Wednesday, October 13, 2010

The Forgetting Curve

As we have discussed previously in this dyslexia blog students with dyslexia often have problems regarding memory.

Hermann Ebbinghaus, a German pyschologist is famous for his research into memory which he carried out in the 1880’s. His experiments give an insight into learning and forgetting and his findings are still valid today. He tested his own memory using a large number of nonsense syllables which he created.

His findings were as follows :

It is harder to memorize material that does not have significance or relevance to the learner.

His data revealed that increasing the amount of material to be learned usually dramatically increases the amount of time it takes to learn it. This is the learning curve.

He established that relearning is easier than initial learning, and that it takes longer to forget material after each subsequent re-learning.

Ebbinghaus’s work also suggested that learning is more effective when it is spaced out over time rather than crammed into a single marathon study session.

Ebbinghaus also discovered that forgetting happens most rapidly right after learning occurs and slows down over time. This is the forgetting curve. It shows that about 80% of what students learn today will be forgotten within 24 hours ,if the material is not gone over.

So what can we learn from this ?

It is important that students regularly review the knowledge that they are learning; this is how things move from short-term to long term memory and become easier to recall at speed.

Effective revision should an ongoing process, not a cramming session just before the exams.

It is important for students to revise at particular points in time in order that they don’t forget the information they have learnt :

They should go over the information they are learning in the same day (in the evening for 10 minutes ) also 24 hours later, one week later and one month later ( or sooner ).

Remember that students with dyslexia will also need to revise even more frequently. The more over learning they do the easier it will become to recall information. It is a good idea if students can make up questions to test themselves on the information they are learning, as this is a good aid to learning.

It would be a useful if parents and teachers explain the importance and implications of the forgetting curve to children in order to encourage them to review material learnt more regularly.

Tuesday, October 12, 2010

Long Multiplication

In this dyslexia blog article there are some tips and advice on long multiplication.

Being able to recall basic multiplication facts is essential for success with long multiplication, therefore it is crucial you make sure your child practices their times tables on a regular basis. Games are a good way to motivate them to learn them !!

Students who have dyslexia will often have a weakness in their working memory. As a result it may be difficult for them to rely solely on mental calculations when solving math problems.The dyslexic student may often forget what they are doing and lose their place . In long multiplication ,of course,there is more of a risk that there will get muddled up since the numbers that they are dealing with are bigger.

When they are are doing long multiplication problems teachers and parents should encourage children to write down every step, including carrying numbers.They should also preferably use scrap paper to help them in their calculations.

Common errors made :

Students make mistakes because they haven’t kept their columns straight. Make sure they line up their numbers correctly and also encourage correct spacing. It is advisable to use squared paper at all times for maths calculations to prevent this problem.
Unfortunately sometimes teachers don’t leave enough space for workings out on worksheets and test papers and this creates problems !!

Forgetting to ‘carry’ numbers A good way to remember the carry number is to write it in a circle.

Forgetting to write down a zero eg :

660 should be 6600
=1650 ( answer should be 7590 )

You could consider teaching your child alternative methods to solve long multiplication problems. One such method is long multiplication using key facts. This method is recommended by Steve Chinn who is one of the leading experts in the area of dyscalculia. With this method your child only needs to know how to double and half numbers and multiple by 10 to get the correct answer.

Long Multiplication using key facts

E.g 78 x 17

1) First set up an easy multiplication table with the key facts :

1 x 17 = 17
2 x 17 = 34
5 x 17 = 85
10 x 17 = 170
20 x 17 = 340
50 x 17 = 850
100x 17 = 1700

1x 17 is easy to find = 17.
To get 2 x 17 just double 17.
After workout 10 x 17 = 170 .Now you can easily find 5 x 17 – just half 170. ( 85 )
For the answer to 20 x 17 double 170 .
100 x 17 is easy just add a zero to 170 ( 10 x 17=170).
For 50 x 17 half the answer to 100 x17 = 1700 ie 850.

2)After find the easy numbers ( or partial products ) in 78 .

78 = 50 + 20 + 5 + 2 + 1

3) After add up these partial products :
50 x 17 = 850
20 x 17 = 340
5 x 17 = 85
2 x 17 = 34
1 x 17 = 17

Answer 78 x 17 = 1326

In Turkey however unfortunately some teachers are reluctant to teach alternative methods of doing maths calculations. Also this method does require more space on the paper for the workings out. In many cases worksheets and test papers provide little space for students to use .It is assumed a lot of workings out will be done mentally. Teachers here in Turkey need to try to be more flexible in their approaches in order to accommodate all children. I would recommend everyone to look at Steve Chinn’s books for more ideas regarding maths.