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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…
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-…
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 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…