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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

Whitacre, Ian – Cognition and Instruction, 2018

I present a viable learning trajectory for prospective elementary teachers' number sense development with a focus on whole-number place value, addition, and subtraction. I document a chronology of classroom mathematical practices in a Number and Operations course. The findings provide insights into prospective elementary teachers' number sense…

Descriptors: Preservice Teachers, Elementary School Teachers, Mathematics Activities, Mathematics

Ghousseini, Hala – Cognition and Instruction, 2017

This study addresses how rehearsals of teaching could support teachers in developing mathematical knowledge for teaching (MKT). The analysis of 30 rehearsals, from elementary methods courses in 3 teacher education programs, attends to what novice teachers and teacher educators did in rehearsal that enlisted MKT. The findings elaborate the tasks…

Descriptors: Knowledge Base for Teaching, Mathematics Instruction, Elementary School Mathematics, Methods Courses

Murata, Aki; Siker, Jody; Kang, Bona; Baldinger, Evra M.; Kim, Hee-Jeong; Scott, Mallika; Lanouette, Kathryn – Cognition and Instruction, 2017

This study investigated different math-talk facilitations, and conceptualized the teachers' talk moves for productive student mathematics discussions. Our findings suggest that students' strategy development is supported by talk moves coordinating a wide range of student strategies, representations and discussions that are at a process-level and…

Descriptors: Grade 1, Elementary School Mathematics, Discussion (Teaching Technique), Teaching Methods

Tsang, Jessica M.; Blair, Kristen P.; Bofferding, Laura; Schwartz, Daniel L. – Cognition and Instruction, 2015

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

Descriptors: Neurological Organization, Mathematics Instruction, Numbers, Grade 4

Stylianides, Gabriel J.; Stylianides, Andreas J. – Cognition and Instruction, 2014

Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In…

Descriptors: Teaching Methods, Learner Engagement, Student Needs, Relevance (Education)

Smith, John P., III; Males, Lorraine M.; Dietiker, Leslie C.; Lee, KoSze; Mosier, Aaron – Cognition and Instruction, 2013

Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students' difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the…

Descriptors: Measurement, Elementary School Mathematics, Primary Education, Mathematical Concepts

Van Dooren, Wim; De Bock, Dirk; Verschaffel, Lieven – Cognition and Instruction, 2010

This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

Descriptors: Numbers, Word Problems (Mathematics), Mathematical Logic, Problem Solving

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

Saxe, Geoffrey B.; Earnest, Darrell; Sitabkhan, Yasmin; Haldar, Lina C.; Lewis, Katherine E.; Zheng, Ying – Cognition and Instruction, 2010

This report provides evidence of the influence of a tutorial "communication game" on fifth graders' generative understanding of the integer number line. Students matched for classroom and pretest score were randomly assigned to a tutorial (n = 19) and control group (n = 19). The tutorial group students played a 13-problem game in which…

Descriptors: Numbers, Tutors, Number Concepts, Grade 5

Morris, Anne K. – Cognition and Instruction, 2007

This study was designed to identify the types of understandings, skills, and beliefs that affect pre-service teachers' evaluations of students' mathematical arguments in classroom contexts. Thirty-four pre-service teachers read a transcript of a third grade lesson in which the students were expected to prove a generalization. To investigate…

Descriptors: Preservice Teacher Education, Validity, Mathematical Logic, Generalization

Baroody, Arthur J.; Brach, Catherine; Tai, Yu-chi – Cognition and Instruction, 2006

A schema based view of addition development is compared with Siegler's latest strategy-choice model, which includes an addition goal sketch (a basic understanding of "the goals and causal relations" of addition; Siegler & Crowley, 1994, p. 196). This metacognitive component in the latter model is presumed to develop as a child practices a basic…

Descriptors: Arithmetic, Mathematics Instruction, Models, Cognitive Development

Arendasy, Martin; Sommer, Markus; Ponocny, Ivo – Cognition and Instruction, 2005

Simple arithmetic word problems are often featured in elementary school education. One type of problem, "compare with unknown reference set," ranks among the most difficult to solve. Differences in item difficulty for compare problems with unknown reference set are observed depending on the direction of the relational statement (more than vs. less…

Descriptors: Psychometrics, Arithmetic, Word Problems (Mathematics), Item Response Theory

Murata, Aki – Cognition and Instruction, 2004

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…

Descriptors: Teaching Methods, Grade 1, Arithmetic, Foreign Countries

Peer reviewed

Nathan, Mitchell J.; Knuth, Eric J. – Cognition and Instruction, 2003

This study compared flow of information and peer- and teacher-directed scaffolding evident in whole class discussions during Years 1 and 2 of a middle school mathematics teacher's efforts to change classroom practices. Results showed that in Year 2, the teacher removed herself as the analytic center to invite greater student participation.…

Descriptors: Change Strategies, Discourse Analysis, Elementary School Mathematics, Group Discussion

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