Quantitative Measures of Mathematical Knowledge : Researching Instruments and Perspectives book cover
1st Edition

Quantitative Measures of Mathematical Knowledge
Researching Instruments and Perspectives

ISBN 9780367670757
Published December 18, 2020 by Routledge
266 Pages

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Book Description

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.

Table of Contents

  1. Validation in Mathematics Education: An Introduction to Quantitative Measures of Mathematical Knowledge: Researching Instruments and Perspectives – Erin E. Krupa, Jonathan Bostic, and Jeff Shih

  2. The Form of Mathematics in Assessment Items: How Items Convey and Measure Multiplicative Reasoning Differently – Karl W. Kosko

  3. Substantiating claims about students’ algebraic reasoning: Initial evidence based on response processes and internal structure – Lindsey Perry, Leanne R. Ketterlin-Geller, and Cassandra Hatfield

  4. A Validation Approach to Middle-grades Learning Trajectories within a Digital Learning System applied to the "Measurement of Characteristics of Circles" – Jere Confrey and Emily Toutkoushian

  5. Assessing college-ready data-based reasoning – Amy Arneson, Diah Wihardini, and Mark Wilson

  6. A Validity Argument for an Undergraduate Mathematics Concept Inventory – Kathleen Melhuish and Michael D. Hicks

  7. Developing a construct map for teacher attentiveness – Michele Carney, Tatia Totorica, Laurie Cavey, and Patrick R. Lowenthal

  8. A validation process for complex knowledge: The Standards for Mathematical Practice Konwledge-Gabriel Matney, Jonathan D. Bostic, and Mathew Lavery

  9. Reflecting on the past and looking ahead at opportunities in quantitative measurement of K-12 students’ content knowledge – Jonathan Bostic, Erin Krupa, Michele Carney, and Jeff Shih

  10. Future Directions in the Measurement of Mathematics Teachers’ Competencies – Heather Howell, Elizabeth Stone, and Michael Kane

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Jonathan Bostic is an associate professor of mathematics education at Bowling Green State University, USA.

Erin Krupa is an assistant professor of mathematics education at North Carolina State University, USA.

Jeffrey Shih is an associate professor of mathematics education at the University of Nevada, Las Vegas, USA.


"The authors of these ten chapters, all experts in mathematics education research, provide a broad yet unified message: increased validity and credibility are achievable via more “robust and rigorous measures in mathematics education.” Each chapter includes extensive references. This book’s audience includes mathematics education researchers, assessment specialists, and interested mathematics education students."
-J. Johnson, emeritus, Western Washington University, CHOICE