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Appendix E: How the Mathematics at Work High-Leverage Team Actions Support the NCTM Principles to Actions: Ensuring Mathematical Success for All

Kanold, Timothy D. Solution Tree Press ePub

APPENDIX E

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

CHAPTER 3

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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Chapter 3 After the Unit

Kanold, Timothy D. Solution Tree Press ePub

CHAPTER 3

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-assessing-learning cycle (see figure 3.1, page 102).

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Appendix B: Standards for Mathematical Practice Evidence Tool

Kanold, Timothy D. Solution Tree Press ePub

APPENDIX B

Standards for Mathematical Practice Evidence Tool

Source: © 2013 by Mona Toncheff & Timothy D. Kanold. All rights reserved.
Source for Mathematical Practices: NGA & CCSSO, 2010, pp. 6–8.

Mathematical Practice 1: “Make Sense of Problems and Persevere in Solving Them”

Students:

•   Check intermediate answers, and change strategy if necessary

•   Think about approaches to solving the problem before beginning

•   Draw pictures or diagrams to represent given information

•   Have the patience to complete multiple examples in trying to identity a solution

•   Start by working a simpler problem

•   Make a plan for solving the problem

In the classroom:

•   Student teams or groups look at a variety of solution approaches and discuss their merits.

•   Student teams or groups compare two different approaches to look for connections.

•   Students discuss with their peers whether a particular answer is possible in a given situation and explain their thinking.

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Appendix D

Kanold, Timothy D. Solution Tree Press PDF

APPENDIX D

Sources for Higher-Level-Cognitive-Demand Tasks

Common Core Conversation www.commoncoreconversation.com/math-resources.html

Common Core Conversation is a collection of more than fifty free website resources for the Common

Core State Standards in mathematics and ELA.

EngageNY Mathematics www.engageny.org/mathematics

The site features curriculum modules from the state of New York that include sample assessment tasks, deep resources, and exemplars for grades preK–12.

Howard County Public School System Secondary Mathematics Common Core https://secondarymathcommoncore.wikispaces.hcpss.org

This site is a sample wiki for a district K–12 mathematics curriculum.

Illustrative Mathematics www.illustrativemathematics.org

The main goal of this project is to provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience upon implementation of the Common Core State Standards for mathematics.

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