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Metacognition- Thoughts on teaching mathematical problem solving skills

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Metacognition- Thoughts on teaching mathematical problem solving skills

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How do you go about teaching problem solving skills? How do you teach pupils the thinking skills necessary to solve mathematical problems in contexts that are unfamiliar to them?

These are difficult questions. I'll declare upfront that I don't have the answers to them fully. Nonetheless I have been researching and formulating possible approaches. This post shares with you where I am at with my current thinking and I hope will spark an interesting debate in the comments section where our readers can extend the ideas further.

I'd like to start by associating problem solving skills within the context of metacognition. Research evidence strongly concludes that the teaching of metacognitive skills has a significant impact on pupil progress. In a recent post about The Education Endowment Foundation I introduced readers to their work that shows which intervention strategies are effective on improving pupil progress. The teaching of metacognition and self-regulation has been found on average to improve pupil progress by +8 months. E.g. a pupil taught metacognitive strategies will progress by 8 months more than one not taught it over the period of one academic year. It's clearly important, but how can it be done?

Let's start by saying what it's not. Metacognition has been a buzzword in the Thinking Skills initiative that many schools have participated in over the last decade. It has often been defined as thinking about thinking, which is a bit too vague to be useful. Lessons that try to develop pupils' problem solving metacognitive skills are often in two forms. Either they are very example-led in the hope that pupils will make links in new problems based on their experience base of knowledge from seeing lots of problems solved, or they are open-ended where pupils are given many problems to solve and then those that solve them share their solution methods. The later case is really a more student-led version of the first type where we assume giving pupils many experiences and examples, that they will extract the common strategies and approaches for themselves. I think this is a big assumption and we need to be more explicit. In the same way that giving a pupil who can't do column addition lots of questions to answer doesn't move them forward if you don't diagnose what their issue is, just throwing lots of open-ended maths problems at pupils won't necessarily allow them to develop their own toolkit of problem solving strategies.

For some pupils we need to show them the toolkit and teach them how to use it one tool at a time.

A better definition of metacognition that I've have read is teaching one's brain to control the thought processes it has for the purpose of directing it towards the management of their own learning. It's like the conscious brain becomes a coach for itself. In the same way that we coach pupils by asking questions such as 'what information is given in the problem?' and 'what areas of maths could we use to solve this?', metacognition is when pupils ask these questions for themselves. This comes naturally to some, but not others.

I have a developing interest in Singapore Maths, the national curriculum and teaching methodologies used in Singapore. In their Ministry of Education document The Singapore Model Method for Learning Mathematicsthey define a set of Heuristics for Problem Solving that I think offer a starting point for categorising the various skills we use to solve problems:

Act it out

Use a diagram or model

Make a systematic list

Look for patterns

Work backwards

Use before/ after concept

Use guess and check

Make suppositions

Restate the problem in another way

Simplify part of the problem

Solve part of the problem

Thinking of a related problem

Use equations

Don't these offer us a scaffolded structure for teaching problem solving skills? I think these heuristics act as a problem solving skillset that it would be possible to explicitly teach pupils. When showing them solutions to problems, couldn't they examine this list and see which explicit strategies helped with the solutions? After seeing a range of different contextual problems where the key to their solutions was to make a systematic list, wouldn't the pupils have a learned a valuable problem solving skill by looking in detail and focus at just one? Next time they could focus on problems that require using a guess and check approach and see the common strategy across different problems and contexts. Another lesson could focus on problems that require the drawing of an accurate diagram or model to solve.

Problem solving is a big skillset and something that needs breaking down into bite-size chunks. I think these heuristics offer a decent starting point. The next step will be to find problems that lend themselves to different heuristics so lessons can focus on just one skill at a time before they are then combined. The final step would be to get pupils to identify which strategies could be useful in solving problems. A flow chart could even be made based on the heuristics of things to ask themselves.

