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July 07, 2013

Auditing Math...

I audited the Math classes in both Udavi and Isai Ambalam for the week of 24-29 Jun 2013. One obvious thing in almost all classes is the spread between the children following the class and those struggling to keep up. The teachers don't feel equipped to keep the 'smart' ones engaged while giving the time the 'slow' learners require. This disparity keeps the class in a bit of flux with the ones that finish not knowing what to do. There is also a strong drive to 'finish' a problem and in doing so have nothing to do with it anymore. There is no dwelling over the problem and once it is finished boredom begins.

The teachers at Udavi were kind enough to give me some 10 mins towards the end of the class. I was showing ways for the children to cross check their answers, areas that the children had difficulty with, puzzles based on what they were working on or just put it in context. A few children seem to see something that can be done with a problem once they are finished it.

At Isai Ambalam three sets of grades were doing work on shapes 3, 4 and 5th grade. The same four shapes triangle, circle, rectangle and square (differentiated from a rectangle) were covered. In the higher standards we gave names to the vertices, but the rules supplied to the children to identify a rectangle were quite limited in all the grades - 4 corners, 4 sides and opposite sides are the same. The rules are not sufficient to differentiate a rectangle from a parallelogram.
Surprisingly it was the younger children were able to come up with a rule that a general parallelogram was not 'L' shaped and they are yet to encounter our definition of an angle.
What was surprising was that most of the time a triangle was represented as a delta (Δ) and most children find it difficult to identify a right angled triangle as a triangle. This time of course I applied their rules and it fit :).
I gave a puzzle of a rectangle with diagonals and asked them to identify all triangles beyond the obvious 4. It took half the class time to identify them. I turned the rectangle around and the children again set off to identify it for the new shape...perhaps, a little more work is required in pattern recognition. We also did the same for a running star (5-line star that you make without lifting your pencil).
In higher grades was that they were also labeling the corners of the triangle and other shapes. I wonder if we are asking enough of children...

Fractions are a heavy source of confusion in both schools. These problems start at and early age and keep getting bigger and bigger as more and more things that can be done with fractions (dividing negative fractions! comes along).

Another common problem are negative numbers and operations based off these. Even if you can get children to associate negative numbers with having money vs having a loan they are soon tied up in knots.
I give stories of many operations, but the multiplication of two negative numbers was tough. I put in a sense of direction with the number line and my frog that jumped two negative steps at a time, where would it land if it started at origin and jumped three time in the opposite direction...I know, the children didn't get it either. Please feel free to post a story for the product of two negative numbers.

I found it very difficult to work with the reallly young kids. I wanted to hit my head against a wall with a kid who would not remember what she said 2 seconds ago and had no association with what she wrote and what she did. It seems she was just pulling out numbers at random. Finally with teaching aids I settled down and asked her to count and realized that she doesn't know what comes after 39 and fills this in with anything she wants 60, 70, 44 (nope no 42). Even though the teacher was there she still doesn't believe that the child doesn't know...

I also notice a lot of what 'us teachers' do when the children are unable to get to the 'right' answer. The children are just fabulous at reading our facial expressions and body language.

Its amazing that even at the Xth class level most of the examples and exercises in the textbook have whole number answers. Apparently, its these questions that will come in verbatim in the examination!

I also had a few funny experiences where I wanted children to use what they knew from other compartmentalized sections of mathematics in their geometry and some of the kids just found the answer by drawing it out. Serves me right for being a smart Alec.

I also kicked off my puzzles sessions - Tue and Thu every week at Udavi. I received a few solutions for them, but by and large the Xth grade seems to have picked it up and at least discuss it. This is thanks to Ramji who was their class teacher in VIII grade and gave them much practice. They keep me on my toes and I need to come up with something they have not encountered. I am yet to get the younger children interested in the same.
I did have my fun by asking them to draw what they did in class, a triangle with zero area called a 'co-linear' triangle. Apparently, they don't look too deep in the names co-linear points. It was like a huge ah, ha moment in class that all points on a line are co-linear!

There are alternative teaching techniques (beyond the text book) in both schools for lower grades. But, these aids completely dry up as the children get to 7th grade as it is assumed that they can now magically abstract all that they see and do.

1 comment:

partha sarathy said...

Sanju
Was reading your blog. Wanted to share thoughts on understanding multiplication of two -ve numbers.

One way is to separate the signs and the multiplication operation. 2 negative numbers would mean moving in the opposite direction twice and hence pointing to default direction (right of numberline). Since the sign can be interpreted as a direction - the multiplication of numbers can be separated from the changes in direction

Not sure if this would help or if you have tried this.

Best wishes
Jiju