## Sunday, January 17, 2010

### Simple arithmetic

A neighbour asked my husband if he would help his 10 year old daughter who was struggling with maths, in particular with subtraction. After a brief lesson, she was able to tackle her homework with confidence but yesterday she came back to ask for more help. Her teacher had refused to give her a mark for the homework because the answers were correct but she had not used his "correct" method to arrive at them.

My husband uses the same method that I was taught in school in the 1950s - equal addition. He asked the little girl to use that method on this question 8157 - 379. It took her 25 seconds to produce the correct answer:

She then attempted the same question using the school's method. She took 7 minutes to arrive at an answer, which turned out to be incorrect.

Here is the recommended method; it goes through a number of stages, each with the potential to mystify and confuse:

Stage 1

Stage 2

Stage 3
The little girl could not do the addition in her head so she had to write out the numbers

The question hanging around chez Random Distractions all weekend is WHY?

1. Oh don't get me started on this one. It's inexplicable!

Chatterbox, who is 8, came home with some subtraction and addition using the new fangled method. Neither me, nor my Dad, nor my hubs could for the life of us work out how to get to the correct answer on one of the questions.

Why make it complicated? The method that your husband used is the method I would use, I'm rubbish at maths and yet it makes sense to me.

If it ain't broke don't mend it. Silly curriculum.

2. I haven't seen that one! The treasures at my school use your (and mine I may add) method. They are always encouraged to 'guesstimate' first as well.
If I were doing the sum in my head I would use the addition method like the school are teaching, but never on paper.

3. Sarah and Rattling On

I'm no great whizz at maths but the basics I learned in primary school have proved very useful and trustworthy ever since. My husband entered teaching as a second career when he retired from the merchant navy. He was shocked by the poor standard of maths teaching and the silly gimmicks that have been introduced to replace good old-fashioned tables and basic procedures. This latest silliness is the one to beat all - not only does it take more time and effort, it made the child produce the wrong answer!

4. When my nephew was in school, arithmetic was taught by using the set method. It wasn't until he got to college (he's 40 now and has a Ph.D in ecological biology, so he's obviously not a dummy) that he learned how to do simple arithmetic and make change. I wonder if this is a variation on that method.

5. erp
Learning by rote went out of fashion in the early 70s and children were expected to understand the how and why of everything. Of course, to get by in life you just need to add your bill and check your change quickly!

In my 40 years in education I never encountered this particular system and I certainly can't understand the reason for it.

6. True. Did your system go through the anti-phonics phase called "sight reading"? It was responsible for the abominable reading, writing and spelling ability of nearly a generation of students.

We were lucky our kids went to non-progressive schools where they learned both by rote and to understand the how and why of things.

7. Yes, e, phonics, tables and other aids to learning were re-introduced a few years ago (as if they were new ideas!) but as most of the teachers grew up with the structureless scemes they didn't know how to teach them.

We didn't put our children through the state education system because there were no reasonable schools where we lived.

8. Smart of you.

We were lucky with the schools our children attended and our grandchildren aren't being subjected to the vagaries of the public/state schools, so we're doubly lucky.

Here's an example of our educational system. A beautiful, intelligent girl (age thirtyish to fortyish) I met is a middle manager and makes a nice living. She admired my watch (an nice example of 'mod' art, but said she couldn't tell time with that kind of watch. The face didn't have numbers or indications where they numbers should be, so I thought that was the reason she couldn't tell time, but that wasn't it.

She doesn't know how to tell time at all!!!

It really stunned me. How do people who don't know the face of a clock know when "incoming are at 2 o'clock" or other important facts associated with time going back to ancient sun dials?

9. I had to have a quiet lie-down after reading this, M. I haven't a clue what is going on in Stages 1, 2 and 3. But then I wasn't even allowed to sit O Level Maths, which was all about algebra and mathematical stuff that was a complete mystery to me, thanks largely to the abysmal quality of maths (and science) teaching at my girls' grammar school.

However, I loved straightforward arithmetic - (yes, as taught in my primary school in the 1950s, using similar methods to that in your example) and this, as it turned out, has been perfectly adequate to enable me to budget for a family, manage family and personal finances, and run a profitable business for 20 years. I even managed, during the years I was working in press relations, to sound reasonably knowledgeable interpreting and quoting statistics in answer to questions from journalists up against a deadline. Where did I go wrong?

10. e, Reading a clock face will probably be another great new idea from a government department in a year or so!

11. D, I don't think I've ever needed to apply my knowledge of simultaneous quadratic equations or trigonometry (just as well since I've forgotten it) but the times tables and basic arithmetic are in constant use. It seems we were among the last of the lucky ones.

12. My husband and I grew up in the 1960s in America and were victims of a trend in mathematics teaching known as the "new math". It was mind-boggling for elementary students, incomprehensible to parents who knew how to do math, and only known to teachers who had just graduated from university. Explanation of just what this was could not fit in this space, but the idea was to understand what you were doing, rather than to get the right answer! It was scrapped after about five years, but left my generation in innumeracy.

Also, this puts me in mind of a scene from Harper Lee's To Kill a Mockingbird:
"...as I read the alphabet a faint line appeared between her eyebrows, and after making me read most of My First Reader and the stock market quotations from The Mobile Register aloud, she discovered that I was literate and looked at me with more than faint distaste. Miss Caroline told me to tell me father not to teach me to read anymore, it would interfere with my reading."

13. Jodi, that sums it up perfectly!

14. Well M, not only Why? but How? I cannot work out how to do this sum by the new and I suppose we must think, better method. I will have to come and have some tuition from the MM! On second thoughts, I will just go on doing it by the old method.

15. Stick to the old ways, Crinny. You know they work!

16. How absurd! If one arrives at the correct answer, what does it matter how she got there?

17. Absurd indeed, Carolyn. I'm afraid that teachers who are insecure in what they are teaching can be very dogmatic!

18. m. do teachers in your state schools have autonomy over what they teach? Here the unions have absolute control over ever aspect of the public schools and teachers do what their told.

19. e, State schools have to follow the National Curriculum which specifies what must be taught. It offers guidelines on how it should be taught but teachers have some degree of autonomy on method unless they have a very controlling head teacher.

20. Oh, dear. The dreaded new math. :( Why can people not leave well enough alone? Ack.

21. I am still trying to work out how to do the sum by the new method. I just don't understand it. No wonder the poor child couldn't get it right; I am mystified!

22. And here I was cribbing all day yesterday that the teachers in my First Grader's school complicate things by teaching them multiple ways of doing the same sun, thereby complicating things.
But this new system is utterly ridiculous- I would enjoy doing it, because I love playing with numbers - what is wrong with the conventional carry forward method?

23. Welcome to Random Distractions, Rayna, and welcome to the band of bewildered people who see absolutely no sense is this complicated method of doing a simple sum!

I love to read your comments and promise that I will reply as soon as I can leave my garden, sewing room or kitchen!