That just about represents the extent of my thoughts so far. I can see an opportunity for the teaching of metacognition to be more scaffolded and bite-sized for the pupils who need it that way, rather than some approaches that just label things as metacognition retrospectively when pupils have shown the skills. These thoughts need taking further. The heuristics need evaluating and possibly adding to. Problems that relate to particular heuristics need finding. There is much more work to do here and I hope you can contribute your thoughts and ideas in the comments section below!

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Metacognition... thoughts on teaching mathematical problem solving skills

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How do you go about teaching problem solving skills? How do you teach pupils the thinking skills necessary to solve mathematical problems in contexts that are unfamiliar to them? These are difficult questions. I'll declare upfront that I don't have the answers to them fully. Nonetheless I have been researching and formulating possible approaches.

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Tips For Grading Math Tests that incorporates Metacognition

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Tips For Grading Math Tests that incorporates Metacognition

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Math.Practice.MP1

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. What does Ms. Alcala mean by "flow through" credit?

2. Why does Ms. Alcala review her favorite mistakes instead of the correct answers before passing back the test?

3. How does this grading strategy foster a class culture that values risks and learning from mistakes?

School Details

Martin Luther King Middle School
1781 Rose Street
Berkeley CA 94703

Data Provided By:

Teachers

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Highlighting Mistakes: A Grading Strategy

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Leah Alcala explains how she helps her students learn from mistakes through a grading strategy. When grading tests, Ms. Alcala highlights student mistakes rather than marking or correcting them. She passes back tests without grades so that the students can focus on learning from their mistakes.

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Edutopia is a free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education. We are published by the George Lucas Educational Foundation, a nonprofit, nonpartisan organization.

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Learning about Learning: Resources for supporting effective learning

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Learning about Learning: Resources for supporting effective learning

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For Students, Why the Question is More Important Than the Answer

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For Students, Why the Question is More Important Than the Answer

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That's the premise of the Right Question Institute and a new book by its co-directors Dan Rothstein and Luz Santana. The book, Make Just One Change: Teach Students to Ask Their Own Questions, documents a step-by-step process to help students formulate and prioritize questions about nearly everything.

Coming up with the right question involves vigorously thinking through the problem, investigating it from various angles, turning closed questions into open-ended ones and prioritizing which are the most important questions to get at the heart of the matter.

"We've been underestimating how well our kids can think."

"We've been underestimating how well our kids can think." Rothstein said in a recent discussion on the talk show Forum. "We see consistently that there are three outcomes. One is that students are more engaged. Second, they take more ownership, which for teachers, this is a huge thing. And the third outcome is they learn more - we see better quality work."

On the teacher's part, the role becomes more a facilitator than an instructor.

"What happens is the teacher plays a different role," Santana said. "They lead students into thinking. The process of teaching students to ask their own questions allows teachers to communicate what they need to around curriculum. The difference is that the students are thinking and doing more, rather than the teacher."

Rothstein and Santana call their method the Question Formulation Technique. The idea is that if students are engaged in deciding what question to answer they will also be invested in discovering the answer. Both teachers and students say the method has been both empowering and difficult. Kids who had long been struggling in school said they felt smart, the authors said.

It's a bit like the Socratic method flipped on its head. Socrates wandered around Athens asking questions to get at a deeper truth. Since then philosophy and law teachers have used questions as a way to get students to think more deeply, rather than giving them the information directly. The Question Formulation Technique turns that dynamic around and asks the students to come up with the questions that speak to the core of a topic. The quest is for the question, not the answer.

If the concept feels a bit opaque, the book lays out a step-by-step process for guiding reticent students along the Socratic path, even laying out potential road blocks and work-arounds, which were developed over years of trial and error. In the end, students develop higher order thinking skills that will help them make decisions and think for themselves in any situation throughout life. Santana calls these "foundational skills" that are rarely taught formally, even though they are used all the time.

An excerpt of Make Just One Change below lays out rules for students to follow as they produce their first set of questions. The questions are focused around what Rothstein and Santana call the "Question Focus" or "QFocus." This is a guiding topic for the questions that students should be producing.

