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

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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…

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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.
A cluster randomized trial design was used to…

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The Advancing Reasoning Covariationally (ARC) curriculum is a curriculum for working pre-service and in-service teachers. ARC targets and develops quantitative and covariational reasoning as connecting threads to major…

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There is strong empirical evidence in support of learning from comparisons in mathematics education research. The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of…

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

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This study examines the design and implementation of a simulated teaching environment in Second Life for prospective teachers.
From the perspectives of Graduate Research Assistants (GRAs), this study…

Scaling up innovative learning in mathematics: exploring the effect of different professional development approaches on teacher knowledge, beliefs, and instructional practice

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The purpose of the current study was to explore different ways for teachers to engage in Professional learning experiences (PLEs) and how these approaches might enable the field to scale up these efforts in a sustainable…

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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…

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The Math Pathways & Pitfalls K-8 curriculum was designed with built-in support for teachers, alignment to the Common Core State Standards and Mathematical Practices. The curriculum can be flexibly used as an…

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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…

Developing Algebra-ready students for Middle School: Exploring the Impact of Early Algebra (Blanton, Knuth)

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This is a 3-year project designed to build the preliminary components for investigating the impacts of early algebra education on students’ algebra readiness in middle grades.
Algebra…

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A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged. For example, f(x, y, z) = xy +xz + yz is a symmetric polynomial. If we interchange…

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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…

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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.
Differentiating…

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

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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…

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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…

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CADRE has compiled sortable Excel lists of DR K-12 projects that work in a particular topic area (e.g., algebra, earth science) or with a particular target audience. These lists can be useful tools in writing proposals for…

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

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

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

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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…

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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…

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On February 10th, 2012, five Fellows presented on the work of their projects. Many thanks to the presenters and to the audience of Fellows who followed up each presentation with great questions and discussion.
Due to…

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The Concord Consortium has developed 19 activities for teaching and learning algebra that are available online or as an app for iPad or Android tablet computers. These activities—which cover a variety of algebra topics,…

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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…

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

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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.
This study examines how sampled…

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Several recent studies have focused on helping students understand the limitations of empirical arguments (e.g., Stylianides, G. J. & Stylianides, A. J., 2009, Brown, 2014). One view is that students use empirical…

A Geometric Path to the Concept of Function: Transformations using dynamic software can provide a unique perspective on a common topic.

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The concept of function spans elementary school through high school. When introducing the topic to elementary school and middle school students, we ask them to work with a variety of examples and representations of…

Knowledge for Algebra Teaching for Equity (KATE) Project: An Examination of Virtual Classroom Simulation Approaches

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In this paper, we present an overview of the National Science Foundation (NSF) funded Knowledge for Algebra Teaching for Equity (KATE) Project and experiences from preservice teachers who are preparing for teaching middle…

Challenges to Using the Regression Discontinuity Design in Educational Evaluations: Lessons from the Transition to Algebra Study

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This article describes the use of RD design to evaluate the impact of a supplemental algebra-readiness curriculum, Transition to Algebra, on students’ mathematics outcomes.
Interest in the regression…

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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 …

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

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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-…

Eliminating counterexamples: A case study intervention for improving adolescents’ ability to critique direct arguments

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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…

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

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

Pre-Service Teachers' Knowledge for Teaching Algebra for Equity in the Middle Grades: A Preliminary Report

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This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science…

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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’…

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Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily…

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Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition about contrapositive reasoning and lack of a meta-argument for the logical equivalence between a conditional claim and its…

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

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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.
In this paper, we share the design…

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Algebra
Presentation
High
Mary Ann Huntley
Maria Terrell
2010…

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

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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…

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

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This presntation addreses 4 research cquestions
•What extant criteria do Grade 8 students use to choose the better line
of fit between two lines “fit” to a set of data, when both lines express
the trend of the data…

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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…

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This session considers teachers’ transitions from teacher-centered mathematics to student-centered mathematics, including issues of meaning, coherence, and learnability, as well as the importance of working with colleagues…