Algebra

Transforming Learning Opportunities in Linguistically Diverse Secondary Classrooms Through Promoting Discussions: Results of an Intervention

This article presents results from a design experiment intended to develop students’ understanding of linear functions and rates of change in a linguistically diverse ninth grade classroom. The intervention focused on fostering classroom discussions. Students’ pre-post assessment gains were higher in the redesigned classrooms than in the pre-intervention classrooms. Additionally, multilingual students who were classified as English Learners (ELs) made larger gains than their non-EL peers, and the majority of student learning gains occurred on conceptually-focused items.

Author/Presenter

William Zahner

Ernesto Daniel Calleros

Lynda Wynn

Kevin Pelaez

Lead Organization(s)
Year
2024
Short Description

This article presents results from a design experiment intended to develop students’ understanding of linear functions and rates of change in a linguistically diverse ninth grade classroom. The intervention focused on fostering classroom discussions.

Transition to Algebra (TTA) Curriculum

The Transition to Algebra (TTA) curriculum seeks to quickly give students the mathematical knowledge, skills, and confidence to succeed in a standard first-year algebra class and to show them that they can explore mathematics and actually enjoy it. TTA is a full-year algebra support curriculum that can run concurrently with first-year algebra.

Author/Presenter

Transition to Algebra Team

Year
2019
Short Description

The Transition to Algebra (TTA) curriculum seeks to quickly give students the mathematical knowledge, skills, and confidence to succeed in a standard first-year algebra class and to show them that they can explore mathematics and actually enjoy it. TTA is a full-year algebra support curriculum that can run concurrently with first-year algebra. It is designed to build students' algebraic habits of mind as they explore algebraic logic puzzles that connect to and extend algebra course topics and learn broadly applicable tools and strategies to help them make sense of what they are learning in algebra. Students discuss and refine their ideas as they work through mental mathematics activities, written puzzles, spoken dialogues, and hands-on explorations that engage them in cultivating mathematical knowledge, intuition, and skills.

Seeds of Algebraic Thinking

Seeds of Algebraic Thinking are sub-conceptual resources coming from life experience that students call upon when responding to mathematical prompts. This site includes resources students could activate when thinking about groups and sets, equality, proportionality and ratio reasoning, and functions.

Author/Presenter

Janet Walkoe

Lead Organization(s)
Year
2024
Short Description

Seeds of Algebraic Thinking are sub-conceptual resources coming from life experience that students call upon when responding to mathematical prompts. This site includes resources students could activate when thinking about groups and sets, equality, proportionality and ratio reasoning, and functions.

Project CARe Student Tasks

This site provides three online activities focused on covariational reasoning as a foundation for middle school students to build more abstract algebraic knowledge. These tasks provide students with opportunities to understand static points, understand dynamic points, and make sense of different amounts of change.

Author/Presenter

Teo Paoletti

Lead Organization(s)
Year
2024
Short Description

This site provides three online activities focused on covariational reasoning as a foundation for middle school students to build more abstract algebraic knowledge. These tasks provide students with opportunities to understand static points, understand dynamic points, and make sense of different amounts of change.

Impact of the Design of an Asynchronous Video-Based Learning Environment on Teacher Noticing and Mathematical Knowledge

In this paper, we share the design and impact of a set of two-hour online mathematics professional development modules adapted from face-to-face video-based materials. The “Video in the Middle” (VIM) modules are aligned with principles of authentic e-learning and can be combined in a variety of ways to form professional development pathways that meet the unique needs of a wide range of professional learning settings and contexts. VIM modules aim to support teacher noticing of student thinking and increase their mathematical knowledge for teaching.

Author/Presenter

Nanette Seago

Angela Knotts

Lead Organization(s)
Year
2021
Short Description

In this paper, we share the design and impact of a set of two-hour online mathematics professional development modules adapted from face-to-face video-based materials.

Resource(s)

Extractive and Inferential Discourses for Equation Solving

We investigate the algebraic discourse of secondary mathematics teachers with respect to the topic of equation solving by analyzing five teachers’ responses to open-ended items on a questionnaire that asks respondents to analyze hypothetical student work related to equation solving and explain related concepts.

Author/Presenter

Cody L. Patterson

Elizabeth Wrightsman

Mehmet Kirmizi

Rebecca McGraw

Lead Organization(s)
Year
2021
Short Description

We investigate the algebraic discourse of secondary mathematics teachers with respect to the topic of equation solving by analyzing five teachers’ responses to open-ended items on a questionnaire that asks respondents to analyze hypothetical student work related to equation solving and explain related concepts.

ReLaTe-SA: An Effort to Understand Teachers’ Reasoning Language in Algebra

The purpose of the Reasoning Language for Teaching Secondary Algebra (ReLaTe-SA) project is to understand teachers' use of reasoning language for teaching concepts and procedures in middle and high school algebra. Previous studies on algebra and algebraic reasoning have investigated other aspects, including students’ conceptions and discourse. The link between students' discourse and conceptual understanding has been explored (Chesnais & Constantin, 2020; Reinhardtsen, 2020). However, less is known about middle and high school teachers' language in the algebra classroom.

Author/Presenter

Mehmet Kirmizi

Lead Organization(s)
Year
2022
Short Description

The ReLaTe-SA project investigates the research question: what language do teachers use to describe and explain routines in algebra classes? The goal of this article is to inform readers about some ways we have learned to describe the discourse that teachers use when solving linear equations.

Perspectives on Algebra I Tutoring Experiences With Students With Learning Disabilities

The researchers conducted a qualitative analysis of the perceptions of school personnel and pre-service teachers about an Algebra I tutoring program for students with learning disabilities. The researchers surveyed and interviewed the participants about the effectiveness of the program for the mathematics learning of the students with LD at the school and as a learning experience for the pre-service teachers. The school personnel indicated there was a mutually beneficial relationship between the tutors and the school.

Author/Presenter

Casey Hord

Anna F. DeJarnette

Lead Organization(s)
Year
2020
Short Description

The researchers conducted a qualitative analysis of the perceptions of school personnel and pre-service teachers about an Algebra I tutoring program for students with learning disabilities. The researchers surveyed and interviewed the participants about the effectiveness of the program for the mathematics learning of the students with LD at the school and as a learning experience for the pre-service teachers.

The Centrality of Student-Generated Representation in Investigating Generalizations about the Operations

This article addresses the nature of student-generated representations that support students’ early algebraic reasoning in the realm of generalized arithmetic. We analyzed representations created by students for the following qualities: representations that distinguish the behavior of one operation from another, that support an explanation of a specific case of a generalization, and that support justification of a generalization.

Author/Presenter

Deborah Schifter

Susan Jo Russell

Year
2022
Short Description

This article addresses the nature of student-generated representations that support students’ early algebraic reasoning in the realm of generalized arithmetic.

Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes.

Author/Presenter

Kristen N. Bieda,
AnnaMarie Conner,
Karl W. Kosko,
Megan Staples

AnnaMarie Conner

Karl W. Kosko

Megan Staples

Lead Organization(s)
Year
2020
Short Description

This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.