Rule 1: Ask As Many Questions as You Can (Gives License to Ask). There are a number of potential stumbling blocks related to this rule, including:

Students struggle trying to produce the questions: Give them time to think. Repeat the QFocus and the rules but do not give examples of questions.

Students ask for examples: Do not give examples. Repeat: Do not give examples. When you give examples you are setting direction for the questions. Students need to struggle with this a bit. If they are completely stuck, you can use question starters. For example: "You can start a question with words like what, when or how. Use one of these words to produce a question about [our QFocus]." Question starters will be a good strategy for when students are stuck or when they have produced very few questions.

Groups are working at different pace: While some of your small groups will have lots of questions, others will not. This is fine. The work during this exercise should not be judged by the number of questions students produced. If some of your groups are slow in producing questions, just make sure they stay on task by reminding them of the rules.

Some students are not participating or one student is producing all the questions: Remind students about the task and the rules. All group members should contribute questions including the scribe. Remind students of this first rule. All questions are welcomed and valued which will allow the reluctant student to participate.

Rule 2: Do Not Stop to Discuss, Judge, or Answer Any Question (Creates Safe Space and Protection). Students want to answer a question as it comes up. This rule says it all: do not stop to answer, judge, or discuss. Let students know that there will be opportunities for discussion and addressing the questions in other steps of the process.

Rule 3: Write Down Every Question Exactly as It Is Stated (Levels the Playing Field So All Questions and Voices Are Respected.) Sometimes it will be difficult for the scribe to keep track of the question and all the words. The challenge is to make sure each question is captured, especially if there's a flurry of questions. Remind students that the whole group is responsible for each question to be written exactly as it was asked. Group members can help the scribe in remembering and recording all the questions.

Rule 4: Change Any Statement into a Question (Insists on the Discipline of Phrasing, Asking, and Thinking in Questions, Not Statement). Potential challenges that may arise with rule 4 include:

Students get off task and start talking: Make sure students stay focused on asking questions. Sometimes you will see students getting off-task -- talking or discussing. other times they might think they have asked a question when they have not, using statements or even phrases rather than questions. If you see any of these happening just ask them to change what they were talking about or the statement they wrote into a question.

Students are confused about the instructions: Confusion could be a result of requesting students to work differently. Repeat the QFocus and the rules to clarify but do not overexplain.

The QFocus is not working: It is important to have a backup plan if the QFocus doesn't work. Plan alternative ways to present the same QFocus. Do not try to explain or give information about the QFocus but give the instructions in a different way. "I want you to ask questions about [alternative QFocus]." Explore with students what is it that they don't understand; this will allow you to restate the instructions in a way they understand.

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For Students, Why the Question is More Important Than the Answer

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In a traditional classroom, the teacher is the center of attention, the owner of knowledge and information. Teachers often ask questions of their students to gauge comprehension, but it's a passive model that relies on students to absorb information they need to reproduce on tests.

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Teach Students to Ask Their Own Questions

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Teach Students to Ask Their Own Questions

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Thanks to a grant from the Library of Congress Teaching with Primary Sources (TPS) program, RQI collaborated with seven classroom teachers to develop a series of lesson snapshots that demonstrate how the Question Formulation Technique (QFT) can be used for primary source learning.

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Thanks to a grant from the Library of Congress Teaching with Primary Sources (TPS) program, RQI collaborated with seven classroom teachers to develop a series of lesson snapshots that demonstrate how the Question Formulation Technique (QFT) can be used for primary source learning.

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The Role of Metacognition in Learning and Achievement

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The Role of Metacognition in Learning and Achievement

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To illustrate the value of metacognition and how it actually plays a role in learning, we can consider an example from mathematics, where it has been shown that metacognition plays a central role in learning and achievement. Specifically, when novice students were compared to seasoned mathematicians, the students selected a seemingly useful strategy and continued to apply it without checking to see if the strategy of choice was actually working well. Thus, a significant amount of time was wasted in fruitless pursuits. The more experienced mathematicians on the other hand, exercised metacognition, monitoring their approach all along the way to see if it was actually leading to a solution or merely to a dead end.Being aware of how one is engaging with the process of learning influences how the student interprets the task at hand, and what strategies are selected and employed in service of achieving learning goals. It can help optimize the problem-solving experience at a very high level, and is thus applicable across a large range of contexts. These metacognitive strategies are powerful tools for any discipline, inter-discipline or for learning in general.

