# Facts

## 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

## 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.

## 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.

## Elementary and Middle School Mathematics: Teaching Developmentally (Sixth Edition)

This resource helps readers make sense of mathematics interweaving content ideas with instructional implications. Sixteen chapters reflect the view that mathematics can be taught through a problem-solving approach that motivates children and builds their confidence as they learn. Chapter 9 (pages 120-137) supplements Section II by providing instructional implications for number development in the early grades.

## Looking at Learning Again Part 1

A short video clip (4 minutes) reflecting estimation and computation skills in a fourth grade classroom setting. Students are shown solving math problems, using multiplication of whole numbers, as a group. Estimation strategies, problem solving and communication skills are stressed. This short video clip could be used to supplement section II.