One of a number of tried and tested technique for teaching work that students learners find hard to learn found in teaching tricks and tips
This is write long-windedly is the opposite of simplify - it helps students learners both understand and remember their work and also helps students learners "get" why mathematicians are always compacting.
Here are a number of situations where students learners writing out their maths "long-windedly" helps.
simplify
When a question asks students learners to simplify it at first glance seems strange to ask students learners to write out the problem long-windedly. However here are a number of situations when it becomes apparent that it does helpdoes
- help identify the structure
- help explain "the why of how some " of some short cuts work
- helps reduce the working memory requirements
- helps improve student learner accuracy
simplify in index form
"Simplify b5 x b3"
Initially we get students learners 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 learner to write this short-windedly or simplify
We are putting our students learners 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 learner to imagine the method of writing the problem out "long-windedly" first - to be sure of their answer, but first actually asking the learners to write out the expression "long-windedly" helps making this method concrete helps. We should continue to ask the learner to write out their working "long-windedly" until the learner achieves mastery learning on these types of question.
The plan for this page is to build up a list of examples, as above, and include links to "teaching Higher work to Foundation studentslearners" videos and more easy on the eye student learner "remind-me" videos. For now though here is a list of situations where we have found asking students learners to "write that out long-windedly" has helped.
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