The goal of this paper is to describe the teaching of initial multiplication concepts and skills, up to the multiplication table, in the Croatian educational system. As Stiegler and Hiebert (1999) concluded, teaching is a complex system rooted in a cultural script of a given society. To describe it without ignoring certain features of it that…

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…

Background: It has been shown that mathematical representations can aid children's understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children's focus of attention and…

South Africa participated in TIMSS from 1995 to 2015. Over these two decades, some positive changes have been reported on the aggregated mathematics performance patterns of South African learners. This paper focuses on the achievement patterns of South Africa's high-performing Grade 9 learners (n = 3378) in comparison with similar subsamples of…

Of the "big four", division is likely to regarded by many learners as "the odd one out", "the difficult one", "the one that is complicated", or "the scary one". It seems to have been that way "for ever", in the perception of many who have trodden the learning pathways through the world of…

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in…

Describes two studies that analyzed the impact of problem type on the understanding of commutativity of multiplication of (n=20) children ages 8-10. The concept seemed poorly understood, but the children did significantly better in the context of rotation than of rearrangement of elements. (Author/MKR)

Examined development of multiplication skills in 8- to 12-year-olds taught by discovery methods. Found a general shift away from less effective strategies across ages 8 to 12, but by 11 years, relatively few used the most effective strategy of retrieval for all operands. Effective strategy development was related to nonverbal reasoning ability and…

Analyzes discussions with teachers (n=26) of Key Stage 2 classes (ages 7-11) during interviews on mathematical tasks based on use of pattern. Finds that pattern was used frequently, but that some teachers had a wider and more sophisticated view of pattern than others. Includes references and an appendix. (CMK)