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In a world of AI, we must rethink the purpose of maths homework

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EEF on Parental Engagement to Support Learning

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EEF on Parental Engagement to Support Learning

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Homework refers to tasks given to pupils by their teachers to be completed outside of usual lessons.

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CPD - Modeling Metacognition Learning Lunch

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CPD - Modeling Metacognition Learning Lunch

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Mindsets are the implicit theories that individuals hold about the malleability of human characteristics. Research indicates that students' beliefs about the nature of intelligence and ability significantly shape their response to academic challenges (Dweck, 2006; Yeager & Dweck, 2012).

The mindset framework summarizes research on how people think, feel, and respond to failure and challenging experiences. Individuals who believe that intelligence and ability are largely immutable ('fixed mindset') respond to failure by withdrawing, disengaging, or persisting with the same set of strategies despite their prior demonstrated ineffectiveness.

On the other hand, students who believe they can substantially increase their intelligence and ability through experience and effort (' growth mindset ') often react to academic challenges by allocating more effort, experimenting with new approaches, and seeking feedback. Students with a growth mindset set mastery goals and increasingly challenging tasks that promote skill development and acquisition.

Students with a fixed mindset, by contrast, tend to select performance goals, safer learning experiences that help them validate their intelligence, and avoid exposing deficiencies to others, as shown in the table below.

Fixed vs. Growth Mindset Attributes

Views on effort
Sees the exertion of effort is a sign of weakness

Sees effort as an integral component of learning

Goals
Performance goals: picks challenges that are easier to meet

Mastery goals: picks increasingly more difficult challenges

Attribution of failure
Internalizes (not enough ability) or externalizes reasons for failure (blames others & situation)

Diagnoses more objectively his/her own responsibility (not enough effort, preparation, or ineffective strategies) vs. the contribution of external factors (ineffective mentoring, poor course design, etc.)

Strategies
Abandons & withdraws due to feelings of helplessness or repeats the same failed strategy

Doubles down on effort, tries new things, asks for help

Feedback
Avoids feedback, acts defensively

Seeks feedback proactively

Mindsets occur in a continuum between the fixed and growth extremes and are domain-specific. For example, a student can have a growth mindset towards developing coding skills while demonstrating fixed mindset beliefs towards public speaking. Even within a certain domain, an individual might initially approach a particular challenge by exerting effort and seeking help-demonstrating a growth mindset, but may subsequently perceive setbacks as a diagnosis of low inherent ability-demonstrating a fixed mindset.

Why is it important?

Effect of mindsets on individuals

Although students with fixed mindsets can succeed academically when their studies are going well, a fixed-mindset approach can hinder individuals when confronted with serious setbacks. Fixed-mindset thinking can result in students:

Interpreting failure as an inherent inability to improve in a challenging domain, which in turn can cause students to 1) feel inadequate (also known as "imposter syndrome") and unable to succeed (leading to a loss of self-efficacy), 2) drop out of a course, major, or educational experience, and/or 3) abandon developing skills that could be beneficial for academic and professional growth.

Underutilizing available resources that could help them overcome the challenging experience (Y. Hong, Chiu, Dweck, & Lin, 1999). Those with a fixed mindset may view the utilization of resources as a confirmation of inadequacies. Additionally, it is hard to see the utility of said resources if one believes that skill in the challenging domain cannot be substantially developed.

Failing to seek feedback from peers and mentors and/or discarding helpful, constructive feedback from others (Mangels, Butterfield, Lamb, Good, & Dweck, 2006; Moser, Schroder, Heeter, Moran, & Lee, 2011).

Experiencing increased anxiety and depression (Shih, 2011; Da Fonseca et al., 2009; Schleider, Abel, & Weisz, 2015).

Beyond helping students to overcome the negative outcomes listed above, teaching students that intelligence/abilities are malleable has been shown to bridge the academic gap for women and underrepresented minorities (Aronson, Fried, & Good, 2002; Good, Aronson, & Inzlicht, 2003) and to increase their sense of belonging (Good, Rattan, & Dweck, 2012).

Practices that support development

The mindset communicated by an instructor's teaching practices can influence students' behavior regardless of the students' original mindset (Park, Gunderson, Tsukayama, Levine, & Beilock, 2016; Rattan, Good, & Dweck, 2012). Therefore, as an instructor, it is important that you model a growth mindset in the classroom.

1. Normalize the experience of mistakes and failure

Use personal examples and examples from others. Interventions that exposed students to narratives of eminent physicists modeling how they themselves overcame failures and struggles improved physics learning (recall of facts and problem solving) and increased their interest in physics (H. Y. Hong & Lin-Siegler, 2012; Lin-Siegler et al., 2016).

Emphasize the importance of failure and iteration in the engineering design process and research. Although the connection between mindset and the research/engineering process has not been rigorously evaluated, explicitly destigmatizing failure in this way may help students adopt a growth mindset orientation and help them embrace educational challenges and risks.

2. Praise student effort and use of study strategies, rather than intelligence

Although we do not have data on how many students at MIT exhibit a fixed-mindset orientation, students may arrive at MIT with a history of success that has been accompanied by "intelligence praise" from parents, teachers, and mentors. Studies that probe the origin of mindset inclinations show that when children are given lots of praise for their intelligence-as opposed to receiving praise for using strategies and allocating effort (i.e., "process praise")-they are more likely to adopt a fixed-mindset orientation (Gunderson et al., 2013; Mueller & Dweck, 1998). If a student is operating primarily with a fixed mindset relating to academics, they may encounter academic struggle for the first time at MIT.

3. Teach students that feedback is an important part of the learning process

In a recent online intervention (Study 3 in Yeager et al., 2016b), students from a highly selective private university were taught that critical feedback from professors and other instructors reflected "high standards and confidence that students can meet those standards, not a negative judgment of the student or his/her potential" (Yeager et al., 2016b). Past research has demonstrated that clarifying the intent of critical feedback can increase students' motivation to revise or improve their work, particularly for students who are more at risk of stereotype threat (Cohen, Steele, & Ross, 1999).

4. Challenge the notion that learning should feel easy

Students who are taught to reframe their interpretations of why a task might be difficult (ex: learning something new can be difficult) improve their performance during demanding tasks (Wilson, Damiani, & Shelton, 2002).

You can help students reframe their interpretations of learning difficulty by using personal examples of times when they struggled to learn something and had to exert effort to learn. Explain to students how learning takes place and that it is normal and expected to have difficulty learning something new.

Deep conceptual understanding-the re-organization of mental frameworks and accommodation for new understanding-requires time and effort.

Many central concepts at the heart of disciplines are not obvious or intuitive to a novice; they are the product of hard-won inquiry.

Emphasize that learning should feel challenging. Behaviors that make studying feel less effortful may not be desirable for learning (E. L. Bjork & Bjork, 2011). For example, testing yourself by doing a new set of problems, rather than reviewing previously solved problems might feel more effortful and difficult, but leads to better performance & deeper learning.

5. Communicate that abilities can grow over time

Mindset interventions demonstrate that teaching students about neuroplasticity has the potential to change their beliefs about the nature of intelligence and ability.

Explain to students how expertise develops. Expertise is achieved by zeroing in on weaknesses and tackling those aggressively-a form of practice called "deliberate practice." Deliberate practice requires focused attention to deficiencies and constant feedback. The goal of deliberate practice is not to just meet someone's potential but to build it by continuing to move beyond someone's current ability level (zone of proximal development) (Ericsson & Pool, 2016).

By communicating the process for increasing competence for a particular skill and by providing examples and strategies to demonstrate skill development within a domain, you can help students understand that 1) abilities and intelligence are not fixed and 2) that struggling and making mistakes are part of the natural process of learning, as they seek experiences that stretch their comfort zones.

Provide assignments and exams where students can show progress over time, such as projects or papers that incorporate cycles of feedback and revision, so that students have the opportunity to improve their work with each iteration and allowing test corrections.

Growth mindset at MIT

Professor Srini Devadas reinforces the message that learning should be challenging in 6.006 Introduction to Algorithms. (The clip of interest ends at 8:28)

Reflection question: Was there anything that you found particularly motivating about how Professor Devadas presented this to the class?

Professor Gunther Roland describes how the 8.13 Experimental Physics I & II "Junior Lab" teaching staff emphasize to students that public speaking is a skill that can be improved through practice. Professor Roland also describes how the course is designed to facilitate that practice. (The clip of interest ends at 4:19)

Reflection question: What activities does Professor Roland describe that help students develop their public speaking skills?

Instructors William Li and Grace Teo designed 6.811 Principles and Practices of Assistive Technology to normalize failure as part of the design process. (The clip of interest ends at 3:01)

Reflection question: What structures and class activities were used to normalize failure and highlight it as an essential component of the design process?

Caveats

Fixed-mindset environments

Mindset interventions may be ineffective if students are mostly operating in fixed-mindset environments.

From the literature on mindset, we understand that student behaviors may be more tightly correlated with the instructor's mindset than students' own mindsets (Park et al., 2016; Rattan et al., 2012). Therefore, it is not enough for faculty and instructors to express a desire to have a growth mindset-their classroom practices and behaviors must also support the development of a growth mindset.

Programs and processes that emphasize grades too much (ex: entrance into medical school) or cultures in which extreme time constraints are the norm (ex: the culture of course and extracurricular overload common at MIT) can contribute to adoption of performance goals rather than mastery goals.

Unknown long-term effects

The long-term effects of scalable interventions are unknown. The most scalable interventions on mindset (i.e., those delivered online) are brief and their effects have only been assessed for a short period of time-from a single semester to approximately one year. We do not know if the effects of these brief interventions can persist over long periods of time, such as for a student's 4 undergraduate years and beyond (Orosz, Péter-Szarka, Bőthe, Tóth-Király, & Berger, 2017)

Overemphasis on mindsets

An overemphasis on teaching about mindsets can backfire.

Be sure you are not focusing on mindset at the expense of teaching students specific strategies to improve performance and learn from feedback. The adoption of a growth mindset is helpful-but not sufficient- in overcoming academic challenges.

It is also critical to be conscious of the changing inequities in our society that make it more difficult for certain students to succeed.

Well-designed curricula, high-quality instruction, and nurturing learning environments where all feel welcomed are also essential to ensure your students are maximizing their potential.

Related initiatives

MIT and various peer institutions have launched initiatives to collect and share experiences from faculty and students that can help normalize struggle and failure, such as:

Flipping Failure: a collection of stories told by MIT students about their experiences of struggle while at MIT.

Stanford Resilience Project: In addition to a host of campus resources, the Resilience Project has a large collection of personal stories of struggle and hosts various events (ex: the annual 'Stanford, I screwed up!' event).

We also offers 2 different types of mindset training to the MIT Community:

1. A short workshop on mindset during TA days, a TA training event that takes place at MIT before the start of each academic term.

2. An IAP course on How to succeed at MIT and beyond- developing a growth mindset. This 4-part workshop series focuses on learning strategies and the development of a growth mindset.

References

Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. Retrieved from http://bjorklab.psych.ucla.edu/pubs/EBjork_RBjork_2011.pdf

Dweck, C. (2006). Mindset. Random House.

Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Essays in Social Psychology.

Ericsson, A., & Pool, R. (2016). Peak. Houghton Mifflin Harcourt.

Hong, H. Y., & Lin-Siegler, X. (2012). How learning about scientists' struggles influences students' interest and learning in physics., 104(2), 469-484. http://doi.org/10.1037/a0026224

Wilson, T. D., Damiani, M., & Shelton, N. (2002). Improving the Academic Performance of College Students with Brief Attributional Interventions. In Improving Academic Achievement Impact of Psychological Factors on Education (pp. 89-108). Elsevier. http://doi.org/10.1016/B978-012064455-1/50008-7

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Mindsets are the implicit theories that individuals hold about the malleability of human characteristics. Research indicates that students' beliefs about the nature of intelligence and ability significantly shape their response to academic challenges (Dweck, 2006; Yeager & Dweck, 2012). The mindset framework summarizes research on how people think, feel, and respond to failure and challenging experiences.

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BBC Article

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How to boost your resilience when studying - BBC Bitesize

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Dr Heather Branigan guides us through the basics of resilience in relation to studying.

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The inner voice and inner ear may be central to consciousness (2). The point is that talking to yourself is a powerful tool for successful living. I have previously described how to use your inner voice in order to practice metacognitive quality-control of your reading and self-regulation of your learning. You can learn how to carry out this activity simply by holding an inner dialogue as you consume academic content. As you read or consume academic content, ask yourself questions such as these:

Does this remind me of anything in another unrelated domain of knowledge?

Can I think of anything else I know that contradicts this concept?

What other things that I already know support the veracity of this concept?

Can I think of any practical examples of this?

Is this the first time that I've come across this nugget of knowledge?

