explain why

One of a number of tried and tested technique for teaching work that learners find hard to learn found in teaching tricks and tips

sometimes explaining why is helpful and sometimes it is not

Sometimes it helps learners to know "why" processes work - but sometimes this makes learning new processes just too hard. 

So the reason why the "trick for multiplying fractions" works is helpful but perhaps the "trick for dividing one fraction by another" is not.

Offering reasons why is helpful if it helps learners follow a process that would otherwise seem arbitrary, when the reason gives more meaning, but is no more complicated than the process being learned. So if working memory load is decreased or memory can be retained longer because it is attached to something that is already learned it can be helpful. 

The plan for this page is to build up examples as above and include links to "teaching Higher work to Foundation learners" videos and more easy on the eye learner "remind-me" videos. For now though here is a list of situations where we have found explaining "why" to some learners has helped.

adding fractions: why we don't add the numerator and add the denominator?

Knowing why is useful - if learners are likely to fall into this trap, and why it is helpful for us to explicitly state why the trap is wrong.

fraction4operations: 1PlusEvery

fraction4operations: 6&10plus

convert between fractions, decimal, percentages and ratio

• FD%RasaFD%R 0.57WHY
• FD%RasaFD%R 0.7asa%WHY
• FD%RasaFD%R Fasa%WHY

probability tree

why one would multiply the fractions on the two branches to find the probability probabilityTree1.pdf

index form 

valueINDEX: 3^0

valueINDEX: 3^1

valueINDEX: 3^-3

sequence 

sequences page 1 NC quick find an expression for the nth term

standard form

intro 7.2 x 10+ve as ordinary number

standard form why better to move the decimal point than the numbers

standard form why 7.2x10^-4 as ordinary number

area

why area of a rectangle is width x height

volume

why volume of a cuboid is width x depth x height

correctly matching the area and circumference of a circle formulas

diagram method to show what πr^2 and 2πr look like for when π =3 and r < < 3 and for r >> 3