don steward
mathematics teaching 10 ~ 16

Sunday, 26 January 2020

long multiplication teaching

Deborah Loewenberg Ball (Michigan, USA) suggests that teaching involves content knowledge (having the skill) and pedagogic knowledge (having an awareness of how to teach it effectively and how to respond to student misconceptions)

the first resource is for teachers
what misconception might students have, to do calculations in this manner?
what might a teacher do in response?

one strategy to aid skill development is to provide examples
it seems helpful for these to be dynamic - either filmed or in a powerpoint loop

the intention is that you have the powerpoint playing whilst students are working
i.e. set the powerpoint to run and leave it to continue, in a loop

loop 1 is here
the shortened algorithm
58 times 73
35 times 67

loop 2 is here
the expanded algorithm
38 times 46
238 times 46

not looped, long multiplication examples are here
dotty grids, grid method, expanded and shortened algorithms

also not looped, lattice ('gelosia') algorithm examples are here
maybe better left until later in a student's life
especially where other methods are fragile
used historically, with good reason

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