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Specific ways to use Webb’s DOK in class

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Specific ways to use Webb’s DOK in class

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Specific ways to use Webb’s DOK in class

Describes all 4 levels of Webb’s DOK

Shows question and stem examples on each level

Describes activities and products on each level

Additional strategies for

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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
Try Prodigy today! 🎉

Create your free teacher account now!

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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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Good to pair with the Hess Cognitive Rigor Matrix

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Compares DOK levels to Bloom’s cognitive process dimensions

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Using data to support implementation of positive classroom behaviour support practices and systems

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Great resource

Will have you click on a behaviour and then find one that describes the student

Shows tier 1, 2, and 3 interventions to try for this behaviour with data tracking forms and strategies

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PBIS World | A Complete Tier 1 Through Tier 3 Positive Behavior Interventions & Supports System

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PBIS World is in no way affiliated, associated, or connected with any other website, entity, organization, or federal, state, local, or other government agency, department, program, policy, organization, or initiative.

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Regular education interventions/at risk documentation PDF

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Regular education interventions/at risk documentation PDF

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Discusses foundation, high-quality instruction, different tier support, data-based decision making, understanding and using data, outcomes

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Includes; definition, characteristics, coexisting disabilities, MTSS, law, Accommodations, effective instruction, social and emotional impact

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Bell curve with different types of scores

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Bell curve with different types of scores

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Bell Curve with Derived Measures and Visual

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Bell Curve with Derived Measures and Visual

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The Reader Self-Perception Scale (RSPS): A New Tool for Measuring How Children Feel about Themselves as Readers

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The Reader Self-Perception Scale (RSPS): A New Tool for Measuring How Children Feel about Themselves as Readers

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Reader self-perception scale

Discussion, explanation, and the actual assessment

Assessment use, why was it created

How to administer and score

Self-efficacy and reading

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Where does self-efficacy come from and how can you get more of it? The originator of the theory, Albert Bandura names four sources of efficacy beliefs.

1. Mastery Experiences

The first and foremost source of self-efficacy is through mastery experiences. However nothing is more powerful than having a direct experience of mastery to increase self-efficacy. Having a success, for example in mastering a task or controlling an environment, will build self- belief in that area whereas a failure will undermine that efficacy belief. To have a resilient sense of self-efficacy requires experience in overcoming obstacles through effort and perseverance.

2. Vicarious Experiences

The second source of self-efficacy comes from our observation of people around us, especially people we consider as role models. Seeing people similar to ourselves succeed by their sustained effort raises our beliefs that we too possess the capabilities to master the activities needed for success in that area.

3. Verbal Persuasion

Influential people in our lives such as parents, teachers, managers or coaches can strengthen our beliefs that we have what it takes to succeed. Being persuaded that we possess the capabilities to master certain activities means that we are more likely to put in the effort and sustain it when problems arise.

4. Emotional & Physiological States

The state you’re in will influence how you judge your self-efficacy. Depression, for example, can dampen confidence in our capabilities. Stress reactions or tension are interpreted as signs of vulnerability to poor performance whereas positive emotions can boost our confidence in our skills.

5. Imaginal Experiences

Psychologist James Maddux has suggested a fifth route to self-efficacy through “imaginal experiences”, the art of visualizing yourself behaving effectively or successfully in a given situation.

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1. Determine Student’s strengths and weaknesses in a topic.

-Repeated failure of a task lowers expectations of ability and success raises them.

-Do they have the skills to succeed?

2. Ask students who they feel their teachers, family members, and parents feel about them.

-An understanding of how they think others view their abilities will help teachers understand direct and indirect input about from people around them (Henk & Melnick, 1995).

3. Ask the students how they view their abilities compared to peers in their class.

-Students naturally compare their abilities to the vicarious experiences that they observe in the classroom.

For example, if they see their peers experience negative consequences when they attempt and fail at performing a task, then the student will most likely not attempt similar task in fear they will experience the same negative stimulus but if they see their peers succeed, they will attempt similar task in the pursuit for the same consequence.

4. Discover their emotional feelings in regard topic.

-Ask the students how they feel about themselves.

Do they feel good or bad about themselves in the topic? Negative feelings about themselves will influence whether or not they will attempt the task and continue to pursue when the task becomes difficult.

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Cooper 1989

Series of meta-analysis evaluating HOMEWORK

•Effect size can be up to .64 for high school

•.29 for junior high

•.15 for elementary

•Positive effects were negatively related to duration-

•Shorter is better

•Correlation of d=-0.04 between time spent on homework and achievement

•Effects were highest in Mathematics and lowest in science and social studies (ELA was in the middle)

•Effects are highest for rote learning tasks vs. learning subject matter

•Effects are greater for high achieving students

•Does not help students develop time management skills

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Tips for creating powerful Assessments for your students 

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Tips for creating powerful Assessments for your students 

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1) Begin with the end in mind
2) Communicate your purpose
3) Blend assessments into your teaching
4) Identify and avoid bias
5) Consider non-traditional assessments
6) Follow up

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By Melissa Maypole
Assessments are no longer simply tests that students fret about or neglect to study for. As you may well know, today's environment of heightened accountability for educators has made assessments stressful for not only students, but for teachers as well. Not to worry, though. Assessments can actually be powerful (and even fun!) tools to evaluate how well your students are mastering the material you're covering in class and how well you're doing covering said material. Just follow these 6 simple tips:

1) Begin with the end in mind.

For years, teachers have planned their lessons in a linear fashion. First, we create daily lessons aligned with objectives followed by tests to assess the objectives each lesson addresses. Logical, right? Sure, but this traditional method of teaching and assessing learning may not necessarily be the most effective way to go about things. Instead, try creating an objectives-based assessment first, and then plan activities that target the learning goals the assessment evaluates. This not only ensures that the assessment aligns to your students' learning objectives, but it also allows the assessment to help drive your instruction, meaning you'll know for sure that you've actually taught the material and skills that require mastery.

2) Communicate your purpose.

The purpose of a traditional pencil and paper test may be fairly cut and dry to your students-I answer a bunch of questions and it tells the teacher if I've learned the material-but this may not be the case for a more open-ended assessment such as a project or essay that a student may see as busy work. In order to get the outcome you want from your students, it's important to let them know why they are doing something, including what skills and knowledge you're expecting them to demonstrate mastery of. One of the best ways to do this is to create a clear rubric and give your students a copy prior to beginning work on the assignment. This way, there will be no question as to what you expect your students to demonstrate, and it may even motivate many to perform.

3) Blend assessments into your teaching.

Highly effective educators use assessments to adapt and enhance instruction. Instead of treating assessments as intimidating bookends to curriculum units, successful teachers assess learning more frequently and less formally with the intention of using the results of the assessment as an arrow toward the next steps in the learning process. Create opportunities for non-threatening, formative checkpoints in your instruction. Give deliberate and targeted mini-quizzes that allow you to assess common misconceptions and truly know in real-time where your students are tracking. Craft your quiz by following assessment-writing best practices outlined in this article.

4) Identify and avoid bias.

Since assessments are such an important tool in your teaching toolbox, it's important to ensure that they are as authentic and targeted as possible. This means making an intentional effort to check for any biases that may affect students' performance or invalidate your results. An assessment should be designed in parts that specifically test single, targeted skills, and unintended bias will quickly invalidate your efforts. Although it may seem impossible to create an assessment with zero bias, we can still do our due diligence to identify and remove bias.

The most common types of bias in assessments are those that inadvertently assume knowledge other than the specific skill being tested. This bias can be blatant such as assuming knowledge of a certain cultural group, for instance, or it could be hidden. Hidden biases are often found in the language of the assessment. Teachers must be especially careful not to create written assessments that are on a higher reading level than their students, so that a mathematics assessment, for example, doesn't unintentionally assess how well the student can read the problem as well as the specific skills.

5) Consider non-traditional assessments.

Nothing crushes classroom morale faster than announcing a pop quiz or traditional paper and pencil test. In order to incorporate some fun into your assessment repertoire and keep your students engaged in their learning, you'll need to think outside of the box. Create a game or activity based on specific learning objectives to mix things up while bringing out the very best in your students. Or consider tying in a cross-curricular semester-long project that connects the material together and forces a higher level application of skills. You can pepper in traditional mini-assessments throughout the span of the project to determine where your students are, but the journey here is much more fun.

