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Chimoni, Maria; Pitta-Pantazi, Demetra; Christou, Constantinos – Educational Studies in Mathematics, 2018

The aim of this study is to better understand the notion of early algebraic thinking by describing differences in grade 4-7 students' thinking about basic algebraic concepts. To achieve this goal, one test that involved generalized arithmetic, functional thinking, and modeling tasks, was administered to 684 students from these grades. Quantitative…

Descriptors: Algebra, Grade 4, Grade 5, Grade 6

Louie, Nicole L. – Educational Studies in Mathematics, 2018

This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin's concept of "professional vision" as a way of bringing analyses of culture and power into studies of…

Descriptors: Mathematics Teachers, Mathematics Instruction, Teaching Methods, Perception

Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés – Educational Studies in Mathematics, 2017

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

Descriptors: Arithmetic, Algebra, Educational Technology, Thinking Skills

Blanton, Maria; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katie; Newman-Owens, Ashley – Educational Studies in Mathematics, 2017

Recent research suggests that children in elementary grades have some facility with variable and variable notation in ways that warrant closer attention. We report here on an empirically developed progression in first-grade children's thinking about these concepts in functional relationships. Using learning trajectories research as a framework for…

Descriptors: Elementary School Mathematics, Grade 1, Mathematics Instruction, Thinking Skills

Downton, Ann; Sullivan, Peter – Educational Studies in Mathematics, 2017

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Descriptors: Problem Solving, Mathematical Aptitude, Mathematics Skills, Difficulty Level

Jeannotte, Doris; Kieran, Carolyn – Educational Studies in Mathematics, 2017

The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR,…

Descriptors: Mathematics Instruction, Thinking Skills, Mathematics Education, Mathematical Models

Dawkins, Paul Christian; Cook, John Paul – Educational Studies in Mathematics, 2017

Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…

Descriptors: Mathematical Logic, Thinking Skills, Undergraduate Students, College Mathematics

Güçler, Beste – Educational Studies in Mathematics, 2016

Despite the existence of extensive literature on functions, fewer studies used sociocultural views to explore the development of student learning about the concept. This study uses a discursive lens to examine whether an instructional approach that specifically attends to particular metalevel rules in the mathematical discourse on functions…

Descriptors: Reflection, Academic Achievement, Mathematics, Mathematics Instruction

Wilkie, Karina J. – Educational Studies in Mathematics, 2016

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

Descriptors: Secondary School Mathematics, Algebra, Thinking Skills, Problem Solving

Kidron, Ivy; Tall, David – Educational Studies in Mathematics, 2015

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

Descriptors: Visualization, Symbols (Mathematics), Graphs, Investigations

Garfield, Joan; Le, Laura; Zieffler, Andrew; Ben-Zvi, Dani – Educational Studies in Mathematics, 2015

This paper describes the importance of developing students' reasoning about samples and sampling variability as a foundation for statistical thinking. Research on expert-novice thinking as well as statistical thinking is reviewed and compared. A case is made that statistical thinking is a type of expert thinking, and as such, research…

Descriptors: Mathematical Logic, Thinking Skills, Statistical Analysis, Cognitive Processes

Yang, Kai-Lin; Hsu, Hui-Yu; Lin, Fou-Lai; Chen, Jian-Cheng; Cheng, Ying-Hao – Educational Studies in Mathematics, 2015

This paper aims to explore the educative power of an experienced mathematics teacher educator-researcher (MTE-R) who displayed his insights and strategies in teacher professional development (TPD) programs. To this end, we propose a framework by first conceptualizing educative power based on three constructs--communication, reasoning, and…

Descriptors: Mathematics Teachers, Teacher Researchers, Faculty Development, Interpersonal Communication

Logan, Tracy; Lowrie, Tom; Diezmann, Carmel M. – Educational Studies in Mathematics, 2014

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged…

Descriptors: Mathematics Activities, Task Analysis, Map Skills, Spatial Ability

Krummheuer, Götz – Educational Studies in Mathematics, 2013

This paper deals with one aspect of the endeavor to generate a theory of the development of mathematical thinking of children in the early years ages 3 to 10. By comparing two scenes, one from preschool and one from a first grade mathematics class, the relationship between diagrammatic and narrative argumentations among children and teachers is…

Descriptors: Mathematics Instruction, Mathematical Logic, Thinking Skills, Young Children

Heng, Mary Anne; Sudarshan, Akhila – Educational Studies in Mathematics, 2013

This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, "Human Development" 52:109-128, 2009) to understand students' mathematical thinking. This study challenged teachers' pedagogical assumptions about what it means to teach for…

Descriptors: Foreign Countries, Mathematics Instruction, Grade 1, Mathematics Teachers