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Kotaro Komatsu; Shogo Murata; Andreas J. Stylianides; Gabriel J. Stylianides – Cognition and Instruction, 2024
"Assumptions" play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in…
Descriptors: Mathematics Instruction, Learning Activities, Student Attitudes, Foreign Countries
Lockwood, Elise – Cognition and Instruction, 2022
In this paper, I discuss undergraduate students' engagement in basic Python programming while solving combinatorial problems. Students solved tasks that were designed to involve programming, and they were encouraged to engage in activities of prediction and reflection. I provide data from two paired teaching experiments, and I outline how the task…
Descriptors: Undergraduate Students, Thinking Skills, Prediction, Teaching Methods
Izsák, Andrew; Beckmann, Sybilla; Stark, Joy – Cognition and Instruction, 2022
The present study is motivated by a significant body of research documenting teachers' perennial difficulties with a critical swath of topics related to multiplication. In response, we track how Nina, a future middle grades mathematics teacher, made progress constructing explanations across topics by reasoning with measurement-based definitions of…
Descriptors: Multiplication, Mathematics Instruction, Pedagogical Content Knowledge, Middle School Teachers
Kelton, Molly L.; Ma, Jasmine Y. – Cognition and Instruction, 2020
In this article, we report on a video-based field study of an intergenerational family's enactment of a mathematical object (a torus) in the context of an immersive mathematics exhibition in a science center. To do this, we center interwoven, multi-party mobilities at multiple scales--walking, gesturing, touching, and postural adjustments -- as…
Descriptors: Mathematics, Exhibits, Science Teaching Centers, Family (Sociological Unit)
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, Analúcia 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
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
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
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