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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

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

Pei, Christina; Weintrop, David; Wilensky, Uri – Mathematical Thinking and Learning: An International Journal, 2018

There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

Descriptors: Problem Solving, Thinking Skills, Mathematics Instruction, Mathematical Logic

Sinclair, Nathalie; Patterson, Margaret – Mathematical Thinking and Learning: An International Journal, 2018

The goal of this paper is to explore dynamic geometry environments (DGE) as a type of computer programming language. Using projects created by secondary students in one particular DGE, we analyse the extent to which the various aspects of computational thinking--including both ways of doing things and particular concepts--were evident in their…

Descriptors: Mathematics Instruction, Programming, Computation, Thinking Skills