
06675840
a
Mason, John
Overcoming the algebra barrier: being particular about the general, and generally looking beyond the particular, in homage to Mary Boole.
Stewart, Sepideh (ed.), And the rest is just algebra. Cham: Springer (ISBN 9783319450520/hbk; 9783319450537/ebook). 97117 (2017).
2017
Cham: Springer
EN
C30
H20
H30
E50
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
doi:10.1007/9783319450537_6
Summary: 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.