We all know that assessments provide feedback to us teachers-they let us know which material students have mastered and which material they still need to work on. They also tell us how well we're delivering the necessary information and facilitating learning in our classrooms. Don't forget, though, that assessments can and should provide vital feedback for your students as well. After all, if we want them to be in charge of their learning (and we do!), then we must give them the necessary information to make and reach their learning goals. Reviewing the results of a quiz or test has the potential to help students realize their deficits and detect meaningful patterns in their errors. These are discoveries that are crucial to correcting misconceptions and directing future learning. When planning a review or follow-up on an assessment, keep in mind that sooner is always better. The quicker you provide learners with feedback on their performance, the more meaningful this information will be.

When crafted carefully, assessments can be incredibly powerful tools for learning. Well-planned assessments provide teachers and students with the necessary information to gauge progress and plan the next steps in the learning process. When we assess learning clearly, frequently and without bias, we get a better picture of how well we're doing with instruction and how to best serve our students in the future.

For more, see:

Melissa Maypole is an English Teacher with a Master's of Science in Education, and is a contributor at .
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6 Tips for Creating Powerful Assessments for Your Students

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By Melissa Maypole - Today's heightened accountability for educators has made assessments stressful for teachers. Here's how to do them right.

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Papers, presentations (individual and group), debate, leading class discussion, problem solving, lab reports

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Included below are sample criteria for you to consider as you develop a grading rubric. As you develop your rubric, consider the essential knowledge and skills required for the assignment/assessment for which you are developing the rubric and develop and define the criteria accordingly. Then consider how you will weight these criteria relative to each other (for a good example and description of weighted rubrics, see page 11 of An Introduction to Rubrics by Stevens & Levi, which is available as an online resource through the Brown library).

This resource from the University of North Carolina Wilmington offers examples of sample grading criteria organized by assignment and discipline: https://uncw.edu/cas/assessment/rubrics/samplerubrics.html ​

clarity, organization, grammar

context of & purpose for writing, content development, genre & disciplinary conventions, sources & evidence, control of syntax & mechanics

communication, critical thinking, content

thesis, structure, use of evidence, analysis, logic and argumentation, mechanics

Presentations (individual)

content, organization, graphics, English, elocution, eye contact

introduction, organization, context, evidence, analysis, presentation

organization, language, delivery, supporting material, central message

organization, subject knowledge, graphics, mechanics, eye contact, elocution

Presentation (group)

individual presentation skills, group presentation skills, group organization, individual organization, individual content

respect for other team, information, rebuttal, use of facts/statistics, organization, understanding of topic, presentation style

Leading a Class Discussion

preparation, content, discussion/debate methods, discussion questions, communication skills

Problem Solving

define problem, identify strategies, propose solutions/hypotheses, evaluate potential solutions, implement solution, evaluate outcomes

statement of problem, correctness of proof

understanding; strategies, reasoning, procedures; communication

analysis, interpretation, application

Lab Reports

organization, content, analysis, interpretation

abstract/summary; introduction; experimental procedure; results (data, figures, graphs, tables, etc.); discussion; conclusions; spelling, grammar & sentence structure; appearance & formatting

introduction, research, purpose/problem, procedure, data & results, conclusion, grammar & spelling, attractiveness, timeliness

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Included below are sample criteria for you to consider as you develop a grading rubric. As you develop your rubric, consider the essential knowledge and skills required for the assignment/assessment for which you are developing the rubric and develop and define the criteria accordingly.

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Defining purpose of the assignment

Holistic vs Analytic rubrics

Design the rating scale

Writing descriptions for each level of the rating scale

How to use a grading rubric

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Why Use Rubrics?

Rubrics help instructors grade and provide feedback on assessments that have more than one correct answer in an efficient and equitable way. They facilitate transparency in grading, as well as increase consistency in scoring. When given alongside an assignment, students can use rubrics to gain understanding about the purpose of an assignment, to provide peer feedback, or to engage in self-assessment. Multiple graders or reviewers produce more consistent results when they have been trained in using the rubric and have been provided with exemplars (for reviews of the research see Jonsson & Svingby, 2007; Reddy & Andrade, 2010).

Three Elements of a Rubric

A rubric involves three elements: 1) the criteria for assessing the product or performance, 2) a range of quality levels, and 3) a scoring strategy. There is enormous flexibility for instructors to construct rubrics that reflect their teaching perspective within these three parameters.

Criteria define the distinct elements of expert or competent performance of the tasks central to the assignment. As the number of criteria increases, so does the amount of time required to review assignments. Too few criteria can lead to a rubric that does not effectively assess the range of knowledge, skills, and attitudes required to complete the task assigned. Generally, 4 to 6 criteria assess the breadth of competencies that are most essential to an assignment.

A single criterion can be used to create a holistic rubric with very general descriptions. Holistic rubrics do not provide targeted feedback and research suggests they are less consistently used. Holistic rubrics work well to speed grading for low stakes activities that only need very general feedback (e.g., discussion forum posts or responses). For more significant assignments, an analytic rubric with multiple criteria is more useful for reviewers and students. Effectively selecting the most important criteria is the first step to designing effective analytic rubrics. For examples of each type of rubric see the resource links below.

Quality Levels

Once the most essential criteria for competently completing the assignment have been identified, different quality levels need to be identified. Selecting the number of quality levels is a critical decision. While a greater number of quality levels allows for finer distinctions, more levels increase the time required to develop the rubric and to review assignments. In addition, research has shown that as the number of quality levels increases, consistency across graders or reviewers decreases. Considering the ultimate grade distinctions that will be made in the course can help determine the appropriate levels of quality for significant assignments.

The labeling of quality levels requires careful reflection. In learning contexts, instructors typically distinguish levels of competence, mastery, or expertise. This framing emphasizes a developmental teaching perspective and communicates a growth mindset. Instructors should beware of quality descriptors that demoralize students (e.g., incompetent, barely adequate, almost competent).

The most equitable rubrics create a detailed table describing the key features for each criteria at each quality level. Criteria are listed along the left-most column (often according to hierarchy of importance or process order) and quality levels are arranged across the top row of the table (either from low to high or high to low). Each of the remaining table cells is filled with a description of key features that can be observed for the specific criteria at that quality level. These often focus on key factors that represent bottlenecks in student learning or critical steps to increased levels of competence.

Scoring Strategy

Rubrics are flexible tools and instructors use a range of strategies to score student work using rubrics including:

1) Setting weights for each criterion, and single scores for each quality level. This approach speeds grading and minimizes discretion that might be a source of bias. Many digital tools support this strategy.

2) Weighting criteria and providing a range of scores for each quality level. This approach supports instructors interested in making more fine-grained distinctions.

3) Focusing on the overall combination of quality levels across criteria to assign a grade. This is a simplified grading structure that focuses on the overall grade and holistic judgment of the instructor or grader. For larger course enrollments, this strategy increases the risk of inconsistent or biased grading.

4) For drafts and formative assessments, focusing on providing students feedback with the rubric and simply assigning a complete or incomplete grade can be an efficient and effective strategy

Suggestions for Creating a Rubric

Determine the purpose of the assignment

Consider what, exactly, you want students to learn from the assignment. Write this down; it will guide the creation of criteria for your rubric.

Clearly establish criteria

Decide how you want to grade students. What elements of the assignment do you want to give them feedback on? This means determining the criteria associated with the task. To determine the criteria, think again about the goals of the assignment. What do you want students to accomplish? What do you want them to learn? Keep these criteria descriptions brief. Also, try to have an even, rather than an odd, number of criteria. This prevents the middle criterion from becoming a catch-all, allowing for more nuance in grading.

Determine the scoring method

Decide whether you will use a letter grade, percentages, points, a rating scale, or some other scoring method in your rubric. How will you label them? With numbers or descriptive labels?

Develop the descriptors of the criteria

Make sure the descriptors follow a logical progression. That is, descriptors indicating poor performance should be distinctly different from descriptors indicating high performance. And there should be consistency within the descriptors, meaning they should focus on particular attributes that carry through all criteria.

Be sensitive to language used

Rubrics offer a more objective means of assessing student work, but that doesn't mean they should assume a negative tone or offer an overly pointed critique of the learner. Try to refer to the assignment rather than the student when developing criteria. Avoid overly subjective language and use active voice where appropriate.

