write long-windedly

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 a list of 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.

simplifypq: b^5 xb^3 and b^5 x b

simplifypq: b^5 div b^3 and b^5 div b

simplifypq: 3a^2b x 4a^3b^5 and ...

simplifypq: (c^2)^3 and (ab^3)^4

simplifypq: (3c^2)^4

simplify algebra simplifypq: 2g x 3g

simplify a fraction

have only 2nd part of 7timesFull etc - so best to record another

simplify a ratio

ratio: simplestform

factorise 

factorise: 3x + 12

factorise: 4x^2 + 6xy

factorise: remind me 2 different letters 

long multiplication

multiply: partitioning

multiply: 28 x £4.70

long division

divide: divide double digit

divide: divide 5Q

find the mean, median, mode or range from a frequency table

(not available yet)

solve

solve: 4e + 22 = 70 (where the function machine is writing out all the things that happen to e  long-windedly)

solve: m - 6 = 8 (where the function machine is writing out what happens to m  long-windedly)