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Mathematics Assessment and Intervention in a PLC at Work™

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Part of the Every Student Can Learn Mathematics series

Harness the power of formative assessment processes within an RTI model (MTSS) to inspire student learning in mathematics. This user-friendly resource is divided into two parts, each covering a key team action for mathematics in a PLC at Work™. First you'll learn how to develop high-quality common assessments. Then discover how to use the mathematics assessments for formative student learning and intervention. The book features unit samples for learning standards, sample unit exams, student performance trackers, and more.

Improve your math assessment methods using RTI Tier 2 interventions and PLC processes as a guide:

  • Explore an assessment model for writing quality common assessments.
  • Utilize RTI Tier 2 intervention strategies for effectively responding to student learning.
  • Make sense of the grade-level content standards and corresponding tasks.
  • Learn how to write quality common unit assessments and score them accurately.
  • Determine how students can reflect and set performance goals using common unit assessment results.
  • Develop a Tier 2 RTI math intervention program to support student learning.


Part 1: Team Action 1 -- Develop High-Quality Common Assessments for the Agreed-On Essential Learning Standards
Chapter 1: The Purpose and Benefit of Common Mathematics Assessments
Chapter 2: Quality Common Mathematics Unit Assessments
Chapter 3: Sample Common Mathematics Unit Assessments and Collaborative Scoring Agreements

Part 2: Team Action 2 -- Use Common Unit Assessments for Formative Student Learning and Intervention
Chapter 4: Quality of Mathematics Assessment Feedback Processes
Chapter 5: Team Response to Student Learning Using Tier 2 Mathematics Intervention Criteria
Chapter 6: Student Action on Assessment Feedback During the Unit

References and Resources

Books in the Every Student Can Learn Mathematics series:

  • Mathematics Assessment and Intervention in a PLC at Work™
  • Mathematics Instruction and Tasks in a PLC at Work™
  • Mathematics Homework and Grading in a PLC at Work™
  • Mathematics Coaching and Collaboration in a PLC at Work™

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Chapter 1



The Purpose and Benefit of Common

Mathematics Assessments

When you’re surrounded by people who share a passionate commitment around a common purpose, anything is possible.

—Howard Schultz


hances are, you already use during-the-unit and end-of-unit assessments to measure and record student learning. You may or may not know the routines your colleagues use to ensure the assessments you create are in common. You also may not have a common strategy for assessing the quality of those assessments.

learning standard, the format of the test questions, the number of test questions, the alignment of those questions to each standard, the strategies students use to demonstrate learning, and the scoring of those assessment questions all depend on your willingness to work together and erase any potential inequities that a lack of transparency with colleagues can cause.

In Learning by Doing, authors DuFour, DuFour,

Eaker, Many, and Mattos (2016) indicate that common assessments:


Chapter 2



Quality Common Mathematics

Unit Assessments

Design is a funny word. Some people think design means how it looks.

But of course, if you dig deeper, it’s really how it works.

—Steve Jobs


ow do you decide if the unit-by-unit common mathematics assessment instruments you design are high quality? This is a question every teacher and leader of mathematics should ask.

Tim Kanold describes his experience at Stevenson HSD

125 when he first asked this question of the middle school mathematics teachers from one of the Stevenson feeder districts.

The mathematics assessment work Tim describes created an early beta model for a test evaluation tool he and his fellow teachers could use to evaluate the quality of their unit-by-unit mathematics assessments. Figure 2.1 (page 14) provides a much deeper

Personal Story

and robust during-the-unit or end-of-unit assessment instrument evaluation tool your collaborative team can use to evaluate quality and build new and revised unit assessment instruments.


Chapter 3



Sample Common Mathematics

Unit Assessments and

Collaborative Scoring Agreements

Through frequent assessment, teachers discover when students need additional support to continue their learning.

—John Hattie, Douglas Fisher, and Nancy Frey


very common mathematics unit assessment, no matter how strong it may be, can still be improved—crafted into a stronger tool to more accurately and effectively gather evidence for you and your students as to which essential learning standards students have learned and which they have not learned yet.

