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consist of a scale based on predetermined criteria with two important functions -- it permits the student to see what is central to excellent performance and it provides the teacher with scoring guidelines that support analysis of students’ work.

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Refers to a variety of written products, including problem-based tasks, journal entries, student self-assessments, and tests.

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Useful Interviews are assessment opportunities, not teaching opportunities.

During diagnostic interviews, it is important to explore whether the student can use models to connect actions to what he/she wrote or explained earlier

During an interview: avoid revealing whether a student’s answer is right or wrong, wait silently for the student to give an answer, remember that you should not interject clues or teach, and let students share their thinking freely without interruption.

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Student is given a problem and asked to verbalize his or her thinking at points in the process.

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Use to note growth in mathematical processes or practices, such as problem solving, modeling, or reasoning.

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Creating Assessments for Learning
By: Emily Nunez-Eddy, Xue Wang, Molly Trapp, Samantha Phillips, and Maria Estrada

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Communicating Grades and Shaping Instruction:

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Communicating Grades and Shaping Instruction:

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Grading must be based on the performance tasks and other activities for which you assigned rubric ratings

The grade at the end of the marking period should reflect a holistic view of where the student is now relative to your goals

Teachers must know how to act on the evidence revealed in an assessment or set of assessments to address the learning needs of students

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1. Permit students to use calculators
2. Use manipulatives and drawings
3. Include opportunities for explanations
4. Use open-ended questions

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Tests should match the goals of your instruction

Quizzes that are done in collaboration with a peer

How to succeed on “high stakes” tests -- teach the big ideas in mathematics curriculum that are aligned with required standards… use a problem-based approach

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Open-Ended Writing Prompts for Self-Assessment:

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Open-Ended Writing Prompts for Self-Assessment:

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How well do you think you understand the work we have been doing on fractions?during the last few days? What is still causing you difficulty with fractions?

Write two of the important things you learned in class today (or this week)

Which problems on the activity sheet did you find the most challenging? Which were the easiest?

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When students assess their own progress and growth they are developing an important life-long learning skill.

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Include specific statements, known as performance indicators, that describe what students’ work should look like at each level of the rubric and establish criteria for acceptable performance on that particular task

Used to predict students’ common misconceptions or the expected thinking or approaches to the same or similar problems

Performance indicators should be shared ahead of time with students.

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Identify broad categories of performance instead of specific criteria for a particular task and therefore can be used for multiple assignments

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Solved the problem accurately and effectively

Justified and explained strategy use or arguments

Used logical reasoning

Expressed a grasp of numerical relationships and structure

Incorporated multiple representations and/or multiple strategies

Demonstrated an ability to appropriately select and use tools and manipulatives

Communicated with precise language and accurate units

Identified general patterns of ideas that repeat, making connections from one big idea to another

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Scoring -- compares students’ work by established criteria set in advance
Grading -- summarizing a student’s performance throughout the accumulation of a variety of scores and data about their understanding of important concepts and skills

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Using seven representations for concepts, students are asked to use more than one representation (e.g. words, tools, and numbers) to demonstrate understanding of a single problem.

Translation tasks can be used when a teacher wants to find out more about a student’s ability to represent ideas in various forms and explain why these representations are similar or different.

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Tasks that are connected to actual problem solving abilities used in instruction

Focus on an important mathematics concept or skill aligned to a valued learning expectation

Stimulate the connection of students’ previous knowledge to new content

Allow multiple solution methods or approaches with a variety of tools

Offer opportunities for students to correct themselves along the way

Encourage students to use reasoning and explain their thinking

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Tasks should include discussion, to develop the habit of sharing, writing, and listening to justifications.

Students should compare and make connections between strategies and debate ideas in order to assist them in organizing their thoughts, thinking about their position, and analyzing the positions of others.

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Diagnostic interviews are a means of getting in-depth information about an individual student’s knowledge and mental strategies about concepts.

Interviews are assessment opportunities, not teaching opportunities.

Useful for gathering information to assess the effectiveness of instruction

Useful for students that you need more information on, especially about how he/she is mentally constructing concepts or using a procedure

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What can you tell me about [today’s topic]?

How can you put the problem in your own words?

What did you do that helped you understand the problem?

How does this problem remind you of another problem we’ve done?

Did you find any numbers or information you didn’t need? How did you know that the information was not important?

How did you decide what to do?

How did you decide whether your answer was right?

Did you try something that didn’t work? How did you figure out it was not going to work?

What is something you did in this problem that you could use to help you solve other problems?

Can you show that idea with [a model, a sketch, an equation]?

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Use anecdotal notes -- write short notes during or immediately after a lesson in a brief narrative style, focusing on about 5 students per day.

Use checklists -- create an individual checklist with several specific processes, mathematical practices, or content objectives.

Use questioning -- probe into students’ thinking through the use of questions to provide helpful data and insights to inform instruction, while also helping students focus on their reasoning.

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Assessments should measure student’s conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.

Assessments should give students the opportunity to demonstrate how they understand essential concepts in more than one way.

Problem solving, reasoning, communication, connections, and representations should be addressed.

Productive disposition -- refers to students’ ability to persevere, as well as their confidence and belief in their own mathematical abilities.

Discuss and explicitly model the expectations for assessments.

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Assessment should be seen as a way to “make learning visible”, in turn helping students grow, not just about tests or quizzes.

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Assessment is a “way to collect evidence about students’ content knowledge, flexibility in applying that knowledge, and disposition or attitudes toward mathematics”.

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1. Identify where learners are

2. Identify goal for learners

3. Identify a path to reach the goal

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used to check the status of students’ development during instructional activities, to preassess, or to attempt to identify students’ native understandings or misconceptions.

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cumulative evaluations that might generate a single score, such as an end-of-unit test or standardized tests

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Students should begin to use their own assessment results to move forward as learners.

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Students should be “informed partners” in understanding their progress in learning and how to enhance their growth in understanding concepts.

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Assessment should enhance students’ learning

Assessment is a valuable tool for making instructional decisions