Explore results with hypothetical scoring combinations

Test your rubrics with a variety of scores for each criteria and see how significantly an outlier in one criterion will impact the overall grade. Consider whether adjustments to the weighting of criteria or the way points are allocated would more accurately reflect the appropriate grade.

Share your rubric with a colleague

Asking a colleague to review the rubric in advance is one of the best ways to ensure that your expectations are clear. You can ask colleagues to focus on specific elements of the rubric or to provide overall feedback.

Rubric Tools

Gradescope

Gradescope is a tool that enables efficient and transparent grading. Foremost, Gradescope prompts instructors to grade by question rather than by student. Within each question, the platform enables graders to create a dynamic, shared digital rubric that allows for expedited, collaborative grading and point altering.

The Canvas Rubrics tool can help you grade more quickly by providing an easy way to select the appropriate feedback, or grade by the same criteria for each student. After you attach a rubric to an assignment and configure it for grading, you can use the same grading criteria for all student submissions. Canvas will then automatically calculate the total score for you in Speedgrader.

Resources and Works Cited

Rubrics for Assessment from Northern Illinois University

Types of Rubrics from DePaul Teaching Commons

Types of Rubrics: Holistic and Analytic from Queen's University

Know Your Terms: Holistic. Analytic. And Single-Point Rubrics

Jonsson, A., & Svingby, G. (2007). The use of scoring rubrics: Reliability, validity and educational consequences. Educational Research Review, 2(2), 130-144. https://doi.org/10.1016/j.edurev.2007.05.002

Reddy, Y. M., & Andrade, H. (2010). A review of rubric use in higher education. Assessment & Evaluation in Higher Education, 35(4), 435-448. https://doi.org/10.1080/02602930902862859

Additionally, Dannelle D. Stevens & Antonia J. Levi, An Introduction to Rubrics (Sterling, VA: Stylus, 2005), is available as an online Brown Library resource and in the Sheridan Center's library.

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Designing Grading Rubrics | Sheridan Center | Brown University

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Rubrics help instructors grade and provide feedback on assessments that have more than one correct answer in an efficient and equitable way. They facilitate transparency in grading, as well as increase consistency in scoring. When given alongside an assignment, students can use rubrics to gain under…

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Participation and discussion, writing, science, psychology philosophy, history, film studies, biology, art, anthropology

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Sample Scoring Rubrics

Here are examples of rubrics designed by faculty at this and other institutions. Besides looking at rubrics created for your discipline, there is also benefit in looking at rubrics for similar assignments in other disciplines. They can help you define the elements of your assignment as well as the quality criteria.

Anthropology

Art

Biology

Film Studies

History

Philosophy

Psychology

Science - Applicable to all sciences

Writing across disciplines

Participation and Discussion Rubrics

Other Rubric Sources

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Sample Scoring Rubrics Here are examples of rubrics designed by faculty at this and other institutions. Besides looking at rubrics created for your discipline, there is also benefit in looking at rubrics for similar assignments in other disciplines. They can help you define the elements of your assignment as well as the quality criteria.

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Click on a grade level to view the Utah Core standards for that grade. Click on the subject title to view all grades for that subject.
Use the UEN Curriculum Search to to search the core and to find lesson plans.

K-12 Standards Career and Technical Education Standards Adult Education College and Career Readiness Standards

K-12 Standards

Career and Technical Education Pathways

Adult Education College and Career Readiness Standards

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Click on a grade level to view the Utah Core standards for that grade. Click on the subject title to view all grades for that subject. Use the UEN Curriculum Search to to search the core and to find lesson plans.

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- Align assessments to learning goals
- Offer authentic opportunities for assessment
- Assess engagement as well as content knowledge
- Include frequent formative assessments
- Reduce unnecessary barriers to access
- Support learner variability through flexible assessments
- Use and share rubrics to clarify expectations
- Involve learners in assessing their learning progress
- Reflect on summative assessments for future design
- Build communities of practice that support
reflective design

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The UDL Guidelines are a tool used in the implementation of Universal Design for Learning, a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn. Learn more about the Universal Design for Learning framework from CAST. The UDL Guidelines can be used by educators, curriculum developers, researchers, parents, and anyone else who wants to implement the UDL framework in a learning environment. These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.

UDL Rising to Equity

Because the UDL Guidelines are meant to be informed by feedback from the field as well as new research, they have been updated several times in the past. We are in the process of updating the Guidelines once again in our UDL Rising to Equity initiative.

This update will focus specifically on addressing systemic barriers that result in inequitable learning opportunities and outcomes. CAST aims to develop a transparent, inclusive, and community-driven process. If you are interested in collaborating and staying updated on our progress, we invite you to complete a brief survey. Do you use social media? Join the conversation happening now in the #UDLrising hashtag.
Meet the UDL Rising to Equity Advisory Board Meet the UDL Rising to Equity Stakeholder Council

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The UDL Guidelines are a tool used in the implementation of Universal Design for Learning, a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn. Learn more about the Universal Design for Learning framework from CAST.

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goals, reflection, questions to ask, strategies of assessment, tracking data, organising data, informing through data, and making data actionable

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What are they?, components, difference between diagnostic and formative, examples, assessment tools

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Diagnostic assessments are pretests. They usually serve as a barometer for how much pre-loaded information a student has about a topic. The word diagnosis is defined as an analysis of the nature or condition of a situation, which is exactly how teachers tend to use them.

Diagnostic tests help to tell the teacher (and the student) how much they know and don't know about an upcoming topic. This helps to inform the teacher's lesson planning, learning objectives, and identify areas that may need more or less time spent on.

Components of a Diagnostic Assessment

Happen at the beginning of a unit, lesson, quarter, or period of time.

Goal of understanding student's current position to inform effective instruction

Identify strengths and areas of improvement for the student

Low-stakes assessments (Usually do not count as a grade)

Difference Between Diagnostic and Formative Assessments

Though both diagnostic assessments and formative assessments aim to inform teachers to instruct more effectively, they emphasize different aspects. Formative assessments are taken during a unit to assess how students are learning the material that the teacher has been teaching ( click here to learn more). Diagnostic assessments come before this, analyzing what students have learned in the past, many times from different teachers or classes. Both are very helpful for the teacher, and the results are used to identify areas that need more attention in future instruction.

Diagnostic Assessments Examples

At the beginning of a unit on Ancient Greece, a teacher may give a pre-test to determine if the class knows the basic geography, history or culture. The class' responses will determine where the teacher begins and how much time is dedicated to certain topics. The teacher may learn from this diagnostic assessment that many students already have knowledge on cultural aspects of Greece, but know little about its history. From this, they may adjust the lesson plan to spend a bit more time on the history and origins of Ancient Greece and slightly less on culture.

Keep In Mind

Another valuable use of a diagnostic pre-test is to give the students an idea of what they will have learned by end of the learning period. When combined with a post test, their score on a pre-test will show students just how much knowledge they have gained. This can be a powerful practice for building esteem in students. In fact, some teachers even use the same pre-test and post-test to make this difference more evident. This strategy provides great data on how students have progressed is a sure-tell way to measure and analyze growth over the year.

The grading scale for a diagnostic assessment is usually not based on the number of correct answers and holds little weight for a student's final grade. You might consider this type of test to be a low-stakes assessment for students.

Diagnostic Assessment Tools

Teachers use Edulastic to find or develop diagnostic assessments in a number of creative ways. Some teachers set up diagnostics in the form of introductory activities, classic multiple-choice assessments, or tech-enhanced "quizzes". The automated grading feature of Edulastic makes it easy to instantly know how much information the class as a whole already knows.

Love using @Edulastic to help prepare for online assessments during a review lesson! pic.twitter.com/hhu8s0HqJM

- Mrs Bell (@MrsBellWHS) December 7, 2017

Diagnostic assessments happen at the start to gauge pre-knowledge.

Access Free Diagnostic Assessments

Start off the year strong and know where student are at when they begin the school year. Access FREE grade level SmartStart diagnostic assessments for grades 3-12 ELA and Math. Click here to learn more or use the button below to log in and explore these diagnostic assessments and more in the Edulastic Test Library.

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A diagnostic assessment is a pre-test or barometer for how much information a student already knows about a topic. Read on to learn more.

