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Mahlaba, Sfiso Cebolenkosi – For the Learning of Mathematics, 2020

Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to…

Descriptors: Geometry, Logical Thinking, Mathematical Logic, Validity

Palatnik, Alik; Koichu, Boris – For the Learning of Mathematics, 2019

This study aims to explore a phenomenon of a one-off manifestation of mathematical creativity on the part of a student, against the background of her normative and not especially creative behavior--a flash of creativity. We seek to elaborate on this phenomenon in terms of the 4P (person, press, process and product) model of creativity. Namely,…

Descriptors: Creativity, Mathematics Instruction, Models, Personality Traits

Tillema, Erik; Gatza, Andrew – For the Learning of Mathematics, 2016

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…

Descriptors: Mathematics Instruction, Multiplication, Mathematics Skills, Thinking Skills

Ulrich, Catherine – For the Learning of Mathematics, 2016

This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite…

Descriptors: Young Children, High School Students, Arithmetic, Algebra

Palatnik, Alik; Koichu, Boris – For the Learning of Mathematics, 2015

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A threeweek long solution process by a pair of ninth-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

Descriptors: Attention, Grade 9, Attention Control, Educational Theories

Ulrich, Catherine – For the Learning of Mathematics, 2015

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Descriptors: Mathematics Education, Secondary School Mathematics, High School Students, Constructivism (Learning)

Hansraj, Sudan – For the Learning of Mathematics, 2010

I argue for the inclusion of topics in high school mathematics curricula that are traditionally reserved for high achieving students preparing for mathematical contests. These include the arithmetic mean--geometric mean inequality which has many practical applications in mathematical modelling. The problem of extremalising functions of more than…

Descriptors: Secondary School Mathematics, Calculus, Arithmetic, Geometry

Bokhove, Christian; Drijvers, Paul – For the Learning of Mathematics, 2010

The algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite…

Descriptors: Mathematics Education, Algebra, Symbols (Mathematics), Student Behavior

Karp, Alexander – For the Learning of Mathematics, 2004

Research conducted during the Trends in International Mathematics and Science Study (TIMSS) and later (Stigler et al. 1999; Stigler and Hiebert 1999) undertook a thorough analysis of lessons in the United States, Japan, and Germany. This article focuses on certain aspects of mathematics lessons in Russia. Specifically, the attempt is made to…

Descriptors: Foreign Countries, Mathematics Instruction, Lesson Plans, Teaching Methods

Hannula, Markku S. – For the Learning of Mathematics, 2003

Understanding and reporting students' affective experiences with mathematics is difficult if those experiences do not resonate with personal experiences. Utilising fiction-writing in narrative reporting can be a technique that helps both the researcher and the reader of the research report to immerse themselves in the student's experiential world.…

Descriptors: Fiction, Learning Experience, Student Experience, Student Centered Curriculum

Castro, Fernando – For the Learning of Mathematics, 2003

The author shares a story of how Luis González, an iron artisan, helped the author build a wooden and iron toy truck. The knowledge required to build the skeleton for the parallelepiped in the construction of the truck is not in the mathematical high school curriculum in Venezuela. Although Luis never received a degree beyond high school,…

Descriptors: Metallurgy, Geometry, Geometric Concepts, Mathematics Skills