# Mathematics Education Book

## Uncovering Student Thinking in Mathematics- 25 K-12 Formative Assessment Probes

The 10 assessment probes in the "Number and Operations" section of this book can be used as a CTS application to examine student thinking after conducting a CTS. Additionally, the teacher background notes provide valuable information on instructional implications (CTS Section II) and research on learning (CTS Section III). For example, the "Comparing FRactions" probe can be used with the "Fractions" CTS to examine student work related to part-whole relationships when comparing fractions.

- Addition and Subtraction
- Addition and Subtraction of Whole Numbers
- Assessment Task
- Comparing and Ordering Numbers
- Computation and Operations
- Counting
- Decimals
- Equivalence
- Estimation
- Exponents
- Facts
- Fractions
- Fractions, Decimals, and Percents
- Large and Small Numbers
- Mathematics Education Book
- Multiplication and Division
- Multiplication and Division of Whole Numbers
- Numbers and Operations
- Percent
- Place Value
- Properties of Operations
- Ratio and Proportion
- Rational Numbers

## The Young Mathematician at Work: Multiplication and Division (2nd in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

## The Young Mathematician at Work: Fractions, Decimals and Perent (3rd in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

## The Young Mathematician at Work: Addition and Subtraction (1st in a series of 3 volumes)

Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents.

## Teaching for K-12 Mathematical Understanding Using the Conceptual Change Model

Chapter 3 of this resource can be used to supplement Section IV: Research on Student Learning for topics in the Numbers and Operations Category. The Chapter includes information about 1) Student difficulties, confusion, and misconceptions and 2) Factors contributing to students' difficulties, confusion, and misconceptions.

## Statistical Literacy at School: Growth and Goals

This book illustrates the development of studentsí understanding of statistical concepts. The author gives many examples that highlight how students think about important statistical concepts and supports findings based on research. Student thinking is explained in relation to a variety of tasks based on sampling, graphical representations, averages and chance. This resource could be used to supplement the readings from section I, II, III and IV.

## Research Ideas for the Classroom: High School Mathematics: pages 140-152

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Sections can be used as supplements for Section IV.

## Reflections on Statistics: Learning, Teaching and Assessment in Grades K-12

A collection of essays which offer insights into the emphasis on statistics in the K-12 mathematics curriculum. Through the investigation of several projects, the authors explore the enhancement and assessment of student learning in the areas of collection, presentation and interpretation of data. The essays cover content, teaching, learning and assessment. The statistics content, the extent of coverage recommended for various grade levels as well as student understandings are highlighted. This resource could be used in conjunction with the readings from section I and II.

## How Students Learn: Mathematics in the Classroom

How Students learn uses the principles and findings from How People Learn within the context of the mathematics classroom. An introduction to the principles as they apply to mathematics is included in chapter 2, whole numbers at the elementary level is the focus of chapter 3, rational numbers at the middle level is the focus of chapter 4 and chapter 5 focuses on functions at the high school level. This would be an additional reference to sections II, III and IV.

## How Students (Mis-)Understand Science and Mathematics

The authors propose 'intuitive rules' that students use to reason about mathematics and science concepts. The book provides many examples how these rules can be used to interpret the misconceptions many students have about mathematical concepts. This resource book can be used to supplement the readings from section IV.