Math Know-How

Answers to Your Most Persistent Teaching Issues, Grades 3-5

Thomasenia Lott Adams, Joanne LaFramenta

• Publisher: Corwin
• Year: 2013
• Print ISBN: 9781452282633
• eBook ISBN: 9781452282626
• Edition: 1
• Topic: Education
• Subtopic: Education General

From two math coaches who really know how
Have you ever wished there were a single resource to help you tackle your most persistent teaching issues once and for all? To engage students in more meaningful ways? To provide the tools you need to increase students' understanding of key mathematical concepts? All at the same time! Math coaches Thomasenia Lott Adams and Joanne LaFramenta have just written it.

Written especially for grade 3-5 teachers, Math Know-How is organized around real questions Adams and LaFramenta have fielded from real teachers—questions that have remained remarkably consistent across the hundreds of educators they have advised . Now these two coaches share their hard-won wisdom with you, including how to

• Employ strategies to connect instruction to the  CCSS, especially the Mathematical Practices
• Negotiate the wide range of lesson planning and instructional choices
• Catch up when you fall behind your pacing guide
• Explore the myriad possibilities for exploiting technology in the classroom
• Engage students with diverse learning needs

Read this book cover to cover and start asking and answering questions of your own about your teaching practice.

"As we shift from individual standards to the Common Core State Standards for Mathematics, this book will be a valuable resource in establishing strategies and instructional techniques to better equip teachers for the overwhelming transition."
—Nena Mathews, Math/Science Teacher, Florence, SC

1	Common Core State Standards for Mathematics Mathematics Content and Mathematical Practices

Dear professor:

I’ve been teaching for fifteen years, and I’m pretty busy. The days at school with the children consume all my attention, and then after school I have to plan for the next day. I’m pretty tired by the time I get home (and I also have school-age children), but I’m a professional and I try to keep abreast of the new happenings in education. Now all the talk is about the Common Core standards. I’m sure there is information about the Common Core on the Internet, but they haven’t given us much information at school, just saying that we need to get ready and we need to get students ready, because it is coming and it will be different. Someone told me that almost all the states will be using Common Core and that our teachers won’t be ready to teach it. Some gloomily predict that vast numbers of our students will fail the new assessments. All this talk is really frustrating, and frankly, frightening. What is actually going on? Why are we changing standards now? I am not the oldest member of the staff here, but I know that this is not the first time that the administration has tried to “reform” our curriculum. It seems as if just about the time we finally learn how to teach a mathematics curriculum, somebody changes it. Are these changes different? What will I have to do now as a teacher? Can we expect this reform to last? I wish someone would help me understand what I should know and do about the Common Core.

Sincerely,
A fourth-grade teacher

Quantitative data and technology were the driving forces behind the global economy in which we are now interacting, which makes mathematics a critical element in both national and international undertakings. Hence mathematics education is a field vibrant with new and paradigm-changing adventures required to support these driving forces. The most recent adventure in the field of mathematics education involves the unveiling of the Common Core State Standards (CCSS) for Grades K–12. The CCSS includes content for language arts and mathematics. We refer to the Common Core State Standards for mathematics as CCSSM. The mission of the CCSS is to

. . . provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy (National Governors Association Center for Best Practices (NGA) & Council of Chief State School Officers (CCSSO), 2010, p. 93).

In this chapter, we address many important and relevant questions: Why do we need the CCSSM? What supported the development of the CCSSM? And how does the CCSSM differ from already existing standards related to the teaching and learning of mathematics? Knowing the answers to these questions equips you to address inquiries from peers, school administrators, parents, and even students. We also recommend that you begin to collect your own additional questions and any questions posed from others so that as you answer these questions, you become more informed about the CCSSM. Table 1.1 is a CCSSM Information Log provided to record questions in order to facilitate building your knowledge of the CCSSM.

CREATING THE COMMON CORE STATE STANDARDS FOR MATHEMATICS

The CCSSM developed quickly, but the antecedents have been in existence for many years. Likewise, concern about the educational issues necessitating adoption of these standards has been the focus of policy makers and educators for several decades. Working together, political and educational leaders joined to develop the CCSSM.

Table 1.1 Sample CCSSM Information Log

Impetus for the CCSSM

There are several reasons why the CCSSM became a reality. One impetus for the CCSSM is supported by examination of historical mathematics achievement data of students in the United States compared with students in other countries around the world. In 2004, the United States Department of Education (USDOE) indicated that

international and domestic comparisons show that American students have not been succeeding in the mathematical part of their education at anything like a level expected of an international leader. Particularly disturbing is the consistency of findings that American students have often achieved in mathematics at a mediocre level by comparison to peers worldwide. (p. 12)

Years of data show that U.S. students struggle behind other nations to achieve in mathematics and this research provided the platform for educators and other leaders to suggest that as a nation, we need to address our standards for what mathematics we expect students to know and execute. The need to have our students do well in mathematics so that they can succeed in a global economy drives the selection of what mathematics we teach and how we teach it.

Another impetus for the CCSSM is the mathematics achievement gap, which is “the difference between the average scores of two student subgroups on the standardized assessment” (National Center for Education Statistics (NCES), 2011, p. 12). In the range of mathematics assessments from 1992 to 2009, the National Assessment for Educational Progress (NAEP) reported that White students in Grades 4, 8, and 12 scored higher in mathematics than Black and Hispanic students in the same grades (NCES, 2011, p. 12).