Where else have I come across this idea?

Who else has tried to teach me this before?

How certain am I that this is true and correct?

Does this relate to anything else that I already know?

Where else in life can I find an example of this?

What other related concepts come to mind?

How difficult was it for me to grasp this?

If this is a WHAT, then can I explain the WHY?

How can this information be applied in my life?

Why is this important to know?

What else do I know about this topic?

What else would I like to learn about this subject?

Do I fully understand this?

Can I break this down into smaller parts?

How would I explain this to a child?

How does this fit in with the rest of what I know about this subject?

Is this information reliable?

Is this totally believable?

What, if anything, surprises me about this?

Is this easy to grasp?

Do I find this interesting and why?

How can I apply this in the real world?

Why is this important to know?

Am I curious to learn more about this?

What else might I want to learn more about because of this?

What does this mean to me?

Do I need to consult another source to better understand this?

What questions does this raise for me?

Does this have any broader implications?

Why is this important?

What other ways could I express this concept?

Does this bring any examples to mind?

Would I like to be able to remember this forever?

Should I consult another source?

How would I succinctly summarize this?

It's widely accepted that metacognition has a central role in achieving academic success. But what role does it have in everyday life?

Every goal we pursue in life requires thought and planning behavior. To the degree that we can bring the skill of metacognition to bear, we can quality-control our thinking and planning in order to optimize our outcomes.

Many of us don't purposely use our inner voice or ear to hold rational and reflective inner dialogues. It's very easy to use them simply to fret, worry, levy blame, relive the past, and complain about our life circumstances. But there are many more useful activities that we can exercise in order to achieve more successful lives. Let me give you a couple of examples.

We can live more successfully by employing metacognition to properly assess for truthiness. Truth must be based on real rather than alternative facts. While we have become a highly polarized society, everyone still needs to embrace reality in order to live successful lives. But how do we test for the truth? Unfortunately, almost everyone falls victim to one of the most pernicious of the cognitive biases, confirmation bias. This is the bias where once we adopt an opinion, we lose the mental agility to change our minds. Instead, we search the world for data and in fact, we tend to interpret all future data in a manner that confirms what we already believe, silently ignoring anything that refutes our existing beliefs. So, how can you employ some metacognition to avoid this trap? We need to ask ourselves "What would this belief look like if it were untrue?", "How can I disprove this opinion?" and "Could those folks with the opposite opinion actually be right?" We need to approach our opinions with vigilance and test them against the real world. It's easy to have an opinion but the most successful people know how to reassess their beliefs. They are able to test their opinions without preconception and change their views when the real world shows them that they are wrong. Learn to develop a falsification bias! Hold metacognitive dialogues and challenge your thinking and beliefs.

This final example somewhat conflates cognition and metacognition. But I think that it is a story worth telling. We sometimes need to invent a solution for a serious everyday life problem. A tool that some of the greatest scientists and philosophers have utilized, throughout history, is the thought experiment.

One of my favorite examples of a thought experiment is the story of "Houston. We have a problem!" in Apollo 13. If you saw the movie version [please watch this short video to refresh your memory] you may recall that the astronauts experienced an oxygen tank failure because of an explosion during a routine stirring operation. They soon were running out of life-sustaining oxygen needed for breathing and the generation of electrical power. A NASA team on the ground used an 8-step approach that saved the lives of the astronauts.

1. Define the problem

2. Determine goals/objectives

3. Generate an array of alternative solutions

4. Evaluate the possible consequences of each solution

5. Use this analysis to choose one or more courses of action

6. Plan the implementation

7. Implement with full commitment

8. Adapt as needed based upon incoming data

While the experiment was actually carried out in the physical world by a team, this story demonstrates how a thought experiment can be used to solve a real-world problem.

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Metacognition is a superpower that helps elite students separate themselves from their peers. I have written about this topic several times including how learners can employ metacognition when reading academic materials in order to deeply engage with the content. It's a practice I employed ...

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from the EEF

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Sketchnote from ImpactWales

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Learning Lunch 6 Nov 2024

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Free to use icons to support dual coding.

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Noun Project: Free Icons & Stock Photos for Everything

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Noun Project has the most diverse collection of free icons and stock photos. Download SVG and PNG. Over 5 million art-quality icons and free photos.

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Stephen Smith & Suzie Condy

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Sonja Smith

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Oliver Caviglioli, @olivercavigliol, is a former special-school head of many years, who later on in his career turned to visualization. Oliver has worked with us on various projects - most notably, the 6 effective learning strategy posters. You can read our interview with Oliver here.
I recently presented at the Derby College Showcase conference, whose theme was inclusion.

Overview

It was easy to place the value of visual communication in the theme of inclusion. I started off with two exercises to immerse the teachers into what it feels like not to understand seemingly simple communication.

The first activity I took from my days of presenting day-long INSET (teacher training) courses on visual teaching techniques. It involves me explaining a concept that I show, piece-by-piece, on the whiteboard, helping to build up understanding. However, only half the audience are able to see this visual counterpart to my oral presentation. The other half have their backs to the board and have to process and store all of the incoming information.

And, that, in essence, was the main point of my presentation - that spoken information is transient. During my previous life as a trainer I used to make this point, but I had no evidence, or indeed language, to back this up. All I had was the teachers' own experiences. But without authority to back up their insights, I can only imagine that this interesting insight simply fell away from their memories the following day.

Last week, while studying John Sweller's magnificent Cognitive Load Theory book, I came upon an explanation of this phenomenon. It's called the Transient Information Effect.

Whenever a teacher orally explains something to a class...the information presented is transient. -- Sweller et al. (1)

The Transient Information Effect

Here is the concept that I explained to the teachers, only half of whom saw the supporting visual build up (the other half had their backs facing the screen). As you can see, the content I explained was about retrieval practice. It is presented here in the form of a concept map that I created in partnership with Megan and Yana (see this blog post for the original concept map and a discussion of how it came about).

After demonstrating the transience of spoken communication, I then moved on to what should have been a simple solution - the use of the written word. While this is the proposed solution put forward by John Sweller and his fellow authors, there still remains a problem with text-only approaches.

Combining Text with Graphics

Elsewhere in the cognitive science evidence, there are many experiments showing that text-only communication can be less effective than a text-and-graphics strategy (2). The following activity showed why that should be so.

I presented the teachers with this very simple, and short, description of the personnel in The Lasagna Project (3). Despite its brevity and simple vocabulary and grammar, very few of the teachers were able to answer the three questions below the description.

But, when the corresponding visual was shown, the answers became self-evident.

The combination of these two activities was - to my thinking - obviously highly significant to the issue of inclusion. But, given that the trainee teachers had trouble, too, with these activities, the transience of spoken communication and the complexity of written communication can't be considered solely as problems for low-knowledge students.

As the presentation continued, I argued that these psychological constraints were pertinent to the professional learning of teachers themselves.

After running the Transient Information Effect activity, I proposed a solution in a second activity by asking the teachers to answer questions based on a simple piece of text. As anticipated, they found this difficult - until, of course, I showed the same information depicted in a diagram.

Here are two quotations that, to some degree, both explain their experience. I still find the Bertrand Russell's explanation most compelling.

"People learn better from graphics and words than from words alone...you can help people learn better if you include appropriately designed graphics in instructional presentations." -- Richard Mayer (4)

"Languages are sequential in nature, and so must have a compensatingly complex syntax to express certain relationships." -- Bertrand Russell (5)

Organizing Visual Information

Just "going visual", however, is insufficient. Pretty much most education strategies have both disadvantages as well as advantages. The danger with using visuals is in using distracting, attention-sapping decorative images that have nothing to do with the concept at hand (see this blog post for more on when too many pictures become too much of a good thing).

At best, visuals should help organize the information (as we saw in the Lasagna Project activity). Organizing information is crucial in helping students encode it into their long-term memories. However, as Reif warns us (5), students are not very able in doing this.

"Poorly organized knowledge cannot readily be remembered or used. But students don't know how to organize their knowledge effectively." -- Frederick Reif (6)

This is not surprising if we remember that students are novices in the context of the material they are learning. So teachers must organize the material for them. This accords with Sweller's view that learning consists of borrowing information, already organized, from others.

The two following slides come from the Further Education section of the special school at which I was head teacher. You can see that the teacher has organized information about the topic she was about to teach; the information is nested.

In the first slide, note the outer branch circled - hygiene.

Now look at the following slide, and see that hygiene is now in the center.

Now, return to the top slide and you can see how the second slide that expands on the hygiene topic could be drawn on its borders. Similarly, every other outer portion of the slide could be expanded in this way. However, and very wisely, the teacher recognized that presenting such a full and complex map to her students with severe learning difficulties would be overwhelming. Some have termed this unskilled use of visuals as map shock.

But, by nesting the information in this layered way, the teacher was able to build up the students' knowledge, layer by layer.

Teacher as Learners

At this point, I switched the attention away from students as learners to teachers as learners, pointing out that all the psychological constraints and solutions we had covered were applicable to adults too, including the area of professional learning.

Teachers are prone to unknowingly misinterpret the verbal descriptions of teaching and learning techniques. They then go on to tweak them even more, back in their classrooms. These distortions are extended and repeated as teachers verbally share their learning with one another.

While this is not a bad thing, it does, however, mean that we don't build an accurate shared understanding of what specific teaching techniques consist of. My explanation of this is because our communication is based on words alone, either spoken or written, and then serially communicated along a path of what could be called a game of broken telephone.

The development of the HOW2s came about to address this problem. The HOW2s include very specific, concrete, step-by-step instructions for how to use evidence-based teaching strategies. Accordingly, I finished off my presentation by showing part of a HOW2 in two of its three visual formats (infographic and presentation slides). The one I showed came from the collaboration with the Yana and Megan. The full set of 6 cognitive science HOW2s are free and available for download here.

In the link below, you can download my full presentation, which includes more of the HOW2 you see partially here.
Resources

This slide shows the books I have been reading these past few months on cognitive science/psychology that have influenced my thinking. Their references are in the handout, which you can download below.

I have summarized every one of the 17 chapters of Sweller et al's 2011 book into both sketch notes and a corresponding PDF presentation slides (that can be imported into your PowerPoint document if needed). Here's what they look like:

You can download the Cognitive Load Sketchnotes here.
Handout
Here is the one-sider handout for my presentation.
Presentation Slides
Here are my presentation slides for the 35 minutes slot.
A version of this post previously appeared on the teachinghow2s blog.

References:

(1) Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive Load Theory. New York, NY: Springer.

(2) Clark, J. M., & Paivio, A. (1991). Dual coding theory and education. Educational Psychology Review, 3, 149-210.

(3) Moyer, D. (2010). The Napkin Sketch Workbook, Blurb.com

(4) Mayer, R.E. (2004) Foreword. In Clark, R. C., & Lyons, C. Graphics for Learning. San Francisco, CA: Pfeiffer.

(5) Russell, B. (1923). Vagueness. The Australasian Journal of Psychology and Philosophy, 1, 84-92.

(6) Reif, F. (2008). Applying Cognitive Science to Education. Cambridge, MA: MIT Press.

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I recently presented at the Derby College Showcase conference, whose theme was inclusion. It was easy to place the value of visual communication in the theme of inclusion. I started off with two exercises to immerse the teachers into what it feels like ...

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Dual Coding | Making Visuals Work | Science of Learning Series

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Dual Coding Theory has been gaining a lot of attention from teachers around the world over the last couple of years, but what exactly is it and how can teachers use it to help their students gain a deeper learning?

What is Dual Coding Theory? Allan Pavio discovered that our memory has two codes (or channels) that deal with visual and verbal stimuli. Whilst it stores them independently, they are linked (linking words to images). These linked memories make retrieval much easier. The word or image stimulates retrieval of the other.

When teachers employ a dual coding mindset to their learning materials, the student's cognitive load is reduced and their working memory capacity is increased, thus, learning is improved.

Whats is Dual Coding Theory?

Back in 1971, Canadian researcher, Allan Paivio, formulated his dual coding theory. And then spent the next four decades researching it, trying to 'break it'.
He didn't manage it.
This learning theory still stands today as one of the most robust ways of understanding the invisible processes that happen in our heads as we attempt to make sense of incoming stimuli.

His most significant discovery was that we have two separate channels that deal with verbal and visual stimuli.

While being independent of each other, they are also able to create what Paivio called "associative connections" between them. So, they are both apart from one another but can cooperate in forming linked pairs of words and images.

By forming such a link, the encoding process is enriched.

It leaves a double memory trace and, in the words of Professor Paul Kirschner, results in "double-barrelled learning" because of the resultant double opportunity of being retrieved by either verbal or visual means.

