Mathematics

Validation: A Burgeoning Methodology for Mathematics Education Scholarship

Validity-related issues are a growing topic within the mathematics education community. Until recently, validation has been treated as something to gather when convenient or is rarely reported in ways that conform to current standards for assessment development. This theoretically-focused proceeding adds to a burgeoning theoretical argument that validation should be considered a methodology within mathematics education scholarship. We connect to design-science research, which is a well-established framework within mathematics education.

Author/Presenter: 
Jonathan Bostic
Gabriel Matney
Toni Sondergeld
Gregory Stone
Lead Organization(s): 
Year: 
2018
Short Description: 
The goal for this proceeding is to foster the conversation about validation using examples and to communicate information about validation in ways that are broadly accessible.

Content validity evidence for new problem-solving measures (PSM3, PSM4, and PSM5)

Bostic, J., Matney, G., Sondergeld, T., & Stone, G. (2018, November). Content validity evidence for new problem-solving measures (PSM3, PSM4, and PSM5). In T. Hodges, G. Roy, & A. Tyminski (Eds.), Proceedings for the 40h Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1641). Greenville, SC.

Author/Presenter: 
Jonathan Bostic
Gabriel Matney
Toni Sondergeld
Gregory Stone
Lead Organization(s): 
Year: 
2018
Short Description: 
The study’s purpose is to describe content validity evidence related to new problem-solving measures currently under development.

Teaching of the associative property: A natural classroom investigation

In this study we investigate the teaching of the associative property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urban school district. Findings indicate that the associative property was often conflated with the commutative property during teaching. The role of the associative property in many computational tasks remained fully implicit, even after the property had been formally introduced.

Author/Presenter: 
Eli Barnett
Meixia Ding
Lead Organization(s): 
Year: 
2018
Short Description: 
In this study we investigate the teaching of the associative property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urban school district.

Transitioning from textbook to classroom instruction in mathematics: The case of an expert Chinese teacher

This study reports how an expert Chinese teacher implements mathematics textbook lessons in enacted instruction. Our video analysis indicates that both textbook and enacted teaching included only one worked example; however, the teacher engaged students in unpacking the example in great depth. Both the textbook and the enacted teaching showed “concreteness fading” in students’ use of representations. However, the Chinese teacher incorporated students’ self-generated representations and facilitated students’ active modeling of quantitative relationships.
Author/Presenter: 
Chen Wei
Meixia Ding
Lead Organization(s): 
Year: 
2018
Short Description: 
This study reports how an expert Chinese teacher implements mathematics textbook lessons in enacted instruction.
Resource(s): 

Modeling with tape diagrams

Two teachers use a powerful, challenging tool in their Chinese classrooms to build, ensure, and solidify students’ understanding of quantitative relationships.
 
Ding, M. (2018). Modeling with tape diagrams. Teaching Children Mathematics, 25, 158-165. doi: 10.5951/teacchilmath.25.3.0158
Author/Presenter: 
Meixia Ding
Lead Organization(s): 
Year: 
2018
Short Description: 
This article describes a tool to build, ensure, and solidify students’ understanding of quantitative relationships.
Resource(s): 

Transferring specialized content knowledge to elementary classrooms: Preservice teachers’ learning to teach the associative property

This study explores how preservice teachers (PSTs) transfer the intended specialized content knowledge (SCK) to elementary classrooms. Focusing on the case of the associative property of multiplication, we compared three PSTs’SCK during enacted lessons in fourth grade classrooms with their own learning in professional development (PD) settings. Findings revealed the PSTs’ successes and challenges in unpacking an example task, especially in areas of making connections between concrete and abstract representations and asking deep questions that target quantitative interactions.

Author/Presenter: 
Meixia Ding
Kayla Heffernan
Lead Organization(s): 
Year: 
2018
Short Description: 
This study explores how preservice teachers (PSTs) transfer the intended specialized content knowledge (SCK) to elementary classrooms.

Most and Least: Differences in Integer Comparisons Based on Temperature Comparison Language

The language involved in de-contextualized integer comparisons poses challenges, as students may interpret “most” based on absolute values rather than on order. Using the context of temperature, we explored how students’ integer value comparisons differed based on question phrasing (which temperature is hottest, most hot, least hot, coldest, most cold, least cold) and on numbers presented (positive, negative, mixed). Participants included 88 second graders and 70 fourth graders from a rural school district in the Midwestern USA, and each student solved 36 integer comparisons.

Author/Presenter: 
Laura Bofferding
Sherri Farmer
Lead Organization(s): 
Year: 
2018
Short Description: 
This article explores how students’ integer value comparisons differed based on question phrasing (which temperature is hottest, most hot, least hot, coldest, most cold, least cold) and on numbers presented (positive, negative, mixed) within the context of temperature.

Variations in coaching knowledge and practice that explain elementary and middle school mathematics teacher change

This study investigated relationships between changes in certain types of coaching knowledge and practices among mathematics classroom coaches and how these explain changes in the attitudes, knowledge, and practice of the teachers they coach. Participants in this study were 51 school-based mathematics classroom coaches in the USA and 180 of the teachers whom they coached between 2009 and 2014. The participating coaches were recruited from schools that hired their own coaches independently from this research project.

Author/Presenter: 
David A. Yopp
Elizabeth A. Burroughs
John T. Sutton
Mark C. Greenwood
Lead Organization(s): 
Year: 
2017
Short Description: 
This study investigated relationships between changes in certain types of coaching knowledge and practices among mathematics classroom coaches and how these explain changes in the attitudes, knowledge, and practice of the teachers they coach.

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