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1. Keep It Small
2. Help Your Students Prepare in Advance
3. Teach Effective Exam Strategies
4. Provide Adequate Time

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What’s the Difference Between Interim and Formative Assessments?

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Today's blog is the first in a series of three blogs about benchmark testing. Many of us are familiar with benchmark tests. They are often given at the start of the year-which is why now is a good time to have this discussion. If your school is like many others, benchmark tests will be administered not only in the fall but also several times throughout the year to gauge student standing relative to well-defined outcomes.

Despite their frequent use, there's a lot of confusion surrounding benchmarks. What are they? What purpose do they serve? Are there different kinds? How can they be used most effectively? These are all questions that we in Edmentum's research department field regularly-and frankly, grapple with ourselves as well. Our goal with this series is to explore some of the nuances of benchmark assessment. Let's start by reviewing the basics and clarifying key definitions.
Why administer benchmark assessments?
All educators know-it's all about student outcomes. One might say that the purpose of a benchmark is to influence well-defined outcomes-they're a form of assessment for learning in preparation for the assessment of learning that summative tests eventually measure. Notice the preposition in the phrasing; benchmark assessments are for learning, not of learning. A benchmark is given when there is still time to intervene, and it should alert the teacher as to how things are going, much like a checkup at the doctor is made to promote good health in the future. Similarly, teachers administer benchmark tests to ensure that students are on track to achieve the relevant learning outcomes, and if they are not on track, it's not too late for a teacher to adjust instruction. That's the point of benchmarks in a nutshell.

To better grasp the very basic distinction we're making between benchmarks and outcomes, think of your college classes. You had a final exam to judge whether you met the required outcomes. You usually had a midterm test to see if you were on track to pass the class. If so, the final exam was the outcome test, and the midterm was the benchmark test.
Are there different types of benchmark assessments?
Of course, K-12 education is quite different than college. The simple distinction between outcome and benchmark lacks sufficient contour. We must introduce a distinction for K-12. Benchmarks can be divided into two kinds: interim tests and formative tests. We will here follow the terminology provided by Dr. Marianne Perie, director of the Center for Assessment and Accountability Research and Design (CAARD). For more detail on evaluating benchmarks, Dr. Perie and her colleagues Scott Marion and Brian Gong published this very interesting article on " Moving Toward a Comprehensive Assessment System: A Framework for Considering Interim Assessments."

An interim assessment is administered during instruction to measure knowledge and skills to inform educator or policymaker decisions at the state, district, or classroom level. Results are reported at the aggregate level. For example, the Measures of Academic Progress (MAP) and the Renaissance Star assessments have been adopted by districts and states as interim assessments. Schools and districts report average scores across students, schools, and districts throughout the year.

The emphasis of an interim assessment tilts toward administration and accountability. Is there another kind of benchmark that is perhaps more organic than interim assessments? Something that feels more intimately related to instruction? Well, some teachers give quizzes frequently during instruction. A quiz is like an interim assessment in that it comes before the final, and it tries to positively influence the results on the final assessment. But quiz scores are not generally used beyond the classroom level. And quiz scores are typically not aggregated to the school or district level. Quizzes are examples of a different kind of assessment known as formative assessments.

A formative assessment is typically used solely by the teacher to check if instruction is having its expected result on individual students, to verify that they are on track to achieve all relevant outcomes, and to diagnose gaps in learning. Thus, formative assessment might be thought of as an essential part of an individualized learning infrastructure. That's not always the case, but thinking about it this way gives us insight into formative assessments.

One more thing needs to be said about formative assessments. Many years ago, the classroom quiz was certainly the prototype of a formative assessment. But, educational technology has matured to the point that we can now automate the preparation and administration of high-quality formative tests. These tests can be as reliable and valid as the well-known end-of-year tests or the third-party interim assessments, yet used strictly at the classroom level, and only for assisting the teacher.

So, one should keep in mind that the simplicity of an assessment is not the indicator that it is a formative assessment. What makes an assessment formative is that it pertains strictly to the individual student and lacks the administrative and accountability aspects of interim assessments.

Formative assessments span a diverse range of techniques, including exit tickets (brief, ungraded questions given at the end of class), quizzes, thought papers, oral preliminary exams in graduate school, and computer-assisted exams. These are widely different in aims, complexity, time, and implementation.
Is one type of benchmark assessment best?
These definitions would seem to suggest that interim tests are of higher quality or more reliable and valid than formative tests. But, as we've seen, it is a mistake to draw that conclusion. In fact, a formative assessment can be a better choice for some settings. Whereas interim assessments tend to be given under highly standardized conditions, formative tests-lacking the high stakes implications-can be administered across a wide variety of technology platforms and settings. Because the purpose is not to compare one child to another, but rather to support the unique needs of each child, formative testing may be the right choice for teachers, schools, districts, and states in many situations where determining student needs and tailoring instruction is the goal.

There is one caveat to be added. Keep in mind that whether a benchmark test is properly designated as interim or formative is determined primarily by use- when the test is administered, how often, under what conditions, where the scores go, and what decisions are made from the data. Indeed, many interim or summative end-of-year tests expose their retired item banks to offer prep courses and practice testing materials. One item in the same test can have different uses.

The goal of this blog was to dig into benchmark testing to clarify the terminology surrounding these tests. We tried to show two very different use cases for benchmark tests. Now that we can speak fluently about formative and interim assessments, we can look forward to the next installments of this blog series where we will look at the different ways that these tests can be administered and used. We will find that it all comes down to what the state, district, school, and teacher hope to accomplish with benchmark testing. And, hopefully, by the time we finish the series, teachers will feel more knowledgeable in making decisions about what kinds of assessments they should choose to best help their students.

Looking for additional resources to support effective assessment in your classroom? Download our Guide to Assessment for Learning!

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The Value of Benchmarking: What's the Difference Between Interim and Formative Assessments?

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We're kicking off a series on benchmarking assessment by defining the two primary types: interim and formative tests.

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What do teachers need to know and do?

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To many of today's teachers, assessment is synonymous with high-stakes standardized tests. But there is an entirely different kind of assessment that can actually transform both teaching and learning. Ms. Heritage describes what the skillful use of formative assessment would look like.

Formative assessment, if used effectively, can provide teachers and their students with the information they need to move learning forward. But after more than a hundred years of exhortations and a significant body of research on the topic, the idea that assessment and teaching are reciprocal activities is still not firmly situated in the practice of educators. Instead, assessment is often viewed as something in competition with teaching, rather than as an integral part of reaching and learning.

In our current accountability environment, assessment is not regarded as a source of information that can be used during instruction. Instead, it has become a tool solely for summarizing what students have learned and for ranking students and schools. In the process, the reciprocal relationship between teaching and assessment has been lost from sight. In a context in which assessment is overwhelmingly identified with the competitive evaluation of schools, teachers, and students, it is scarcely surprising that classroom teachers identify assessment as something external co their everyday practice.

Educators recognize that annual state tests provide too little information that arrives too late for planning instruction, and this has prompted districts and schools to supplement state assessments with interim or benchmark assessments. These typically consist of item banks, administration tools, and customized reports, and they usually are administered uniformly co all students three to four times a year. Their greater frequency notwithstanding, these assessments still do not provide teachers with information they can use for ongoing instruction. Despite the enthusiasm for these assessments at the district level and the considerable resources that are being expended on chem, the face remains chat they cover too long a period of instruction and provide coo little detail for effective use in ongoing instructional planning. At best, they function more as snapshots of student progress and as predictors of student performance on the end-of-year, statewide tests. Indeed, Dylan Wiliam and Marnie Thompson suggest that they might better be described as "early warning summative" tools rather than as tools chat can be formative co instruction. ¹ Furthermore, teachers do not control how or when these tests occur, what the purpose of the assessment is, or who is assessed. Yet these are the assessments that "count," even though they offer little help to teachers in their daily practice.

Compounding these difficulties is the fact that assessment has traditionally not been a focus of preservice and inservice courses. As Richard Stiggins laments, U.S. educators are "a national faculty unschooled in the principles of sound assessment." ² Teachers learn how to teach without learning much about how to assess. Moreover, their administrators also lack training in assessment and therefore do not have the skills to support the development of assessment competencies.

