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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

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

Liu, Chunhua; Carraher, David W.; Schliemann, AnalĂșcia D.; Wagoner, Paul – Cognition and Instruction, 2017

In a 1-hour teaching interview, 20 children (aged 7 to 11) discovered how to tell whether objects might be made of the same material by using ratios of measures of weight and size. We examine progress in the children's reasoning about measurement and proportional relations, as well as design features of instruments, materials, and tasks crafted to…

Descriptors: Children, Preadolescents, Measurement, Cognitive Development

Rubel, Laurie H.; Lim, Vivian Y.; Hall-Wieckert, Maren; Sullivan, Mathew – Cognition and Instruction, 2016

This article explores integrating place-based education with critical mathematics toward teaching mathematics for spatial justice. "Local Lotto," a curricular module with associated digital tools, was designed to investigate the lottery as a critical spatial phenomenon and piloted in urban high schools. This article describes findings…

Descriptors: Mathematics, Social Justice, Geographic Information Systems, Mathematics Instruction

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

Braithwaite, David W.; Goldstone, Robert L. – Cognition and Instruction, 2015

Learning abstract concepts through concrete examples may promote learning at the cost of inhibiting transfer. The present study investigated one approach to solving this problem: systematically varying superficial features of the examples. Participants learned to solve problems involving a mathematical concept by studying either superficially…

Descriptors: Concept Formation, Prior Learning, Problem Solving, Mathematical Concepts

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

Norton, Anderson; Wilkins, Jesse L. M. – Cognition and Instruction, 2013

Previous research has demonstrated the effectiveness of particular instructional practices that support students' constructions of the partitive unit fraction scheme and measurement concepts for fractions. Another body of research has demonstrated the power of a particular mental operation--the splitting operation--in supporting students'…

Descriptors: Teaching Methods, Grade 6, Grade 7, Algebra

Sfard, Anna – Cognition and Instruction, 2010

There are infinitely many ways of talking about infinity. The assortment of discourses on learning infinity is infinite as well. When the author says "way of talking" or "discourse," she is concerned with much more than the question of how words are chosen and combined. Ways of talking are not just innocent "auxiliaries" to thinking--they shape…

Descriptors: Mathematical Concepts, Academic Discourse, Theories, Concept Formation

Carlson, Marilyn; Oehrtman, Michael; Engelke, Nicole – Cognition and Instruction, 2010

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

Descriptors: Calculus, Algebra, Thinking Skills, Cognitive Processes

Shechtman, Nicole; Roschelle, Jeremy; Haertel, Geneva; Knudsen, Jennifer – Cognition and Instruction, 2010

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the "Scaling Up SimCalc" research project in 2005-07, we examined relationships between teachers' mathematics knowledge, teachers' classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear…

Descriptors: Mathematics Instruction, Mathematics Curriculum, Teacher Characteristics, Decision Making

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

Vamvakoussi, Xenia; Vosniadou, Stella – Cognition and Instruction, 2010

We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…

Descriptors: Secondary School Students, Intervals, Numbers, 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