The aim of this book is to explore measures of mathematics knowledge, spanning K-16 grade levels. By focusing solely on mathematics content, such as knowledge of mathematical practices, knowledge of ratio and proportions, and knowledge of abstract algebra, this volume offers detailed discussions of specific instruments and tools meant for measuring student learning. Written for assessment scholars and students both in mathematics education and across educational contexts, this book presents innovative research and perspectives on quantitative measures, including their associated purpose statements and validity arguments.

chapter 1|13 pages

Validation in Mathematics Education

An Introduction to Quantitative Measures of Mathematical Knowledge: Researching Instruments and Perspectives
ByErin E. Krupa, Jonathan D. Bostic, Jeffrey C. Shih

chapter 2|27 pages

The Form of Mathematics in Assessment Items

How Items Convey and Measure Multiplicative Reasoning Differently
ByKarl W. Kosko

chapter 3|26 pages

Substantiating Claims About Students’ Algebraic Reasoning

Initial Evidence Based on Response Processes and Internal Structure
ByLindsey Perry, Leanne R. Ketterlin-Geller, Cassandra Hatfield

chapter 5|28 pages

Assessing College-Ready Data-Based Reasoning

ByAmy Arneson, Diah Wihardini, Mark Wilson

chapter 6|31 pages

A Validity Argument for an Undergraduate Mathematics Concept Inventory

ByKathleen Melhuish, Michael D. Hicks

chapter 7|27 pages

Developing a Construct Map for Teacher Attentiveness

ByMichele B. Carney, Tatia Totorica, Laurie O. Cavey, Patrick R. Lowenthal

chapter 8|26 pages

A Validation Process for Complex Knowledge

The Standards for Mathematical Practice Knowledge Assessment
ByGabriel Matney, Jonathan D. Bostic, Matthew Lavery

chapter 9|25 pages

Reflecting on the Past and Looking Ahead at Opportunities in Quantitative Measurement of K-12 Students’ Content Knowledge

ByJonathan D. Bostic, Erin E. Krupa, Michele B. Carney, Jeffrey C. Shih

chapter 10|23 pages

Future Directions in the Measurement of Mathematics Teachers’ Competencies

ByHeather Howell, Elizabeth Stone, Michael Kane