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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'…

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The Centrality of Student-Generated Representation in Investigating Generalizations about the Operations
This article addresses the nature of student-generated representations that support…

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Backward Transfer Influences from Quadratic Functions Instruction on Students’ Prior Ways of Covariational Reasoning about Linear Functions
The study reported in this article examined the ways…

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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…

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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…

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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…

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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…

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Eliminating counterexamples: An intervention for improving adolescents’ contrapositive reasoning
Students’ difficulties with contrapositive reasoning are well documented. Lack of intuition…

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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…

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Cognitive Instructional Principles in Elementary Mathematics Classrooms: A Case of Teaching Inverse Relations
Instructional principles gleaned from cognitive science play a critical role in…

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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…

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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…

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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…

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Tiering Instruction for Middle School Students
Differentiating instruction (DI) is a pedagogical approach to managing classroom diversity in which teachers proactively adapt curricula,…

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Domain appropriateness and skepticism in viable argumentation
https://pmena2020.cinvestav.mx/Program-Proceedings/Proceedings

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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…

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Eliminating counterexamples: A case study intervention for improving adolescents’ ability to critique direct arguments
Students’ difficulties with argumentation, proving, and the role of…

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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…

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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…

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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…

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Thinking Scientifically in a Changing World
Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative…

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Eliminating Counterexamples: A Case Study Intervention for Improving Adolescents’ Ability to Critique Direct Arguments
Students’ difficulties with argumentation, proving, and the role of…

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Math Pathways & Pitfalls Algebra Readiness: Lessons and Teaching Guide, Grades 7–8
The Math Pathways & Pitfalls Algebra Readiness mathematics intervention is intended to help students…

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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…

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NCTM Presentation Line of "Good" Fit in Grade 8 Classrooms
NCTM 2018 Modeling Presentation 4.15.18.pdf

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Advancing Reasoning Covariationally (ARC) Curriculum
The Advancing Reasoning Covariationally (ARC) curriculum is a curriculum for working pre-service and in-service teachers. ARC targets and…

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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…

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“Approximate” Multiplicative Relationships between Quantitative Unknowns
Three 18-session design experiments were conducted, each with 6–9 7th and 8th grade students, to investigate…

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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…

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Illuminating Coordinate Geometry with Algebraic Symmetry
A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged…

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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…

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SmartGraphs: Algebra
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…

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Intensified Algebra I--poster
http://cadrek12.org/sites/default/files/An%20architecture%20of%20intensificatio…

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Pre-Service Teachers' Knowledge for Teaching Algebra for Equity in the Middle Grades: A Preliminary Report
http://www.eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true…

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What is Algebra? Cross-Curricular Textbook Analyses
http://cadrek12.org/sites/default/files/Poster%20-%20NSF%20PI%20Mtg%202010%20%2…

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Teaching Mathematics, Teaching Students, Teaching Mathematics to Students (Thompson, Miller)
http://cadrek12.org/sites/default/files/THOMPSON%202009-11%20NSF%20DRk-12.pdf…

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Developing Algebra-ready students for Middle School: Exploring the Impact of Early Algebra (Blanton, Knuth)
BLANTON Algebra_DRK-12_poster_2009.ppt