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White, Tobin – Cognition and Instruction, 2019

This article analyzes an episode of classroom mathematics activity mediated by graphing technology from 3 different theoretical perspectives. An important line of research in the learning sciences focuses on graphs as "inscriptions", foregrounding learners' interactions with and around the material properties of graphical displays.…

Descriptors: Mathematics Education, Educational Technology, Technology Uses in Education, Teaching Methods

Steier, Rolf; Kersting, Magdalena – Cognition and Instruction, 2019

Though we live in a 4-dimensional universe, our minds and bodies are not particularly good at perceiving and depicting 4 dimensions. This study contributes to our understanding of collaboration with abstract concepts by examining particular activities where bodily and experiential understandings may conflict with the conceptual domain.…

Descriptors: Metacognition, Imagination, Secondary School Science, Secondary School Students

Fonger, Nicole L.; Stephens, Ana; Blanton, Maria; Isler, Isil; Knuth, Eric; Gardiner, Angela Murphy – Cognition and Instruction, 2018

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked…

Descriptors: Academic Achievement, Mathematics Education, Algebra, Research and Development

Kainulainen, Mikko; McMullen, Jake; Lehtinen, Erno – Cognition and Instruction, 2017

Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…

Descriptors: Numbers, Foreign Countries, Grade 3, Grade 4

Lai, Yvonne; Weber, Keith; Mejia-Ramos, Juan Pablo – Cognition and Instruction, 2012

In this article, we report two studies investigating what mathematicians value in a pedagogical proof. Study 1 is a qualitative study of how eight mathematicians revised two proofs that would be presented in a course for mathematics majors. These mathematicians thought that introductory and concluding sentences should be included in the proofs,…

Descriptors: Sentences, Mathematics Education, Qualitative Research, Mathematics Instruction

Rogat, Toni Kempler; Linnenbrink-Garcia, Lisa – Cognition and Instruction, 2011

This study extends prior research on both individual self-regulation and socially shared regulation during group learning to examine the range and quality of the cognitive and behavioral social regulatory sub-processes employed by six small collaborative groups of upper-elementary students (n = 24). Qualitative analyses were conducted based on…

Descriptors: Social Control, Cooperation, Group Dynamics, Elementary School Students

Simon, Martin; Saldanha, Luis; McClintock, Evan; Akar, Gulseren Karagoz; Watanabe, Tad; Zembat, Ismail Ozgur – Cognition and Instruction, 2010

We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which…

Descriptors: Mathematics Education, Learning Processes, Research Methodology, Mathematics Activities

Ding, Meixia; Li, Xiaobao – Cognition and Instruction, 2010

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…

Descriptors: Comparative Analysis, Mathematics Education, Textbooks, Elementary School Mathematics

Izsak, Andrew – Cognition and Instruction, 2008

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

Descriptors: Mathematics Education, Mathematics Instruction, Grade 6, Teacher Attitudes

Li, Xiaobao; Ding, Meixia; Capraro, Mary Margaret; Capraro, Robert M. – Cognition and Instruction, 2008

This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level.…

Descriptors: Foreign Countries, Comparative Analysis, Symbols (Mathematics), Grade 6

Staples, Megan – Cognition and Instruction, 2007

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can…

Descriptors: Educational Strategies, Academic Achievement, Educational Change, Mathematics Education

Wagner, Joseph F. – Cognition and Instruction, 2006

The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical…

Descriptors: Case Studies, Undergraduate Students, Problem Solving, Statistics

Van Dooren, Wim; De Bock, Dirk; Hessels, An; Janssens, Dirk; Verschaffel, Lieven – Cognition and Instruction, 2005

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

Descriptors: Age Differences, Mathematics Education, Arithmetic, Mathematical Concepts

Izsak, Andrew – Cognition and Instruction, 2004

In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct…

Descriptors: Grade 8, Cognitive Processes, Mathematics Education, Algebra

diSessa, Andrea A. – Cognition and Instruction, 2004

The premise of this article is that the study of representation is valuable and important for mathematics and science students. Learning about representation should go beyond learning specific, sanctioned representations emphasized in standard curricula (graphs, tables, etc.) to include principles and design strategies that apply to any scientific…

Descriptors: Science Education, Mathematics Education, Cognitive Development, Learning Problems

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