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Tillema, Erik S. – Mathematical Thinking and Learning: An International Journal, 2020

Two-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11-12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented…

Descriptors: Mathematics Instruction, Multiplication, Mathematical Concepts, Teaching Methods

Ayalon, Michal; Wilkie, Karina – Mathematical Thinking and Learning: An International Journal, 2020

Researching students' responses to tasks at different year levels and in varied curriculum contexts can provide insights that relate their understandings to prior learning experiences and teaching approaches. In this article, we discuss evidence of students from three curriculum contexts (English, Australian, and Israeli) (n = 350) ways of…

Descriptors: Secondary School Mathematics, Comparative Education, Foreign Countries, Mathematical Logic

Baldinger, Erin E. – Mathematical Thinking and Learning: An International Journal, 2020

Analyzing and interpreting student thinking through written work is a key, often challenging, practice of teaching. It entails noticing students' mathematical thinking and drawing on mathematical knowledge for teaching. This study investigates how pre-service secondary teachers at the beginning of their preparation reason about students' written…

Descriptors: Preservice Teachers, Secondary School Teachers, Problem Solving, Logical Thinking

Simon, Martin A. – Mathematical Thinking and Learning: An International Journal, 2020

The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then…

Descriptors: Instructional Design, Mathematics Instruction, Mathematical Concepts, Abstract Reasoning

van Dijke-Droogers, Marianne; Drijvers, Paul; Bakker, Arthur – Mathematical Thinking and Learning: An International Journal, 2020

While various studies suggest that informal statistical inference (ISI) can be developed by young students, more research is needed to translate this claim into a well-founded learning trajectory (LT). As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation, and evaluation of the…

Descriptors: Statistical Inference, Grade 9, Sampling, Statistical Distributions

Calculus Students' Quantitative Reasoning in the Context of Solving Related Rates of Change Problems

Mkhatshwa, Thembinkosi P. – Mathematical Thinking and Learning: An International Journal, 2020

Despite the increasing amount of research on students' quantitative reasoning at the secondary level, research on students' quantitative reasoning at the undergraduate level is scarce. The present study used task-based interviews to examine 16 high-performing undergraduate calculus students' quantitative reasoning in the context of solving three…

Descriptors: Calculus, Logical Thinking, Problem Solving, Undergraduate Students

Cullen, Amanda L.; Barrett, Jeffrey E. – Mathematical Thinking and Learning: An International Journal, 2020

In this article, we describe how students structured 2-dimensional space with square and nonsquare units. We employed a cross-sectional design, interviewing 5 students from each of 4 different grade groups: Grades 1, 3, 5, and 7 (ages 7, 9, 11, and 13) in structured, task-based interviews. Our findings about students' ways of measuring area fit a…

Descriptors: Geometric Concepts, Grade 1, Grade 3, Grade 5

Munter, Charles; Haines, Cara – Mathematical Thinking and Learning: An International Journal, 2019

This study examined whether secondary students in an urban school district perceived racial differences in opportunity to be successful in mathematics, whether those perceptions differed between students of color and white students, and the relation of those perceptions to teachers' choice and implementation of mathematical tasks. The results of…

Descriptors: Mathematics Teachers, Difficulty Level, Student Attitudes, Racial Differences

Kobiela, Marta; Lehrer, Richard – Mathematical Thinking and Learning: An International Journal, 2019

Design research was conducted to investigate the development of dynamic conceptions of area. Students used simple physical instruments, squeegees, and paint, to generate rectangular areas continuously as a sweeping motion of one length through another. Then, they dissected the resulting swept space into discrete units of measure by coordinating…

Descriptors: Geometric Concepts, Measurement, Concept Formation, Spatial Ability

Kertil, Mahmut; Erbas, Ayhan Kursat; Cetinkaya, Bulent – Mathematical Thinking and Learning: An International Journal, 2019

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers' ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented…

Descriptors: Preservice Teachers, Student Attitudes, Middle School Mathematics, Mathematics Education

Visnovska, Jana; Cobb, Paul – Mathematical Thinking and Learning: An International Journal, 2019

We report on five-year professional development collaboration with a group of middle-school mathematics teachers during which their views of what constitutes a productive classroom statistical activity changed. The teachers' statistics instruction was initially typical in the US context and focused on producing calculations and following…

Descriptors: Teacher Attitudes, Attitude Change, Statistics, Mathematics Activities

Johnson, Nicholas C.; Turrou, Angela C.; McMillan, Brandon G.; Raygoza, Mary C.; Franke, Megan L. – Mathematical Thinking and Learning: An International Journal, 2019

Capturing the breadth and variety of children's understanding is critical if studies of children's mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children's counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed…

Descriptors: Preschool Children, Preschool Education, Computation, Comprehension

Reinke, Luke T. – Mathematical Thinking and Learning: An International Journal, 2019

Scholars propose that contextual problems can be used to ground students' understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as…

Descriptors: Problem Based Learning, Mathematics Instruction, Mathematical Models, Mathematics Curriculum

Hadar, Linor L.; Ruby, T. Lefcourt – Mathematical Thinking and Learning: An International Journal, 2019

The cognitive domain in mathematics, defined as thinking and understanding in the process of learning mathematics, is a main focus of curricula in many countries. This study explores breadth and depth of understanding as addressed in mathematics textbooks certified as aligned to Israeli national mathematics curricula. We compare opportunities for…

Descriptors: Foreign Countries, Grade 4, Grade 8, Mathematics Instruction

Dobie, Tracy E. – Mathematical Thinking and Learning: An International Journal, 2019

This research explores how adolescents conceptualize the usefulness of mathematics. Integrating sociocultural theory with the study of utility value, this study uses open-ended survey items and interview tasks to examine conceptions of usefulness among a group of predominantly Latinx middle school students. Findings reveal that students primarily…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Hispanic American Students, Middle School Students