Title: HOW CAN TEACHING AIDS IMPROVE THE QUALITY OF MATHEMATICS EDUCATION? by Ahmed Afzal
1HOW CAN TEACHING AIDS IMPROVE THE QUALITY OF
MATHEMATICS EDUCATION? by Ahmed Afzal
- Melanie Schmid
- summer term 2006
- Prof. Schlüter Prof. Ludwig
2Introduction
- Afzal The interplay among and connections
between objects, images, language and symbols
that lead to mathematical reasoning and the
stating of mathematical propositions of very wide
generality is well worth closer study.
3Index of contents
- 1. Teaching aids and their use
- 2. Aims of teaching mathematics influence the use
of teaching aids - 3. Characteristics of teaching aids
- 4. Computer as a medium for teaching aids
- 4.1. Examples from a project on linking algebraic
and geometric reasoning - 4.2. Making the power of computer tools
accessible to teachers
41. Teaching aids and their use
- UK teachers tend to look for tools and good
ideas for teaching - ?if they work? repertoire
- ?if not? look for sth. else
5example use of fraction blocks
6result of the example
- Dickson(1984) One of the difficulties with
fractions, decimals and percentages is that they
have a multiplicity of meanings. - ? interpretation
- ? in contrast whole numbers, which are used
mainly either for counting or for measuring
7example triangle? interior angle sum
- draw a triangle
- proof aß?180
- How can we state with a particular triangle such
proof? - ?In this case the triangle really is an idea,
not an object. - ?Papert (1980) object-to-think-with
- many questions? constant research with the active
involvement of teachers
82. Aims of teaching mathematics influence the use
of teaching aids
- Mathematical procedures are taught to all the
school pupils because they will help them in
everyday life as well as in application. - BUT 95 of the population will need less than
5 of the procedures for everyday life or for
applying for sciences, industry and commerce. - ?main task of teaching mathematics not the
contents, but processes e.g. abstractions,
generalisation, logical thinking
93. Characteristics of teaching aids
- Biggs (1972) 5 categories in the process of
discovering mathematics fortuitous, free and
exploratory, guided, directed, programmed - but fortuitous cannot be planned, and
programmed is a directed learning sequence - ?need for material which encourages pupils and
supports their mathematical development
10- Dewey (1966) PLAY as being value at all levels
of development and maturation - 2 goals
short-term goal complete freedom of the solvers
long-term goal solution of the problem
11Characteristics of mathematical tools
- They must allow student-centred activity with the
student in charge of the process. - They utilise students current knowledge.
- They help develop links between students current
mental scheme while they are interacting with the
tools. - They reinforce their current knowledge.
- They assist future problem solving/mathematical
activity through enhancing future access to
knowledge.
12Result
- BUT Tools cannot ensure that a particular
understanding will come about.
134. Computer as a medium for teaching aids
- The computer is able to provide connections
between aspects of mathematics and experiences
planted in everyday life. - We have to find ways to exploit these linkings
for using them in school.
144.1. Examples from a project on linking algebraic
and geometric reasoning
- Examples from a current project for the UKs
Qualifications and Curriculum Authority (QCA) - Linking algebraic and geometric reasoning with
dynamic geometry software - Possibility to bring images from the outside
world into the mathematics classroom
15Using geometric software
Picture of the roof structure of Stockport
railway station, near Manchester
16Possible tasks
- explore geometric ideas of perspective by
drawing lines joining corresponding points - explore numerical ideas of perspective by taking
measurememts from the image
17(No Transcript)
18(No Transcript)
19Possible tasks
- find out the height of the fountain
- ?afterwards compare the results with the actual
height (use the Internet) - velocity with which the water leaves the dragons
mouth - angle at which the water enters the harbour
20- Quadratic function f(x) ax2
- utilities to vary a
21Result
- Thats an example where we have the technology,
but not yet a clear body of what we would call
best-practice in its educational use. - seldom and rare use in the classroom
224.2. Making the power of computer tools
accessible to teachers
- UK between 1999 and 2003 320,000,000 for
additional training for school teachers - of course they (teachers) know the general
advantages, but remain unaware of the potential
of specific software and tools - two questions? How do the technological tools
enhance the teaching and learning process?? How
do teachers perceive the technology in relation
to the mathematics that is being learned?
23Professional development of activities for
teachers
- two linear functions y1(x) and y2(x)
- Teachers are asked to predict what the resulting
graph of y1(x)y2(x) might look like.
24Results
- Most teachers knew the result, but other said
that they had never approached the teaching of
quadratic functions in this way with their
pupils. - Laborde (2001) The role played by technology
moved from being a useful amplifier towards being
an essential constituent of the meaning of
tasks. - Papert (1980) We are learning how to make
computers with which children love to
communicate. When this communication occurs,
children learn mathematics as a living language.
255. Final remarks
- Afzal How materials are used is the most
important factor, since teachers can use good
materials well, good materials badly, bad
materials well and bad materials badly. - ?dependence on the classroom tasks, role of the
teacher and the climate and atmosphere of the
classroom
26Thanks for your attention!