What is missing in assessment practice in this country is the recognition that, to be valuable for instructional planning, assessment needs to be a moving picture - a video stream rather than a periodic snapshot. If assessment is used to inform effective instruction, then that assessment is quickly rendered out of date. Student learning will have progressed and will need to be assessed again so that instruction can be planned to extend the students' new growth.

Formative assessment practices, if implemented effectively, can provide teachers and their students with the data that they need. Moreover, there is empirical evidence that formative assessment, unlike benchmark assessments, is effective in improving student achievement. ³ However, in a profession that already feels burdened by the amount of assessment, there is a danger that teachers will see formative assessment as yet another external demand that takes time away from teaching.
What is formative assessment?
Formative assessment is a systematic process to continuously gather evidence about learning. The data are used to identify a student's current level of learning and to adapt lessons to help the student reach the desired learning goal. In formative assessment, students are active participants with their teachers, sharing learning goals and understanding how their learning is progressing, what next steps they need to take, and how to take them.

Formative assessment involves a variety of strategies for evidence gathering, which can be categorized into three broad types: on-the-fly assessment, planned-for interaction, and curriculum-embedded assessment. ⁴

On-the-f ly assessment. On-the-fly assessment occurs spontaneously during the course of a lesson. For example, a teacher listening.to group discussions hears students expressing misconceptions about the science concept she has been teaching. She then changes the direction of her lesson to provide a quick "pop-up" lesson. ⁵ The pop-up lesson enables the teacher to clear up the misconceptions before proceeding with her planned instructional sequence.

Planned-for interaction. In planned-for interaction, teachers decide beforehand how they will elicit students' thinking during the course of instruction. For example, teachers plan the questions they will ask during the course of the lesson in order to enable students to explore ideas, and these questions can elicit valuable assessment information. ⁶

C urriculum-embedded assessments. There are two kinds of curriculum-embedded assessments, those that teachers and curriculum developers embed in the ongoing curriculum to solicit feedback at key points in a learning sequence and those that are part of ongoing classroom activities. For example, student mathematical representations created during lessons can function as formative assessments, as can students' science notebooks that are also part of students' regular classroom activity. ⁷
Elements of formative assessment
There are four core elements of formative assessment: 1) identifying the "gap," 2) feedback, 3) student involvement, and 4) learning progressions. Teachers need to have a clear understanding of each of these elements.

Identifying the gap. In a seminal paper in 1989, Royce Sadler established the essential purpose of formative assessment as the means to identify the gap between a student's current status in learning and some desired educational goal. He stressed that this gap will vary from student to student and spelled out the consequence for pedagogy: "If the gap is perceived as too large by a student, the goal may be unattainable, resulting in a sense of failure and discouragement on the part of the student. Similarly, if the gap is perceived as too 'small,' closing it might not be worth any individual effort. Hence, to borrow from Goldilocks, formative assessment is a process that needs to identify the 'just right gap.'" ⁸

Educational psychologists call this "just right gap" the zone of proximal development (ZPD). Originating with Lev Vygotsky's still-influential formulation, the ZPD is defined as the distance between what the child can accomplish during independent problem solving and the level of problem solving that can be accomplished under the guidance of an adult or in collaboration with a more expert peer. ⁹ The teacher's task is to identify and build on immature but maturing structures and, through collaboration and guidance, to facilitate cognitive growth. In the process, the child internalizes the resources required for solving a particular problem, and these resources become part of the child's independent developmental achievement. The term "scaffolding" characterizes the support that adults give to learners in the ZPD to move them from what they already know to what they can do next. ¹⁰ Effective formative assessments, then, should identify what a student might achieve in his or her ZPD and enable teachers to adapt teaching to close the gap between the student's current state of learning and the desired state.

Feedback. Formative assessment is designed to provide feedback at multiple levels. First, it provides feedback to the teacher about current levels of student understanding. This feedback also informs what the next steps in learning should be.

Feedback also is central to guiding students through their own next steps. Sadler's model strongly emphasizes feedback to students through the use of the feedback loop. This loop involves teachers and their students in an ongoing process. Effective feedback from teachers provides clear, descriptive, criterion-based information that indicates to the students where they are in a learning progression (defined below), how their understanding differs from the desired learning goal, and how they can move forward. The teacher takes steps to close the gap between the students' current learning and the goal by modifying instruction, assessing again to give further information about learning, modifying instruction again, and so on. In formative assessment, learners must be able to use feedback to improve their learning. ¹¹ Another important aspect of the relationship between feedback and learning is that feedback has a strong effect on students' motivation and their sense of self-efficacy - how they feel about their various abilities -both of which are major influences on learning.

Student involvement. Improving learning through formative assessment also depends on the active involvement of students in their own assessment. ¹² In formative assessment, students learn the skills of self- and peer assessment so that, as Sadler suggests, they collaborate with their teachers in developing a shared understanding of their current learning status and what they need to do to move forward in their learning. In doing so, they are using metacognitive processes. They reflect on their learning, monitoring what they know and understand and determining when they need more information. They also develop self-regulation strategies and are able to adapt their learning tactics to meet their own learning needs. Students must also collaborate with their teachers to determine the criteria for success for each step along the learning progression.

Most state standards, by themselves, do not provide a clear progression for understanding where students are relative to desired goals.

Learning progressions. If formative assessment is to provide guidance to teachers and students, it must be linked to a learning progression. The learning progression should clearly articulate the subgoals that constitute progress toward the ultimate goal. Most state standards, by themselves, do not provide a clear progression for understanding where students are relative to desired goals. In fact, many state standards do not even provide a clear picture of what learning is expected. Developing learning progressions toward standards is a critical element of formative assessment. Learning progressions provide the big picture of what is to be learned, and they help teachers locate students' current learning status on the continuum along which students are expected to progress.

Students also need to have short-term goals, which are derived from the learning progression and described in terms of success criteria. Success criteria are the guide to learning while the student is engaged in the learning tasks. The success criteria provide the framework within which formative assessment takes place and make possible the interpretation of evidence. ¹³
The knowledge teachers need
To use formative assessment successfully in the classroom, teachers need specific knowledge and skills. Four basic elements of teacher knowledge are critical: 1) domain knowledge, 2) pedagogical content knowledge, knowledge of students' previous learning, and 4) knowledge of assessment.

Domain knowledge. Teachers must know the concepts, knowledge, and skills to be taught within a domain, the precursors necessary for students to acquire them, and what a successful performance in each looks like. With this knowledge, they are able to define a learning progression of subgoals toward the desired learning that will act as the framework to guide assessment and instruction. A sufficiently detailed progression will also supply the success criteria for recognizing when students have demonstrated a successful performance and when they have not and for providing students with substantive feedback.

Teachers also need to understand student metacognition as it relates to assessment. As noted earlier, students develop the ability to monitor and assess their own learning so that they recognize when they are learning and when they are not. Linked to self-assessment is self-regulation, the will to act in ways that result in learning. And when students recognize they are not learning, they have the strategies to do something about it. Finally, teachers need to know that students' motivational beliefs - for example, beliefs about their general level of competence or self-efficacy - may influence their learning. ¹⁴

Pedagogical content knowledge. To effectively adapt instruction to student learning, teachers' pedagogical content knowledge must include familiarity with multiple models of teaching for student achievement in a specific domain and knowledge of which model of teaching is appropriate for what purpose. As already noted, the gap between current status and learning goals will differ from student to student, so teachers will need differentiated instructional strategies and a knowledge of how to use them in the classroom. To support student self-assessment, teachers will also need to be familiar with multiple models of teaching metacognitive processes and self-assessment skills.

Students' previous learning. If teachers are to build on students' previous learning, they need to know what that previous learning is. Students' previous learning includes: 1) their level of knowledge in a specific content area, 2) their understanding of concepts in the content area (i.e., the degree to which they can make generalizations through a process of abstraction from a number of discrete examples), 3) the level of their skills specific to the content area (i.e., the capacity or competence to perform a task), 4) the attitudes the students are developing (e.g., the value the students place on the subject, the interest they display, and their levels of initiative and self-reliance), and 5) their level of language proficiency.