Dual Coding and Cognitive Load

Encoding, of course, is psychologists' term for learning and, so, such a powering up of the encoding and retrieval processes deserves teachers' close attention.

It's no surprise then that John Sweller - the originator of the related Cognitive Load Theory - concludes that:

"Working memory capacity can be effectively increased, and learning improved, by using a dual-mode presentation."

( Cognitive Load Theory, 2011, Sweller, Ayres & Kalyuga)

Often, cognitive science brings bad news to students. They are confronted by the facts that learning happens through thinking hard (Coe), that the comforting habit of rereading and highlighting is very inefficient, and that studying one topic at a time is less than optimal.

Dual coding is quite different in that pairing words and images don't incur any additional cognitive load and also greatly helps retrieval.

It's a 'freebie'!

But, as good as this news is, it's only half the story.

When Paivio found that the two channels worked as separate systems, he also noted that they were also fundamentally different in structure.

Verbal information, you won't be surprised to learn, is sequential in construction. Words are joined together in "concatenation" as philosopher, Bertrand Russell, described it when comparing the relative merits of text and diagrams in conveying meaning.

Why are Visual Aids Important in the Classroom?

Visual information was defined by Paivio as being synchronous, or simultaneous' in structure.

These two synonymous terms were used to explain that with diagrams, several, if not all, the elements could be viewed in one go.

Words, by contrast, have to be processed one at a time.

While Paivio noted these important structural differences, he didn't devote his research to exploring them much further.

Others did, I'm glad to say, and we will shortly meet them and learn what they discovered. But, for now, we'll stay with Paivio's studies of the associative links between the two modality systems.

As robust as his findings were over several decades, we ought not to forget that the nature of the content learned by his laboratory subjects was cognitively unchallenging.

Like Ebbinghaus in the century before him, Paivio used simple content in order to discount any element of comprehension messing up his pure work on retrieval.

That's not how schools work though, they do deal with cognitively challenging content.

The knowledge organizer with its lists of facts -let's acknowledge it-while a very useful document, hardly represents the apex of schools' intellectual aspirations.

Instead, different approaches are needed to mesh together such isolated facts into coherent networks and integrated concepts.

The Visual Argument (Larkin and Simon).

That's where Jill Larkin and Herbert Simon come into the picture.

In 1987, they wrote a paper that developed Paivio's distinction of sequential and synchronous information structures.

By comparing the time, effort and accuracy involved in understanding concepts communicated in either verbal or visual format, they arrived at what is now called " The Visual Argument".

In their study, well-constructed diagrams were judged to be more computationally efficient than text.

Behind this somewhat technical term, lies this reasoning.

Because of the sequential nature of verbal information, each word is addressed one at a time. That, of course, isn't all that's entailed. To make sense of each word, they need to relate to others.

Sometimes this is simply the ones directly preceding them. But others may well be further apart in a previous phrase or sentence. Such distances require cognitive effort in searching and connecting in order to make the necessary inferences to make sense of the text as a whole.

Diagrams don't work that way!

Constituent parts of a diagram are all significant, unlike the words in a piece of text. In addition, these visual elements can be perceived in one go, and not serially.

This is why Paivio described visual information being synchronous or simultaneous in structure. And this is why psychologists argue ( Clark & Lyons 2004) that diagrams can be largely understood by using our everyday perception.

Graphics for Learning

Gestalt psychology, for nearly a century, has shown us that we immediately understand that proximity of elements represent commonality, as indeed does inclusion within a border (think Euler and Venn diagrams).

Analogy: Things closer together are more related. People living in the same house are more likely to be related in some way than people in separate houses.

These natural capacities are at play in the reading of diagrams and require considerably less cognitive resources than in reading texts.

The two cognitive, or computational, tasks that are more efficient with diagrams are the reduced need to search for relevant items within sentences and, correspondingly, the easier use of inference because metacognition is able to take place.
Put simply...
Reading texts involves an almost constant traveling back and forth searching which parts relate to which. This, then, makes inferences so much more difficult, or effortful, to make.

An Example of Dual Coding Theory

The example below, that I use in my presentations to make the concept of computational efficiency come alive, makes the point more effectively than my explanations.

From the text on the left, try and answer the questions. Difficult isn't it!

Now try to answer the same questions by looking at the image below...
Much easier right?
Convinced of this you may be but, as always, there's more to it than just presenting a diagram to your students.

As cognitive science authors, Clark and Lyons (2004) warn: "Visuals ignored, don't teach".

It's all very well to give your students diagrams that convey information that require less effort to understand, but if you don't then use them to make your students think, not much will be learned.
Diagrams should be thought of as platforms from which to better analyze texts and prepare for speaking and writing.
And then there are other problems to overcome.

The Visual Argument only happens when teachers have chosen an appropriate visual tool. Exploring the differences between rural and urban settings is not best represented by a timeline for example. And plotting the plot of Hamlet becomes confusing if a mind map is used.

Deductive Reasoning in Dual Coding Theory

Graphic organizers can usefully be grouped along these four types of deductive reasoning:

Identifying the nature of the knowledge task is essential before moving on to choose an appropriate visual tool.

As you might now expect, there's one more danger to avoid.

Supposing the correct organizer is chosen to fit the nature of the task, its execution needs to be adequate.

Clark and Lyons (2004) highlight poor execution as a major factor behind dual coding's diminished impact.

Above all, teachers need to make their handwriting legible. To be confident of this, printing in a clear, bold style with no flourishes or elaborations, is essential.

Forcing students to decipher a rushed handwritten script is an unnecessary cognitive burden that clearly bears an extraneous, unproductive load.

Other graphic considerations when creating dual coded communications involve the following four principles I devised after responding to requests for feedback from teachers on Twitter.

How to do Dual Coding
Firstly...
Simply to cut-reduce the volume presented on page or slide. It's the easiest and most effective of all the principles.
Next...
Chunk the selected content. Identify the categories so it's easier to make sense. And signal the chunks by providing more headings than you normally would.
Then..
Aligning the chunks, and any other element on the page -line or image- makes scanning and search so much easier for the reader.

In other words, don't make them 'artistic' and random in placement. Order makes reading and scanning so very much easier.
Finally...
And lastly, continuing on the non-artistic perspective, practice restraint in the number and intensity of colors used, along with the use of a single typeface (font) ensuring it isn't a fancy, hard-to-read display font or Comic Sans.

Typographers have a long history of theory, research and practice as to what makes reading easy.

Just look closely at any newspaper or magazine design and you will see these principles in action.

For a more detailed explanation of dual coding theory and examples of how it can be included in your classroom practice, Oliver's book; " Dual Coding with Teachers " is perfect, it will be hugely useful to any teacher.

Similar Posts:

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Dual Coding Theory: The Complete Guide for Teachers

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Dual coding theory explains and simplifies how we can teach students to get information into their long term memory easier and retrieve the information quicker.

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How to Give Feedback | Teaching + Learning Lab

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Feedback has been known to be an important part of the learning process. Especially when coupled with deliberate practice, feedback can help students spend their time mastering aspects that they need to focus on most rather than practicing what they already know. Effective feedback works as a map to guide students by letting them know where they are now and what to work on in order to get to their goal. Without good feedback, students may carry misconceptions that they did not even realize they had while learning the material and walk aimlessly towards a goal without being sure how they can get there.

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all school leaders understand the importance of providing meaningful feedback. done well

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and thereby closing the gap between where a pupil is and where the teacher wants them to be.  however

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not all feedback has positive effects. done badly

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feedback can even harm progress. nor is feedback ‘free’. large amounts of time are spent providing pupils with feedback

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perhaps not always productively.  historically

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much consideration has been given to the methods by which feedback is delivered. specifically

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or should it be verbal? this guidance report aims to move beyond this and focus on what really matters: the principles of good feedback rather than the written or verbal methods of feedback delivery.  the guidance report is based on the best available international evidence

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in addition to a review of current practice

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and refined through consultation with teachers and other experts.

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Teacher Feedback to Improve Pupil Learning

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Six recommendations for using teacher feedback to improve pupil learning

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John Hattie Learning Intentions and Success Criteria

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A blog about something really obvious but worth spelling out.

After 25 years of teaching, I've been through a fair amount of dodgy INSET/CPD. As a result I am something of a 'visiting speaker' sceptic. However, it hasn't all been bad; far from it. Some ideas have been very influential such as the ideas behind CASE (Cognitive Acceleration through Science Education) developed at Kings in the 1990s; also the principles of formative assessment that have trickled into our collective consciousness as teachers since 'Inside the Black Box'. Whilst some ideas have helped me to frame an overarching philosophy for teaching or have augmented my armoury of teaching tools, there is one simple strategy that has transformed the way I teach every lesson, every day:
Think, Pair, Share.
I used to be a 'hands up' merchant just like a lot of people. Then, at an INSET session about 10 years ago, delivered by a superb trainer from Haringey LA (employed through National Strategies - imagine!) the seed was sown that 'hands up' might not be such a great idea. It is so obvious when you think about it. In fact it is rather alarming that such a poor and even harmful strategy is still so deeply ingrained in pedagogical practice. For years I'd fought my way through the forest of hands- "Oo, oo, oo, me, me, me!!!" OR faced the tumbleweed of deathly silence; those 'blood out of stone' moments when you scan the room desperately looking for someone willing to give you an answer and everyone is staring at the floor. And of course there would often have been kids at the back wishing 'please, please, don't ask me, I haven't got a clue.'

But the solution came: Every time you ask a question, get the students to think first, then discuss it in pairs before they answer. Lightening bolt. This simple strategy has transformed how I teach - and helped develop an entirely new way of thinking about teaching. I've since often referred to this as the 'washing hands' of teaching. This is the hospital analogy where the single simplest act with the greatest impact is to ensure every hospital worker washes their hands after each patient contact; i.e. changing something that you do all the time every day has an enormous impact.

I think it is worth revisiting just why 'hands up' is such a poor strategy:

Only one person gets to answer at a time so you have no idea what most people are thinking.

The answer can be offered before others have had a chance to work it out for themselves.

Students can opt out of answering or thinking altogether if they choose to. They can hide.

It is difficult to express confusion or simply to say that you don't know the answer.

In the 'forest of hands' scenario, the competitiveness inhibits less confident students (and there are gender-specific behaviours here that can't be ignored).

In the 'blood out of a stone' scenario, you can't tell if students are really stuck or just too unsure of themselves to offer a public answer.

Very often 'Hands up' goes together with closed questions with very short 'think time. We are not comfortable with silence -and expect responses within seconds of asking a question.

Ingrained patterns of behaviour develop; students who always put a hand up and students who never do.

So, what changes when you ask routinely, 'in your pairs, discuss.....':

Crucially, in doing this you are creating a small bubble of security around each pair; a safe space where they can think for a while and say whatever they like. 'I think X', 'No, I think Y'...'I haven't got a clue', 'I wasn't really listening' 'It is more complicated than that... maybe it is X except when it is Y?'

In this bubble it is safe to admit you don't understand and the pair can pluck up the courage together to report this back. Easier to say 'we don't get it' rather than 'I don't get it'.

Every single student can engage in answering the question; they are all generating answers simultaneously - and there is less chance of hiding. Shy students will speak to their partner; the blood comes out of the stone! It has an immediate effect.

Two heads are better than one. If the question is a good one, pairs can debate their answer. They can then rehearse it and feedback to each other..'yes, that sounds good but maybe also say this....'

When the teacher brings the class together to hear answers, the students are repeating something they have rehearsed. It is easy to report back 'we thought that maybe it is XYZ' when you have already thought this through... compared to being put on the spot with a cold question. It is crucial in the report-back phase to ask selected pairs directly to share their discussion; it means everyone needs to be prepared to report back in case they are asked. Using a building process is also key here - anything to add, to challenge, any better or different answers? And so on. (It is not always time-efficient to get each pair to share their answer.)

I could go on.... it is just such a powerful change. Still now, it is by far the most common piece of feedback I give after lesson observations: 'If you had asked them to discuss in pairs, the learning would have been better'. The question is, why do teachers still ask for hands up or accept it when students take them down the 'hands up' cul-de-sac? What are the barriers to adopting 'in your pairs' as the default mode of questioning?

For some it is about behaviour management. To repeatedly stop and start a class -full of kids talking is more difficult than keeping a lid on them and taking one answer at a time. Good stop-start strategies need to be developed and rehearsed.

It can be overwhelming dealing with all the answers that are generated. After 15 paired discussions - what do you do then? The key is to encourage active listening and the process of building on previous answers as you sample the responses. Sampling is valid - and much much better than only taking a couple of cold hands-up responses.

Students default to hands-up themselves and have to be trained out of it - which can be a drag. Yes, it can, but it soon works if you ignore students with hands up and get the pair discussion going. If you reward 'hands up', that is what you'll get.

