Algebra

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

Lead Organization(s)
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

Lead Organization(s)
Year
2021
Short Description

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).

The Role of Balance Scales in Supporting Productive Thinking about Equations Among Diverse Learners

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks.

Author/Presenter

Ana Stephens

Yewon Sung

Susanne Strachota

Ranza Veltri Torres

Karisma Morton

Angela Murphy Gardiner

Maria Blanton

Eric Knuth

Rena Stroud

Year
2020
Short Description

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign.

Does Early Algebra Matter? The Effectiveness of an Early Algebra Intervention in Grades 3 to 5

A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population. Forty-six schools in three school districts participated. Students in treatment schools were taught the intervention by classroom teachers during regular mathematics instruction. Students in control schools received only regular mathematics instruction.

Author/Presenter

Maria Blanton

Rena Stroud

Ana Stephens

Angela Murphy Gardiner

Despina A. Stylianou

Eric Knuth

Isil Isler-Baykal

Susanne Strachota

Lead Organization(s)
Year
2019
Short Description

A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population.

Does Early Algebra Matter? The Effectiveness of an Early Algebra Intervention in Grades 3 to 5

A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population. Forty-six schools in three school districts participated. Students in treatment schools were taught the intervention by classroom teachers during regular mathematics instruction. Students in control schools received only regular mathematics instruction.

Author/Presenter

Maria Blanton

Rena Stroud

Ana Stephens

Angela Murphy Gardiner

Despina A. Stylianou

Eric Knuth

Isil Isler-Baykal

Susanne Strachota

Lead Organization(s)
Year
2019
Short Description

A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population.

“Approximate” Multiplicative Relationships between Quantitative Unknowns

Three 18-session design experiments were conducted, each with 6–9 7th and 8th grade students, to investigate relationships between students’ rational number knowledge and algebraic reasoning. Students were to represent in drawings and equations two multiplicatively related unknown heights (e.g., one was 5 times another). Twelve of the 22 participating students operated with the second multiplicative concept, which meant they viewed known quantities as units of units, or two-levels-of-units structures, but not as three-levels-of-units structures.

Author/Presenter

Amy J. Hackenberg

Robin Jones

Ayfer Eker

Mark Creager

Lead Organization(s)
Year
2017
Short Description

Three 18-session design experiments were conducted, each with 6–9 7th and 8th grade students, to investigate relationships between students’ rational number knowledge and algebraic reasoning. Implications for teaching are explored in this article.

Tiering Instruction for Middle School Students

Differentiating instruction (DI) is a pedagogical approach to managing classroom diversity in which teachers proactively adapt curricula, teaching methods, and products of learning to address individual students' needs in an effort to maximize learning for all (Tomlinson, 2005). DI is rooted in formative assessment, positions teachers and students together as learners, and involves providing choices and different pathways for students. Although teachers can differentiate for many characteristics of students, we differentiate for students' diverse ways of thinking.

Author/Presenter

Amy J. Hackenberg

Robin Jones

Rebecca Borowski

Lead Organization(s)
Year
2020
Short Description

In this article, we describe an example of differentiating instruction (DI) involving middle school students from a five-year project funded by the National Science Foundation.

Backward Transfer Effects when Learning about Quadratic Functions

Presentation slides from the 42nd Conference of the International Group for the Psychology of Mathematics Education.

Hohensee, C., Willoughby, L., & Gartland, S. (2018, July). Backward transfer effects when learning about quadratic functions. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, p. 65). Umeå, Sweden: PME.

Author/Presenter

Charles Hohensee

Laura Willoughby

Sara Gartland

Lead Organization(s)
Year
2018
Short Description

Presentation slides from the 42nd Conference of the International Group for the Psychology of Mathematics Education.

Backward Transfer Effects on Action and Process Views of Functions

Presentation slides from the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

Hohensee, C., Gartland, S., & Willoughby, L. (2019, November). Backward transfer effects on action and process views of functions. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. St Louis, MO: University of Missouri.

Author/Presenter

Charles Hohensee

Sara Gartland

Laura Willoughby

Lead Organization(s)
Year
2019
Short Description

Presentation slides from the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

LEAP Early Algebra Curriculum

The LEAP program is the first early algebra curriculum for students in grades 3-5. The program includes 18-20 one-hour lessons at each grade level and teacher support and assessment. Professional development  is also available. 

Author/Presenter

The LEAP Team

Lead Organization(s)
Year
2020
Short Description

The LEAP program is the first early algebra curriculum for students in grades 3-5. The program includes 18-20 one-hour lessons at each grade level and teacher support and assessment. Professional development  is also available.