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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

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

Gadanidis, George; Clements, Erin; Yiu, Chris – Mathematical Thinking and Learning: An International Journal, 2018

In this article, we investigate the artistic puzzle of designing mathematics experiences (MEs) to engage young children with ideas of group theory, using a combination of hands-on and computational thinking (CT) tools. We elaborate on: (1) group theory and why we chose it as a context for young mathematicians' experiences with symmetry and…

Descriptors: Mathematics, Professional Personnel, Mathematics Instruction, Geometry

diSessa, Andrea A. – Mathematical Thinking and Learning: An International Journal, 2018

This article develops some ideas concerning the "big picture" of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of "computation as a new literacy" in some detail and with concrete examples of sixth grade students…

Descriptors: Computers, Computation, Computer Literacy, Mathematics Instruction

Blanton, Maria; Otálora, Yenny; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katharine B.; Gibbins, Aliska; Kim, Yangsook – Mathematical Thinking and Learning: An International Journal, 2018

This study explores kindergarten students' early notions of mathematical equivalence in the United States. In particular, it uses qualitative methods to examine the understandings children hold about the equal sign prior to formal instruction and how these understandings shift throughout an 8-week classroom teaching experiment designed to develop…

Descriptors: Kindergarten, Knowledge Level, Mathematical Concepts, Symbols (Mathematics)

Anhalt, Cynthia Oropesa; Cortez, Ricardo; Bennett, Amy Been – Mathematical Thinking and Learning: An International Journal, 2018

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to…

Descriptors: Preservice Teachers, Secondary Education, Mathematical Models, Secondary School Mathematics

Pittalis, Marios; Pitta-Pantazi, Demetra; Christou, Constantinos – Mathematical Thinking and Learning: An International Journal, 2018

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students' (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early…

Descriptors: Numbers, Arithmetic, Algebra, Elementary School Students

Montenegro, Paula; Costa, Cecília; Lopes, Bernardino – Mathematical Thinking and Learning: An International Journal, 2018

Multiple representations of a given mathematical object/concept are one of the biggest difficulties encountered by students. The aim of this study is to investigate the impact of the use of visual representations in teaching and learning algebra. In this paper, we analyze the transformations from and to visual representations that were performed…

Descriptors: Mathematics Instruction, Mathematical Concepts, Algebra, Middle School Students