The achievement gap between Black and White 4th-grade students in 2009 (-26 points) was not measurably different from the gap in 2007, but it was smaller than the gap in 1990 (-32 points). The 21-point achievement gap between White and Hispanic 4th-grade students in 2009 was not measurably different from the gap in 2007 or the gap in 1990. (NCES, 2011, p.12)

As we make progress in the field of mathematics education, making certain that we are giving attention to every subgroup of learners is important to the goal of overall academic success for our students. The CCSSM provides clarity on the mathematics that every student needs to learn in order to be a productive and active citizen in an increasingly complex society.

We do know that improvement in students’ mathematics achievement is possible. As Table 1.2 indicates,

In 2011, the average NAEP mathematics scores for 4th-grade and 8th-grade students were higher than their average scores in all previous assessment years, and from 1990 to 2011, the average 4th-grade NAEP mathematics score increased by 28 points, from 213 to 241. During that same time period, the average 8th-grade score increased by 21 points, from 263 to 284. (NCES, 2011, p. 1)

The changes in the positive direction provide support for engaging in more efforts to improve students’ mathematics achievement. These efforts include work by the National Council of Teachers of Mathematics (NCTM) and efforts by teachers of mathematics to transform research to practice.

Twelfth-graders were most recently assessed in 2009; in that year, the average 12th-grade mathematics score was 3 points higher than in 2005, the first year that the revised assessment was administered (NCES, 2011, para. 4).

Having the ability to capture at specific grade levels the trajectory of growth in students’ mathematics achievement and targeting students’ mathematical needs is an advantage for the CCSSM’s mission of preparing students for college and career readiness.

Table 1.2 Trend in NAEP Mathematics Average Scores

Source: National Center for Education Statistics, 2011, p.1.

A third impetus for the CCSSM is the goal of being able to deliver mathematics instruction that is deliberate and consistent throughout the United States. A review of previous mathematics standards and mathematics instruction from state to state revealed a lack of consistency between individual state standards (Hirsch & Reys, 2009). However “a focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula” (USDOE, 2008, p. 16). The lack of consistency in mathematics content and instruction from state to state directly influences mathematics teaching and learning in response to the active mobility of students across the United States. “Students who move often between schools may experience a range of problems, such as: lower achievement levels due to discontinuity of curriculum between schools” (Education Week, 2004). The problem of students learning different mathematics based on where they happen to reside at any particular time can be tackled by presenting mathematics standards that are acknowledged more broadly across the United States. Finally, there is more of a need to further strengthen the mathematics curricula as students are expected to become more proficient in mathematics. We recognize that “A curriculum is more than a collection of activities: It must be coherent, focused on important mathematics, and well articulated across the grades” (NCTM, 2009a, para. 3). When we consider avenues of improvement, we can look to the CCSSM to determine the quality of mathematics content and learning experiences that are essential for students as they progress through the years of their mathematics learning. The changing needs of the national and international careers provide more incentive for the CCSSM.

The U.S. education system must be improved, top to bottom so that our most precious resource—our children—can compete in the increasingly global world economy. Statistically, our K–12 students are falling farther behind students in Korea, China and elsewhere in the physical sciences. We can and must do better (Case, Doerr, Otellini, & Sandberg, 2011, para. 5).

The CCSSM provides clarity on how we can do better teaching the mathematics necessary for our students to engage in careers and post-secondary education that require mathematics as a foundation.

Ultimately, when we consider that our aim for schools is to prepare students to be active, informed, literate, and productive citizens who contribute to the good of themselves and society at large, it is critical that we consider any and every opportunity to propel our students forward. This is the opportunity offered by the CCSSM. The challenge, of course, is to make the best use of this opportunity to empower students as they pursue college and careers to be mathematically proficient.

Developers of the Common Core State Standards for Mathematics

The Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practices (NGA) sponsored the development of the CCSSM. However, individuals who invested in the writing of the CCSSM included William McCallum, Phil Daro, and Jason Zimba. Numerous stakeholders also contributed to the development of the CCSSM. These stakeholders included educators at various levels (e.g., schools, colleges, and universities), content experts, researchers, national professional organizations (e.g., ACT, a college readiness assessment test, the Achieve organization, which provides standard-setting and benchmarking services, and the College Board), classroom teachers, parents, community organizations, and industry leaders. The fact that the CCSSM had broad participation for its development is an indicator of the range of support and diversity of ideas that are reflected in the CCSSM. In addition, this broad contribution to the development of the CCSSM provided the opportunity for the content of the CCSSM to represent both academic and workforce positions.

Adoption of the Common Core State Standards for Mathematics

As of 2013, 45 states, the District of Colu...

Table of contents

• Front Cover
• Halftitle
• Title
• Copyright
• Contents
• Preface
• Acknowledgments
• About the Authors
• Chapter 1: Common Core State Standards for Mathematics: Mathematics Content and Mathematical Practices
• Chapter 2: Making Mathematics Teaching Decisions
• Chapter 3: Using the Pacing Guide Effectively
• Chapter 4: Approach to Planning Mathematics Instruction
• Chapter 5: Facilitating Differentiated Instruction
• Chapter 6: Teaching and Learning Mathematics With Manipulatives
• Chapter 7: Appropriate Use of Technology
• Chapter 8: Reflecting on the Teaching Practice of Mathematics
• Chapter 9: Understanding the Learner
• Chapter 10: Mathematics Assessment 101
• Chapter 11: Conclusion
• Appendix: Resources for Teachers
• References
• Index
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