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Epilogue: Taking Your Next Steps

Kanold, Timothy D. Solution Tree Press ePub


Taking Your Next Steps

So now what? Your collaborative teams have moved through the five stages of the PLC teaching-assessing-learning cycle and should now be ready to start the process again with the next unit. Some of the considerations from this handbook relative to your teams’ work with the instructional unit include:

•   Was the size of the unit manageable within the teaching-assessing-learning cycle?

•   How did the team discussion of essential learning standards help support student understanding?

•   How did the design of the mathematical tasks and assessment instruments work? Were they aligned? Did they require demonstrations of student understanding?

•   How did the unit formative assessment plan fit with the end-of-unit assessment?

•   What was the student and teacher response at the end of the unit?

•   Did the team have the proper amount of time needed to complete its work?

The daily expectations of preparing class, scoring and grading student assessments, dealing with students who need extra help, meeting with parents, and having other school meetings often overwhelm teachers. Part of your responsibility as a leader within a PLC culture is to provide the team time necessary to support their work around the ten high-leverage team actions.

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Appendix E

Kanold, Timothy D. Solution Tree Press PDF


How the Mathematics at Work High-Leverage

Team Actions Support the NCTM �Principles to

Actions: Ensuring Mathematical Success for All

The Beyond the Common Core: A Handbook for Mathematics in a PLC at Work series and the Mathematics at Work process include ten high-leverage team actions teachers should pursue collaboratively every day, in every unit, and every year. The goals of these actions are to eliminate inequities, inconsistencies, and lack of coherence so the focus is on teachers’ expectations, instructional practices, assessment practices, and responses to student-demonstrated learning. Therefore, the Mathematics at Work process provides support for NCTM’s Guiding Practices for School Mathematics as outlined in the 2014 publication

Principles to Actions: Ensuring Mathematical Success for All (p. 5). Those principles are:







Curriculum principle—An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world.

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Chapter 3

Kanold, Timothy D. Solution Tree Press PDF


After the Unit

You can’t learn without feedback. . . . It’s not teaching that causes learning. It’s the attempts by the learner to perform that cause learning, dependent upon the quality of the feedback and opportunities to use it. A single test of anything is, therefore, an incomplete assessment. We need to know whether the student can use the feedback from the results.

—Grant Wiggins

Teachers have just taught the unit and given the common end-of-unit assessment (developed through high-leverage team actions 3 and 4). What should happen next? Did the students reach the proficiency targets for the essential learning standards of the unit? As a school leader, how do you know? More important, what are the responsibilities for each of your collaborative teams after the unit ends?

The after-the-unit high-leverage team actions support steps four and five of the PLC teaching-assessinglearning cycle (see figure 3.1, page 102).

Think about when your teachers pass back an end-of-unit assessment to their students. Did assigning the students a score or grade motivate them to continue to learn and to use the results as part of a formative learning process? Did the process of learning the essential standards from the previous unit stop for the students as the next unit began? In a PLC culture, the process of student growth and demonstrations of learning never stop.

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Appendix C: Cognitive-Demand-Level Task-Analysis Guide

Kanold, Timothy D. Solution Tree Press ePub


Cognitive-Demand-Level Task-Analysis Guide

Source: Smith & Stein, 1998. © 1998, National Council of Teachers of Mathematics. Used with permission.

Table C.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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Chapter 1

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Before the Unit

Teacher: Know thy impact.

—John Hattie

As a school leader, you are and always will be a teacher—of adults. Thus, the Hattie quote that opens this chapter is for you too. What will be your impact on the adults in your school or district, every month, every day, and on every unit of instruction? The ultimate outcome of before-the-unit planning is for your teachers to develop a clear understanding of the shared expectations for student learning during the unit.

Do you expect a teacher learning culture that understands mathematics as an effort-based and not an ability-based discipline? Do you have high expectations that every teacher can ensure all students learn?

Your collaborative teams, in conjunction with district mathematics curriculum team leaders, prepare a roadmap that describes the knowledge students will know and be able to demonstrate at the conclusion of the unit. To create this roadmap, each collaborative team prepares and organizes work around five before-the-unit high-leverage team actions that you will need to monitor.

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