It can feel like a sledgehammer to crack a nut if you only want to know 'what is the capital of Spain 'or 'what is 3 x 4'. Well it is. But is that a good question in the first place?

This is the crux; think-pair-share forces us to ask better questions. There is room for a few sharp closed questions in a lesson but if we are looking for higher order thinking, answers that model literacy skills as well as content and, generally, are probing to a deeper level of understanding, then 'hands up' with closed questioning, is never going to be enough.

Once you are into the groove of routine 'in your pairs' questioning, you find yourself asking better questions -it all flows.

So, thank you to Alison from Haringey for showing me the light! I've never looked back.... My hands are clean - are yours!!??

(Thanks to Paul L for providing the illustration...)

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The 'Washing Hands' of Learning: Think Pair Share

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A blog about something really obvious but worth spelling out. After 25 years of teaching, I've been through a fair amount of dodgy INSET/CPD. As a result I am something of a 'visiting speaker' sceptic. However, it hasn't all been bad; far from it. Some ideas have been very influential such as the ideas behind...

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From Bruce Robertson

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Teachers across the country are tying themselves in knots with learning intentions and success criteria. Some are using them well; some are not. Some aren't using them at all.

So why isn't everyone using them and using them well? A significant factor it is because many teachers are unsure about what these should look like. This Five Minute Guide aims to address that.

Learning Intentions

Learning intentions are statements which summarise the purpose of a lesson in terms of learning. A useful acronym is WALT: 'What we Are Learning Today'.

In writing them, it is usually useful to include the terms ' know', ' understand' or ' be able to', which helps communicate that the learning will relate to knowledge, understanding or skills, respectively.

An example might be:

Over the course of several lessons, the class will be learning about the structure of an atom. For that reason, this statement will appear as part of the learning intention in lessons which follow. In this particular lesson, the specific focus is on the sub-atomic particles which make up atoms. The learning intention for the next lesson two lessons might be:

We are learning about the structure of an atom, specifically to understand:

The electron arrangements of the first 20 elements

Because every lesson is about learning, every lesson should have a clear learning intention, whether this be for students to learn something new, to consolidate their learning (through practice or revision) or to demonstrate their learning.

Learning intentions should make clear what students will be learning about, not how this learning will be achieved, that is, to the activities and tasks of the lesson. For example, 'Complete all of the questions on page 45 of your textbook' is not a learning intention - it is a statement about an activity. Learning intentions should be about what is to be learned.

Communicating learning intentions

It is important that learning intentions are clearly communicated with students. Good practice is to do this both verbally and visually. However, saying this is very different from saying that students need to copy down the learning intentions (and success criteria) for lessons. Some schools insist that teachers get students to do that, but students learn nothing from doing so and it just wastes valuable learning time.

Revisiting learning intentions

It can be useful to revisit learning intentions during lessons, reminding students of the learning focus. By the end of the lesson, something should have changed: students should know something that they didn't before, they should be able to do something that they couldn't before, or they should have improved at something. Every lesson should impact on learning; every lesson should count.

Success Criteria

Success criteria relate to the evidence you are looking for to determine if students have learned what you intended. A useful acronym is WILF: 'What I am Looking For'.

Success criteria can take different forms, including:

The principal purpose of success criteria is to support assessment and feedback. When assessing learning, it isn't enough for a teacher to ask, 'Have you learned this?' and then just to accept 'yes' as an answer. There needs to be evidence of learning; students need to prove it. Success criteria can make clear what that evidence should be. In this way, success criteria become tools to support teacher assessment, peer assessment and self-assessment. Without being clear about what you are looking for, meaningful assessment and feedback is not possible.

'I can...' statements

When success criteria are written as ' I can...' statements, they include verbs which make clear the evidence required to demonstrate learning. Rather than being about 'knowing', 'understanding' or 'being able to' - which is the language of learning intentions - they should be about what you are looking for in order for students to demonstrate that they have learned what was intended.

If students can 'state', 'write', 'describe', 'explain' or 'draw', this can evidence learning. Saying that 'I know', 'I understand' or 'I am able to' doesn't evidence learning. While it might be true, it isn't evidence. Success criteria should make clear what evidence of learning needs to be produced.

To appreciate this, consider the learning intention used earlier:

We are learning about the structure of an atom, specifically to know about:

The sub-atomic particles which make up atoms

Possible success criteria are:

1. I candraw a labelled diagram of an atom, showing the arrangement of the three sub-atomic particles which make it up

2. I can state the charge of each of the sub-atomic particles

3. I can state the mass of each of the sub-atomic particles

Occasionally, I hear people argue that success criteria shouldn't be quantified. For example, if success criteria relate to being able to identify advantages and disadvantages of something, teachers shouldn't specify how manyadvantages and disadvantages. The rationale is that, by quantifying, you limit student learning. However, I would argue that, if success criteria are going to be used to assess learning and to guide feedback, they need to be as specific as possible. Sometimes, this will mean quantifying them. The way to get around any issue of 'limiting learning' is to include the phrase 'at least' in front of the quantity (for example, 'I can identify at least two advantages and two disadvantages of...')

Key features

Sometimes, rather than writing success criteria as 'I can' statements, they are better written as ' key features '. This tends to be when they relate to 'Be able to...' learning intentions. For example, a learning intention might be:

Success criteria could be that:

It has two columns

Each column has an appropriate heading

Each heading has correct units

The data has been entered correctly

It has been drawn with a ruler

Confusing learning intentions and success criteria

A common mistake I see teachers make is that they confuse learning intentions and success criteria. Below is an example of a learning intention which does this:

Be able to define and describe 'deforestation'

I see this sort of learning intention quite often. In writing it, the teacher has confused the learning (which relates to deforestation) with the evidence students need to produce to demonstrate their learning. A far better learning intention would be:

Understand what 'deforestation' is

This is focused on learning.

Possible success criteria could be:

I can write a definition for 'deforestation'

I can describe three causes of deforestation

These are focused on evidence of learning. In checking that students understand what deforestation is, the teacher would be looking to see evidence relating to each success criterion.
Taken from The Teaching Delusion: Why Teaching In Our Schools Isn't Good Enough (And How We Can Make It Better), published by John Catt Educational. Available at:

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A Five Minute Guide To... Learning Intentions & Success Criteria

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Teachers across the country are tying themselves in knots with learning intentions and success criteria. Some are using them well; some are not. Some aren't using them at all. So why isn't everyone using them and using them well? A significant factor it is because many teachers are unsure about what these should look like....

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Rosenshine's principle of independent practice states that students should be given plenty of opportunities to practice skills and concepts independently. This can be done by providing activities such as worksheets, problem sets, or independent projects for students to complete. With independent practice, students can expand their understanding of concepts and develop the ability to apply them in new contexts.

1. Scaffolding: Scaffolding is a teaching strategy that can be used to help A-level students become more independent. The teacher provides support and guidance to the student as they progress through a task, then gradually reduces the amount of support over time to allow the student to take the lead. For example, a teacher could provide a student with a list of key terms and questions while they complete a reading assignment and then slowly withdraw support as the student begins to understand the material.

2. Differentiated Instruction: Differentiated instruction is a strategy that allows teachers to tailor their instruction to the individual needs of their students. For example, a teacher can give A-level students different reading material based on their reading levels and abilities, allowing them more independence in the learning process.

3. Collaborative Learning: Collaborative learning allows A-level students to work together to complete tasks, leading to increased independence and a greater understanding of the material. For example, a teacher can assign two students to work together on a project, with one student providing guidance to the other.

4. Problem-Based Learning: Problem-based learning is a strategy that encourages students to think critically and independently to solve a given problem. For example, a teacher can provide A-level students with a scenario and ask them to come up with a solution, giving them the opportunity to practice their independent problem-solving skills.

5. Inquiry-Based Learning: Inquiry-based learning is a strategy that encourages students to ask questions and do their own research to come up with their own conclusions. For example, a teacher can assign A-level students to research a topic and present their findings, allowing them to become more independent in their learning.

6. Experiential Learning: Experiential learning is a strategy that encourages A-level students to learn through hands-on activities such as field trips, simulations, and projects. For example, a teacher can assign a group of students to create a project based on a given topic, allowing them to practice their independent research and problem-solving skills.

7. Project-Based Learning: Project-based learning is a strategy that allows A-level students to work independently on a project from start to finish. For example, a teacher can assign a group of A-level students to research a topic and create a presentation, giving them the opportunity to practice their independent problem-solving and research skills.

8. Directed Reading-Thinking Activity: Directed reading-thinking activities are a strategy that encourages A-level students to read and think critically about a given topic. For example, a teacher can provide a group of A-level students with a text and ask them to answer questions related to the text, allowing them to practice their independent thinking skills.

9. Peer Tutoring: Peer tutoring is a strategy that allows A-level students to tutor one another, leading to increased independence and a greater understanding of the material. For example, a teacher can assign two A-level students to work together on an assignment, with one student providing guidance to the other.

10. Self-Assessment: Self-assessment is a strategy that allows A-level students to assess their own progress and understanding of the material. For example, a teacher can assign A-level students to complete a quiz or task and then ask them to reflect on their performance, giving them the opportunity to practice their independent problem-solving and self-assessment skills.

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10 practical ways to use Rosenshine's 'independent practice' principle

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Rosenshine's principle of independent practice states that students should be given plenty of opportunities to practice skills and concepts independently. This can be done by providing activities such as worksheets, problem sets, or independent projects for students to complete. With independent practice, students can expand their understanding of concepts and develop the ability to apply...

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State of New South Wales, Department of Education, Australia

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The Digital learning selector helps you make fast decisions about a technology you can use for learning with your class. Find support to get started, contribute new tools and share them with your colleagues.

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Take a low effort, high impact approach to task and question design - Tips for Teachers

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Top 20 Principles from Psychology on Teaching & Learning

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Top 20 Principles from Psychology on Teaching & Learning

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Deans for Impact Summary

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From Dan Willingham

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Rosie Culkin-Smith, history teacher at Whalley Range High School espouses, the joys of the visualiser. She explains how it can be an effective tool to help raise attainment in the classroom.
What is a visualiser?

Using a visualiser is nothing new. In short, a visualiser is basically a camera with the ability to connect to an interactive screen, projector, interactive whiteboard, or PC monitor.

They can be incredibly useful but are often underused. One issue is that they are often misused and can foster passive learning.

What this article aims to show is that, used at the right time for the right element of learning, a visualiser could quickly become your best friend!

My visualiser and me

If you're new to visualisers then you may need to move that big pile of textbooks, whiteboard pens (or hand sanitizer) off your desk or follow one of the many wires going into the back of your PC (as I did in my first few years of teaching).

Admittedly, and ashamedly in the first two years of my teaching career, my visualiser was a perfect shelf for which to store my ever-growing pile of worksheets and lesson plans (remember those!).

These days, I use my visualiser at least once in every single lesson.

Why I like visualisers

Firstly, the position of the visualiser being situated at your desk allows you to face the class as you demonstrate the annotation of piece of evidence or scaffold the structure of an exam question.

It allows you to maintain a connection with a) your class and b) the concept or idea being discussed. It allows them to see your thought process, and most importantly the human element of your working memory.

By this, I mean the crossings out and rephrasing. Greg Thornton (@MrThorntonTeach), in the History How To-s series builds on a long tradition of modelling by explaining that visualisers can become a "window into teaching" - giving the students an insight "into the mind for a teacher, who demonstrate their own vulnerabilities to pupils in real time""

This is not new, many of you will have done this with an overhead projector (OHP) before computers.

Many more of you will remember your teacher writing essays out and rubbing out the mistakes with a wet finger.

"I have had classes I also would not dare turn my back to - so the visualiser provided a perfect antidote to this."
Rosie Culkin-Smith

Teachers have always modelled and shared their thought process. I like to show my students that the goal is realistic and achievable, rather than presenting them with a pre-written answer displayed on perfectly-edited PowerPoint slides.

But I can do this on my whiteboard, I hear you say? Yes, this is completely possible - and there are times I absolutely love mapping out a mega timeline or essay plan on my board with my multi-coloured board pens.

However, I always felt disconnected from my class every time I turned my back.

Additionally, in quite simple terms, I have had classes I also would not dare
turn my back to - so the visualiser provided a perfect antidote to this.

Also, using a visualiser is straightforward and simple. Most visualisers are now connected to your PC or IWB by USB, which is run by an app or programme on your computer.

In most cases it is simply a click-and-go kind of thing, and one that I have a lot of time for in a contest of ever-changing technologies and ideas.

Finally, my main love for the visualiser is that it has student outcomes and achievement at its core.

The visualiser makes possible what I think is one of the most important parts of teaching and learning in the history classroom - modelling.

The case for the visualiser

The evidence to support the use of visualisers is largely informed by the scholarship behind modelling and feedback.