Of course, with such an abstract learning goal, it is important for educators to be precise with how they teach it. Traditional methods for improving students' learning strategies often focus on prescribed procedures (note-taking, self-testing, scheduling, etc.) and typically result in initial motivation and some short-term improvement, but ultimately a reversion to old habits happens. While these tactics may work in the short term (e.g., to cram for an exam), once the context changes, successful transfer of these methods is less likely to occur. More strategic methods that focus on metacognition for deeper learning- such as developing a growth mindset (discussed later), setting and monitoring one's learning goals, and growing one's capacity to persist despite difficulties-have been shown to result in more permanent learning gains.

It is important to note that since metacognition involves higher-level thinking overseeing lower-level thoughts, there is actually a range of mental processes that fall under its definition. Effects of metacognitive training vary based on what kind of lower-level thoughts are being overseen, and how they are being overseen. Research has identified three levels of reporting on metacognitive processes:

1. Verbalization of knowledge that is already in a verbal state (such as recalling what happened in a story).

2. Verbalization of nonverbal knowledge (such as recalling how one solved a Rubik's Cube).

3. Verbalization of explanations of verbal or nonverbal knowledge (such as explaining how one makes use of the rhetorical structures of a story as one reads).

Only this third level of metacognitive process has been linked to improved results in problem solving.

Metacognition can be developed in students in the context of their current goals and can enhance their learning of competenciesas well as transfer of learning, no matter their starting achievement level. In fact, it may be most useful for lower-achieving students, as the higher-achieving students are already employing strategies that have proven successful for them. For learning disabled and low - achieving students, metacognitive training has been shown to improve behavior more effectively than traditional attention-control training.

Students who have higher levels of self-efficacy (more confidence in their ability to achieve their goals) are more likely to engage in metacognition and, in turn, are more likely to perform at higher levels. This strongly indicates a positive feedback loop for high-achieving students-they are more successful by using metacognitive strategies, which increases their confidence and in turn leads them to continue to increase their performance. Metacognition is an integral part of this virtuous learning cycle, and one that is amenable to further improvement through instruction.

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The Role of Metacognition in Learning and Achievement

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To illustrate the value of metacognition and how it actually plays a role in learning, we can consider an example from mathematics, where it has been shown that metacognition plays a central role in learning and achievement.

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15 ways to spark student reflection in your classroom

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15 ways to spark student reflection in your classroom

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In a recent survey of educators conducted by THE Journal, an overwhelming number - 81 percent - considered reflection skills very important. This doesn't come as a surprise. The ability to learn from mistakes and recognize strengths and weaknesses can make the difference between success and failure, in school and beyond.

Are you looking for some new ways to increase student reflection in the classroom? Here are 15 ideas you can try tomorrow:

Help students get started by providing sentence starters like "I was surprised when..." or "I'm still wondering about...." Here's a great source for many more.

Try getting your students to sketch a picture that represents what they've learned from a project. Remember it's not about the quality of the art - it's about how drawing prompts students to look at their learning from a different perspective.

Especially with young students, putting reflection questions on dice is a fun way to vary the reflection experience. Here's a virtual die that a teacher created using QR codes, but you can also do this the old-fashioned way by writing questions on a blank cube.

4. Teach a peer, a younger classmate or a parent

It's often said that the best way to learn something is to teach it to someone else - it's also a natural way to reflect. Plus encouraging students to teach each other is just another way to create a student-centered collaborative classroom.
Opening up a reflective dialog with parents can deepen the experience for your students. With a digital portfolio,LMS or other cloud-based solution, students can post a project, add a reflection and then get their parents to add comments.
Journaling is a tried-and-true reflection activity, but these days there's no need to restrict yourself to paper and pencil. Blogs and vlogs work just as well for getting students to regularly reflect.

