I ran into this little letter in the community paper last night:

I quote:

"What I am about to tell you is going to blow your socks off. Some school have been teaching the wrong way of adding, subtracting, multiplying and dividing fractions and in fact whole numbers for decades.

If your child is in Grade 6, he or she will learn how to add, subtract, multiply and divide fractions using the BODMAS system. This system is supposed to remind them of the order in which to do these operations. That is, first do ‘B’, the numbers in Brackets, then do ‘O’, or ‘of’ (eg. 1\4 of 12), then ‘D’, Division and ‘M’, Multiplication, and lastly ‘A’, Addition and ‘S’, Subtraction.

The important point to remember is that the BODMAS system tells you to do division and multiplication before addition and subtraction, and then to work from left to right. It does not mean that you must do division before multiplication and addition before subtraction. In fact in many cases, if you do addition before subtraction, you will get the wrong answer. And this is where many schools are getting it wrong. They are taking BODMAS to mean that you do Division first, then Multiplication, then Addition followed by Subtraction.

The following example will demonstrate how some schools are getting it wrong:

Eg. 3/4 - 3/8 + 1/8

According to the incorrect interpretation of BODMAS, you do addition first.

So, = 3/4 –( 3/8 + 1/(8 )) = 3/4 - 4/8= 3/4 - 2/4 = 1/4 ,

which is absolutely the wrong answer.

According to the correct mathematical method, you do subtraction first.

So, = ( 3/4 - 3/8 ) + 1/8 = ( 6/8 - 3/8 ) + 1/8 = 3/8 + 1/8 = 4/8 = 1/2 ,

which is definitely the correct answer.

(For the more mathematically minded, the + and – signs must not be treated as an

operation between two numbers, but rather as a positive or a negative sign belonging to the number after it. So by putting brackets after a negative sign, you are making everything within the brackets negative.)

The situation gets even worse when you consider the Afrikaans ‘help you to remember’ sentence, which is : “Hier Vlieg My Dooie Oom Andries”. Taking the first letter of each word gives you: H V M D O A, which gives the order: Hackies (brackets), Van (of), Maal (multiplication), Deel (division), Optel (add), Aftrek (subtraction).

Or in universal language: () ‘of’ × ÷ + - .

Now the unfortunate and disturbing thing about this is that this Afrikaans order is different from the English BODMAS order, which is: () ‘of’ ÷ × + - . This should make no difference if it is used correctly, by doing multiplication and division before addition and subtraction and then working from left to right. But if it is used by following the order in “Hier Vlieg My Dooie Oom Andries”, as some schools are doing, you will sometimes get the wrong answer, by doing Multiplication before Division.

The following example will demonstrate how some Afrikaans schools are also getting sums involving multiplication and division wrong.

eg. 5/8 ÷ 3/4 × 2/5

According to the incorrect interpretation of the Afrikaans method, you do multiplication first.

So, = 5/8 ÷( 3/4 × 2/5 ) = 5/8 ÷ 3/10 = 5/8 × 10/3 = 25/12 ,

which is absolutely the wrong answer.

According to the correct mathematical method, you do division first.

So, = ( 5/8 ÷ 3/4) × 2/5 = ( 5/8 × 4/3 ) × 2/5 = 40/120

( or, if you cancel first; = 1/3 ) , which is definitely the correct answer.

Schools should stop using the BODMAS system or “Hier Vlieg My Dooie Oom Andries” system, as pupils are using it incorrectly and teachers, in many cases, are not correcting them as they are not aware of the error.

If students always use the order: Division, Multiplication, Subtraction, Addition, as the order of operation in which to calculate sums, they will always get the correct answer. To help remember the order, teachers and students need only to remember the mnemonic: “Disciplined Maths Students Achieve”, and take the first letter of each word. (i.e. D M S A). Or pupils may prefer: “Dead Mice Smell Awful”. Or, if you want to include the bits about Brackets and Of, then use: “Bits Of Dead Mice Smell Awful”."

Unquote

http://www.tametimes.co.za/index.php?option=com_content&view=article&id=4789:1--1--2--schools-get-it-wrong-or-beware-of-bodmas&catid=37:schools&Itemid=200The problem is, even if the kids and parents take notice of this guideline, if they implement it, it is likely that the teacher in question willl mark their results as incorrect. Its a no-win situation.