Way back in 2008, the Department for Children, Schools and Families, published, Get Going, generating, shaping and developing ideas in writing.

This report advocated supporting pupils via modelling at the point of writing.

Indeed, for the history teaching community modelling is essential for student outcomes, as the very nature of our discipline means we, as experts, have to help our students transform very abstract concepts and ideas into concrete ones, which are then to be written logically and grammatically on the pages of exercise books and exam papers.

There is no shortage of excellent History Scholarship on building the sequence of learning, showing connections and linking to previously taught content and concepts

The practical examples of this are everywhere in the History community - one example from The History Association from 2009 shows the importance explicitly planning the links and responses required for an enquiry on Magna Carta.

Your visualiser can support this: "A range of teaching methods was used, including short sketches...to portray simple scenarios from which the students could infer generalisations...".

Most of the time the way I use my visualiser is supporting this idea. It is helping me to make links, push thinking, and support students critically evaluating the subject.

The History teachers have been confident adopters of pedagogical theories such as Rosenshine's Principles of Instruction.

Rosenshine suggests that teachers should: present learning in small steps, model steps towards the goal, time to apply. Clearly there is nothing revolutionary about Rosenshine's principles.

It is, es sentially good practice. Moreover, it supports the great tradition of planning and teaching history via enquiry questions which was advocated by Michael Riley 20 years ago.

After all, an enquiry question approach, presents work in small steps. The skilled history teacher will also model how pupils should approach each step AND, she will model the type of writing or thinking required in the end task.

Four ways to use visualisers in the history classroom

Live Modelling - writing an essay or exam question under the visualiser in timed conditions in which students simply sit, watch and listen to my thought process.

Thinking aloud here is important as it shows your students the processes needed, and the selection of knowledge as part of the process.

I particularly like completing a 'Walking Talking Mock' in this fashion, as it also adds an instructional element to the worked example, including the planning element, utilisation of time, the structure and order of the paper etc.

This process also supports assessment and exam feedback.

Dictagloss - This was an idea presented by Lesley Ann McDermott
(@LA_McDermott) at one of my very first SHP conferences, in which the teacher would read aloud an excellent answer and the students would listen and write down as many key phrases as they can.

This is repeated until they think they have a comparable answer.

I developed this idea, by presenting my class with an average piece of writing (often referred to as a partially worked example), in which we would, by crowd sourcing (whole class participation) 'gloss it up' by deconstructing it, adding evidence, quotes, explanation etc. until we had a finished piece that we were pleased with.

I find this particularly useful as not only does it give students an opportunity for scaffolded guided deliberate practice, it also builds confidence and gives them ownership of the completed piece.

Modelling Book - Create a modelling book, that is an exercise book in which all the work in it has been entirely modelled by you.

Not only does this give you an opportunity to create beautifully handwritten and highlighted notes, it becomes a resource of which you can display excellence.

I found that many of the things I was modelling I would repeat later in the week or term.

It was useful to have to hand a finished version, of which we could then deconstruct as a class, or model in reverse. My modelling book is my pride and joy!

Exemplifying Excellence and Misconceptions - Live Marking
One of the best ways to use your visualiser is to share first class examples of students work with the class.

Not only does this offer praise, and explicitly showcase gold standard work,
but it raises expectations from your students as they aim to meet that excellence.

I would signpost this until the students are confident with the content and structure, then I would encourage their comments.

However, as the work of Dylan Wiliam shows that feedback has more impact when it is showing something specific that is missing.

This must not be generic statements such as; "more detail" or "key terminology needed".

The feedback must be precise, given early in the learning process, and acted on immediately.

When to step away from the visualiser.

I know I have proved to you throughout this article just how in love I am with my visualiser.

However, there are times it has the opposite effect to the one described.

Over-reliance on it can lead to passive children who don't try - why would they if you are going to give them the right answer eventually?

Being up and out our seats is so important when teaching, we have to see our students and look at those nodding heads to see who really gets it and who is just nodding the seconds away until lunch.

Sometimes the whole class don't need the feedback, it is more appropriate for it to be delivered individually.

Furthermore, praise and showing off good work must be balanced with summative pieces of work.

We need students to understand the difference between intrinsic and extrinsic motivation if we want this to pay off when they sit their exams.

Finally, we don't want children to leave school and think about their History lessons as time spent watching their teacher write under the visualiser.

They want you up in front of them, telling them the stories, giving them that explicit and direct instructions, and talking to them individually about how they are doing.

The Return!

As we return to the classroom we know that feedback and scaffolding are going to be important for helping students get ahead.

Your visualiser can play a massive part of that, but remember, the students have missed you so know when to get up and perform; that's what teaching is!

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Visualisers in the history classroom: when to use them and when to step away

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The joys of the visualiser for history teachers - how it can be an effective tool to help raise attainment.

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This blog will look at the concept of Variation Theory and attempt to demystify the confusing language surrounding it. It is hoped that this will make Variation Theory an accessible and exciting tool that you can begin to use in your math lessons, or give you an understanding of what is happening if you recognize the principles, despite never having heard of Variation Theory before!
What is Variation Theory in elementary math?

Variation Theory is a general theory of learning that is used predominantly in mathematics teaching and pedagogy. It emphasizes a concept's essential features by focusing on what is kept the same and what changes, which offers the opportunity to make meaningful connections.

Origins of Variation Theory

The study of Variation Theory arises mainly from work across two groups of researchers who arrived at similar, but not exactly the same conclusions.

One was Swedish researcher Marton, F. and colleagues who worked on the concept of phenomenography, which developed into Variation Theory; the other was Gu Ling Yuan and his team in Shanghai who called it Bianchi (teaching with variation).

As one would expect, the emergence of two similar theories has caused confusion in some areas of the sector and educational research. In the context of the US, the distinction between them is rarely made and so aspects of Bianchi are used under Variation Theory.

They both agree that 'the central idea of teaching with variation is to highlight the essential features of the concepts through varying the non-essential features'. (Gu, Huang & Marton, 2004). This blog will mainly draw on the learning study of Gu and his team.

The application of Variation Theory is much wider than just the domain of mathematics teaching, but rather is a theory that underpins how students learn anything. The principle that underpins the theory is that new learning occurs when learners understand how a critical aspect of a new concept changes (varies) against something that does not change (invariance).

By adjusting their perception of what has remained the same and what has changed, students are more likely to learn the object of learning and understand the underlying mathematical structures being studied.

In other words, it is when an educator carefully constructs questions, considers the order in which they appear, and brings the thinking process between questions to the forefront for the learners, so that meaningful connections to the mathematical structures can be made from the task.
It is unlikely that a worksheet on its own will bring about the required cognitive process in students needed to benefit from the advantages that Variation Theory offers students in their conceptualization of mathematical structures.
Do not be deceived into purchasing paid resources that promise to bring about Variation Theory with just a worksheet, unless you can specifically identify how the pattern of variation enacts the principles of the object of learning, and you feel confident that you can bring out these mathematical structures to the students through your questioning in a very deliberate way.

Indeed, as you will see through some examples, attempts at Variation Theory through only a worksheet approach and no dialogue risks student learning less than not trying to use Variation Theory.

What are the types of Variation Theory?

There are two types of Variation Theory; conceptual variation and procedural variation.

What is procedural variation in math?

Procedural variation is a process for the formation of mathematical ideas stage by stage, in which students' experience in solving problems is manifested by the richness of varying problems and the variety of transferring strategies.

It is derived from three parts:

1. Varying the problem

2. Multiple methods for solving a problem

3. Multiple applications of a methodology to similar problems

As with conceptual variation, the key to success is to teach students to look for connections within the mathematical structures from an early age.

What is conceptual variation in math?

Conceptual variation is a process that looks at providing students with multiple perspectives and experiences within a given concept or object of learning. It refers to the strategies a teacher may employ to bring to the forefront critical aspects of the desired learning outcome, and increase their understanding by demonstrating it from different perspectives.

Marton and his team of researchers concluded that students notice difference between different objects of learning before they notice sameness.

When employing conceptual variation pedagogy in classroom discourse, it is best to provide examples that are totally different before looking at examples that are similar. For example, if you wanted to demonstrate to students what a triangle was, it would be best to present a triangle along with other shapes that are not triangles to help students distinguish what it is that makes a triangle.
Is this an elephant?
A common non-mathematical approach to explain this is to look at the animal kingdom.

How is it that we are acutely aware of what an elephant is? We are able to distinguish it quite easily from the countless other members of the animal kingdom. If pressed to answer how we know the picture above is an elephant, the first two features that people describe to explain their certainty are the trunk and tusks.

To which my reply is this: is this therefore NOT an elephant? In order to be aware of certain aspects of a phenomenon, we must experience variation.

Clearly, it is an elephant. But this is a tuskless elephant, and tusks are one of the distinguishing features of an elephant that many people claim. Perhaps we could go on to explain that the size of an elephant is a distinguishable feature, or the gray color. An elephant must be gray, have a trunk, be big, and can have tusks, but this is not a requirement.

My reply is: if that is the case, is this an elephant?

Patently it is. Yet, this is hardly a big animal and so would not meet the conditions placed upon it to characterize it as an elephant from above. Therefore, an elephant can be large or small, have tusks or not have tusks, be gray and have a trunk. The necessary conditions of what constitutes an elephant become ever clearer.

We also know, instinctively, that this picture is not an elephant despite it being small, gray and not having tusks. We know it cannot be because of the ears, the shape of the head and the lack of trunk. And here, through our visual perception, the idea of Variation Theory comes to life.

By seeing what it is to be something in as many different forms as possible and in forms that are related, be it closely or otherwise, we are able to see that concept from multiple perspectives and experiences to truly know it. At its most basic level, this is conceptual variation.

Examples and non-examples of Variation Theory

As mentioned above, we tend to recognize sameness before we recognize difference. It is from this principle that we can consider introducing critical aspects of mathematical structures through examples and non-examples that we share with students.

In this instance, to remain true to Marton's findings, the examples that demonstrate the critical object of learning that we want students to learn will be invariant, but the background in which we teach will vary. Subsequently, when we show non-examples they act, as one might imagine, to define what the critical aspect is not.

For example, if teaching the meaning of the equal sign, you could have examples of different equations using all four operations where the answer was correct and examples using all four operations where the answers were incorrect and so the equivalence sign could not be used.

Standard and non-standard in Variation Theory

Once students have developed a sense of what the critical aspect is and is not, it is important to then demonstrate this aspect in both standard and non-standard forms.

I remember the first time that students I was teaching came across an equation on where the equal sign came before any digits and other symbols '__ = 8 + 9'. There were looks of bewilderment as if they had been tasked with the impossible. The fault of this confusion was entirely my own as every question I had ever asked focused on the standard form when writing equation '8 + 9 =__'.

This meant that students had not fully grasped the concept of the symbol and its critical feature; that it is there to represent equivalence, not just as a symbol that is used to write down an answer afterwards.

In my teaching sequence for teaching equivalence and the equals sign, after looking at examples and non-examples, I should have then looked at standard and non-standard forms like those below:

__ = 8 + 9

10 + 7 = 8 + 9

This graphic might be useful in highlighting how these components fit together.

Procedural variation: what's the same, what's different and what do you notice?

We can use procedural variation to highlight patterns within a set of questions that bring about a critical learning point or object of learning. Say we wanted to draw students' attention to one of the field axioms of multiplication - distributivity - so that they can employ it at will when dealing with any multiplication. We may present this in the following way:

The incorrect way to go about this would be to treat this as a worksheet, in which you deliver an input and tell the students to go ahead and complete it. There would be no method to that madness, and the opportunities for bringing out new and previous learned relationships between the numbers would likely fall by the wayside for all students, or would only be found by those who are high attaining in mathematics.

Rather, a more controlled approach should be taken. You should ask students to complete the first two questions and then ask them, 'what is the same, what is different and what do you notice?' This will provide the opportunity to pick up on what the design of these minimally different questions is attempting to draw out.

Procedural variation steps

Firstly, you would want students to notice the relationship between the multiplicand from the given statement (12) and the combination of the multiplicands from the first two equations (11 + 1 and 10 + 2). Students will be drawn to the fact that they all total the same and that the product is also going to be 96.

From here, students can see if that holds true for the next two questions. The danger of letting students complete all 4 questions first without discussing it could result in students seeing that the product is the same, but not understanding the relationship between the multiplicands.

Notice that the 5th question in the sequence does not maintain the same pattern exactly. The multiplicands total 12, but the multiplier is now half of the original. This is to stop students aimlessly writing 96 down without giving any thought.

Crucially though, the statement at the beginning can still be used to solve this as the answer will be half of 96. This relationship between the multipliers can also be brought out. Question 6 allows the commutative property of multiplication to come through, as well as the associative property, and the final question reinforces division as the inverse of multiplication.