Assessment knowledge. Teachers must know about the range of formative assessment strategies so that they can maximize the opportunities for gathering evidence. In addition, even though formative assessment strategies will not always meet accepted standards of validity and reliability, teachers need to understand that the quality of the assessment is an important concern. The overriding issue is consequential validity. Because the purpose of formative assessment is to promote further learning, its validity hinges on how effectively learning takes place in subsequent instruction. Teachers also need to know how to align formative assessments with instructional goals, and they need to ensure that the evidence from the formative assessment and the inferences they draw from it are of sufficient quality to enable them to understand where the learner is along a learning progression. ¹⁵ Finally, teachers need to know that their own assessments of learning are not the only available sources of evidence; students' self- and peer assessments provide important opportunities for establishing their current learning status.
The skills teachers need
In addition to an appropriate knowledge base, the successful implementation of formative assessment requires specific teacher skills. Teachers need to be able to 1) create classroom conditions that allow for successful assessment, 2) teach the students to assess their own learning and the learning of others, 3) interpret the evidence, and 4) match their instruction to the gap.

Creating the conditions. If students are going to be involved in assessment, two things need to happen. First, teachers must create a classroom culture that supports self- and peer assessment. This means that the classroom is a place where all students feel that they are respected and valued and that they have an important contribution to make. Second, teachers must have the skills to build a community of learners, characterized by a recognition and appreciation of individual differences. Classroom norms of listening respectfully to one another, responding positively and constructively, and appreciating the different skill levels among peers will enable all students to. feel safe in the learning environment and to learn with and from one another. Above all, teachers will need the skills to model the "safety" norms of the classroom in their own behavior.

Student self-assessment. Teachers must teach students to assess their own learning and the learning of others. This involves helping students to set goals and criteria for success, to reflect on their own and others' understanding, and to evaluate learning according to the criteria. Strategies to involve students in self-assessment can be as simple as asking students to reflect on their performance through such questions as "Do you think that your response demonstrated understanding? If so, why do you think this? If not, why do you think you did not demonstrate understanding?" From this basis, students can learn to be more independent and can recognize when they do not understand, when they need to do something about it, and what they can do to improve.

Teacher skills also include helping students learn to give constructive feedback to their peers that can provide for future growth. From simple beginnings like sayming, "It wasn't clear to me when. . ." or "I didn't understand your point about . . . ," students can progress to a detailed analysis of their peers' performance against specific criteria. Once again, the teacher must model all of this in the classroom so that students see that they are collaborators with their teacher and peers in developing a shared understanding of their current learning status and what they need to do to move forward.

Interpreting evidence. Teachers' skills in drawing inferences from students' responses are crucial to the effectiveness of formative assessment. No matter what the assessment strategy -observation, dialogue, asking for a demonstration or a written response -teachers must examine students' responses from the perspective of what they show about their conceptions, misconceptions, skills, and knowledge. This involves a careful analysis of the responses in relation to the criteria for success. In essence, teachers need to infer what the "just right gap" is between the current learning and desired goals, identifying students' emerging understanding or skills so that they can build on these by modifying instruction to facilitate growth.

The analysis of student responses takes place in different time frames, depending on the method of assessment. In on-the-fly assessments, teachers have to make inferences on a moment-by-moment basis. A curriculum-embedded analysis of student work might take place after the lesson and will provide more time for close examination. In both instances the importance of domain knowledge to analysis cannot be overstated; the success of the analysis is wholly dependent on it. Without a strong base of domain knowledge there is a danger that teachers' analyses will focus on the surface aspects of learning at the expense of deeper levels of understanding. An inaccurate analysis of the students' learning status will lead to errors in what the next instructional steps will be.

The analysis of student responses also provides the substance for feedback to students. Teachers need the skills to translate their analyses into clear and descriptive feedback, matched to the criteria for success, that can be used by students to further their learning.

Matchin g instruction to the gap. It is axiomatic to formative assessment that, if the next instructional steps to close the gap are too hard for the student, frustration will almost certainly result, and if they are too easy, boredom and disaffection are potential outcomes. Therefore, teachers need the skills to translate their interpretations of the assessment results into instructional actions that are matched to the learning needs of their students. This involves selecting the learning experiences that will place appropriate demands on the student and ordering these experiences so that each successive element leads the student toward realizing the desired outcome. Having matched the next steps in learning to the gap, teachers' scaffolding skills come into play. Their skills in deciding on the appropriate strategy must be complemented by their skills in executing the strategy. Their job is to ensure that the student receives appropriate support so that new learning is incrementally internalized and ultimately becomes pan of the student's independent achievement.

Matching the instruction to the gap cannot be done successfully without differentiating classroom instruction. In any classroom, one student's "just right gap" will not always be the same as another's. Clearly it is not practical for teachers to engage in one-on-one instruction with each student. However, strategic questioning in a whole-class lesson can provide scaffolding for a range of learning levels, while forming subgroups for instruction, assigning individual activities, and employing a combination of didactic and exploratory approaches help accommodate differences.
Conclusion
Even if teachers have all the required knowledge and skills for formative assessment, without the appropriate attitudes toward the role that formative assessment can play in teaching and learning, their knowledge and skills will lie dormant.

Teachers must view formative assessment as a worthwhile process that yields valuable and actionable information about students' learning. If they do not, formative assessment will be seen as "yet another thing" that is being externally imposed on them. Teachers must view formative assessment and the teaching process as inseparable and must recognize that one cannot happen without the other.

Also, if students are going to be successfully involved in monitoring and assessing their own and their peers' learning, then they need to be regarded by their teachers as partners in learning. This is not an attitude that has traditionally been prevalent in the profession.

If formative assessment is to be an integral pan of professional practice, there needs to be a major investment made in teachers. This investment must begin with changes in preservice training. No teacher should exit a professional training program without the knowledge to assess student learning. Furthermore, beginning teachers must have opportunities to develop and practice the skills of assessing before they are responsible for a class of students. Teacher educators have a significant role to play in ensuring that teacher education programs equip their students with the knowledge and skills necessary to integrate teaching and assessment in classroom practice.

The investment in teachers must continue with inservice professional development that involves a commitment by leaders at all levels of the education system. Rather than providing teachers with more tests, leaders at the state, district, and school levels should invest in a coordinated effort to establish structures and provide resources that support effective professional development.

This investment is a long-term project that should not be shortchanged. The payoff will be improved teacher practices and improved student learning, and that is surely worth it.
References

1. Dylan Wiliam and Marnie Thompson, "Integrating Assessment with Learning: What Will It Take to Make It Work?," in Carol Dwyer, ed., The Future of Assessment: Shaping, Teaching and Learning (Mahwah, N.J.: Erlbaum, 2006).

2. Richard Stiggins, "Assessment Crisis: The Absence of Assessment FOR Learning," Phi Delta Kappan, June 2002, pp. 758-65.

3. Paul Black and Dylan Wiliam, ".Assessment and Classroom Learning," Assessment in Education: Principles, Policy and Practice, 5, November 1998, pp. 7-73.

4. Richard J. Shavelson, "On the Integration of Formative Assessment in Teaching and Learning with Implications for Teacher Education," paper prepared for the Stanford Education Assessment Laboratory and the University of Hawaii Curriculum Research and Development Group, 2006, available at www.stanford.edu/dept/SUSE/SEAL.

5. H. Margaret Heritage, Norma Silva, and Mary Pierce, "Academic Language: A View from the Classroom," in Alison L. Bailey, ed., Language Demands of Students Learning English in School· Putting Academic Language to the Test (New Haven, Conn.: Yale University Press, 2006).

6. Paul Black et al., Assessment for Learning: Putting It into Practice (New York: Open University Press, 2003).

7. H. Margaret Heritage and David Niemi, "Toward a Framework for Using Student Mathematical Representations as Formative Assessments," Educational Assessment, vol. 11, 2006, pp. 265-82; and Pamela Aschbacher and Alicia Alonzo, "Examining the Utility of Elementary Science Notebooks for Formative Assessment Purposes," Educational Assessment, vol. 11, 2006, pp. 179-203.

8. D. Royce Sadler, "Formative Assessment and the Design of Instructional Systems," Instructional Science, vol. 18, 1989, p. 130.

9. Lev Vygotsky, Mind in Society (Cambridge, Mass.: Harvard University Press, 1978); and idem, Thought and Language (Cambridge, Mass.: MIT Press, 1986).

10. David Wood, Jerome Bruner, and Gail Ross, "The Role of Tutoring in Problem Solving," journal of Child Psychology and Psychiatry, 17, 1976, pp. 89-100.

