One of a number of tried and tested technique for teaching work that students find hard to learn found in teaching tricks and tips
This is the opposite of simplify - it helps students both understand and remember their work and also helps students "get" why mathematicians are always compacting.
Here are a number of situations where students writing out their maths "long-windedly" helps.
simplify
When a question asks students to simplify it at first glance seems strange to ask students to write out the problem long-windedly. However here are a number of situations when it becomes apparent that it does help
- help identify the structure
- help explain the why of how some short cuts work
- helps reduce the working memory requirements
- helps improve student accuracy
simplify in index form
"Simplify b5 x b3"
Initially we get students to "write it out long-windedly first" that is b x b x b x b x b x b x b x b now when we ask a student to write this short-windedly or simplify
We are putting our students in a position where they
- can create a generalisation for themselves (be a mathematician)
- can answer similar questions accurately
- be more likely to deal with "odd" cases such as "Simplify b5 x b"
- be more likely to remember a method, rather than half remember a rule
Ultimately we want the student to imagine the method of writing the problem out "long-windedly" first - to be sure of their answer, but first making this method concrete helps.
The plan for this page is to build up examples as above and include links to "teaching Higher work to Foundation students" videos and more easy on the eye student "remind-me" videos. For now though here is a list of situations where we have found asking students to "write that out long-windedly" has helped.
simplify a fraction
simplify a ratio
factorise
long multiplication
long division
find the mean, median, mode or range from a frequency table
solve
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