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 Volume 2008, Issue 6, 2008
Learning and Teaching Mathematics  Volume 2008, Issue 6, June 2008
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Volume 2008, Issue 6, June 2008

From the editors
Authors: Mellony Graven and Marcus BizonySource: Learning and Teaching Mathematics 2008 (2008)More LessThis edition is full of interesting articles with inspiring ideas for implementation in the classroom.

Talking geometry : a classroom episode
Author Erna LampenSource: Learning and Teaching Mathematics 2008, pp 3 –8 (2008)More LessThe course is based on geometric constructions and the students were very comfortable with the basic compass constructions by the time this episode happened. In addition, the students had been introduced to The Geometer's Sketchpad early in the course and they used the programme to investigate their conjectures in an informal way outside class time.

Approaches to generalising quadratic sequences
Author Duncan SamsonSource: Learning and Teaching Mathematics 2008, pp 9 –15 (2008)More LessThe study of pattern has become an integral component across all Grades of the South African school Mathematics curriculum (Department of Education, 2002; Department of Education, 2003b). In the Intermediate Phase (Grades 46) the importance of number pattern activities is in "laying the foundation for the study of formal algebra in the Senior Phase while at the same time developing important mathematical thinking skills" (Department of Education, 2003a:37).

Should we expect certainty from probability classroom experiments?
Author Mercy KazimaSource: Learning and Teaching Mathematics 2008, pp 16 –19 (2008)More LessI have had the opportunity and privilege of observing probability lessons in one township school in South Africa and in some schools in Malawi. In all cases I observed similar activities taking place where their teacher asked learners for example to toss coins or throw dice and record the outcomes. I will discuss two examples of activities that I observed; one in Malawi and the other in South Africa.

What is the South African Mathematics Foundation?
Author Lynn BowieSource: Learning and Teaching Mathematics 2008 (2008)More LessThe professional mathematics community in South Africa is represented by the South African Mathematical Society (SAMS) and the Association for Mathematics Education in South Africa (AMESA). The South African Mathematics Foundation (SAMF) was formed to assist in the areas of common interest to both SAMS and AMESA. So SAMF serves as a national office to promote the effective coordination, administration and advancement of mathematics in South Africa.

Photographs as inspiration for mathematical activity : Sproule, Stephen
Author Stephen SprouleSource: Learning and Teaching Mathematics 2008, pp 21 –22 (2008)More LessPhotographs as inspiration for mathematical activity

Computers for experiments in the classroom
Author Marcus BizonySource: Learning and Teaching Mathematics 2008, pp 23 –24 (2008)More LessSome years ago I decided to have some pupils (they weren't learners in those days) experiment with rightangled triangles, hoping that Pythagoras' Theorem would appear. So 24 kids drew rightangled triangles fairly carefully, measured fairly carefully, squared, added and ... . not one of them found that the property described by Pythagoras was apparent in their triangle.

Getting the most out of your keyboard a compilation of tips from various people
Source: Learning and Teaching Mathematics 2008, pp 25 –27 (2008)More LessEverything that can be done with a mouse can be done by keystrokes. In Excel, for instance, one very often wants to Paste Values rather than simply copy cells: CtrlV does the full copy, which carries over formulae, formatting and everything, but if you want merely to copy the results of the formulae then the standard approach is to highlight your cells, type CtrlC, go to the destination, then use the mouse to click Edit / Paste Special / Values. But for this last stage you could simply have typed AltE S V (so you press the E while you are pressing Alt). This can save a lot of time since it means you do not have to reach for the mouse and then manoeuvre it.

Web review
Author Marcus BizonySource: Learning and Teaching Mathematics 2008 (2008)More LessMany of the mathematical discussions are supported by applets. At the site you can enter the CTK Exchange, which is where people post their queries, and you can read the conversation as it builds up. The Exchange is divided into sections according to the level of maths (e.g. Early Maths, Middle School, High School and so on) and when you go into one of these you see various queries that have been submitted as well as the number of replies that they generated: so you know immediately which are the contentious ones.

The great Mugg & Bean mystery
Author Marc NorthSource: Learning and Teaching Mathematics 2008, pp 29 –35 (2008)More LessIn discussions with Mathematical Literacy teachers, there is a great deal of difference of opinion in how we should be teaching Mathematical Literacy and what we should be focussing on in our teaching. Some teachers argue that exploring reallife contexts are the most important aspect of the subject. Others argue that the mathematical content of the subject is primary. Still others argue that a balanced focus on context and content is important (Graven and Venekat).

A useful failure
Author Marcus BizonySource: Learning and Teaching Mathematics 2008 (2008)More LessI have always enjoyed the theorem that says the bisector of an angle of a triangle divides the opposite side in the ratio of the sides forming the angle. One day I decided to play with the converse idea: how might the bisector of a side from a vertex (in other words a median) divide the angle it runs through?

Senior certificate examinations for mathematical literacy : findings from a small study
Authors: Hamsa Venkat and Mvelo PhungulaSource: Learning and Teaching Mathematics 2008, pp 37 –39 (2008)More LessGuidelines have been issued for the structure of ML Senior Certificate examinations (DoE, 2007). Textbooks and exemplar papers interpreting these guidelines (often in slightly different ways) are also available. In this article, we share findings from an Honours research project  designed by the two authors with data collected by the second author in 2007 in the area of ML assessment. The formulation of this project followed discussion about the structure of ML summative assessment as detailed in the Subject Assessment Guidelines (DoE, 2007). This document states that ML will be assessed by two examination papers, each 2½ hours long. Unlike the situation in Mathematics, these two papers are not split by content area but by complexity. Complexity in ML is outlined in terms of the following taxonomy :

Pick's theorem : tasks, expectations and outcomes
Authors: Beverly S. Rich and Sherry L. MeierSource: Learning and Teaching Mathematics 2008, pp 40 –46 (2008)More LessSchroeder and Lester (1989) referred to this as ''teaching for problem solving''. An alternative instructional approach could more aptly be described as ''teaching via problem solving'', where the problems are carefully constructed to highlight an advance mathematical concepts already discussed.

Turning myself around  experiences of teaching mathematical literacy
Author Cylia ZengelaSource: Learning and Teaching Mathematics 2008, pp 47 –48 (2008)More LessI currently teach Mathematical Literacy at a school in southern Johannesburg. I started teaching the new subject in grade 10 in 2006 when it was first introduced, and have followed my group through into grades 11 and 12.

Proof without words
Author Sanjay K. KhattriSource: Learning and Teaching Mathematics 2008 (2008)More LessProof without words