### Balancing the Equation: A Guide to School Mathematics for Educators and Parents, Matthew R. Larson & Timothy D. Kanold

## Chapter 4: The Equilibrium Position and Effective Mathematics Instruction

*“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

The primary audience of Unit 2 is parents, although it is certainly critical information for educators as well. The authors seek to explain to parents what is meant by mathematical literacy and describe the components of balanced, effective mathematics instruction. As educators, we can use the information in this section to help explain to parents the different look and feel of current math instruction.

### What is Mathematical Literacy?

The authors propose a definition for mathematical literacy that includes “student development of skills and procedures, conceptual understanding, problem solving, and a disposition to expend effort and persevere when learning mathematics and solving problems.” This closely parallels the definition of *mathematical proficiency* outlined by the National Research Council (NRC) in their 2001 publication Adding It Up which describes five “interwoven and interdependent” strands.

### Finding a Balance

Before laying out what effective mathematics instruction looks like, the authors provide a glimpse of the current state of mathematics instruction in far too many classrooms in the United States: low-level tasks, limited communication among students, and an emphasis on memorizing procedures. This traditional style of teaching, however, is not providing our students with the skills they need to compete in the 21st century.

A mathematics program that is balanced, or in equilibrium, should include the following elements:

- Conceptual understanding
*and*procedural skills - Communication
- Perseverance
- Feedback
- Technology

### Students Develop Conceptual Understanding and Procedural Skills

The authors are very clear in this section that in a balanced program students *are* expected to learn procedural skills. The example they give contrasts the traditional method for teaching the standard algorithm for multiplication (as a procedure) versus teaching the same skill using various models, such as base-ten blocks or arrays, which still lead to the standard algorithm, but also develop a conceptual understanding of the process.

*“The goal (or standard) remains for students to learn the mathematics you learned when you were in school. The difference is that teachers use conceptual instructional strategies, such as the open array model, to build understanding of the traditional algorithm.”*

### Students Communicate With Peers About Mathematics

Once again we visit the traditional math classroom–if the teacher is not explaining the day’s lesson, then it’s quiet and students are likely working individually. That is not an environment that encourages deep thinking and problem solving. We learn best when we communicate.

*“Students who communicate with their classmates and teacher about their thinking, solution pathways, and insights into how they solved a problem, or who analyze another student’s solution, develop a deeper understanding of mathematics.”*

Educators will find this chapter extremely helpful for explaining the changes in math standards and instruction to parents. If we expect parents to be our allies, then we must open the lines of communication and help them understand the reasons behind and the value of the methods we are using. The authors give us the words to use to accomplish that!

Be sure to visit The Recovering Traditionalist for a discussion of the rest of this chapter.

### Use these links to view the entire book study:

- Table of Contents, About the Authors, and Introduction
- Evil Math Wizard — Chapter 1: Why Mathematics Education Needs to Improve
- The Math Spot — Chapter 2: A Brief History of Mathematics Education
- The Research Based Classroom — Chapter 3: The Common Core Mathematics Debate
- Math Coach’s Corner — First half Chapter 4: The Equilibrium Position and Effective Mathematics Instruction
- LIVE WEBINAR with Matthew Larson (register here)
- The Recovering Traditionalist — Second half Chapter 4: The Equilibrium Position and Effective Mathematics Instruction
- Guided Math Adventures — Chapter 5: How to Help Your Child Learn Mathematics
- Kids Math Teacher — Epilogue, Appendix, and Recap

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