Your continual improvement gathering dependable evidence occurs both during and at the end of assessments.

For some mathematics units or modules, your team may want to create more frequent common assessments to use during a unit. Your team can use the assessment evaluation tool described in chapter 2 to evaluate the quality of these during-the-unit assessments. However, sometimes due to the intent of the essential learning standard, during-the-unit assessments (think quizzes) may not contain a variety of assessment formats and may have a different balance of higher- to lower-levelcognitive-demand tasks.


Chapter 4



Quality Mathematics

Assessment Feedback Processes

Assessment is a process that should help students become better judges of their own work, assist them in recognizing high-quality work when they produce it, and support them in using evidence to advance their own learning.

—NCTM, Principles to Actions


here are two important elements to consider when using your mathematics assessment results effectively. First, students must receive meaningful impact feedback on their work in order to improve their mathematical understanding. For the purposes of this book, meaningful assessment feedback refers to the

FAST feedback elements described in this chapter.

Second, students must use tools or protocols requiring them to take action on during-the-unit and end-of-unit mathematics assessment feedback in formative ways. To repeat: they take action on your feedback.

Dylan Wiliam (2016) states it this way, “If our feedback doesn’t change the students in some way, it has probably been a waste of time” (p. 14).


Chapter 5



Team Response to Student Learning

Using Tier 2 Mathematics

Intervention Criteria

As long as interventions are viewed as an appendage to a school’s traditional instructional program, instead of an integral part of a school’s collaborative efforts to ensure all students succeed, interventions will continue to be ineffective.

—Richard DuFour


ot all students learn the same way or at the same rate, as evidenced by the student work on your end-of-unit common mathematics assessments.

When students have not yet learned essential standards, the collaborative teacher team response in a PLC culture is not to stop and reteach all students. Such an action would be done at the expense of students learning the remaining essential standards that are part of the guaranteed and viable curriculum for your grade level or mathematics course.

Instead, the PLC response is to work together to design a quality mathematics intervention program that provides additional time and support to students needing to still learn grade-level or course-based essential learning standards, while continuing to teach the essential learning standards in the next unit. Such a mandate requires a team effort to ensure every student is learning from an intentional mathematics intervention. Quality systematic interventions are not pull-out programs or initial differentiated instruction variety, but rather a value-added model of continued instruction.


Chapter 6



Student Action on Assessment

Feedback During the Unit

When students engage in their learning and take ownership of the process, they are able to set goals, evaluate their progress, and determine what course of action to take to reach the highest level of achievement.

—Sharon V. Kramer


here is a final assessment and intervention for you and your colleagues to consider as part of your unit-by-unit work in mathematics. In addition to end-of-unit common formative assessments, students can also learn and benefit from shorter common assessments provided during a mathematics unit. Since each assessment closely aligns to one or two essential learning standards, students can use your feedback to determine whether they have learned the standard yet before the final end-of-unit assessment. It is important that students take action on and ownership of the assessment feedback they receive during the unit. They will then be able to engage in Tier 2 mathematics interventions before the unit ends as you help them respond to PLC critical question 3 (DuFour et al., 2016): How will we respond when some students do not learn (in this case, during the unit)? Thus, learning during the unit becomes more formative.






Task Analysis Guide

This appendix provides criteria you can use to evaluate the cognitive-demand level of the tasks you choose each day. As you develop your unit plans, use this tool to ensure a balance of lower-level and higher-level tasks for students as they learn the standards.

Table A.1: Cognitive-Demand Levels of Mathematical Tasks

Lower-Level Cognitive Demand

Higher-Level Cognitive Demand

Memorization Tasks

• These tasks involve reproducing previously learned facts, rules, formulae, or definitions to memory.

• They cannot be solved using procedures because a procedure does not exist or because the time frame in which the task is being completed is too short to use the procedure.

• They are not ambiguous; such tasks involve exact reproduction of previously seen material and what is to be reproduced is clearly and directly stated.

• They have no connection to the concepts or meaning that underlie the facts, rules, formulae, or definitions being learned or reproduced.



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