The Aims of Teaching Mathematics

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The Aims of Teaching Mathematics
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Questions for discussions

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Reasons for constantly Review of Educational Aims

• What we see taking place in our classrooms does
  not always, on careful reflection, seem
  justifiable.
• Pupils do express concern about the end-points of
  their current studies
• situations and circumstances do change, new
  content and new teaching methods are proposed.

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Examples that require justification

• The use of calculators
• fractions
• IT

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Primary and Secondary Aims

• Primary aims we have to have reasons for
  including mathematics in the school curriculum.
• Secondary aims
• so that the content and methods can be decided.
• Important general aims of education which can be
  pursued within mathematics

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Example of Aims HMI (1985)

• Mathematics as an essential element of
  communication
• mathematics as a powerful tool
• appreciation of relationships with mathematics
• awareness of the fascination of mathematics
• imagination, initiative and flexibility of mind
  in mathematics
• working in a systematic way
• working independently
• working cooperatively
• in-depth study in mathematics
• pupils confidence in their mathematical
  abilities

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The Aims of Education

• Spens (1938), any educational aims which are
  concrete enough to give definite guidance are
  correlative to ideals of life
• NCTM(1989), the goals all school try to achieve
  are both a reflection of the needs of society and
  the needs of students
• Warnock (1978), The goals are first, to
  enlarge a childs knowledge, experience and
  imaginative understanding, and thus his awareness
  of moral values and capacity for enjoyment and
  secondly, to enable him to enter the world after
  formal education is over as an active
  participants in society and a responsible
  contributor to it, capable of achieving as much
  independence as possible.

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HMI (1985)

• To help pupils to develop lively, enquiring
  minds, the ability to question and argue
  rationally and to apply themselves to tasks, and
  physical skills
• to help pupils to acquire knowledge and skills
  relevant to adult life and employment in a fast
  changing world
• to help pupils to use language and number
  effectively
• to instil respect for religious and moral values,
  and tolerance of other races, religions and ways
  of life
• to help pupils to understand the world in which
  they live, and the interdependence of
  individuals, groups and nations
• to help pupils to appreciate human achievements
  and aspirations.

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Malaysia (Curriculum Development Centre, 1975)

• To nurture a balanced development in each
  individual by providing for the growth of
  physical, intellectual, emotional, moral and
  aesthetic potentials as a Malaysian upholding the
  tanets of Rukunegara National Principles
• to assist the individual to obtain greater
  insights and understanding into our eco-logical
  and cultural heritage, social institutions,
  values and practices, societal pressures and
  chalenges, to enable the individual to function
  and fulfil his commitments and responsibilities
  as a citizen

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• To develop the human resources of the nation by
  assisting the individual to be a skilled,
  competent, rational and responsive planner,
  producer and consumer, to enable him to improve
  his personal well-being and contribute to the
  progress and development of the nation
• to develop in the individual understanding and
  acceptance of the democratic ideas and ideals
  under the Constitution, loyalty to the King,
  patriotism to the nation, awareness of the rights
  and responsibilities as a citizen in a democracy
  and commitment to exercise these rights and
  responsibilities.

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• To develop in the individual positive attitude
  towards scientific enquiry and technical
  processes and progress, self-reliance, desire and
  capability for life-long education to enable him
  to initiate and adapt to changes compatible with
  the cultural and ethnical values and aspirations
  of the nation

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The Nature of Mathematics

• The study of number, form, arrangement and
  associated relationships using clearly defined
  literal, numerical and operational symbols
• science of space and number
• mathematics is what mathematicians do
• pure mathematics may be defined as the subject in
  which we never know what we are talking about,
  nor whether what we are saying is true

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• Mathematics as an expression of the human mind
  reflects the active will, the contemplative
  reason, and the desire for aesthetic perfection.
  Its basic elements are logic and intuition,
  analysis and construction, generality and
  individuality.

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Reasons for teaching mathematics (Smith, 1928)

• Every educated persons should know what
  mathematics means to society and to our race,
  what its greatest uses are
• it has high value as a mental discipline
• it has intrinsic interest and value of its own -
  it has its own beauty and magic
• it possesses truth which, in an ever changing
  world, is eternal and enduring
• it came into being through the yearning to solve
  the mysteries of the universe and still works for
  us in that way
• the history of mathematics is the history of the
  human race.

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The Cockcroft Report (1982)
Emphasis on usefulness

• Of enabling each pupil to develop the
  mathematical skills and understanding required
  for adult life, for employment and for further
  study and training
• of providing each pupil with such mathematics as
  may be needed for his study of other subjects
• of helping each pupil to develop .. Appreciation
  and enjoyment of mathematics itself and .. Of the
  role which it has played and will continue to
  play both in the development of science and
  technology and of our civilization
• above all, of making each pupil aware that
  mathematics provides him with a powerful means of
  communication

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NCTM (1989)

• Society goals mathematically literate workers,
  lifelong learning, opportunity for all, an
  informed electorate
• goals for students learn to value mathematics,
  become confident in their ability to do
  mathematics, become mathematics problem solvers,
  learn to communicate mathematically, learn to
  reason mathematically

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Five areas selected

• Mathematics is useful
• mathematics is important in our lives and its
  place needs to be understood
• mathematics trains the mind
• mathematics is a powerful means of communication
• mathematics is enjoyable and has aesthetic value.

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Utilitarian Aims

• Practical arithmetic skills needed in everyday
  life?
• Mathematically literate workers?
• Set up problems variety of techniques to
  approach and work on problems understanding the
  underlying mathematical features of a problem .
• Two faces
• foundations for subsequent more advanced study of
  mathmatics
• tools for other subject

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Importance of Mathematics in the World

• Mathematics is vital to the maintenance of
  satisfactory living standards
• in order to make an informed decision about
  continued study

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Mathematics trains the Mind

• Strengthening the powers of reasoning or in
  inducing a general accuracy of mind
• in brain development
• in producing logical way of thinking
• blind belief in the value of mathematics as a
  mental discipline is dangerous (Godfrey, 1931)

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Importance of Mathematics as a Language

• Mathematics is a unique universal language which
  transcends social, cultural and linguistic
  barriers, having symbols and syntax that are
  accepted the world over.

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The Importance of Deeper Appreciation

• Mathematics can provide pleasure and enjoyment,
  but most students do not see it this way.