11. Assessment Reform Group, Assessment for Learning: Beyond the Black Box (Cambridge: University of Cambridge, School of Education, 1999).

12. Ibid.

13. Shirley Clarke, Formative Assessment in the Secondary Classroom (London: Hodder Murray, 2005).

14. Wynne Harlen, "The Role of Assessment in Developing Motivation for Learning," in John Gardner, , Assessment and Learning (London: SAGE, 2006), pp. 61-80.

15. Gordon Stobart, "The Validity of Formative Assessment," in Gardner, 133-46.

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Formative assessment: What do teachers need to know and do? - kappanonline.org

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To many of today's teachers, assessment is synonymous with high-stakes standardized tests. But there is an entirely different kind of assessment that can actually transform both teaching and learning . Ms . Heritage describes what the skillful use of formative assessment would look like.

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Example DIBELs.docx

Sample spelling test- WTW.docx

WTW- Check your grading.docx

WTW- primary_fg.doc

WTW-upper_fg.doc

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evaluating strengths and weaknesses

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Awesome resource
Definitions, Areas of Impact, and Recommended Strategies/Accommodations

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The Construct of Adaptive Behavior:Its Conceptualization, Measurement, and Use in theField of Intellectual Disability

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The Construct of Adaptive Behavior:Its Conceptualization, Measurement, and Use in theField of Intellectual Disability

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Key Words: adaptive behavior assessment; adaptive behavior skills; adaptive behavior construct; diagnosis;
intellectual disability

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The construct of adaptive behavior: its conceptualization, measurement, and use in the field of intellectual disability.

Abstract

This article updates the current conceptualization, measurement, and use of the adaptive behavior construct. Major sections of the article address an understanding of the construct, the current approaches to its measurement, four assessment issues and challenges related to the use of adaptive behavior information for the diagnosis of intellectual disability, and two future issues regarding the relations of adaptive behavior to multidimensional models of personal competence and the distribution of adaptive behavior scores. An understanding of the construct of adaptive behavior and its measurement is critical to clinicians and practitioners in the field because of its role in understanding the phenomenon of intellectual disability, diagnosing a person with intellectual disability, providing a framework for person-referenced education and habilitation goals, and focusing on an essential dimension of human functioning.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

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The construct of adaptive behavior: its conceptualization, measurement, and use in the field of intellectual disability.

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Author(s): Tassé, Marc J; Schalock, Robert L; Balboni, Giulia; Bersani, Hank; Borthwick-Duffy, Sharon A; Spreat, Scott; Thissen, David; Widaman, Keith F; Zhang, Dalun | Abstract: This article updates the current conceptualization, measurement, and use of the adaptive behavior construct.

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Vineland adaptive Behaviour Scales

Sara S. Sparrow, David A. Balla, and Domenic V. Cicchetti

Interview Edition survey form

file:///Users/lizzyw/Downloads/Vineland%20(1).pdf
Download Vineland.pdf

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Download CBCL Child Behavior Checklist(2).pdf

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Monitoring Student Progress in Individualized Educational ProgramsUsing Curriculum-Based Measurement 

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Monitoring Student Progress in Individualized Educational ProgramsUsing Curriculum-Based Measurement 

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Includes:
Critical Features of CBM
CBM procedures in reading and math
Describing present levels of performance on The IEP using CBM
Developing long term goals and short term objectives using CBM
Monitoring student progress using CBM

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Progress Monitoring Within a Response-to-Intervention Model

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Progress Monitoring Within a Response-to-Intervention Model

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1. What is progress monitoring?

2. How does progress monitoring work in RTI?

3. What are the elements of effective progress-monitoring measures?

4. What are some common progress-monitoring measures?

5. What progress-monitoring measures were used in the RTI models in the research review of RTI field studies?

6. What can we conclude from the research and what directions look promising for future research?

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Get Email Updates

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Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2007).

Additional Articles

Additional Resources

The purpose of this article is to discuss progress monitoring within a Response-to-Intervention (RTI) model and to assist the reader in making informed decisions when selecting and interpreting progress-monitoring measures. To that end, this article answers the following questions:

1. What is progress monitoring?

2. How does progress monitoring work in RTI?

3. What are the elements of effective progress-monitoring measures?

4. What are some common progress-monitoring measures?

5. What progress-monitoring measures were used in the RTI models in the research review of RTI field studies?

6. What can we conclude from the research and what directions look promising for future research?

What Is Progress Monitoring?

In the context of an RTI prevention model, progress monitoring is used to assess student progress or performance in those areas in which they were identified by universal screening as being at-risk for failure (e.g., reading, mathematics, social behavior). It is the method by which teachers or other school personnel determine if students are benefitting appropriately from the typical (e.g., grade level, locally determined, etc.) instructional program, identify students who are not making adequate progress, and help guide the construction of effective intervention programs for students who are not profiting from typical instruction (Fuchs & Stecker, 2003). Although progress monitoring is typically implemented to follow the performance of individual students who are at risk for learning difficulties, it can also follow an entire classroom of students (Fuchs & Fuchs, 2006).

How Does Progress Monitoring Work in RTI?

As soon as a student is identified as at risk for achievement deficits by the universal screening measure, his or her progress should be monitored in relation to Tier 1 instruction (Fletcher, Lyon, Fuchs, & Barnes, 2007). Progress should be monitored frequently, at least monthly, but ideally weekly or biweekly (Fuchs & Fuchs, 2006). A student's progress is measured by comparing his or her expected rate of learning (e.g., local or national norms) and actual rate of learning (Fuchs, Fuchs, & Zumeta, 2008). A teacher can use these measurements to gauge the effectiveness of teaching and to adjust instructional techniques to meet the needs of the individual student. A student who is not responding adequately to Tier 1 instruction moves on to Tier 2 and increasingly intensive levels of intervention and instruction. The current recommended time period for measuring response to Tier 1 instruction is 8-10 weeks (McMaster & Wagner, 2007; Fuchs & Fuchs, 2005; Vaughn, Linan-Thompson, & Hickman, 2003) and nonresponsiveness is typically determined by a percentile cut on norm-referenced tests (e.g., < 20 th percentile) or cut score on a curriculum based measurement (CBM).

According to the National Center on Student Progress Monitoring, progress monitoring has the following benefits when it is implemented correctly: 1) students learn more quickly because they are receiving more appropriate instruction; 2) teachers make more informed instructional decisions; 3) documentation of student progress is available for accountability purposes; 4) communication improves between families and professionals about student progress; 5) teachers have higher expectations for their students; and, in many cases, 6) there is a decrease in special education referrals. Overall, progress monitoring is relevant for classroom teachers, special educators, and school psychologists alike because the interpretation of this assessment data is vital when making decisions about the adequacy of student progress and formulating effective instructional programs (Fuchs, Compton, Fuchs et al., 2008).

Elements of Effective Progress-Monitoring Measures

To be effective, progress-monitoring measures must be available in alternate forms, comparable in difficulty and conceptualization, and representative of the performance desired at the end of the year (Fuchs, Compton, Fuchs et al., 2008). Measures that vary in difficulty and conceptualization over time could possibly produce inconsistent results that may be difficult to quantify and interpret. Likewise, using the same measure for each administration may produce a testing effect, wherein performance on a subsequent administration is influenced by student familiarity with the content.
By using measures that have alternate forms and are comparable in difficulty and conceptualization, a teacher can use slope (e.g., academic performance across time) to quantify rate of learning (Fuchs & Fuchs, 2008). Slope can also be used to measure a student's response to a specific instructional program, signaling a need for program adjustment when responsiveness is inadequate (Fuchs et al., 2008).

Effective progress-monitoring measures should also be short and easily administered by a classroom teacher, special education teacher, or school psychologist (Fuchs & Stecker, 2003). According to Fletcher et al. (2007), there is much research to support the use of short, fluency-based probes in deficit areas such as word reading fluency and accuracy, mathematics, and spelling. However, for areas such as reading comprehension and composition, there is less research support for specific kinds of probes because these domains demonstrate less rapid change and require methods for assessing progress over longer periods of time (Fletcher et al., 2007; McMaster & Wagner, 2007).

