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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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Part 5: Developing Heart—T Is for Thought

Kanold, Timothy D. Solution Tree Press ePub



Essential Heartprint Question: Are you a person with surface and deep knowledge capacity, thought, and wisdom?

It is not enough to do your best; you must first know what to do, and then do your best.

—W. Edwards Deming

In part 5, “T Is for Thought,” we explore the role that thought—wisdom about knowing what to do—plays in our growth as professional educators. We explore how to find our professional voice: What do we really understand about the content of our curriculum? What do we care about, believe, and expect from others and ourselves each and every day of our work? What are the principles we will defend and teach our students and colleagues throughout our careers?

When you speak, why should we listen? When you teach, why would we follow? You can’t teach and lead others—your students or your colleagues—to places you do not want to go to yourself.

If you think about the academic nature of our profession, then you understand we need both surface and deep pedagogical knowledge about our subject area—or in the case of elementary school teachers, across a broad range of subject areas. We should develop our wisdom about the content and the process of our work. We need to know the best strategies, representations, and ways to make complex ideas simpler.

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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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Part 3: Developing Heart—A Is for Alliances

Kanold, Timothy D. Solution Tree Press ePub



Essential Heartprint Question: Are you a person open to influence and shared values, able to become more relationally intelligent and interdependent with others?

The first order of business is to build a group of people who, under the influence of the institution, grow taller and become healthier, stronger, more autonomous together.

—Robert Greenleaf

In part 3 of this book, we explore the role alliances play as part of our heartprint in pursuit of an effective and fully engaged professional life. Our intentional effort to effectively collaborate and engage with our colleagues and to honor the covenants and agreements of a team helps to at best erase causes of inequity in our school, and at worse allows our teaching and leading life to expand its impact and find its full and realized potential.

What a payoff! You become both an inequity eraser for your students, and you begin the journey of maximizing the greatest potential that lies within you as a teacher of others.

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Part 2: Developing Heart—E Is for Engagement

Kanold, Timothy D. Solution Tree Press ePub



Essential Heartprint Question: Are you an inspiring person with the day-to-day energy required to be fully engaged in your work life?

We cannot dream of a utopia in which all arrangements are ideal and everyone is flawless. Life is tumultuous—an endless losing and regaining of balance, a continuous struggle, never an assured victory…. Every important battle is fought and re-fought. We need to develop a resilient, indomitable morale that enables us to face those realities and still strive for every ounce of energy to prevail.

—John W. Gardner

In part 2, “E Is for Engagement,” we explore the role that energy and effort play in your pursuit of a fully formed and exceptional professional life. What are the heartprint actions you can take and the conditions you create if you choose to be fully engaged in your work life every day? Will you choose to fight and re-fight every battle? Will you choose to use and reuse every ounce of energy and effort necessary to positively impact children and adults? Will you choose to become great at managing your energy resources?

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