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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

Mkhatshwa, Thembinkosi Peter; Doerr, Helen M. – Mathematical Thinking and Learning: An International Journal, 2018

Contributing to a growing body of research on undergraduate students' quantitative reasoning, the study reported in this article used task-based interviews to investigate business calculus students' quantitative reasoning when solving two optimization tasks situated in the context of revenue and profit maximization. Analysis of verbal responses…

Descriptors: Undergraduate Students, Calculus, Mathematics Instruction, Mathematical Logic

Schulz, Andreas – Mathematical Thinking and Learning: An International Journal, 2018

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

Descriptors: Computation, Mathematics Instruction, Multiplication, Arithmetic

Patterson, Cody L.; McGraw, Rebecca – Mathematical Thinking and Learning: An International Journal, 2018

In this study, we investigate students' ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14-16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise…

Descriptors: Mathematics Achievement, Mathematics Instruction, Graphs, Knowledge Level

Groth, Randall E.; Jones, Matthew; Knaub, Mary – Mathematical Thinking and Learning: An International Journal, 2018

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

Descriptors: Models, Cognitive Processes, Student Attitudes, Graphs

Shanley, Lina; Clarke, Ben; Doabler, Christian; Kurtz-Nelson, Evangeline; Fien, Hank – Mathematical Thinking and Learning: An International Journal, 2018

Early number skills are a critical aspect of early mathematics development. However, the constructs that comprise early number skills differ across assessments, and previous studies have proposed various models of early mathematics skills comprised of formal and informal tasks. This study explored the factor structure of a researcher-developed…

Descriptors: Number Concepts, Mathematics Skills, Kindergarten, At Risk Students

Kanellos, Ioannis; Nardi, Elena; Biza, Irene – Mathematical Thinking and Learning: An International Journal, 2018

In this paper, we propose an enriched and extended application of Harel and Sowder's proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students' emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14-15) secondary students. We capture…

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

Wernet, Jamie L. W. – Mathematical Thinking and Learning: An International Journal, 2017

It has been theorized that contextual tasks support student engagement and sense making. Yet, contradictory ideas exist about the role of these tasks in lessons, and further research is needed to explore how classroom interactions can help achieve their intended purposes. Through video observation of lessons in three eighth-grade classrooms using…

Descriptors: Mathematics Education, Classroom Environment, Classroom Techniques, Interaction