Many Grade 9 mathematics learners face difficulties in solving number-pattern problems due to insufficient exposure to strategies in solving such problems. The aim of this exploratory qualitative study was to investigate Grade 9 mathematics learners' strategies in solving number-pattern problems. The problem-solving conceptual framework of Singer…

In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses…

The study was designed to probe students' thinking about which numerical values can be assigned to algebraic letters. The data from students in Year 7 (n = 533), Year 8 (n = 377) and Year 9 (n = 172) was analysed using response patterns. The data confirmed that each year contained students with two misconceptions; "Different Letter means…

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

Observation of patterns constructed on geoboards can lead to discussions of properties of primes, number sequences, and complex numbers. (SD)

The origin of the magic square, its numerical concepts, and some procedures for its construction are discussed. (JT)

Activity questions based on the prime factorization of numbers can be answered by reference to the lattice structure of factors. (SD)

Use of graphs in studying greatest common divisors, least common multiples, and other concepts can illustrate patterns related to the definitions of these concepts. (SD)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

An algebraic development of the Fibonnaci sequence, appropriate for use in beginning algebra classes, is presented. (SD)

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)