Common Progress-Monitoring Measures

Progress can be monitored by a variety of methods. From a norm-referenced standpoint, it is possible to use widely available assessments such as the Test of Word Reading Efficiency (TOWRE; Torgesen et al., 1999) or the Woodcock-Johnson Achievement Battery (Woodcock, McGrew, & Mather, 2001). With such tests, alternate forms are available to demonstrate student improvement over time, but usually there is at least three months between administrations (Fletcher et al., 2007). Other measures, such as the Dynamic Indicators of Basic Literacy Skills (DIBELS; Good, Simmons, & Kame'enui, 2001), have been reviewed by the National Center for Student Progress Monitoring and vary considerably in reliability, validity, and other key progress-monitoring standards.

CBM, one approach to progress monitoring, has the most well supported measures in the research base. According to Fuchs and Fuchs (2006),

More than 200 empirical studies published in peer-review journals (a) provide evidence of CBM's reliability and validity for assessing the development of competence in reading, spelling, and mathematics and (b) document CBM's capacity to help teachers improve student outcomes at the elementary grades (p. 1).

CBM is a form of classroom assessment that 1) describes academic competence in reading, spelling, and mathematics; 2) tracks academic development; and 3) improves student achievement (Fuchs & Stecker, 2003). It can be used to determine the effectiveness of the instruction for all students and to enhance educational programs for students who are struggling (McMaster & Wagner, 2007). Finally, findings of over 200 empirical studies indicate that CBM produces accurate, meaningful information about students' academic levels and growth, is sensitive to student improvement, and when teachers use CBM to inform their instructional decisions, students achieve better (Fuchs & Fuchs, 2006).

Fuchs and Stecker (2003) warn that most classroom assessment is based on mastery of a series of short-term instructional objectives or "mastery measurement." To implement this type of assessment the teacher determines the educational sequence for the school year and designs criterion-referenced tests to match each step in that educational sequence. According to Fuchs and Stecker, problems with mastery measurement include: 1) the hierarchy of skills is logical, not empirical; 2) assessment does not reflect maintenance or generalization; 3) measurement methods are designed by teachers, with unknown reliability and validity; and 4) the measurement framework is highly associated with a set of instructional methods. CBM combats these problems by making no assumptions about instructional hierarchy for measurement, so it fits with any instructional approach and by incorporating automatic tests of retention and generalization. According to Fuchs and Fuchs (2006), CBM and mastery measurement have another significant difference:

CBM also differs from mastery measurement because it is standardized; that is, the progress monitoring procedures for creating tests, for administering and scoring those tests, and for summarizing and interpreting the resulting database are prescribed. By relying on standardized methods and by sampling the annual curriculum on every test, CBM produces a broad range of scores across individuals of the same age. The rank ordering of students on CBM corresponds with rank orderings on other important criteria of student competence. For example, students who score high (or low) on CBM are the same students who score high (or low) on the annual state tests. For these reasons, CBM demonstrates strong reliability and validity. At the same time, because each CBM test assesses the many skills embedded in the annual curriculum, CBM yields descriptions of students' strengths and weaknesses on each of the many skills contained in the curriculum. These skills profiles also demonstrate reliability and validity (p. 2).

The tasks measured by CBM include 1) pre-reading (phoneme segmentation fluency; letter sound fluency); 2) reading (word identification fluency; passage reading fluency; maze fluency); 3) mathematics (computation; concepts and applications); 4) spelling; and 5) written expression (correct word sequences).

Progress Monitoring in Field Studies

In our research review of RTI field studies, all but one mentioned progress monitoring. However, the specific progress-monitoring measures and frequency of use varied significantly between studies. Table 1 provides information (e.g., type of measure and frequency) on progress-monitoring measures used in each of the 11 studies found in our research review.

Table 1: Progress Monitoring in the Field Studies

Authors*Model Name**Progress Monitoring Mentioned? Type How Often?

O'Connor et al. (2005)
TRI

Yes

WRMT-R sub-tests; CBM Reading

Not reported

*Click author name to view field study
**Model name

SPMM - Standard-protocol mathematics model
SCRED - St. Croix River education district model
RBM - Idaho results-based model
BSM - Behavior support model
IST - Pennsylvania instructional support teams
MPSM - Minneapolis problem-solving model TRI - Tiers of reading intervention
FSDS - Illinois flexible service delivery system model
IBA - Ohio intervention-based assessment
STEEP - System to enhance educational performance
EGM - Exit group model

Conclusion and Directions for Future Research

Progress monitoring is paramount in determining if students are benefitting appropriately from the typical instructional program, identifying students who are not making adequate progress and guiding the construction of effective intervention programs for students who are not profiting from typical instruction. However, it is important to note that while CBM and other measures can be helpful tools for monitoring progress; there are some potential challenges to successful implementation. Teachers must be trained to use these assessments effectively, as well as to use the data to quantify rates of progress and, subsequently, adjust the educational program for struggling students (Fuchs, Fuchs, & Zumeta, 2008). Without that training, the usefulness of any progress monitoring-measure is greatly limited. It is crucial that schools and districts support data-driven approaches and make training available to all teachers.

References

Learning disabilities: From identification to intervention. New York: The Guilford Press.

Fuchs, D., Compton, D. L., Fuchs, L. S., & Bryant, J. (2008). Making "secondary intervention" work in a three-tier responsiveness-to-intervention model: Findings from the first-grade longitudinal reading study at the National Research Center on Learning Disabilities. Reading and Writing: An Interdisciplinary Journal, 21, 413-436.

Fuchs, D., & Fuchs, L. S. (2005). Responsiveness-to-intervention: A blueprint for practitioners, policymakers, and parents. Teaching Exceptional Children, 38, 57-61.

Fuchs, D., & Fuchs, L. S. (2006). Introduction to responsiveness-to-intervention: What, why, and how valid is it? Reading Research Quarterly, 4, 93-99.

Fuchs, L. S., & Fuchs, D. (2008). The role of assessment within the RTI framework. In D. Fuchs, L. S. Fuchs, & S. Vaughn (Eds.), Response to intervention: A framework for reading educators (pp. 27-49). Newark, DE: International Reading Association.

Fuchs, L. S., & Stecker, P. M. (2003). Scientifically based progress monitoring. National Center on Student Progress Monitoring: Washington, DC. Retrieved May 15, 2009.

Good, R. H., Simmons, D. C., & Kame'enui, E.J. (2001). The importance and decision-making utility of a continuum of fluency-based indicators of foundational reading skills for third-grade high-stakes outcomes. S cientific Studies of Reading, 5, 257-288.

McMaster, K. L., & Wagner, D. (2007). Monitoring response to general education instruction. In S. R. Jimerson, M. K. Burns, & A. M. VanDerHeyden (Eds.). Handbook of response to intervention: The science and practice of assessment and intervention (pp. 223-233). New York: Springer.

Torgesen, J. K., Alexander, A. W., Wagner, R. K., Rashotte, C. A., Voeller, K., & Conway, T. (2001). Intensive remedial instruction for children with severe reading disabilities: Immediate and long-term outcomes from two instructional approaches. Journal of Learning Disabilities, 34, 33-58.

Torgesen, J. K., Wagner, R. K., Rashotte, C. A., Rose, E., Lindamood, P., & Conway, T. (1999). Preventing reading failure in young children with phonological processing disabilities: Group and individual responses to instruction. Journal of Educational Psychology, 91, 579-593.

Vaughn, S., Linan-Thompson, S., & Hickman, P. (2003). Response to instruction as a means of identifying students with reading/learning disabilities. Exceptional Children, 69, 391-409.

Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson III. Itasca, IL: Riverside Publishing.
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Progress Monitoring Within a Response-to-Intervention Model

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Progress monitoring is implemented in RTI to follow the performance of students who are at risk for learning difficulties.

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The following Documents come from a spelling program called Words Their Way

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The following Documents come from a spelling program called Words Their Way

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It is a great tool to use as a diagnostic (determining where students need help in spelling instruction) and as a progress monitoring tool

WTW- feature_guides.doc.pdf

WTW- primary_fg.doc

WTW elem_fg_rev.doc

WTW-upper_fg.doc

WTW- Check your grading.docx

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Glossary of Testing, Measurement, and Statistical Terms

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Glossary of Testing, Measurement, and Statistical Terms

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Glossary of Terms Used in Assessments (1) (2)

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PLAAFP and Goals Templates With Examples (1) (1)