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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

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

Sharpe, Sheree T. – Mathematical Thinking and Learning: An International Journal, 2019

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school…

Descriptors: Word Problems (Mathematics), Algebra, Mathematics Instruction, Problem Solving

Turner, Erin; Roth McDuffie, Amy; Sugimoto, Amanda; Aguirre, Julia; Bartell, Tonya Gau; Drake, Corey; Foote, Mary; Stoehr, Kathleen; Witters, Angela – Mathematical Thinking and Learning: An International Journal, 2019

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers', and especially early career teachers' (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related…

Descriptors: Mathematics Instruction, Beginning Teachers, Language Usage, Elementary School Mathematics

Ahmadpour, Fatemeh; Reid, David; Reza Fadaee, Mohammad – Mathematical Thinking and Learning: An International Journal, 2019

We present a model for describing the growth of students' understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Secondary School Mathematics

Ding, Meixia; Chen, Wei; Hassler, Ryan Scott – Mathematical Thinking and Learning: An International Journal, 2019

Linear quantity models such as pre-tapes, tape diagrams, and number line diagrams have drawn increasing attention in mathematics education around the world. However, we still know relatively little about how teachers actually use these models in the classroom. This study explores how exemplary US and Chinese elementary teachers use linear quantity…

Descriptors: Mathematics Instruction, Foreign Countries, Elementary School Teachers, Elementary School Mathematics

Leiss, Dominik; Plath, Jennifer; Schwippert, Knut – Mathematical Thinking and Learning: An International Journal, 2019

Solving reality-based tasks is an important goal in mathematics instruction and is anchored in education standards determined by mathematical modeling skills. These tasks demand a serious examination of the real-world as well as text comprehension to successfully solve them. Therefore, this study empirically reconstructed the comprehension process…

Descriptors: Mathematics Instruction, Reading Ability, Mathematical Models, Grade 7

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