ED455: Advanced Curriculum

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• ED455 Advanced Curriculum
• INDIGENISING THE MATHEMATICS CURRICULUM
• What will it look like?

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• Statement 1
• The perceptions of the nature and role of
  mathematics held by our society have a major
  influence on the development of school
  mathematics curriculum, instruction and research
  
• (Dossey, 1992 39)

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• Statement 2
• the mathematical activities in the culture of
  the child should be seen as the principal entries
  to (school) mathematics. These function as a
  means to handle the world in each culture, they
  should be the cornerstone of mathematics
  education in schools. A net result of such a
  position is that curricula should be specific
  to the cultural group.
• (Bishop, 1988 p 2)

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• Changing Views of Mathematics
• ? an abstract science
• ? a body of knowledge a subject about
  numbers operations, computations manipulation
  of formulae and rules
• ? a powerful system for understanding the
  world
• ? a social or cultural construct

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View 1 of Mathematicsformalist view

• Mathematics is absolute, consisting of
  immutable truths and unquestionable certainty
  without a human face
• (Lakatos, 1976)
• Mathematics is universal knowledge

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View 1 Resultant Mathematics Curriculum

• 1. Homogenous curriculum one size fits all
• 2. Universal mathematics curriculum is a
  particular conception - of Western beliefs
  values
• 3. Culturally blind curriculum (Bishop, 1994).
  
• 4. Causes cultural conflicts.

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View 2 of Mathematicssocially mediated view

• Mathematics a cultural product, with a cultural
  history and created by humans in socially
  interactive situations (Keitel et al, 1989).
• Mathematics is a way of knowing a cultural
  product (Bishop, 1988) a lens through which
  people see the world (Barton, 19932).

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Implications of this view

• the different uses of mathematics in various
  cultures can be decisive as to whether the
  members of one culture learn the mathematics of a
  curriculum or not. Such a position implies that,
  as educationists, we not only have to include the
  cultural aspects when developing a curriculum, we
  also have to realise the impact of possible
  conflicts between the various cultures to which
  the pupils relate.
• (Mellin-Olsen, 1987 15-16)

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What is Mellin-Ollsen saying?

• ? There are math ideas in peoples cultures that
  makes sense to the people
• ? These math ideas must feature in the
  mathematics of the school curriculum
• ? If cultural ideas do not feature in maths
  curriculum, it will affect how students from that
  culture learn understand maths
• ? Be conscious of possible conflicts

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View 2 Resultant Curriculum

• 1. Heterogenous/multicultural curricula
• Allows for expression inclusion of ideas and
  examples from the mathematical traditions of all
  student groups.
• 2. Culturally-responsive curricula
  
• Inclusion of cultural ways of knowing
  language as well as culturally responsive
  teaching.

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Culturally responsive Curriculum

• Ethnomathematics - any form of cultural
  knowledge or social activity of particular groups
  that can be recognized by other groups as
  mathematical (Pompeu, 1994 3)
• 2. Culturally-responsive teaching
• - teachers as cultural bridge
• - flexibility sensitivity
• - bilingualism

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CURRICULUM

• includes the educational experiences that are
  planned to take place in a classroom as well as
  the practical application of the planning in the
  classroom (McGee, 2001)
• Intended curriculum learning and teaching
  plans
• (ii) Operational curriculum activities that
  actually happen in the classroom under the
  leadership of a teacher.

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INTENDED CURRICULUM

• includes the learning and teaching plans
  (Eisner, 1994)
• planned at the national, provincial or local
  levels by curriculum committees and consultants,
  and as codified in curriculum guides (Robitaille
  Dirks, 1982 17)

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IMPLEMENTED/OPERATIONAL CURRICULUM

• those activities that actually happen in the
• classroom under the leadership of a teacher
  (McGee, 2001 87)
• curriculum as contained in the various texts and
  materials which are selected and approved for use
  in the schools and as communicated to students by
  teachers in their classrooms (Robitaille
  Dirks, 1982 17)

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Where does indigenising the curriculum happen?