At all points of getting students to answer these questions in a controlled environment, the questions, 'what is the same, what is different and what do you notice?' are the ones used most, so that students can attend to those differences and similarities. Indeed, completing the above exercise could take up the vast majority of the lesson and students would get more from completing it than a whole worksheet.

Problem solving in procedural variation

At the heart of procedural variation are three forms of problem solving:

1. Varying a problem - extending the original problem by varying the conditions, changing the results and generalization;

2. The use of multiple methods of solving a problem by varying the different processes of solving a problem and associating different methods of solving a problem;

3. Multiple applications of a method by applying the same method to a group of similar problems.

1. Procedural variation: varying the problem

This form of variation aims to consolidate a concept by varying certain conditions to bring information, often information that is in conflict with students' current understanding of the concept, to light. Look at the example below:

The variation within these problems should be self-evident. The amount of apple juice remains a constant, with only the amount that each jar holds getting varied question by question. Students are often comfortable with division as sharing into equal groups (especially at elementary school), where students may generalize that dividing results in making something smaller.

It is this misconception that the example above attempts to exploit through the last three questions. Indeed, we see that dividing by a whole number and decimal produces a quotient greater than the dividend.

2. Procedural variation: varying the method

This type of variation is one that many teachers do, but may not be aware of. Simply teaching and demonstrating different methods in solving a problem is the first step in this type of variation, but its success lies in being able to draw out what students notice about the similarities and differences between each representation. Here are a few worked examples to vary the method for solving 12 × 5.

3. Procedural variation: multiple application of a method to similar problems

This final example looks at bringing about variation, not through changing the method, but with the application of a method or representation against a group of varied yet similar problems.
Variation Theory examples for elementary school
In elementary school, this may look like the following:
1) James has 8 flowers and Julie has 5 flowers. How many flowers are there altogether? 2) James has 5 flowers and Julie has 8 flowers. How many flowers are there altogether? 3) There are 13 flowers, some are red and some are blue. 8 are red. How many are blue? 4) There are 13 flowers, some are red and some are blue. 8 are blue. How many are red?
Here the problems are varied, yet placed within a similar context, and the numbers used are the same, yet what each question is asking students to do differs slightly.

For example, for question one, students may use Cuisenaire rods to visualize the problem. They would lay down the yellow rod and the brown rod to make a train and then the orange and the green above (or below) to help solve the total.

Question two enables students to experiment with the commutative property of addition. Notice how all the rods used are the same, but the order in which the bottom train has been constructed has changed. The underlying structure remains unchanged.

Question three tells us that there are thirteen flowers altogether and 8 of them are red. The next step would be to see how many more are needed to take 8 up to 13. Students may initially use white rods before exchanging it for a yellow rod of equal value. Again, the underlying structure of the problem remains unchanged.

The final question is merely the inverse of question 3. We know the total amount of flowers and that a certain subset of them equals 5. Therefore, to find the missing amount, we need to count up from 5 until we get to 13. Again, students may need to use 8 white rods first, but they will see that this can be exchanged for a brown rod.

By the end of this exercise, students will be able to see that the 4 questions have similar underlying structures despite the variation within the problems.

Variation Theory worked examples

As mentioned above, just providing students with questions that contain aspects of Variation Theory will not bring along the benefits of the approach. Therefore, if you do not understand the variation taking place, it would probably be best not to use those examples.

For each of these, we need lots of examples of what the type of variation you're referring to looks like 'in practice'. In other words, with reference to regular sorts of questions and learning objectives from your school's curriculum, so teachers can read it and see how they could try implementing it in their own lesson.

If you can pull from different topics in your curriculum that would be great, but it's really just a case of showing the wide variety of ways people can think about including this practice in their teaching.

Number examples: number and place value

The examples below vary the representations to give access to the same idea. This approach can be easily transferred across all grade levels to look at place value objectives. Using this in an elementary class would involve looking at each representation and guiding the students through the process of asking 'what is the same, what is different, and what do you notice?'

Introducing students to these questions early on will hopefully result in them becoming internalized automatically and so students will come to naturally ask themselves these questions.

The use of color is particularly useful here as it supports connections between the place value counters, cards and base 10, but the presence of the Cuisenaire rod and the Numicon (whose colors do not conform to this) stops the association of 'tens' being green etc.

A crucial element to draw out of students is the unitization of 2 in some representations or where the 2 has been conserved as 2 ones. The number grid provides an opportunity to link these representations within the abstract number system.

Number examples: addition and subtraction

563 - 100 = ___ - 200

387 - 100 = ___ - 200

983 - 100 = ___ - 200

___ - 100 = 874 - 200

This question focuses on subtracting by multiples of 100 and students' understanding of the equal sign. It is the subtrahend that remains invariant while the minuend varies. This is done so that generalizations can be brought about in regard to the subtraction of multiples of 100. The minuends themselves play no major role in bringing about the effects of Variation Theory.

Here, we would want students to understand that 'equals' does not mean 'answer', but rather that two mathematical statements are balanced and produce a product that is the same as each other.

We can also bring about the relationship between the two minuends, one of which is unknown, when compared to the effect of subtracting the first one by one hundred. Namely, that the tens and ones do not change and that as the subtrahend has increased by 100 from 100 to 200. In order for the proportionality to remain constant between each statement, the minuend must also increase by 100.

It would be in the interest of students to quickly subtract a multiple of 100 from a 4-digit number where the difference is a 3-digit number in subsequent lessons so then they can see the impact this can have on the generalizations they are producing.

Number examples: multiplication and division
What is the same/different and what do you notice?

__ × 5 =__

5 × __ =__

__ =__ × __

__ + __ + __ + __ + __ = __

__ × 7 =__

7 × __ = __

__ =__ × __

__ + __ + __ + __ + __ + __ + __ = __
Write what you notice below.
This task links multiplication to the array/area model of multiplication, the understanding of the equal sign, the commutative property of multiplication and multiplication as repeated addition.

Students will recognize that the answer is 35 and that in the first model they can see 7 groups of 5 when looking vertically across from left to right. When looking at it horizontally from top to bottom, 5 groups of 7 can be seen.

They can use these facts to write a multiplication equation where the product is written first to bring about their understanding of the equal sign, and relate the multiplication of each vertical column to repeated addition of the number of columns in total.

The opposite is the case with the second representation where there are 5 groups of 7 on the horizontal and 7 groups of 5. Such activities will aid in students' understanding of the difference in visual representation when the same numbers are used as multiplicand and multiplier across two different equations.

Number examples: fractions, ratio and proportion

This series of questions is designed to link all the above areas of fraction as well as ratio. This is important as the connections between percentages and ratio can be missed and so more time than needed is used to teach the concept of ratio.

Here the methods used vary but the question is exactly the same, albeit in the context of the concept that it is drawing out.

As such, the answer will be exactly the same for each question (24), but the methods and mathematical thinking behind each approach will draw out the connection between the question, as well as the different representations that have been used, such as the numerator and denominator of a fraction. Notice how all of the above are either concrete or pictorial.

Measurement examples

The following task comes from @J0shMartin and his contribution to Craig Barton's Variation Theory website. Although this is predominantly a high school-based website, there are some examples that are relevant to elementary school. The following task requires students to notice patterns when converting between measurements (something students should have some understanding of doing BEFORE they embark on this task).

The answers are provided below:

As this is a context that many teachers are familiar with, here it would be best for you to try and consider how the questions have been carefully crafted to bring about variation, and how you might go about using this sequence within your own lesson.

Consider the questions you would ask, the number of questions you would get the students to answer before stopping them to discuss the task so far, and how you would explain the patterns to the students.

Geometry examples: properties of shapes

Property of shape is a particularly useful curriculum area to deploy Variation Theory and can be used from kindergarten onwards to great effect. Below is a sequence of slides used in a lesson on describing rectangles with some kindergarten students.

The rotation, color and the type of shape have all varied so that students can generalize about the properties of rectangles (many believed that the ones on slide 17 and 19 were not), so they can really see the distinguishing features of the shape and not get caught on elements that are not important.

This is the conceptual variation as outlined at the start of this blog in action. It uses examples and non-examples, standard and non-standard examples to draw out what it means for a shape to be a rectangle.

What is variation theory?
Enjoyed this? Why not try our 'How I Wish I'd Taught Math' series, inspired by Craig Barton's bestselling book:
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The content in this article was originally written by primary school lead teacher Neil Almond and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza

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What Is Variation Theory? A Guide For Elementary Maths Teachers

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In this blog, we demystify Variation Theory for teachers and share examples of how to bring this to life in the classroom.

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All Posts

In theory, Norman Webb's Depth of Knowledge (DoK) makes sense. But, many teachers feel they're missing a puzzle piece.

That's because there are hurdles to consistently applying each of the four DoK levels in your classroom, from recall and reproduction to extended critical thinking.

Above all, it demands creativity and calculated preparation to deliver engaging tasks that range in complexity - all while providing scaffolding.

This resource will help.

All about applying Webb's Depth of Knowledge in your classroom at different DoK levels, it offers definitions, questions, examples, activities and strategies you can use.

What is Webb's Depth of Knowledge definition?

Based on his 1997 study, Webb's Depth of Knowledge is a framework that categorizes contexts - prompts, scenarios and challenges - into four levels of rigor. As students progress through the DoK levels, they will face contexts in assessments that demand learning and thinking at deeper cognitive stages.

A first-level challenge may only require reciting a math fact. A final-level scenario may involve solving a real-world issue using content from different subjects. Keep in mind:

In action, these context levels look different between subjects and age groups

A student doesn't have to "master" learning and thinking at one level to progress to the next

As a teacher, you can deliver different levels to your students through diverse activities, assessments and assignments

The Depth of Knowledge wheel (and why educators shouldn't use it)

As you'll soon see below in depth, there are four DoK levels:

1. Recall

2. Knowledge application

3. Strategic thinking

4. Extended thinking

Referencing DoK levels should help you create an engaging classroom environment, filled with distinct thinking and learning experiences.

But, before we go on, there's something you should know about the "Depth of Knowledge wheel". You've likely seen the circular DOK diagram, broken into four parts, with accompanying activities attributed to each level.

Webb does not endorse the DOK Wheel Chart

Fun fact: While it may be an interesting (and popular) visual, the DOK wheel that's commonly referenced as Webb's work was not actually endorsed by Webb himself.

As John Walkup, Ph.D. and founder of The Standards Company, writes:

Understanding DoK levels 1 to 4

Recall: DoK level 1

The first Depth of Knowledge level is defined as recollection and reproduction.

Rooted in simple exercises and procedures, students must remember facts, terms and formulas. There is little to no need for extended processing, as there aren't opportunities to "solve" anything. A student will or will not know the answer.

Application: DoK level 2

The second Depth of Knowledge level is defined as knowledge application.

Students must choose the appropriate route to correctly solve a question, making decisions and completing distinct steps along the way. For example, as opposed to reciting a math fact, they may have to solve a multi-step equation. To successfully do so, they may have to apply information in a different way or scenario than they learned it.

Strategic thinking: DoK level 3

The third Depth of Knowledge level is defined as strategic thinking.

Students must face problems and scenarios that are more abstract than those in the previous level. Often, there may be different correct steps and answers. For example, writing an essay based on a defined topic can lead students in unique directions. As a result, they'll likely reach dissimilar conclusions.

Critical thinking: DoK level 4

The fourth Depth of Knowledge level is defined as extended critical thinking.

Students will get a mental workout. To complete a given challenge, they must typically gather information from different sources and disciplines.

These challenges - such as problem-based learning activities - are usually linked to real-world problems without clear solutions, requiring students to justify their ideas and address counterpoints. As a result, students must critically think over relatively-long periods of time.

Webb's Depth of Knowledge questions for every level

1st level Depth of Knowledge question stems

Asking specific questions can launch activities, exercises and assessments that only require recollection and reproduction. For example:

How would you use these questions in, for example, math class? You could ask each student to reproduce a specific formula on paper. Then, test recollection of math facts by calling out numbers for them to plug into the formula.

How about language arts class? If the class recently explored a book's theme, ask students if they remember the activity. Then, everyone can write down steps the class took to identify the theme. As a bonus, the product serves as a template to help them determine elements of future stories.

Just make sure your questions are basic. This helps ensure exercises don't require deep thinking levels.

2nd level Depth of Knowledge question stems

Like the first Depth of Knowledge level, you can ask specific questions to launch exercises that build skills and understandings of concepts.

To get students in the proper mindset, ask:

Returning to the example of math class, you can reinforce concepts by holding a classwide discussion around the different ways to use a formula. You can subsequently provide worksheets that require solving questions with the formula.