This one's not for the faint of heart, but in the right class it can be a fun way to shake things up. After a lesson, all your students write a key reflection on a sheet of paper and crumple it up. Then they toss their papers to the other side of the room. Once students catch a "snowball," they read it, add something new and repeat.

8. Use videos

To give your students a fresh perspective on a presentation, performance or evensocial skill development, pull out your phone or tablet and record it. Watching themselves can give them (and you) incredible insights into their progress.

9. Write exit slips

This idea has been popular for a while for a reason - it's a good one. Before students leave your class, ask them to quickly jot down what they've learned (or answer another reflection question) - it can be that simple. And if you're looking for new ways to use exit slips, check out this Edutopia blog post.

10. Capture weekly learning highlights

On Fridays, have each student capture their number one insight of the week and post it to a shared space - you could use sticky notes on a wall or take the process digital with Nureva visual collaboration solutions. You'll not only build reflection skills, you'll also see at a glance what's resonating with your students. Here's how one school used their Nureva™ Wall and Span™ software to make student thinking visible.

11. Take reflection breaks

Reflection can't be forced, but it is a habit that can be instilled. Build reflective practice by stopping work periodically and encouraging students to record their thoughts. Eventually, students will start to reflect on their own, without teacher direction.

12. Use a reflective taxonomy

Peter Pappas' taxonomy of reflection is a gold mine if you're looking to approach reflection from some different angles. He's taken Bloom's more familiar model and mapped reflection questions to it.

13. Incorporate revision into assessment

Some of the best opportunities for reflection occur during the assessment process. Rather than having students submit work for a grade and then promptly forget about it, try giving them descriptive feedback instead and let them resubmit until they achieve mastery.

14. Teach the growth mindset

Reflection only works if students truly believe they can get better results with hard work and that intelligence isn't a fixed trait. To help students internalize these ideas, try introducing Carol Dweck's growth mindset concept and talk specifically about how you can talk back to the fixed mindset voice they might have.

15. Model your own reflection

Actions speak louder than words. So make sure to model the same reflection skills you teach. Don't be quiet about it either - talk out loud through your thought process to show students that reflecting doesn't stop once schooling is done.

Let's keep adding to this list. What are you doing in the classroom to get students reflecting?

FREE EBOOK

Are you looking for new student-led learning ideas? In this eBook, you'll find more than 20 collaborative activities you can try in your classroom right away.

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15 ways to spark student reflection in your classroom

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In a recent survey of educators conducted by THE Journal, an overwhelming number - 81 percent - considered reflection skills very important. This doesn't come as a surprise. The ability to learn from mistakes and recognize strengths and weaknesses can make the difference between success and failure, in school and beyond.

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Project Zero: Visible Thinking in Action

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Project Zero: Visible Thinking in Action

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What Meaningful Reflection On Student Work Can Do for Learning

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What Meaningful Reflection On Student Work Can Do for Learning

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The following excerpt is from "Authentic Learning in the Digital Age: Engaging Students Through Inquiry," by Larissa Pahomov. This excerpt is from the chapter entitled "Making Reflection Relevant." Characteristics of Meaningful Reflection
For student reflection to be meaningful, it must be metacognitive, applicable, and shared with others. Let's look at each of these characteristics in turn.
Metacognitive
Although it's something of a buzz word, "metacognition" is a state of mind that can be useful for all the core values presented in this book. If students are metacognitive about inquiry, then they're thinking about exactly how they are going to phrase that question; if they're metacognitive about collaboration, then they're considering how their introvert or extrovert personality will affect the group. Metacognition is essentially reflection on the micro level, an awareness of our own thought processes as we complete them. So what does metacognitive reflection look like?

By sharing their reflections on their academic work, students can both advise and seek help from their peers. Sharing their achievements helps those who struggled with that particular task, and sharing their weak spots helps them troubleshoot as they work through a problem set or have a peer edit a rough draft.

