Balancing the Equation: A Guide to School Mathematics for Educators and Parents (Contexts for Effective Student Learning in the Common Core)

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Copublished with the National Council of Teachers of Mathematics, this book focuses on individuals involved in K–12 mathematics education who seek to help children achieve success. The authors tackle popular misconceptions and misguided discourse about mathematics education and draw on peer-reviewed research about instruction that can significantly improve students’ conceptual understanding.

 

Benefits

 

  • Explore reasons why expectations for mathematics teaching and learning must be raised.
  • Study the history of the progression, changes, and disputes in K–12 mathematics education.
  • Discover insights about mathematics education in an era of mathematics reform.
  • Define mathematical literacy and what elements are part of effective mathematics instruction.
  • Learn the steps that must be taken to support the teaching and learning of mathematics so all students can be college and career ready.

 

Contents

 

Introduction

  1. Why Mathematics Education Needs to Improve
  2. A Brief History of Mathematics Education: Lessons to Learn
  3. The Equilibrium Position and Effective Mathematics Instruction
  4. How to Help Your Child Learn Mathematics
  5. Conclusion and Action Steps for Educators and Parents

Epilogue: Conclusion and Action Steps for Educators and Parents

Appendix: Additional Resources for Parents

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Introduction

ePub

e·qui·lib·ri·um

A state in which opposing forces or influences are balanced.

NEW OXFORD AMERICAN DICTIONARY,
THIRD EDITION

We love mathematics. We love students—all of the roughly fifty-four million going to school in the United States each year. We love and admire mathematics teachers. And we deeply appreciate the critical role that parents play in their children’s education. We know it is every parent’s desire for his or her child to succeed in learning mathematics. We also believe it is every educator’s desire—teachers, administrators, teacher leaders, central office personnel, and school board members—to see each and every student in his or her school or school district succeed in learning K–12 mathematics. And yet, this goal of mathematics success for each student is often very difficult to achieve.

We are parents or relatives of parents; we have been mathematics teachers and have served as teacher leaders; and we have dedicated our entire professional lives in the service of K–12 mathematics education. We have witnessed student, parent, and teacher frustration, and we also have observed student, parent, and teacher joy when students effectively learn mathematics.

 

Chapter 1 Why Mathematics Education Needs to Improve

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We are systematically underestimating what our kids can do in math.

—AMANDA RIPLEY,
INVESTIGATIVE JOURNALIST AND AUTHOR

Since the 1990s, efforts to improve mathematics teaching and learning have focused on state adoption and implementation of increasingly more rigorous K–12 mathematics standards. These state standards represent the guaranteed and viable curriculum that every student should learn—what we expect students to know and be able to do in each grade level and course. In addition, each state implemented accountability measures attached to attainment of those standards.

The standards movement was kick-started by the National Council of Teachers of Mathematics (NCTM) in 1989, when it published Curriculum and Evaluation Standards for School Mathematics. This document and the subsequent edition, Principles and Standards for School Mathematics (NCTM, 2000), as well as Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics (NCTM, 2006), served as the blueprints for various state mathematics standards produced over a two-decade period beginning in the early 1990s. NCTM presented a new sense of rigor in terms of both the what and the how of learning school mathematics.

 

Chapter 2 A Brief History of Mathematics Education

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The issues in mathematics education tend to endure, to change slowly if at all.

—PHILIP S. JONES AND ARTHUR F. COXFORD,
EDITORS, THE HISTORY OF MATHEMATICS
EDUCATION IN THE UNITED STATES AND CANADA

A brief history of mathematics education since 1788 illustrates the recurrent underpinnings of the debates in mathematics education. As Christopher Phillips (2015) points out, these issues are “cyclical and seemingly intractable” (p. 20). Table 2.1 (pages 28–29) outlines select major events in the history of mathematics education discussed in this chapter, including some of the intractable issues since 1788.

The two most persistent questions in mathematics education have been and continue to be the following (Jones & Coxford, 1970).

1.What should be the nature of mathematics that students learn—facts, skills, and procedures, or concepts and understanding?

2.How should students learn mathematics—teacher directed with a focus on memorization, or student centered through reasoning and discovery?

 

Chapter 3 The Common Core Mathematics Debate

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

—NCTM

This chapter will help you better understand and speak to the original intent, hope, and promise of the Common Core as well as the arguments against them. As you read through these issues, ask yourself, “How will or does this affect the students in my class or my school, the current high school graduates in my district, or any graduating class moving forward? What is the truth about the expectations of the revised mathematics standards?”

