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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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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…
Poster
Middle School
High School
Mathematics
How do we design small meaningful suggestions for instructional improvement that are easy to…
Poster
Pre-Kindergarten
Elementary School
Mathematics
This study uses an RCT design to test the effectiveness of a Grades K-2 early algebra…
Poster
Elementary School
Middle School
Mathematics
Maria Blanton
Eric Knuth
Resource
Algebra
Presentation
High
Mary Ann Huntley
Maria Terrell
2010…
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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…
Teaching and Learning Algebraic Thinking Across the Middle Grades: A Research-based Approach Using PhET Interactive Simulations
Poster
Middle School
High School
Mathematics
Katherine Perkins
2016 PI Arcade
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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 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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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…
Poster
Elementary School
Mathematics
This project explores how children in grades K-2 understand visual representations of algebraic concepts. For instance,…
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A classroom study was conducted to understand how to engage in responsive teaching with 18 seventh grade students at three stages of units coordination during a unit on proportional reasoning co-taught by the first author…
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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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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…
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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,…
Poster
Elementary School
DRK-12
Algebra
Mathematics
Meixia Ding
Early Career…
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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-…
CAREER: Investigating Changes in Students' Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra
Poster
Middle School
High School
Mathematics
Curriculum
The main issue our project addresses is how students' reasoning about…
Resource
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…
CAREER: Investigating Changes in Students' Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra
Poster
High School
Mathematics
This project examines how instructional activities involving quadratic functions influence students’ prior ways of reasoning…
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Professional development (PD) for mathematics teachers often emphasizes transformative instructional change. However, a more modest, incremental approach may offer a higher likelihood of success in ways that complement…
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…
Poster
Middle School
Mathematics
Jodi Davenport
Yvonne Kao
Alma Ramirez
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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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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…
Poster
High School
Mathematics
Assessment
Broadening Participation
Curriculum
We are studying the implementation and…
Resource
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…
CAREER: From Research to Meta-Research to Practice - The Development of an Educational Learning Environment Framework for School Algebra
Poster
Elementary School
Middle School
High School
Mathematics
This project advances the understanding of teaching and learning of…
Transforming Learning Opportunities in Linguistically Diverse Secondary Classrooms Through Promoting Discussions: Results of an Intervention
Resource
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…
Examining Different Curricular Approaches and Their Impact on High-school Students' Understanding of Algebra: Phase 1 - Studying the Intended Curriculum
Poster
Mathematics
Mary Ann Huntley
Maria Terrell
Developing Algebra-ready students for Middle School: Exploring the Impact of Early Algebra (Blanton, Knuth)
Resource
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…
Poster
Elementary School
Mathematics
Eric Knuth
Ana Stephens
AERA 2017 Poster: Teaching and Learning Algebraic Thinking Across the Middle Grades Using PhET Interactive Simulations
Poster
Click image to see poster.
Abstract
Objectives: This project aims to develop an integration of resources, models, and tools that overcome the tendency for superficial use of computer simulations and enable more mathematics…
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…
Poster
High School
Mathematics
Broadening Participation
Classroom Practice
Pedagogical Content Knowledge
Professional Development…
Resource
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…
Poster
Middle School
Mathematics
Project CARe’s goal is to explore how new technologies create a path into algebra that allows students to build algebraic…
Resource
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…
Poster
Mathematics
E. Paul Goldenberg
June Mark
Deborah Spencer
Gateways to Algebraic Motivation, Engagement and Success (GAMES): Supporting and Assessing Fraction Proficiency with Game-Based, Mobile Applications and Devices
Poster
Middle School
Mathematics
Michael Evans
Gaming Spotlight
http://ltrg.centers.vt.…
Poster
Click image to see poster.
Abstract
The Using Math Pathways & Pitfalls to Promote Algebra Readiness project aims to create and test student activities and professional development that specifically target key…
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…
Understanding How Integrated Computational Thinking, Engineering Design, and Mathematics Can Help Students Solve Scientific and Technical Problems in Career Technical Education
Poster
High School
Computer Science
Engineering
Mathematics
Science
Technology
Broadening Participation…
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…
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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…
Closing the Math Achievement Gap for English Language Learners: Technology Resources for Pre-algebra
Poster
Middle School
Achievement
Algebra
Multilingual Learners
Mathematics
Technology
Carole…
An Architecture of Intensification: Building a Comprehensive Program for Struggling Students in Double-period Algebra Classes
Poster
High School
Mathematics
Alison Castro-SuperfineSusan GoldmanLinda Chaput
James Lynn…
Poster
Middle School
Mathematics
Gerald Kulm
Gaming Spotlight
http://kate.tamu.edu/index.…
Poster
Click image to see poster.
Abstract
Purpose of Study: Comparison plays a critical role in the cognitive process (Goldstone, Day, & Son, 2010; Kotovsky & Genterner, 1996), and supports effective learning of…
Resource
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…
Poster
Middle School
High School
Mathematics
Assessment
Classroom Practice
Curriculum
Disciplinary Content…
Resource
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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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…
An Architecture of Intensification: Building a Comprehensive Program for Struggling Students in Double-period Algebra Classes
Poster
High School
Mathematics
Technology
James Lynn
Martin Gartzman
James Pellegrino…
Examining Different Curricular Approaches and Their Impact on High-school Students' Understanding of Algebra: Phase 1 - Studying the Intended Curriculum
Poster
High School
Mathematics
Mary Ann Huntley
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…
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…
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…
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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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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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…
Poster
Middle School
High School
Mathematics
We investigate teacher beliefs about discourses employed with equation solving and the challenges…
Poster
Elementary School
Middle School
Mathematics
Technology
Daniel Scher
Steve…
Poster
Elementary School
Middle School
Mathematics
Daniel Scher
Steve Rasmussen
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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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…
Poster
Middle School
Mathematics
Jodi Davenport
Yvonne Kao
Alma Ramirez
Resource
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…