One of a number of tried and tested technique for teaching work that students find hard to learn found in teaching tricks and tips
sometimes explaining why is helpful and sometimes it is not
Sometimes it helps students 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.
"trick for multiplying fractions" | "trick for dividing one fraction by another" |
---|---|
fraction4operations 2Full | fraction4operations 5Full |
Offering reasons why is helpful if it helps students 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 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 explaining "why" to some students has helped.
adding fractions: why we don't add the numerator and add the denominator?
Knowing why is useful - if students 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