When children are first learning to reflect on their work, their educators use simple prompts to get them thinking: Do you like what you made? Did you do a good job? Eventually, they are also asked to consider the process: What did you learn from this task? Usually these questions are posed by an outsider-a parent or a preschool teacher, for example-who asks the learner for a simple assessment of the outcome. Metacognitive reflection, however, takes this process to the next level because it is concerned not with assessment, but with self-improvement: Could this be better? How? What steps should you take? As a result, metacognitive reflection can be used to develop resilience in the face of a challenge. Many young children (and some adults) will throw down their work when they become frustrated with it, unable to transcend the struggle. By contrast, a student who has learned the value of metacognitive reflection will recognize frustration as a signal to pause and think through the situation instead of plowing ahead with the same approach or giving up entirely.

Of course, there's a danger of this metacognition turning into a kind of feedback loop: Am I reflecting adequately on my reflection? The better question to keep in mind is, How is this reflection going to help me in the future? In many cases, "the future" is just a few minutes away, but this mindset can also apply to cumulative reflection over a unit, a school year, or a lifetime.

➤ The digital connection. Students who are not naturally inclined to stop and think need explicit practices to nudge themselves toward quality reflection-and digital tools to make it easier. Keeping a log of tasks and habits, for example, gives students a rich source of data to mine when reflecting on their progress, and there are many apps that will collect and aggregate this information in accessible and attractive ways. The myriad of daily journals, goal-setting programs, and "productivity" apps help to create a regular time and place for reflection, which students can use toward academic or personal projects. Even using a simple timer can help students chunk out their work so they take a reflective break, and some programs have breaks built into the timer cycle, so that a pause from the work is guaranteed.
Applicable
The reflective question in the SLA admissions interview is a great tool for getting to know the student, but it doesn't do much to actually serve their learning process. It's completely divorced from the setting where the student actually did the work, and besides, the student already completed the project.

This kind of isolated, after-the-fact reflection dominates our understanding of the process. When asked to imagine a person reflecting, you probably conjure up an image of an individual alone, in a comfortable place, staring off into the distance, plaintively contemplating some earlier life event. This scene is likely set at the end of a calendar year, or at the end of a lifetime-or, if you imagined a professional setting, at a retirement party. These kinds of personal reflections contribute to the richness of life, because through them we are able to appreciate how our path has shaped our existence. But what about the life that is still to be lived and the work that is still to be done? Unfortunately, this sentimental notion of reflection for reflection's sake keeps the practice from being used for active improvement in the here and now. Academic reflections, for example, often take place at the very end of the course, when both the professor and the student will be moving on to other courses and teaching loads. Students are not typically asked to consider how their performance evolves over the years either. Even though teachers often have a very clear notion of how the curriculum builds on itself and how students must develop their skills in a particular sequence, they often keep this structure hidden from their students. Occupied with the daily grind of delivering curriculum, it often doesn't occur to them that their students might benefit from seeing the big picture.

If this structure is revealed to students, though, then they suddenly have a framework for assessing how their past performance will influence their future work. By being transparent about future tasks and assignments, teachers remind students that they're going to have to use at least some of these skills again, so there's no sense in making the same mistakes. Reflection suddenly has a real and immediate purpose: You know where this course is going, so how are you going to improve the quality of your own journey?

➤ The digital connection. If students are going to really benefit from their reflections and apply them to future work, those thoughts have to get out of their heads and into some form of documentation. Proximity here is key; reviewing a previous reflection can be most instructive when students are working on the next task, so their reflection should be stored wherever that work is happening. Paper portfolios can approximate this, although that method forces students to carry a year's worth of work and reflection with them at all times (which is why most teachers choose to keep portfolios in the classroom-logical, but limiting). By contrast, online homes for student reflection are universally accessible and can be organized to accompany student work, so that the past reflection is right in front of students as they start a new task. Digital tools also provide different mediums for students to capture their thoughts-they can type or tag, or talk into the microphone or camera.