If you are an elementary educator, students’ parents might have expressed concern about the nature of homework labeled Common Core. This chapter will help you better understand the intent of the Common Core, gain insight into the arguments some parents and politicians make against the Common Core, equip you to discuss those issues and concerns with parents, and help you determine if elementary-level math homework really has anything to do with the actual content standards of the Common Core. (See Issue 3: Challenges of Authentic Implementation, page 50, for more insight.)

 

Chapter 4 The Equilibrium Position and Effective Mathematics Instruction

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Let us teach our children mathematics the honest way by teaching both skills and understanding.

—HUNG-HSI WU,
PROFESSOR EMERITUS OF MATHEMATICS,
UNIVERSITY OF CALIFORNIA, BERKELEY

In a 2012 NRC report, Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century, the expert panel argues that the competencies necessary to be successful in the 21st century require deeper learning by students—a “process through which an individual becomes capable of taking what was learned in one situation and applying it to new situations (i.e., transfer)” (NRC, 2012a, p. 5). The panel points out that transferable knowledge by students is the product of deeper learning and includes:

content knowledge in a domain and knowledge of how, why, and when to apply this knowledge to answer questions and solve problems. . . . [The needed competencies] are structured around fundamental principles of the content area and their relationships rather than disparate, superficial facts or procedures. (NRC, 2012a, p. 6)

 

Chapter 5 How to Help Your Child Learn Mathematics

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While all parents want to find ways to co-educate their children, not all parents know how to do this.

—JOHN HATTIE,
PROFESSOR OF EDUCATION, DIRECTOR OF THE
MELBOURNE EDUCATION RESEARCH INSTITUTE

As a parent, you are your child’s first teacher, and you are in a prime position to have a significant influence on his or her academic development. Through the values you communicate about education, effort, persistence, and responsibility, you influence your child’s mathematics achievement.

With respect to mathematics, Nancy Kober (1991) asserts that parental attitudes toward mathematics are a good predictor of children’s mathematics achievement at all grade levels. As she notes, “Children’s self-concept and confidence in their own mathematics aptitude is more directly related to their parents’ perceptions of their competence than to children’s own achievement record” (Kober, 1991, p. 47).

With this in mind, we believe you should always talk about mathematics in positive ways. Regardless of your mathematics background or experiences, let your child know that learning mathematics well is an important life skill. Communicating a positive “can do” attitude and message about mathematics promotes your child’s success. Your child is a mirror—he or she reflects back to you exactly the mindset you present to him or her. If you complain or say you hated mathematics in school, your child will most likely reflect that mindset back to you and his or her teacher.

 

Epilogue Conclusion and Action Steps for Educators and Parents

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Regardless of how difficult you think it is to improve classroom mathematics teaching on a wide scale, it is more difficult than that.

—JAMES HIEBERT,
PROFESSOR, SCHOOL OF EDUCATION,
UNIVERSITY OF DELAWARE

Although many aspects of mathematics education in society must change for us to achieve the vision of teaching and learning that all students deserve and the United States needs, we believe a critical strategy in achieving this vision is for both educators and parents to support and advocate for an equilibrium experience in classrooms, schools, and districts. This includes supporting more rigorous and common mathematics standards for all students and implementing effective instructional strategies, as outlined in chapter 4.

If we know what effective mathematics instruction is, why is it so hard to implement (and accept) in the classroom? James Hiebert (2013), a highly respected mathematics educator at the University of Delaware, offers a couple of explanations, including the following.

 

Appendix: Additional Resources for Parents

ePub

This appendix provides an annotated list of additional resources parents might find useful as they support their child’s mathematics learning. The resources include print materials to further their understanding of mathematics education, online games, and websites offering additional mathematics sources.

Figure This! (http://figurethis.nctm.org): NCTM developed this resource to help families enjoy mathematics outside of school through a series of fun and engaging, high-quality challenges. Check out the Family Corner for tips on helping your child with mathematics.

Gamequarium (www.gamequarium.org/dir/Gamequarium/Math): This free web resource provides grade-level practice for all mathematics standards and supports student practice at home for additional skill building.

Helping Your Child Learn Mathematics (U.S. Department of Education, 2005) www2.ed.gov/parents/academic/help/math/math.pdf): This free guide discusses what it means to be a problem solver, communicate mathematically, and demonstrate reasoning ability. It also includes many suggestions for activities you can use to help your child develop mathematics skills. The activities are arranged by level of difficulty and grade level and include a tip box as well as an explanation of the mathematics concept behind each activity. It includes a reference list of mathematics-related resources, including websites, books, computer software, and magazines.

 



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