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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

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

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

Finesilver, Carla – Mathematical Thinking and Learning: An International Journal, 2017

The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D…

Descriptors: Multiplication, Computation, Numeracy, Number Concepts

Sengupta-Irving, Tesha; Agarwal, Priyanka – Mathematical Thinking and Learning: An International Journal, 2017

Students are expected to learn mathematics such that when they encounter challenging problems they will persist. Creating opportunities for students to persist in problem solving is therefore argued as essential to effective teaching and to children developing positive dispositions in mathematical learning. This analysis takes a novel approach to…

Descriptors: Problem Solving, Persistence, Mathematics Education, Elementary School Mathematics

Hopkins, Sarah; Bayliss, Donna – Mathematical Thinking and Learning: An International Journal, 2017

In this research, we examined how 200 students in seventh grade (around 12 years old) solved simple addition problems. A cluster approach revealed that less than half of the cohort displayed proficiency with simple addition: 35% predominantly used min-counting and were accurate, and 16% frequently made min-counting errors. Students who frequently…

Descriptors: Middle School Students, Grade 7, Problem Solving, Mathematics Skills

Bergwall, Andreas; Hemmi, Kirsti – Mathematical Thinking and Learning: An International Journal, 2017

Students' difficulties with proof, scholars' calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related…

Descriptors: Foreign Countries, Comparative Education, Textbook Content, Mathematical Logic

Van Zoest, Laura R.; Stockero, Shari L.; Leatham, Keith R.; Peterson, Blake E.; Atanga, Napthalin A.; Ochieng, Mary A. – Mathematical Thinking and Learning: An International Journal, 2017

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners' understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative…

Descriptors: Mathematics Instruction, Mathematical Logic, Thinking Skills, Discussion (Teaching Technique)

Kotsopoulos, Donna; Zambrzycka, Joanna; Makosz, Samantha – Mathematical Thinking and Learning: An International Journal, 2017

The purpose of the present study was to determine whether there are visual-spatial gender differences in two-year-olds, to investigate the environmental and cognitive factors that contribute to two-year-olds' visual-spatial skills, and to explore whether these factors differ for boys and girls. Children (N = 63; M[subscript age] = 28.17 months)…

Descriptors: Gender Differences, Toddlers, Spatial Ability, Visual Acuity

Stephens, Ana C.; Fonger, Nicole; Strachota, Susanne; Isler, Isil; Blanton, Maria; Knuth, Eric; Murphy Gardiner, Angela – Mathematical Thinking and Learning: An International Journal, 2017

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…

Descriptors: Elementary School Students, Algebra, Generalization, Thinking Skills