Electronic tools of analysis can also play a big role here. Just as athletes track their physical performance using a specific set of metrics, students may benefit from reviewing their academic achievements in different areas, like the categories of a rubric or a list of discrete skills. When used by outside forces as the exclusive criteria for judging a school, this kind of "data-driven" approach can be myopic, but when used by students as one of several tools for measuring success, the process can be empowering. The standards-based grading movement has a multitude of resources available online, including free online grade books for teachers. By tying a numerical score to specific skills, students are naturally encouraged to reflect on their past performance so that they can improve the work, not just the grade.
Shared
Let's go back to that image of the lone person lost in reflection. Once they are done collecting their thoughts, who are they going to share them with? Most likely a trusted confidant or private journal-a safe place with no chance of betrayal. This tendency toward secrecy is natural. In the interest of keeping up appearances, we don't really like to share our weaknesses and past failures (although we do love gawking at the problems and misfortunes of others). But if we are really seeking to take action based on our reflections, then we will likely need some help, and that means we have to own up about what needs work. To make students comfortable with this practice, the classroom has to become a place where each student is recognized as being on an individual path of improvement-and, an important point, no student has reached the end of the path, because there is no end. And if there is no finish line, it becomes more difficult for students to compare their relative positions on the journey.

Once that culture has been established, the classroom can become a place of collective support instead of individual competition. By sharing their reflections on their academic work, students can both advise and seek help from their peers. Sharing their achievements helps those who struggled with that particular task, and sharing their weak spots helps them troubleshoot as they work through a problem set or have a peer edit a rough draft.

➤ The digital connection. Just as electronic tools make reflections easy to access for an individual, so, too, do they make it easy to share. Sharing becomes instantaneous when material is available online; the collection of commentary from an entire class can also be indexed, searched, and organized by theme-a feature that may be of great use for the teacher, who will want to look at both individual goals and the class's experience as a whole. If students are sensitive about sharing their reflections, the work can also be posted anonymously. Like writing in to an advice column with a pseudonym, the practice allows them to receive guidance and support without embarrassing themselves.
Larissa Pahomov teaches students English and Journalism at the Science Leadership Academy in Philadelphia, an inquiry-driven, project-based, 1:1 laptop school.

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What Meaningful Reflection On Student Work Can Do for Learning

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The following excerpt is from "Authentic Learning in the Digital Age: Engaging Students Through Inquiry," by Larissa Pahomov. This excerpt is from the chapter entitled "Making Reflection Relevant." Characteristics of Meaningful Reflection For student reflection to be meaningful, it must be metacognitive, applicable, and shared with others.

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"Be Sure To": A powerful reflection strategy

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"Be Sure To": A powerful reflection strategy

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Discussion and Supporting Materials

Thought starters

1. How does this strategy serve as both a reflection tool and an action plan?

2. Notice how this reflection continues to push students towards deep understanding of the text. How can Be Sure To statements act as an assessment tool?

School Details

Chinook Middle School
2001 98th Ave NE
Bellevue WA 98004

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Teachers

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"Be Sure To": A Powerful Reflection Strategy

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After teaching a lesson on argumentative elements in persuasive texts, 8th grade ELA teacher Julie Manley has her students reflect on their learning by crafting "Be Sure To" statements. Through these statements, students articulate what they have learned and create action items for the future.

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Thinking Notes: A Strategy to Encourage Close Reading

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Thinking Notes: A Strategy to Encourage Close Reading

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Discussion and Supporting Materials

Thought starters

1. In what ways do 'thinking notes' require students to track their response to a text and engage in more thoughtful reading?

2. What other reactions might you have students track when reading?

3. How do 'thinking notes' help students prepare for and structure discussions?

School Details

International School
445 128th Ave Se
Bellevue WA 98005

Data Provided By:

Teachers

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Thinking Notes: A Strategy to Encourage Close Reading

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By highlighting or underlining elements of the text and noting their responses to these elements, students use symbols to identify points to discuss further, confusing or unclear passages, strong writing elements, and ideas to which they had strong reactions.

