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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…
Poster
Elementary School
DRK-12
Algebra
Mathematics
Meixia Ding
Early Career…
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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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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…
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…
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 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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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 …
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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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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…
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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…
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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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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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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…
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-…
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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…
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…
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 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 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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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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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…
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…
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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…
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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…