Learning and Teaching Mathematics - latest Issue
Volume 2016, Issue 20, 2016
Source: Learning and Teaching Mathematics 2016 (2016)More Less
We hope you enjoy the wonderfully diverse array of articles in this issue, and remind you that we are always eager to receive submissions. Suggestions to authors, as well as a breakdown of the different types of article you could consider, can be found at the end of this journal.
Author Debbie StottSource: Learning and Teaching Mathematics 2016, pp 3 –6 (2016)More Less
Research has shown that arrays are a useful tool for developing learners' conceptual understanding of multiplication and division across both the Foundation and Intermediate phases. Because arrays lend themselves to multiplicative understanding rather than additive understanding, they are a useful way of 'unitising' - i.e. seeing items in groups rather than as individual items. They are an important conceptual step between modelling multiplication with physical objects and using more algorithmic methods. Arrays also provide a way to make close connections between multiplication and division.
Author Ronit Bassan-CincinatusSource: Learning and Teaching Mathematics 2016, pp 7 –9 (2016)More Less
Fostering creativity in our pupils is essential if they are to successfully engage with the dynamic and rapidly changing world around us. Working with shape and space is one area of the curriculum where one can potentially encourage creative thinking through more open-ended activities and investigations. In junior grades, one of the goals of working with space and shape is the fostering of geometrical insight through the exploration of shapes, their properties and interrelations. In addition to fundamental properties such as area and perimeter, pupils should develop their visual and spatial perception skills in order to make the transition from basic to more complex shapes.
Author Laura De LangeSource: Learning and Teaching Mathematics 2016, pp 10 –13 (2016)More Less
The Curriculum and Assessment Policy Statement (CAPS) describes Mathematics as:
...a language that makes use of symbols and notations for describing numerical, geometric and graphical relationships. It is a human activity that involves observing, representing and investigating patterns and qualitative relationships in physical and social phenomena and between mathematical objects themselves. It helps to develop mental processes that enhance logical and critical thinking, accuracy and problem solving that will contribute in decision-making. (Department of Basic Education, 2011, p. 8)
The above description is multi-faceted, incorporating notions of Mathematics as a language of symbols; a human activity involving processes such as investigation and generalisation; a means of describing the physical and social world in which we find ourselves; a deductive system of abstraction; and a means of improving broader decision-making processes. The above description incorporates ideas from a variety of different philosophies of mathematics. However, as a teacher, what is your own philosophy of mathematics?
Author Nicholas KroonSource: Learning and Teaching Mathematics 2016, pp 14 –15 (2016)More Less
A few years ago, when learning about 3-dimensional shapes, my Grade 9 Maths class was tasked with building containers to hold four ping pong balls of radius 2 cm so that the four balls fitted snugly inside the container. The simplest and most popular ways of doing this were to construct cuboids or cylinders with the correct dimensions. If you were ambitious you could try other shapes, such as a triangular prism, but whatever shape you chose it was important for the dimensions to be mathematically accurate. Calculating the dimensions of these shapes is well within the means of a competent Grade 9 learner.
Author Michael De VilliersSource: Learning and Teaching Mathematics 2016, pp 18 –20 (2016)More Less
Exploring and engaging with multiple solution tasks (MSTs), where students are given rich mathematical tasks and encouraged to find multiple solutions (or proofs), has been an interesting and productive trend in problem solving research in recent years. A longitudinal comparative study by Levav-Waynberg and Leikin (2012) suggests that an MST approach in the classroom provides a greater educational opportunity for potentially creative students when compared with a conventional learning environment.
Author Andrew MaffessantiSource: Learning and Teaching Mathematics 2016, pp 21 –22 (2016)More Less
One of the many joys of teaching is seeing how different pupils tackle problems in different, and often unexpected, ways. In formal assessments this of course makes the marking process a little more complex as one needs to be vigilant about properly engaging with unexpected responses - particularly if the solution provided by the pupil is different to the marking guidelines. When pupils approach questions in unexpected ways we have a duty to be open-minded and to take the time necessary to properly explore and attempt to understand the reasoning behind the solution provided. In this article I share a recent episode that illustrates how engaging with the unexpected can lead to opportunities for deep learning.
Author Alan ChristisonSource: Learning and Teaching Mathematics 2016, pp 27 –29 (2016)More Less
Author Marcus BizonySource: Learning and Teaching Mathematics 2016, pp 30 –34 (2016)More Less
One of the difficulties in finding suitable investigations for secondary school pupils is that interesting scenarios are likely to be too difficult, while those that are manageable are potentially uninteresting. More than that, in order to know whether a particular scenario is suitable, one must have worked through it oneself. Having done so, the temptation is then to scaffold the investigation process so as to lead students to the conclusions one found oneself - thereby eliminating the 'open-ended' nature of a proper investigative approach.
Author Yiu-Kwong ManSource: Learning and Teaching Mathematics 2016, pp 35 –37 (2016)More Less
Source: Learning and Teaching Mathematics 2016, pp 38 –42 (2016)More Less
The world of mathematics is constantly evolving. However, the mathematics included in school curricula seldom reflects this evolving nature of the discipline. Appreciating the importance of exposing students to contemporary mathematics, we identified fractal geometry as a topic that could meaningfully be integrated into the regular curriculum. In this article we briefly introduce the idea of fractals and demonstrate how they can be integrated into the teaching of infinite geometric series.