Algebra

Teaching Practices for Differentiating Mathematics Instruction for Middle School Students

Three iterative, 18-episode design experiments were conducted after school with groups of 6–9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students’ mathematical thinking while developing a cohesive classroom community.

Author/Presenter

Amy J. Hackenberg

Mark Creager

Ayfer Eker

Lead Organization(s)
Year
2020
Short Description

This study is a case of using second-order models of students’ mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students’ thinking are at the heart of differentiating mathematics instruction.

Eliminating Counterexamples: A Case Study Intervention for Improving Adolescents’ Ability to Critique Direct Arguments

Students’ difficulties with argumentation, proving, and the role of counterexamples in proving are well documented. Students in this study experienced an intervention for improving their argumentation and proving practices. The intervention included the eliminating counterexamples (ECE) framework as a means of constructing and critiquing viable arguments for a general claim. This framework involves constructing descriptions of all possible counterexamples to a conditional claim and determining whether or not a direct argument eliminates the possibility of counterexamples.

Author/Presenter

David A. Yopp

Rob Ely

Anne E. Adams

Annelise W. Nielsen

Erin C. Corwine

Lead Organization(s)
Year
2019
Short Description

This case study investigates U.S. eighth-grade (age 13) mathematics students’ conceptions about the validity of a direct argument after the students received instruction on the eliminating counterexamples (ECE) framework.

Growth in Children’s Understanding of Generalizing and Representing Mathematical Structure and Relationships

We share here results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5.

Author/Presenter

Maria Blanton

Isil Isler-Baykal

Rena Stroud

Ana Stephens

Eric Knuth

Angela Murphy Gardiner

Lead Organization(s)
Year
2019
Short Description

Authors share results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5.

Growth in Children’s Understanding of Generalizing and Representing Mathematical Structure and Relationships

We share here results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5.

Author/Presenter

Maria Blanton

Isil Isler-Baykal

Rena Stroud

Ana Stephens

Eric Knuth

Angela Murphy Gardiner

Lead Organization(s)
Year
2019
Short Description

Authors share results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5.

Linear Algebra and Geometry

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. 

Author/Presenter

Al Cuoco

Kevin Waterman

Bowen Kerins

Elena Kaczorowski

Michelle Manes

Year
2019
Short Description

Linear Algebra and Geometry is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. The materials are organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

Thinking Scientifically in a Changing World

Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

Lombardi, D. (2019). Thinking scientifically in a changing world. Science Brief: Psychological Science Agenda, 33(1). Retrieved from https://www.apa.org/science/about/psa/2019/01/changing-world.aspx

Author/Presenter

Doug Lombardi

Lead Organization(s)
Year
2019
Short Description

Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

A Student Asks About (-5)!

A first-year algebra student’s curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics.
Author/Presenter

E. Paul Goldenberg

Cynthia J. Carter

Year
2017
Short Description

A first-year algebra student’s curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics.

Problematizing and Assessing Secondary Mathematics Teachers’ Ways of Thinking

STEM Categorization
Day
Thu

Engage with presenters as they discuss assessment and rubrics designed to measure secondary teachers’ mathematical habits of mind.

Date/Time
-

Work in secondary mathematics education takes many approaches to content, pedagogy, professional development and assessment. This session aims to illuminate the richness of hte content of secondary mathematics and the field of secondary mathematics education by sharing two such approaches and reflecting on the differences and commonalities between the two.   

Session Types

Constructing and Role-Playing Student Avatars in a Simulation of Teaching Algebra for Diverse Learners

From the perspectives of Graduate Research Assistants (GRAs), this study examines the design and implementation of a simulated teaching environment in Second Life (SL) for prospective teachers to teach algebra for diverse learners. Drawing upon the Learning-for-Use framework, the analyses provide evidence on the development of student avatars in construction and role-playing activities. The study reveals challenges, procedures, and suggestions for future simulations. This study also calls for research efforts toward preparing mathematics teachers for cultural diversity.

Author/Presenter

Tingting Ma

Irving A. Brown

Gerald Kulm

Trina J. Davis

Chance W. Lewis

G. Donald Allen

Lead Organization(s)
Year
2014
Short Description

This study examines the design and implementation of a simulated teaching environment in Second Life for prospective teachers.