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Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him – International Journal of Mathematical Education in Science and Technology, 2014

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

Descriptors: Problem Solving, Number Concepts, Numbers, Teaching Methods

Kimani, Patrick M.; Olanoff, Dana; Masingila, Joanna O. – Mathematics Teaching in the Middle School, 2016

This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…

Descriptors: Problem Solving, Mathematics Instruction, Mathematics Activities, Task Analysis

Pathak, H. K. – International Journal of Mathematical Education in Science and Technology, 2008

In this article, we shall discuss some interesting, viable, meaningful, applicable and productive conjectures and methods to deal with some fundamental results in the theory of numbers.

Descriptors: Number Concepts, Theories, Mathematical Logic, Validity

Papadopoulos, Ioannis; Iatridou, Maria – Mathematics Education Research Journal, 2010

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

Descriptors: Number Concepts, Grade 10, Problem Solving, Geometric Concepts

Gauthier, N. – International Journal of Mathematical Education in Science and Technology, 2011

Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…

Descriptors: Introductory Courses, Numbers, Number Concepts, Calculus

Bair, Sherry L.; Rich, Beverly S. – Mathematical Thinking and Learning: An International Journal, 2011

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

Descriptors: Grounded Theory, Mathematics Education, Teacher Education Programs, Data Analysis

Aabrandt, Andreas; Hansen, Vagn Lundsgaard – International Journal of Mathematical Education in Science and Technology, 2016

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…

Descriptors: Mathematical Formulas, Algebra, Mathematical Applications, Equations (Mathematics)

Ernst, Dana C.; Hodge, Angie; Schultz, Andrew – PRIMUS, 2015

In the Spring of 2011, two of the authors of this paper taught number theory courses at their respective institutions. Twice during the semester, students in each class submitted proofs of two to three theorems to be peer reviewed by students in the other class. Each student wrote anonymous and formal referee reports of the submitted theorems,…

Descriptors: Mathematics Instruction, College Mathematics, Mathematical Logic, Validity

Bossé, Michael J.; Bayaga, Anass; Fountain, Catherine; Young, Erica Slate; DeMarte, Ashley – International Electronic Journal of Elementary Education, 2019

Previous theoretical research has revealed conceptual similarities among a number of mathematical learning theories and theories regarding language acquisition. This intersection of ideas led to a novel framework defining four stages of mathematical learning: Receiving, Replicating, Negotiating Meaning, and Producing. Through qualitative research…

Descriptors: Mathematics Instruction, Teaching Methods, Language Acquisition, Mathematics Skills

Teker, Gülsen Tasdelen; Güler, Nese – International Journal of Assessment Tools in Education, 2019

One of the important theories in education and psychology is Generalizability (G) Theory and various properties distinguish it from the other measurement theories. To better understand methodological trends of G theory, a thematic content analysis was conducted. This study analyzes the studies using generalizability theory in the field of…

Descriptors: Generalizability Theory, Content Analysis, Foreign Countries, Education

Firozzaman, Firoz; Firoz, Fahim – International Journal of Mathematical Education in Science and Technology, 2017

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…

Descriptors: Mathematics Instruction, Numbers, Mathematical Concepts, Equations (Mathematics)

Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2012

It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

Descriptors: Introductory Courses, Number Concepts, Numbers, Algebra

Watkins, John J. – College Mathematics Journal, 2012

Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…

Descriptors: Number Concepts, Numbers, Puzzles, College Mathematics

Holbrook, Robert L., Jr.; Chappell, David – Management Teaching Review, 2019

Motivation is a fundamental component in management and organizational behavior courses. At the same time, it can be a complicated topic for teaching and learning due to the number of popular models and theories. The activity described here is a simple and fast way to illustrate the components of two of the most important and practical motivation…

Descriptors: Motivation, Theories, Administrator Education, Class Activities

Srinivasan, V. K. – International Journal of Mathematical Education in Science and Technology, 2013

Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…

Descriptors: Mathematics Instruction, Mathematical Concepts, Geometric Concepts, Numbers