Thursday, 20 June 2013

What is a decimal?

A difficult question

Fractions to decimals
What is a decimal? Can you answer in one sentence? If there was a pause for thought good, because it is a really difficult question to answer, we are so used to decimals we forget what they are. If you did struggle imagine pupils’ confusion when you start to talk about decimal fractions or changing fractions into decimals.

We have all at one time or another thought ‘decimals should be easy to understand’. After all no matter where we are in the world money is based upon the decimal system, which child has not experienced that? Yet if you ask a student what is the value of 7 in 0.12379 the answers given will probably be not what you want.

Root of the problem

A decimal is a fraction where the denominator is restricted to powers of ten. Children do not think of decimals this way. They do not see decimals being linked to place value at all, yet when you mention hundreds, tens and units a smile comes to there face remembering younger days when life was easy. Why do they quite comfortably understand ad cope with place value on the left hand side of the decimal point yet when we come to the right hand side it all seems to go wrong, confusion and lack of understanding.

What to do

We need to be really explicit about place value and decimals. One brief lesson is not enough. Constant reinforcement and being very clear about the links between decimals and fractions is vital to success.

Here are your 3 easy actions to take. Do these and their understanding of decimals and fractions will become far more secure.
1. The obvious first solution is to constantly emphasise place values when writing decimals. I always write the place value in a different colour to the decimal. This simple action will separate the two sets of numbers, aid memory and make your teaching more effective.

2. Secondly I would persistently practice asking what do numbers represent in a decimal number, in other words what is their place value. For example what does the 3 stand for in 0.436. This is easy to do as a starting activity, doesn't take long but done over a few weeks will pay rich dividends.

3. Thirdly I would place a big emphasise the ‘ths’. Some learners will not hear the difference between a hundred and hundredths as the ‘ths’ is a very soft sound. You do not want  misunderstanding because of mishearing your pronunciation. Avoid confusion and uncertainty by over emphasising the 'ths'.

4. Ensure that when pupils talk about numbers like 0.29 they say point two nine not twenty nine. Correct them becuse if they believe the number is twenty nine then this additional errors could occur. For example you ay ask which is bigger 0.29 or 0.3? The student may reply 0.29 because twenty nine is bigger tha 3.

Follow this simple and what may appear trivial steps when teaching fractions and decimals and you are laying a firm foundation for greater success in the future.

Further reading

I recently came across a book which will help all us hard pressed teachers in the daily struggle to educte, entertain and stimulate the kids. It is called Outstanding Teaching: Engaging Learners by Andy Griffiths.
'A class can be skilled and motivated to learn without a teacher always having to lead. Engaging learners in this way unpicks intrinsic motivation, the foundation that underpins a productive learning environment and helps to develop independent learning, creativity and improved behaviour management. Based on five years of intensive research through Osiris Education's award-winning Outstanding Teaching Intervention programme, during which the authors have trained more than 500 teachers to teach over 1,300 lessons in schools nationwide, this book is packed with proven advice and innovative tools developed in these successful outstanding lessons. Written in the same humorous, thought-provoking style with which they both teach and train, Andy and Mark aim to challenge all who teach, from NQTs to seasoned professionals, to reflect on their day-to-day practise and set an agenda for sustainable teacher and leadership improvement. Outstanding Teaching: Engaging Learners was short listed for Educational Resources best Educational Book Award 2013'

It has been reviewed by 27 people and given 4.5 stars out of 5. Well worth investigating I think.

Has anyone got further ideas that will help us all for teaching fractions and decimals?

Please leave a comment.

Why not follow me on Twitter at @croftsr1?