In language arts or a similar subject, you can ask students to work in small groups to identify and explain a book's core plot points. This helps them understand concepts surrounding plot devices while developing analytical skills to dissect them.

You can use such questions to frame activities across grades and disciplines.

3rd level Depth of Knowledge question stems

Question stems that promote strategic thinking include:
Strategic Thinking
How would you test ____?

What would happen if ____? Why?

Can you predict the outcome of ___? How?

What conclusions can you draw from ____? What

facts would you use to support the argument that ____?

What is your interpretation of ____? Support your theory or ideas.

Explain and justify the single best answer to this open question: ____?

The goal of such questions isn't solely to gauge a student's understanding of lesson material, but to have them link concepts through independent thought.

Active learning strategies use a similar tactic.

4th level Depth of Knowledge question stems

To encourage continuous strategic thinking, questions must be open-ended. This requires students to independently research and - in the spirit of interdisciplinary learning - fuse information from different classes and subjects.

Some examples include:
Extended Critical Thinking
What information can you find and use to support your idea about ____?

Follow the scientific method to design and conduct an experiment, using ____.

Write and defend a thesis, forming your conclusion based on at least __ number of sources.

Apply information from one source to another source in a different subject. Develop an argument about the overarching topic.

From this list of topics I provide, pick one you know nothing about. Research the topic using at least __ number of sources.

Whereas the third level aims to spur strategic thinking, fourth-level questions should result in products born from longer periods of critical thought.

DoK questions for math

Adaptive and curriculum-aligned, Prodigy Math delivers questions that reflect Webb's DoK levels one to three.

This helps students build skills and exercise strategic thinking in an exciting fantasy world where answering math questions correctly allows them to progress through the story.

Plus you can make your teacher account for free and start enjoying all of its time-saving tools and features.

Try Prodigy today! 🎉

Depth of Knowledge activities for any subject

Level 1 DoK

Despite a question's simplicity, you can still provide your class with many activities, having them finish a range of products. Depending on the question's purpose, students can:

Paraphrase a passage or chapter of a book

Outline and re-iterate the main points of a recent lesson

Complete a quiz or series of questions that only requires fact recall or fluency

Make a timeline that maps historical or storybook events in relation to each other

Deliver a short presentation to classmates that doesn't require independent research

While focusing on the first Depth of Knowledge level, you can differentiate your instruction by rotating through this blend of exercises.

Level 2 DoK

Requiring deeper thought than recollection and reproduction, there are many activities that stop just short of the third Depth of Knowledge level. Using questions as starting points, your class can:

Write blog, diary or journal entries

Review texts in pairs or small groups

Complete isolated, multi-step calculations

Synthesize an explanation of a complex concept

Create mind maps that show relationships between topics

Design a physical model to demonstrate a scientific concept or historical event

These activities are time-flexible, lending themselves to many kinds of lessons and assignments.

Level 3 DoK

Activities and products associated with the above questions shouldn't inherently involve long-term research or drawing ideas from different subjects. That would extend into the final Depth of Knowledge level. Keeping this in mind, third-level activities include:

Writing an essay

Composing venn diagrams

Exploring a research question

Delivering a persuasive speech

Preparing and participating in a debate

Completing complex equations related to real-world problems

These may all seem like solo assignments, but some - such as preparing debate points - can involve cooperative learning. Keep this in mind if you feel classroom engagement dwindle due to lack of group work.

Level 4 DoK

Activities that require these longer periods of critical thought lend themselves to high school or older elementary students. But, with a few changes, you can offer similar activities to younger pupils. For example, students can work in small groups to form and test hypotheses under in-class supervision. They can also:

Debate on one side of a contentious issue

Partner or group with other students to complete a cross-subject research report and presentation

Apply lessons from different subjects to pinpoint a problem's underlying issues, subsequently solving it

As they finish products, you'll gain clear insight into each student's distinct thought processes.

Additional Depth of Knowledge questioning strategies to apply in the classroom

Referencing question stems and activity lists are useful steps in designing lessons, but there are other helpful strategies for teaching at each Depth of Knowledge level. Consider:

Keep these strategies in mind as you strive to establish an environment rich with distinct learning and thinking levels.

Final thoughts about Webb's Depth of Knowledge and DoK levels

Whether you see it as basic or complex, effectively applying Depth of Knowledge theory in your classroom takes practice.

Using the questions, examples, activities and strategies in this guide should help you consistently craft engaging lessons that vary in cognitive effort.

So, don't be skeptical if a colleague's strategic thinking exercises have little in common with yours.

It's likely a sign of properly recognizing your students' distinct learning needs and styles.
Join over 2.5 million teachers who also use Prodigy to help engage their students' learning.
Create your free teacher account now!

This resource will help.

The problem with the DOK wheel chart rests on the fundamental, but completely false, premise that teachers can simply select certain action verbs to raise and lower the DOK level of their instruction... In December 2013, I emailed Norman Webb for his views on the DOK wheel chart. Apparently, he is asked quite regularly for permission to use the chart in the mistaken belief that he created it. In his response, Webb explicitly stated that he considers the wheel chart misleading and has always discouraged its use.

Strategic Thinking
How would you test ____?

What would happen if ____? Why?

Some examples include:
Extended Critical Thinking
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Depth of Knowledge: 4 DoK Levels & Proven Strategies to Increase Rigor

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All Posts In theory, Norman Webb's Depth of Knowledge (DoK) makes sense. But, many teachers feel they're missing a puzzle piece. That's because there are hurdles to consistently applying each of the four DoK levels in your classroom, from recall and reproduction to extended critical thinking.

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When I worked with student teachers on developing effective lesson plans, one thing I always asked them to revise was the phrase "We will discuss."
We will discuss the video. We will discuss the story. We will discuss our results.
Every time I saw it in a lesson plan, I would add a note: "What format will you use? What questions will you ask? How will you ensure that all students participate?" I was pretty sure that We will discuss actually meant the teacher would do most of the talking; He would throw out a couple of questions like "So what did you think about the video?" or "What was the theme of the story?" and a few students would respond, resulting in something that looked like a discussion, but was ultimately just a conversation between the teacher and a handful of extroverted students; a classic case of Fisheye Teaching.

The problem wasn't them; in most of the classrooms where they'd sat as students, that's exactly what a class discussion looked like. They didn't know any other "formats." I have only ever been familiar with a few myself. But when teachers began contacting me recently asking for a more comprehensive list, I knew it was time to do some serious research.

So here they are: 15 formats for structuring a class discussion to make it more engaging, more organized, more equitable, and more academically challenging. If you've struggled to find effective ways to develop students' speaking and listening skills, this is your lucky day.

I've separated the strategies into three groups. The first batch contains the higher-prep strategies, formats that require teachers to do some planning or gathering of materials ahead of time. Next come the low-prep strategies, which can be used on the fly when you have a few extra minutes or just want your students to get more active. Note that these are not strict categories; it's certainly possible to simplify or add more meat to any of these structures and still make them work. The last group is the ongoing strategies. These are smaller techniques that can be integrated with other instructional strategies and don't really stand alone. For each strategy, you'll find a list of other names it sometimes goes by, a description of its basic structure, and an explanation of variations that exist, if any. To watch each strategy in action, click on its name and a new window will open with a video that demonstrates it.

Enjoy!
a.k.a. Chat Stations
Basic Structure: Stations or posters are set up around the classroom, on the walls or on tables. Small groups of students travel from station to station together, performing some kind of task or responding to a prompt, either of which will result in a conversation.

Variations: Some Gallery Walks stay true to the term gallery, where groups of students create informative posters, then act as tour guides or docents, giving other students a short presentation about their poster and conducting a Q&A about it. In Starr Sackstein's high school classroom, her stations consisted of video tutorials created by the students themselves. Before I knew the term Gallery Walk, I shared a strategy similar to it called Chat Stations, where the teacher prepares discussion prompts or content-related tasks and sets them up around the room for students to visit in small groups.
a.k.a. Values Continuum, Forced Debate, Physical Barometer, This or That
Basic Structure: A statement that has two possible responses-agree or disagree-is read out loud. Depending on whether they agree or disagree with this statement, students move to one side of the room or the other. From that spot, students take turns defending their positions.

Variations: Often a Philosophical Chairs debate will be based around a text or group of texts students have read ahead of time; students are required to cite textual evidence to support their claims and usually hold the texts in their hands during the discussion. Some teachers set up one hot seat to represent each side, and students must take turns in the seat. In less formal variations (which require less prep), a teacher may simply read provocative statements students are likely to disagree on, and a debate can occur spontaneously without a text to refer to (I call this variation This or That in my classroom icebreakers post). Teachers may also opt to offer a continuum of choices, ranging from "Strongly Agree" on one side of the room, all the way to "Strongly Disagree" on the other, and have students place themselves along that continuum based on the strength of their convictions.

Basic Structure: Students are divided into 4 groups. Three of these groups are assigned to represent specific points of view. Members of the fourth group are designated as "provocateurs," tasked with making sure the discussion keeps going and stays challenging. One person from each group (the "speaker") sits in a desk facing speakers from the other groups, so they form a square in the center of the room. Behind each speaker, the remaining group members are seated: two right behind the speaker, then three behind them, and so on, forming a kind of triangle. From above, this would look like a pinwheel. The four speakers introduce and discuss questions they prepared ahead of time (this preparation is done with their groups). After some time passes, new students rotate from the seats behind the speaker into the center seats and continue the conversation.

Variations: When high school English teacher Sarah Brown Wessling introduced this strategy in the featured video (click Pinwheel Discussion above), she used it as a device for talking about literature, where each group represented a different author, plus one provocateur group. But in the comments that follow the video, Wessling adds that she also uses the strategy with non-fiction, where students represent authors of different non-fiction texts or are assigned to take on different perspectives about an issue.
a.k.a. Socratic Circles
Basic Structure: Students prepare by reading a text or group of texts and writing some higher-order discussion questions about the text. On seminar day, students sit in a circle and an introductory, open-ended question is posed by the teacher or student discussion leader. From there, students continue the conversation, prompting one another to support their claims with textual evidence. There is no particular order to how students speak, but they are encouraged to respectfully share the floor with others. Discussion is meant to happen naturally and students do not need to raise their hands to speak. This overview of Socratic Seminar from the website Facing History and Ourselves provides a list of appropriate questions, plus more information about how to prepare for a seminar.

Variations: If students are beginners, the teacher may write the discussion questions, or the question creation can be a joint effort. For larger classes, teachers may need to set up seminars in more of a fishbowl-like arrangement, dividing students into one inner circle that will participate in the discussion, and one outer circle that silently observes, takes notes, and may eventually trade places with those in the inner circle, sometimes all at once, and sometimes by "tapping in" as the urge strikes them.
a.k.a. Affinity Diagramming
Basic Structure: Give students a broad question or problem that is likely to result in lots of different ideas, such as "What were the impacts of the Great Depression?" or "What literary works should every person read?" Have students generate responses by writing ideas on post-it notes (one idea per note) and placing them in no particular arrangement on a wall, whiteboard, or chart paper. Once lots of ideas have been generated, have students begin grouping them into similar categories, then label the categories and discuss why the ideas fit within them, how the categories relate to one another, and so on.

Variations: Some teachers have students do much of this exercise-recording their ideas and arranging them into categories- without talking at first. In other variations, participants are asked to re-combine the ideas into new, different categories after the first round of organization occurs. Often, this activity serves as a good pre-writing exercise, after which students will write some kind of analysis or position paper.
a.k.a. Speed Dating
Basic Structure: Students form two circles, one inside circle and one outside circle. Each student on the inside is paired with a student on the outside; they face each other. The teacher poses a question to the whole group and pairs discuss their responses with each other. Then the teacher signals students to rotate: Students on the outside circle move one space to the right so they are standing in front of a new person (or sitting, as they are in the video). Now the teacher poses a new question, and the process is repeated.

Variations: Instead of two circles, students could also form two straight lines facing one another. Instead of "rotating" to switch partners, one line just slides over one spot, and the leftover person on the end comes around to the beginning of the line. Some teachers use this strategy to have students teach one piece of content to their fellow students, making it less of a discussion strategy and more of a peer teaching format. In fact, many of these protocols could be used for peer teaching as well.

Basic Structure: Another great idea from Sarah Brown Wessling, this is a small-group discussion strategy that gives students exposure to more of their peers' ideas and prevents the stagnation that can happen when a group doesn't happen to have the right chemistry. Students are placed into a few groups of 4-6 students each and are given a discussion question to talk about. After sufficient time has passed for the discussion to develop, one or two students from each group rotate to a different group, while the other group members remain where they are. Once in their new group, they will discuss a different, but related question, and they may also share some of the key points from their last group's conversation. For the next rotation, students who have not rotated before may be chosen to move, resulting in groups that are continually evolving.

