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Appendix D: Sources for Higher-Level-Cognitive-Demand Tasks

Kanold, Timothy D. Solution Tree Press ePub


Sources for Higher-Level-Cognitive-Demand Tasks

Common Core Conversation


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


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


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

Illustrative Mathematics


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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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 2

Kanold, Timothy D. Solution Tree Press PDF


During the Unit

The choice of classroom instruction and learning activities to maximize the outcome of surface knowledge and deeper processes is a hallmark of quality teaching.

—Mary Kennedy

Learning is experience. Everything else is just information.

—Albert Einstein

Much of the daily work of your teacher teams occurs during the unit of instruction. This makes sense, as it is during the unit that teachers place into action much of the team effort put forth in their beforethe-unit work.

Your role is to support teachers’ efforts in data gathering, sharing, feedback, and action regarding student learning that forms the basis of an in-class formative assessment process throughout the unit. The teacher sharing of in-class formative assessment processes provides the platform that allows your collaborative teams to make needed adjustments to instruction, tasks, and activities that will better support student learning during the unit.

A teacher team–led effective formative assessment process also empowers and motivates students to make needed adjustments during class in their ways of thinking about and doing mathematics that lead to further learning.

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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 A: Standards for Mathematical Practice

Kanold, Timothy D. Solution Tree Press ePub


Standards for Mathematical Practice

Source: NGA & CCSSO, 2010, pp. 6–8. © 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Used with permission.

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

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