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Jungic, Veselin; Yan, Xiaoheng – For the Learning of Mathematics, 2020

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

Descriptors: Number Concepts, Mathematics Instruction, Cognitive Processes, Numbers

Thouless, Helen; Gifford, Sue – For the Learning of Mathematics, 2019

In this article we compare two frameworks for analysing young children's responses to the task of copying and extending a 6-dot triangle pattern. We used Mulligan & Mitchelmore's Awareness of Mathematical Pattern and Structure (AMPS) and then Biggs & Collis' SOLO taxonomy, both of which provide criteria for assigning levels. In comparison…

Descriptors: Preschool Children, Pattern Recognition, Geometric Concepts, Disadvantaged Youth

Oktaç, Asuman; Trigueros, María; Romo, Avenilde – For the Learning of Mathematics, 2019

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Descriptors: Mathematics Instruction, Learning Theories, Knowledge Level, Constructivism (Learning)

Ejersbo, Lisser Rye; Leron, Uri; Arcavi, Abraham – For the Learning of Mathematics, 2014

The observation that the human mind operates in two distinct thinking modes--intuitive and analytical- have occupied psychological and educational researchers for several decades now. Much of this research has focused on the explanatory power of intuitive thinking as source of errors and misconceptions, but in this article, in contrast, we view…

Descriptors: Intuition, Cognitive Processes, Mathematics Instruction, Workshops

Papademetri-Kachrimani, Chrystalla – For the Learning of Mathematics, 2012

In this paper I argue my opposition to the consensus which has dominated the literature that young children view shapes as a whole and pay no attention to shape structure and that geometrical thinking can be described through a hierarchical model formed by levels. This consensus is linked to van Hiele's weok by van Hiele-based research. In the…

Descriptors: Young Children, Geometric Concepts, Cognitive Processes, Mathematics Education

Abrahamson, Dor – For the Learning of Mathematics, 2012

Motivated by the question, "What exactly about a mathematical concept should students discover, when they study it via discovery learning?", I present and demonstrate an interpretation of discovery pedagogy that attempts to address its criticism. My approach hinges on decoupling the solution process from its resultant product. Whereas theories of…

Descriptors: Learning Theories, Discovery Learning, Mathematical Concepts, Teaching Methods

Tillema, Erik; Hackenberg, Amy – For the Learning of Mathematics, 2011

In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in…

Descriptors: Educational Research, Experiments, Mathematics, Learning

Maheux, Jean-Francois; Roth, Wolff-Michael – For the Learning of Mathematics, 2011

Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

Descriptors: Mathematics Instruction, Geometry, Learning, Critical Thinking

Foster, Colin – For the Learning of Mathematics, 2011

In this paper I take a positive view of ambiguity in the learning of mathematics. Following Grosholz (2007), I argue that it is not only the arts which exploit ambiguity for creative ends but science and mathematics too. By enabling the juxtaposition of multiple conflicting frames of reference, ambiguity allows novel connections to be made. I…

Descriptors: Mathematics Education, Figurative Language, Scientific Concepts, Mathematics Instruction

Gascon, Josep – For the Learning of Mathematics, 2003

In the International Commission on Mathematical Instruction (ICMI) study, "Mathematics Education as a Research Domain: A Search for Identity" (Sierpinska and Kilpatrick, 1998), an eclectic point of view is adopted in terms of both the object of study in mathematics education and the objectives of research, the types of problems that it…

Descriptors: Mathematics Education, Intellectual Disciplines, Research Methodology, Educational Research

Peer reviewed

Hasegawa, Junichi – For the Learning of Mathematics, 2002

Discusses a class on subtraction or difference-finding, problems such as "There are eight white flowers and five red flowers, how many more white flowers are there than red flowers?" used in the teaching of Japanese first grade children. Describes three instances of introductory teaching of "difference-finding" problems in the…

Descriptors: Arithmetic, Cognitive Processes, Concept Formation, Elementary Education

Peer reviewed

Smith, John P., III; Hungwe, Kedmon – For the Learning of Mathematics, 1998

Explores the mathematical practices of three young mathematicians in an extended interview setting. Focuses on the interaction of discovery and verification, the role of conjecture in discovery, and the place of intuition and understanding in research. Indicates an interesting mismatch between how they valued their own guesses and how they reacted…

Descriptors: Cognitive Processes, Discovery Processes, Elementary Secondary Education, Learning Strategies

Peer reviewed

Villarreal, Monica – For the Learning of Mathematics, 2000

Presents a study to describe and understand the thinking processes of students in a computer environment while undertaking mathematical tasks related to the differentiation of functions defined on real numbers. Describes two different approaches, the visual and the algebraic approach, in the thinking processes of calculus students. (Contains 19…

Descriptors: Calculus, Cognitive Processes, Computer Uses in Education, Differential Equations

Peer reviewed

Cruz, Ines; Febles, Maria; Diaz, Jose – For the Learning of Mathematics, 2000

Presents a case study that aimed to obtain information on students' mathematical comprehension levels and on whether students may or may not make use of visualization processes in solving mathematical problems. Discovers students' beliefs about teaching and learning processes in general, and mathematics in particular. (Contains 25 references.)…

Descriptors: Cognitive Processes, Elementary Secondary Education, Mathematics Education, Spatial Ability

Peer reviewed

Van Den Heuvel-Panhuizen, Marja; And Others – For the Learning of Mathematics, 1995

Reports on the knowledge of fifth-grade students about what they are learning about percentage. Reveals the range of comfort students had in the instructional sequence and provides suggestions for developing assessment tasks, especially student-generated problems. An appendix of sample tasks is included. (MKR)

Descriptors: Cognitive Processes, Elementary School Students, Grade 5, Intermediate Grades