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Overcoming the Algebra Barrier: Being Particular About the General, and Generally Looking Beyond the Particular, in Homage to Mary Boole

Abstract

Consistent with a phenomenographic approach valuing lived experience as the basis for future actions, a collection of pedagogic strategies for introducing and developing algebraic thinking are exemplified and described. They are drawn from experience over many years working with students of all ages, teachers and other colleagues, and reading algebra texts from the fifteenth century to the present. Attention in this chapter is mainly focused on invoking learners’ powers to express generality, to instantiate generalities in particular cases, and to treat all generalities as conjectures which need to be justified. Learning to manipulate algebra is actually straightforward once you have begun to appreciate where algebraic expressions come from.

Keywords

  • Expressing generality
  • Pedagogic strategies
  • Tracking arithmetic
  • Watch What You Do
  • Say What You See
  • Reasoning without numbers
  • Same and different
  • Invariance in the midst of change

Algebra consists in preserving a constant, reverent, and conscientious awareness of our own ignorance [p. 56]

Teaching involves preventing mechanicalness from reaching a degree fatal to progress [p. 15]

The use of algebra is to free people from bondage [p. 56]

[all quotes are from Mary Boole , extracted in Tahta, 1972]

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Mason, J. (2017). Overcoming the Algebra Barrier: Being Particular About the General, and Generally Looking Beyond the Particular, in Homage to Mary Boole. In: Stewart, S. (eds) And the Rest is Just Algebra. Springer, Cham. https://doi.org/10.1007/978-3-319-45053-7_6

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