• Intended Curriculum Level
• 1. Historically difficult at this level
  guarded by mathematicians
• 2. Change must be made at thist level because
  only then can it affect examinations
• 3. National examinations assessments must
  treat cultural issues seriously
• 4. Learning Outcomes must address cultural
  issues and systems
• 5. History of mathematics important component
  

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Where does indigenising the curriculum happen?

• Implemented/Operational Curriculum Level
• (schools teachers have freedom to select
  materials)
• 1. Teachers role is critical
• teachers shape the learning of their students
  through the selection they make, the emphases
  they place, and their delivery of the range of
  topics included in the intended curriculum
  (Leder Forgasz, 1992 17)
• a new curriculum is only as good as the
  teachers who implement it because the quality of
  interaction between teacher and pupil is a
  critical factor in the latters ability to
  achieve in school
• (Thaman, 1997 p. 14)

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• 2. What resources are available? What texts are
  being used?
• 3. Teachers must be resourceful, must create own
  materials for culturally responsive teaching
• 4. Culturally responsive teaching
• - use variety of materials activities
• - be aware of and celebrate difference
• - allow students to share ideas traditions in
  projects etc
• - introduce historical references where possible
  e.g. fishermen traditions
• - use biographies and stories of different
  mathematicians in Math projects or when
  introducing topics e.g. Pythagoras, Bernoulli

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• Teachers remember
• even if the content is specified by the
  intended curriculum, the context is open to
  decision and choice, Teachers have the
  opportunity to get away from meaningless and
  arbitrary contexts in mathematics questions, and
  to develop more meaningful and relevant contexts
  from todays pluralistic societies (Bishop,
  1992 178)

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• Table 8.1 Differences in the canonical-
  structuralist and ethnomathematical approaches
  (Bishop, 1992 180)

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• Canonical- structuralist Ethnomathematical

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• Canonical- structuralist Ethnomathematical

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• Conclusion
• The following points must be emphasised
• Mathematics is a critical filter for employment
  and full participation in society. We cannot
  afford to have the majority of our population
  mathematically illiterate. Equity has become an
  economic necessity
• The homogenous curriculum is no longer tenable
  given the diversity in student population.
  Diversity is not a challenge but a gift that
  must be celebrated
• A multicultural mathematics curriculum emphasizes
  both the mathematical and the sociocultural
  aspects of the topics under consideration
• The changes can happen both at the Intended and
  the Operational curriculum levels

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• References
• Barton, B. (1993) Ethnomathematics and its place
  in the
• classroom. SAME Papers, 46-68.
• Bishop, A. (1992) Cultural issues in the
  intended, implemented
• and attained curriculum. In G. Leder (Ed)
  Assessment and Learning of Mathematics. ACER.
  169-189.
• 3. Bishop, A. (1988) Mathematics education in its
  cultural context.
• Educational Studies in Mathematics 19(2),
  179-191.
• Dossey, J. A. The nature of mathematics its role
  and its influence.
• In D. A Grouws (Ed) Handbook of Research on
  Mathematics Teaching and Learning. NY Macmillan.
  39-48.
• 5. Eisner, E. W. (1994) The Educational
  Imagination 3rd edition. NY Macmillan.
• Leder, G. C. and Forgasz, H. J. (1992)
  Perspectives on learning, teaching and
  assessment. In G. Leder (Ed) ) Assessment and
  Learning of Mathematics. ACER. 1-23.

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7. Lakatos, I. (1976) Proofs and refutations
The Logic of Mathematical Discovery. Cambridge
Cambridge University Press. 8. McGee, C. (2001)
Understanding Curriculum. In C. McGee D. Fraser
(Eds) The Professional Practice of Teaching 2nd
Edition. Dunmore Press.85-105.   9.
Mellin-Olsen, S. (1987) The Politics of
Mathematics Education. Dordrecht Reidel. 10.
Pompeu, G. Jr. (1994) Another definition of
Ethnomathematics? Newsletter of the International
Study Group on Ethnomathematics, 9(2), 3. 11.
Robitaille, D. Dirks, M. (1982) Models for the
mathematics curriculum. For the Learning of
Mathematics, 2(3), 3-21. 12. Thaman, K. H.
(1997) The Best of Whose Culture? Curriculum
Development in Oceania. Keynorte Address,
Curicula Pasifika Workshop. University of
Waikato, Hamilton.