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5 Strategies For Teaching Students To Use Metacognition

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5 Strategies For Teaching Students To Use Metacognition

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5 Strategies For Teaching Students To Use Metacognition by Donna Wilson and Marcus Conyers
As educational researchers, we have seen that by empowering all students with the metacognitive and cognitive skills they need to achieve in school.

With their application, schools can more consistently achieve the goals of the Every Student Succeeds Act (ESSA) to improve both excellence and equity. Over the past two decades, we have been inspired by the positive results that have been achieved by educators who have put our frameworks for teaching students metacognitive skills into practice in their classrooms and schools.

Metacognitive skills enable students to regulate their thinking and to become independent learners who can enhance their school and life experiences. Wherever the ambitions of our youth lead them, they will benefit from being able to solve problems creatively, think analytically, communicate effectively, and collaborate with others. As we conducted research for our latest book, we found that studies simultaneously indicate that metacognition is one of the most important skillsets students need, yet often is not taught.

When students are metacognitive, they can take a step back and observe their thinking. Sometimes this is called the reflective process. When using this approach, they might ask themselves questions like these: What is the problem to be solved? How should I solve the problem? How well am I doing? How well did I do? How can I do it better the next time? The metaphor we developed as a way to help educators teach metacognition to children and youth across grade levels is that of "driving your brain."

Teaching students to drive their brains and become self-directed learners can be compared to driver's education, in which students receive explicit instruction on how to guide their thinking, when to slow down, when it's okay to speed up, and how to avoid wrong turns.

Many students yearn for the day they will get their driver's license, but developing the mindset and ability to take charge of their learning will take them further in life than the keys to any car. And younger students don't have to wait until they are old enough for driver's education to take "brain-driving lessons." They can and should start learning about metacognition at an early age and apply it across all content areas and in life lessons.
5 Practical Strategies for Explicitly Teaching Students to Use Metacognition
1. Start by defining the term. We recommend the simple definition "thinking about your thinking as a pathway to better learning." Especially with younger students, a metaphor such as driving their brains concretizes this abstract concept.

2. Early in the discussion about metacognition, ask students to describe the benefits and supply examples of driving their brains well. For example, sometimes we might need to review a reading passage to make sure we understand it, or jot down and organize notes for an essay instead of getting stuck on how to start writing. In communication with others, it is important to think before you speak so as not to risk hurting someone's feelings.

3. Catch students being metacognitive, perhaps when they reflect on their individual learning or engage in metacognitive discourse in class. Celebrate the use of this important skill in large and small groups as a way to underscore the many ways this approach comes in handy at school and in other aspects of life.

4. Lead class discussions that encourage students to share examples about how metacognition can be used inside and outside of school. When Donna teaches metacognition to children in elementary school, she encourages them to explain how their parents might use this skill at work. High school students might think about applying metacognition in their jobs or in personal relationships.

5. Model the use of metacognition by talking through problems so that students can learn how to use higher-order thinking strategies by listening as you problem solve aloud.

The strategies shared in this blog post are adapted from the book Teaching Students to Drive Their Brains: Metacognitive Strategies, Activities, and Lesson Ideas (ASCD, 2016).
Donna Wilson, PhD, is a psychologist, professional developer, and author. Marcus Conyers is an author, professional developer, and doctoral researcher at the University of Westminster in London, England. Their latest book is Teaching Students to Drive Their Brains: Metacognitive Strategies, Activities, and Lesson Ideas (ASCD, 2016). They are cofounders of BrainSMART, Inc., and the Center for Innovative Education and Prevention (CIEP). Learn more about their work at www.brainsmart.org

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5 Strategies For Teaching Students To Use Metacognition -

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5 Strategies For Teaching Students To Use Metacognition by Donna Wilson and Marcus Conyers As educational researchers, we have seen that by empowering all students with the metacognitive and cognitive skills they need to achieve in school. With their application, schools can more consistently achieve the goals of the Every Student Succeeds Act (ESSA) to ...

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Metacognition: The Gift That Keeps Giving

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Metacognition: The Gift That Keeps Giving

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Edutopia is a free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education. We are published by the George Lucas Educational Foundation, a nonprofit, nonpartisan organization.