The module Teaching and Learning Mathematics in Diverse Classrooms is intended as a guide to teaching mathematics for in-service teachers in primary schools. It is informed by the inclusive education policy (Education White Paper 6 Special Needs Education, 2001) and supports teachers in dealing with the diversity of learners in South African classrooms.
In order to teach mathematics in South Africa today, teachers need an awareness of where we (the teachers and the learners) have come from as well as where we are going. To help learners, we need to be able to answer a few key questions:
- What is mathematics? What is mathematics learning and teaching in South Africa about today?
- How does mathematical learning take place?
- How can we teach mathematics effectively, particularly in diverse classrooms?
- What is ‘basic’ in mathematics? What is the fundamental mathematical knowledge that all learners need, irrespective of the level of mathematics learning they will ultimately achieve?
- How do we assess mathematics learning most effectively?
These questions are important for all learning and teaching, but particularly for learning and teaching mathematics in diverse classrooms. In terms of the policy on inclusive education, all learners – whatever their barriers to learning or their particular circumstances in life – must learn mathematics.
ACEMaths Units
The units in this module were adapted from a module entitled Learning and Teaching of Intermediate and Senior Mathematics, produced in 2006 as one of the study guide for UNISA’s Advanced Certificate in Education programme.
The module is divided into six units, each of which addresses the above questions, from a different perspective. Although the units can be studied separately, they should be read together to provide comprehensive guidance in answering the above questions.
Unit 1: Exploring what it means to ‘do’ mathematics
This unit gives a historical background to mathematics education in South Africa, to outcomes-based education and to the national curriculum statement for mathematics. The traditional approach to teaching mathematics is then contrasted with an approach to teaching mathematics that focuses on ‘doing’ mathematics, and mathematics as a science of pattern and order, in which learners actively explore mathematical ideas in a conducive classroom environment. The solutions unit consists of the following:
- General points for discussion relating to the teaching of the mathematical content in the activities.
- Step-by-step mathematical solutions to the activities.
- Annotations to the solutions to assist teachers in their understanding the maths as well as teaching issues relating to the mathematical content represented in the activities.
- Suggestions of links to alternative activities for the teaching of the mathematical content represented in the activities.
| Unit One: Exploring What It Means To ‘Do’ Mathematics |  1.40MB |  611KB |
| Solutions Unit One: Exploring What It Means to 'Do' Mathematics |
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Unit 2: Developing understanding in mathematics
In this unit, the theoretical basis for teaching mathematics – constructivism – is explored. Varieties of teaching strategies based on constructivist understandings of how learning best takes place are described. The solutions unit consists of the following:
- General points for discussion relating to the teaching of the mathematical content in the activities.
- Step-by-step mathematical solutions to the activities.
- Annotations to the solutions to assist teachers in their understanding the maths as well as teaching issues relating to the mathematical content represented in the activities.
- Suggestions of links to alternative activities for the teaching of the mathematical content represented in the activities.
1.40MB | 534KB | |
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Unit 3: Teaching through problem solving
In this unit, the shift from the rule-based, teaching by telling approach to a problem-solving approach to mathematics teaching is explained and illustrated with numerous mathematics examples.
1.35MB | 416KB |
Unit 4: Planning in the problem-based classroom
In addition to outlining a step-by-step approach for a problem-based lesson, this unit looks at the role of group work and co-operative learning in the mathematics class, as well as the role of practice in problem-based mathematics classes.
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Unit 5: Building assessment into teaching and learning
This unit explores outcomes-based assessment of mathematics in terms of five main questions – Why assess? (the purposes of assessment); What to assess? (achievement of outcomes, but also understanding, reasoning and problem-solving ability); How to assess? (methods, tools and techniques); How to interpret the results of assessment? (the importance of criteria and rubrics for outcomes-based assessment) ; and How to report on assessment? (developing meaningful report cards). The solutions unit consists of the following:
- General points for discussion relating to the teaching of the mathematical content in the activities.
- Step-by-step mathematical solutions to the activities.
- Annotations to the solutions to assist teachers in their understanding the maths as well as teaching issues relating to the mathematical content represented in the activities.
- Suggestions of links to alternative activities for the teaching of the mathematical content represented in the activities.
1.34MB | 507KB | |
1.12MB | 248KB | |
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Unit 6: Teaching all children mathematics
This unit explores the implications of the fundamental assumption in this module – that ALL children can learn mathematics, whatever their background or language or sex, and regardless of learning disabilities they may have. It gives practical guidance on how teachers can adapt their lessons according to the specific needs of their learners.
1.28MB | 475KB | |
300KB | 138KB | |
10.5MB | 1.00MB |
During the course of this module we engage with the ideas of three teachers - Bobo Diphoko, Jackson Segoe and Millicent Sekesi. Bobo, Jackson and Millicent are all teachers and close neighbours.
- Bobo teaches Senior Phase and Grade 10-12 Mathematics in the former Model C High School in town;
- Jackson is actually an Economics teacher but has been co-opted to teach Intermediate Phase Mathematics and Grade 10-12 Mathematical Literacy at the public Combined High School in the township;
- Millicent is the principal of a small farm-based primary school just outside town. Together with two other teachers, she provides Foundation Phase learning to an average 200 learners a year.
Each unit in the module begins with a conversation between these three teachers that will help you to begin to reflect upon the issues that will be explored further in that unit. This should help you to build the framework on which to peg your new understandings about teaching and learning Mathematics in diverse classrooms.