Basic Structure: Two students sit facing each other in the center of the room; the remaining students sit in a circle around them. The two central students have a conversation based on a pre-determined topic and often using specific skills the class is practicing (such as asking follow-up questions, paraphrasing, or elaborating on another person's point). Students on the outside observe, take notes, or perform some other discussion-related task assigned by the teacher.

Variations: One variation of this strategy allows students in the outer circle to trade places with those in the fishbowl, doing kind of a relay-style discussion, or they may periodically "coach" the fishbowl talkers from the sidelines. Teachers may also opt to have students in the outside circle grade the participants' conversation with a rubric, then give feedback on what they saw in a debriefing afterward, as mentioned in the featured video.

Basic Structure: One student assumes the role of a book character, significant figure in history, or concept (such as a tornado, an animal, or the Titanic). Sitting in front of the rest of the class, the student responds to classmates' questions while staying in character in that role.

Variations: Give more students the opportunity to be in the hot seat while increasing everyone's participation by having students do hot seat discussions in small groups, where one person per group acts as the "character" and three or four others ask them questions. In another variation, several students could form a panel of different characters, taking questions from the class all together and interacting with one another like guests on a TV talk show.
a.k.a. Pyramid Discussion
Basic Structure: Students begin in pairs, responding to a discussion question only with a single partner. After each person has had a chance to share their ideas, the pair joins another pair, creating a group of four. Pairs share their ideas with the pair they just joined. Next, groups of four join together to form groups of eight, and so on, until the whole class is joined up in one large discussion.

Variations: This structure could simply be used to share ideas on a topic, or students could be required to reach consensus every time they join up with a new group.

Whereas the other formats in this list have a distinct shape-specific activities you do with students-the strategies in this section are more like plug-ins, working discussion into other instructional activities and improving the quality and reach of existing conversations.

One of the limitations of discussion is that rich, face-to-face conversations can only happen when all parties are available, so we're limited to the time we have in class. With a tool like Voxer, those limitations disappear. Like a private voice mailbox that you set up with just one person or a group (but SOOOO much easier), Voxer allows users to have conversations at whatever time is most convenient for each participant. So a group of four students can "discuss" a topic from 3pm until bedtime-asynchronously-each member contributing whenever they have a moment, and if the teacher makes herself part of the group, she can listen in, offer feedback, or contribute her own discussion points. Voxer is also invaluable for collaborating on projects and for having one-on-one discussions with students, parents, and your own colleagues. Like many other educators, Peter DeWitt took a while to really understand the potential of Voxer, but in this EdWeek piece, he explains what turned him around.

A backchannel is a conversation that happens right alongside another activity. The first time I saw a backchannel in action was at my first unconference: While those of us in the audience listened to presenters and watched a few short video clips, a separate screen was up beside the main screen, projecting something called TodaysMeet (update: TodaysMeet has shut down. Use YoTeach! instead.) It looked a lot like those chat rooms from back in the day, basically a blank screen where people would contribute a few lines of text, the lines stacking up one after the other, no other bells or whistles. Anyone in the room could participate in this conversation on their phone, laptop, or tablet, asking questions, offering commentary, and sharing links to related resources without ever interrupting the flow of the presentations. This kind of tool allows for a completely silent discussion, one that doesn't have to move at a super-fast pace, and it gives students who may be reluctant to speak up or who process their thoughts more slowly a chance to fully contribute. For a deeper discussion of how this kind of tool can be used, read this thoughtful overview of using backchannel discussions in the classroom by Edutopia's Beth Holland.
a.k.a. Accountable Talk
Talk moves are sentence frames we supply to our students that help them express ideas and interact with one another in respectful, academically appropriate ways. From kindergarten all the way through college, students can benefit from explicit instruction in the skills of summarizing another person's argument before presenting an alternate view, asking clarifying questions, and expressing agreement or partial agreement with the stance of another participant. Talk moves can be incorporated into any of the other discussion formats listed here.

Whole Brain Teaching is a set of teaching and classroom management methods that has grown in popularity over the past 10 years. One of WBT's foundational techniques is Teach-OK, a peer teaching strategy that begins with the teacher spending a few minutes introducing a concept to the class. Next, the teacher says Teach!, the class responds with Okay!, and pairs of students take turns re-teaching the concept to each other. It's a bit like think-pair-share, but it's faster-paced, it focuses more on re-teaching than general sharing, and students are encouraged to use gestures to animate their discussion. Although WBT is most popular in elementary schools, this featured video shows the creator of WBT, Chris Biffle, using it quite successfully with college students. I have also used Teach-OK with college students, and most of my students said they were happy for a change from the sit-and-listen they were used to in college classrooms.

An oldie but a goodie, think-pair-share can be used any time you want to plug interactivity into a lesson: Simply have students think about their response to a question, form a pair with another person, discuss their response, then share it with the larger group. Because I feel this strategy has so many uses and can be way more powerful than we give it credit for, I devoted a whole post to think-pair-share; everything you need to know about it is right there.

TWO MORE YOU'LL LOVE

Since writing this post, I have learned about two more discussion strategies that teachers are finding to be incredibly effective and powerful for getting students to talk, especially about books and other texts:

This protocol has students come up with their own Thoughts, lingering Questions, and Epiphanies from an assigned reading. Teachers who have used this method say it has generated some of the richest conversations they have ever heard from students!

This strategy places students into one-on-one conversations, getting them to learn each others' names better and create a track record of what they talked about. Excellent for classes where you want to assess for discussion and help students get more comfortable with each other.

So what else do you have? I would like to think this is a pretty complete list, but I'm sure more strategies are out there. If you use a discussion strategy that's not mentioned here, please share it below.

Come back for more.
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The Big List of Class Discussion Strategies

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Here they are: 15 formats for structuring a class discussion to make it more engaging, more organized, more equitable, and more academically challenging.

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We are cognitive psychological scientists interested in research on education. Our main research focus is on the science of learning. (Hence, "The Learning Scientists"!). Our Vision is to make scientific research on learning more accessible to students, teachers, and other educators.

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The 11 BEST Types of Questions in the Classroom: In-depth Guide

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The types of questions in the classroom can hugely affect classroom engagement. Learn to plan your classroom questioning like a guru!

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I've written about retrieval practice several times in other posts but here I just want to make it easy to lay out various alternative methods for the process of reviewing your students' knowledge and understanding. Before doing that, I would suggest that there are some key principles:

1. Involve everyone: Good techniques involve all students checking their knowledge, not just a few and not just one at a time as you might do when questioning.

2. Make checking accurate and easy: it should be possible for all students to find out what they got right and wrong, what they know well and where they have gaps. Every technique involves students testing their knowledge and then checking their work for accuracy and completeness. (This is not the same as giving students extended mark schemes to mark longer assessments which, for me goes beyond a simple retrieval practice activity)

3. Specify the knowledge: Where appropriate, it's better if students know the set of knowledge any retrieval will be based on, so they can study, prepare and self-check. It must be possible for students to check their own answers which has implications for the way the knowledge requirements are laid out.

4. Keep it generative: students need to explore their memory to check what they know and understand; this means removing cue-cards, prompts, scaffolds and cheat-sheets; it means closing the books and thinking for themselves.

5. Make it time efficient: The idea of each technique is that they can be used repeatedly in an efficient manner without dominating whole lessons.

6. Make it workload efficient: None of these methods involve the teacher checking the students' answers, creating unsustainable workload. A teacher might choose to check the occasional test but that's no use for routine practice.

1. Quick Fire Quiz
Everyone know this one but it can still be done well or badly: Teacher reads out the question or presents them via slides or an audio tape (eg in MFL). The questions can be spontaneously generated or prepared. Questions can be simple factual recall, mental maths or multiple choice;

All students write down their answers. Teacher reveals the answers, one by one or all at once. Students check which they got right. Swapping answers to check is an option but it can be a faff and takes away from the message that students need to be evaluating the depth of their own learning. If you've prepared this in advance, it is much more time efficient if students can see the answers all at once to check rather than wait for each to be read out.

It's important that the teacher discusses common wrong answers - which is one of the main functions. If you can do lots of confidence-building questions quickly (rather than deliberately hard ones) - you can get a great buzz of enjoyment. Knowing things is fun!
2. Paper Quiz
Everyone gets a copy of the questions and writes down answers at their own pace within a time limit. This is much less teacher-directed. It frees the teacher up to circulate and spot common errors as they emerge. It allows for a wider range of question types and makes it easier to engage in with worded questions that can be hard to read from a slide.

The checking process is much better done with pre-prepared answers rather than reading out answers one by one. Why? Because it is quicker, allows for more detail in the answers, it allows students to focus on things they got wrong and helps to build their capacity for self-assessment.
3. Silent Self-Quiz
Try this. Which ones do you know? (Answer provided)

How well can you learn these labels? (Test and then check)

In a test like this, students can generate answers and then check if they were right, silently and privately. They can repeat this multiple times. Any number of resources can be used - blanked diagrams, cue cards with answers on the back, maths questions with answers kept separately. This process keeps the outcome of the assessment with the student - the most important place! They learn what they know and don't know. You can then discuss common errors and problems. It saves a lot of time with asking questions and marking them - all of that is done mentally by the students.
4. Paired Quiz.
Here, we start using Dylan Wiliam's excellent strategy: Activating students as resources for one another. In order to maximise the extent of retrieval practice that goes on, it is fantastic to get students to quiz each other in pairs. One student has the material - questions, answers, cue cards, knowledge organiser, text - and asks the other student questions. "Test me" - it's a well-used technique and can be harnessed in lessons. Give a time limit and then get them to swap around. You get a room full of students checking their knowledge. I've seen this done in superbly well in languages where the teacher circulated to check for accent issues and common errors listening in to the multiple paired quizzing dialogues.
5. Self-Explanation
Beyond simple recall, ask students to explain something to themselves. You simply give students a few silent moments to complete a mental task. They have to generate a version of what they understand that they can either then self-check or write down or use to respond to further question. However the process of mental rehearsal is important.. making this explicit helps to train those who don't do it spontaneously.

What is the story of Henry VIII's Six Wives? Run through it... then check.
6. Demonstration and Performance
Of course LOTS of knowledge isn't simply quiz-able declarative knowledge. You can ask students to show what they know: a procedure; a technique; a routine. Have you learned it? Show me... Of course as a student shows what they can do to a teacher, they are showing themselves what they can do. This is important. Again, the intensity and frequency can be amplified by getting students to show each other in pairs rather than one-by-one with the teacher, as long as they have the tools to evaluate success. This is common in practical areas and performance areas - sport, music, art - but it also has a role in science, maths, English where the modelling process could be framed as 'teaching'. eg teaching the class how to answer a maths problem.
7. Paired or individual elaborative-interrogation
A form of quizzing that can be done in pairs or as a silent private process, is elaborative interrogation. This is where students explore their schema by answering How and Why questions.

Why does this happen? How does it work? Why does it work? Why did she say that? Why do you use that structure? Why is that the most important reason? How do you know?

If you train students to use some of these question stems and give them resources that help them to verify the answers, this makes for a deep retrieval practice exercise
8: Tell the story; rehearse the explanation
Lots of knowledge forms a narrative structure - a series of events, a process, cause and effect. So, the retrieval practice can be formed as 'telling the story' to someone else who can play the role of verifier. Any explanation can then be improved and rehearsed. You can get better at telling a story in more detail.

Here are some examples. Tell the story of a water molecule as if follows the water cycle: (with or without key words provided)

Why does the sun rise in the East?.... How good was your friend's answer? Now you have a go...

Of course this material can be used for self-explanation in the first instance.
9: Summarising
This is a useful recall process although it is less precise in terms of checking - because every summary can be different. A retrieval process can be something like:

Last week we looked at renewable energy. Summarise the main advantages and disadvantages of a wind farm: Go! .

Then show your definitive response for checking:
10. Map and Compare
This method is where you want to check students' capacity to make links. Ask them to make a memory map of the key aspects of a topic... eg: Reactions of Metals OR Themes in Hamlet OR Generating Electricity. These things can be much tighter sections of knowledge too: Types of radiation; the key events and figures in the Cuban Missile Crisis.

Students then make mind-maps in a quick, memory -dump style before checking against a good resource - their knowledge organiser, exercise book or a teacher-completed version: What did you get right? What did you miss out completely?

Trial by Ordeal? What can you remember? Go.....

Further reading: Check out these documents. The summaries by @olicav are superb but also read the original papers they relate to.

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Image Credit: https://emptechgroup.com/the-internet-of-things/ I've written about retrieval practice several times in other posts but here I just want to make it easy to lay out various alternative methods for the process of reviewing your students' knowledge and understanding. Before doing that, I would suggest that there are some key principles: Involve everyone: Good techniques involve...