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

plan

Our growing evidence from timely practice is that it is better to ensure that at least one layer of e.g. area is mastered before teaching any layers of perimeter. However often we are too late - the learner has learned them both before and is already confused. The strategy is the same, just teach one to mastery - you may will probably need to remove the other from the learners timely practice to do this. Once the layer is mastered you may move on to teach the other topic or you may prefer to teach a couple of layers from the first topic before teaching the second topic. However if learners know a lot, such as how to calculate the area and circumference of a circle - you may want to use the "look at the units on the answer line" to avoid loosing these skills. The jury is out on this point.

accept

Accepting that learning of some topics will interfere with other topics is the first step to recovery.

By accepting that learning of some topics will interfere with the learning of other topics and embracing this - we are able to help the learners correctly match the ideas and the names attached to those ideas. 

When designing the lay out of the questions we ensure that the questions looked exactly the same apart from the essential key differences for example the word area or perimeter and the units on the answer line - so the learner must focus on mastery, if for no other reason that they become "bored" by getting their answers wrong and then "challenged" to get the questions correct. 

We also encourage teachers to get learners to reflect on situations where the learner has succeeded in overcoming this confusion before such as "Remember when you used to be confused between area and perimeter and now you get these correct every time, well, I think it will be the same with  b x b x b and b + b + b"

This is more than just encouragement, the teacher is getting the learner to recall the "feeling of pride in a job well done" and establishing both the learner and the teachers belief in a "growth mindset". 

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 asking learners to focus on the difference between two problems has helped.

Here are a number of problems that will interfere with each other initially

simplify sum and/or product

Once we start to teach how to simplify h x h x h x h learners lose their confidence  in knowing that h + h + h + h = 4h  .... so as soon as you teach h x h x h x h get learners to work on and compare with h + h + h + h type problems, ideally in a mixed bag over time.

simplifypq: g x h and h x h and h + h

simplifypq: h x h x h x h intro 

area and/or perimeter

With two concepts are ubiquitously confused by learners such as area and perimeter, we know that after teaching one carefully - to what seems like mastery - when the other is introduced most learners will become confused. We encourage learners to embrace this confusion and encourage them to self reflect 

• if this question was about finding the area - what would I have to do?
• if this question was about finding the perimeter - what would I have to do?

and then finally to think

• OK this question is area - perhaps use the clue on the answer line " .... m²  - so I want to work out the number of squares" - to give their answer confidently

If learners believe that most people run into the confusion that they have encountered, and that there is a logical way through the problem, and that a pause for thought leads to an accurate answer and most importantly the learners encounter as many instances in their timely practice assignments as required to accurately match the name of the concept with the concept then the teaching and learning process will succeed.

factor and/or multiple

Teach multiple typeOFnumber1.pdf but as soon as you begin to teach factor compare the two typeOFnumber2.pdf and give a hint of how to distinguish.

all the factors of ... and/or write ... as a product of its prime factors

Personally (assuming learners find division hard to do) I like to teach learners to write a number as its prime factors before I get them to find all the factors of the number, as

• I think the strategy for finding a product of prime factors requires easier division skills than finding all the factors
• the product of prime factors skill is useful in many situations (unlike the factor finding method) and the picture of the prime factor tree can then be used to find all the factors

factorPRIME - FACTORproductOFprime FFMcomparePPFM

HCF and/or LCM

factorPRIME - HCF 84 and 90 quick

factorPRIME - HCF 84 and 90 all the factors

factorPRIME - LCM 1Fully