don steward
mathematics teaching 10 ~ 16

Tuesday, 4 June 2013

geometry steering algebra

Hans Freudenthal advocates utilising the compelling image of a straight line of integer points when establishing directed number rules for addition and subtraction (e.g. in chapter 15 of 'Didactical Phenomenology of Mathematical Structures')

in Freudenthal's words:
'the justification of the numerical operations and their laws by the simplicity of the algebraic description of geometrical figures and relations'

a rule e.g. y = 3  -  x generates some points, by inputting some positive x values
  • initially less than or equal to 3
  • then bigger than 3
  • then negative ("where does the line say the result should be?")
as plotted coordinates are joined the line formed can then be extended into the negative quadrants
some (directed number) calculation results emerge

this work is better managed with talk but the resources intend to nudge in the desired direction

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