# Mathematics

## Theory to Practice: Prospective Mathematics Teachers’ Recontextualizing Discourses Surrounding Collective Argumentation

Teacher education programs have a critical role in supporting prospective teachers’ connections between theory and practice. In this study, we examined three prospective secondary mathematics teachers’ discourses regarding collective argumentation during and after a unit of instruction addressing collective argumentation and ways they recontextualized their on-campus coursework (theory) into their student teaching (practice) as demonstrated by their support for students’ mathematical arguments during student teaching.
Author/Presenter:
Carlos Nicolas Gomez Marchant
Hyejin Park
Yuling Zhuang
Jonathan K. Foster
AnnaMarie Conner
Year:
2021
Short Description:

Teacher education programs have a critical role in supporting prospective teachers’ connections between theory and practice. In this study, authors examined three prospective secondary mathematics teachers’ discourses regarding collective argumentation during and after a unit of instruction addressing collective argumentation and ways they recontextualized their on-campus coursework (theory) into their student teaching (practice) as demonstrated by their support for students’ mathematical arguments during student teaching.

## Backward Transfer Influences from Quadratic Functions Instruction on Students’ Prior Ways of Covariational Reasoning about Linear Functions

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. We conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of our study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions. The subjects were 57 students from two authentic algebra classrooms at two local high schools.

Author/Presenter:
Charles Hohensee
Sara Gartland
Laura Willoughby
Matthew Melville
Year:
2021
Short Description:

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. Authors conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of the study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions.

## Cognitive Instructional Principles in Elementary Mathematics Classrooms: A Case of Teaching Inverse Relations

Instructional principles gleaned from cognitive science play a critical role in improving classroom teaching. This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers’ early algebra lessons in the U.S. Based on the analysis of 32 videotaped lessons of inverse relations, we found that most teachers spent sufficient class time on worked examples; however, some lessons included repetitive examples that also included irrelevant practice problems.

Author/Presenter:
Meixia Ding
Ryan Hassler
Xiaobao Li
Year:
2020
Short Description:

This study examines how three cognitive instructional principles including worked examples, representations, and deep questions are used in eight experienced elementary teachers’ early algebra lessons in the U.S.

## Understanding of the Properties of Operations: A Cross-Cultural Analysis

This study examines how sampled Chinese and U.S. third and fourth grade students (NChina=167,NUS=97) understand the commutative, associative, and distributive properties. These students took both pre- and post-tests conducted at the beginning and end of a school year. Comparisons between students’ pre- and post-tests within and across countries indicate different learning patterns. Overall, Chinese students demonstrate a much better understanding than their U.S. counterparts.
Author/Presenter:
Meixia Ding
Xiaobao Li
Ryan Hassler
Eli Barnett
Year:
2021
Short Description:

This study examines how sampled Chinese and U.S. third and fourth grade students (NChina=167,NUS=97) understand the commutative, associative, and distributive properties.

## Teaching Early Algebra through Example-based Problem Solving: Insights from Chinese and U.S. Elementary Classrooms

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS).

Author/Presenter:
Meixia Ding