At Udavi school I observed math classes for about three weeks. This gave me a good idea of what was missing and which children were having the toughest time. The children in 6 and 7 grade had the most difficult time. They were expected to be comfortable with fractions, decimals, the corresponding arithmetic operations and required to abstract in algebra, etc. They had also started quantifying their learnings in science including knowledge of speed, density, acceleration, light years, etc.
By the time children get to Xth grade abstraction is assumed to such an extent that a teacher would work on coordinate geometry for 1-1/2 hrs without drawing much on the board. When something is drawn is called a rough sketch e.g. to demonstrate mid point of (x1,y1) and (x2,y2) a straight horizontal line would be drawn with these two points and (x,y) would be the mid point, given by the formula...x = (x1+x2)/2, y = (y1+y2)/2.
I'm not convinced that we can assume that the children have already developed this ability to abstract as well. Here is an example of what I experienced:
The teachers were kind enough to give me 10 -15 mins towards the end of a 1-1/2 hr class to do 'what I wanted'. Generally, I connected concepts they had learnt in different Math classes (e.g. geometry with algebra) and sometimes beyond.
After a class of coordinate geometry, I had talked about the characteristic of a straight line of holding a ratio i.e. from a point on the line, if you move some distance x away then a point on the line moves a certain distance y away and this ratio holds, so if you move 2x away then point on the line would have moved 2y away. They had been able to co-relate this to what they had learnt from Physics of how the image of an object keeps getting bigger as they moved away from the focal point.
After a little more than a week I enquired about the characteristics of a straight line are and after the customary shortest distance between two points (ahem, not what I'm looking for and that's a line segment), has no beginning and no ending (my Goth! sounds philosophical) one kid says hey it holds a ratio. By now other kids are going, oh yeah that's obvious, is that what you wanted?
I probed further and let them jog their memory about lenses and their images with distance and one kid even brings up a shadow (whao, more material for later). Then I asked if they knew what this ratio was called. Of course, they came back with, but you haven't told us (and of course, I had, but you can't expect them to remember a name when they just found out that Physics may tally with mathematics in 10 mins!). I let them know that they know this name, now they give me every name they know associated with geometry till my previous discussion (ray, angle, line-segment, co-linear)...but no slope.
This was their second full class (1-1/2 hrs each) of learning and solving most the exercises in their text regarding slopes with the formula m = (y2-y1)/(x2-x1). I was talking at the end of the class they had learnt that lines are parallel if m1=m2 and perpendicular if m1*m2=-1.
When I finally told them that this 'ratio' is slope, they were shocked that it was something related to what they were doing in class.
After the observation period I have been working primarily with 6th and 7th graders, but the above instance convinced me to stay involved with the Xth grade math for one slot in the week. I was pleasantly surprised when one of the teachers asked me to take geometry for them. I wondered if it was because I drew so much in algebra classes. He said because the students four it very dry. Whatever the reason, I accepted the offer this became my Math connection with the kids (I also have one slot for electronics)
Public (state board) examinations are conducted for the children of the Xth grade. These examinations are taken seriously and decide if you will be allowed to pursue science, commerce or arts (usually in that order). The questions in Mathematics are picked up as is from the exercises in the book (apparently, verbatim).
Accordingly the present teaching methodology is that the teachers parse the text and peel off any proofs, theory to boil the lesson down to a set of formulae. They sometimes put some context to the formulae (what will be given and what will be asked) and then proceed to solve all the problems in the exercises. The teacher may even try to give some time for the 'brilliant' students to solve the exercises, but soon the teacher relents and solves the exercise on the board for the benefit of all children. At the time the teacher solves the problem the children are expected to pay attention and not copy (yet). Copying happens soon after, often exceptionally well.
I went through the geometry text and realized that it had 'theory' and proofs. The teachers are a little squeamish about proofs, the children freeze on the same. Each theorem has corollaries, converse theorems and builds on what is done before. I was going to enjoy myself and the children are going to be blank, unless,...
By the time children get to Xth grade abstraction is assumed to such an extent that a teacher would work on coordinate geometry for 1-1/2 hrs without drawing much on the board. When something is drawn is called a rough sketch e.g. to demonstrate mid point of (x1,y1) and (x2,y2) a straight horizontal line would be drawn with these two points and (x,y) would be the mid point, given by the formula...x = (x1+x2)/2, y = (y1+y2)/2.
I'm not convinced that we can assume that the children have already developed this ability to abstract as well. Here is an example of what I experienced:
The teachers were kind enough to give me 10 -15 mins towards the end of a 1-1/2 hr class to do 'what I wanted'. Generally, I connected concepts they had learnt in different Math classes (e.g. geometry with algebra) and sometimes beyond.
After a class of coordinate geometry, I had talked about the characteristic of a straight line of holding a ratio i.e. from a point on the line, if you move some distance x away then a point on the line moves a certain distance y away and this ratio holds, so if you move 2x away then point on the line would have moved 2y away. They had been able to co-relate this to what they had learnt from Physics of how the image of an object keeps getting bigger as they moved away from the focal point.
After a little more than a week I enquired about the characteristics of a straight line are and after the customary shortest distance between two points (ahem, not what I'm looking for and that's a line segment), has no beginning and no ending (my Goth! sounds philosophical) one kid says hey it holds a ratio. By now other kids are going, oh yeah that's obvious, is that what you wanted?
I probed further and let them jog their memory about lenses and their images with distance and one kid even brings up a shadow (whao, more material for later). Then I asked if they knew what this ratio was called. Of course, they came back with, but you haven't told us (and of course, I had, but you can't expect them to remember a name when they just found out that Physics may tally with mathematics in 10 mins!). I let them know that they know this name, now they give me every name they know associated with geometry till my previous discussion (ray, angle, line-segment, co-linear)...but no slope.
This was their second full class (1-1/2 hrs each) of learning and solving most the exercises in their text regarding slopes with the formula m = (y2-y1)/(x2-x1). I was talking at the end of the class they had learnt that lines are parallel if m1=m2 and perpendicular if m1*m2=-1.
When I finally told them that this 'ratio' is slope, they were shocked that it was something related to what they were doing in class.
After the observation period I have been working primarily with 6th and 7th graders, but the above instance convinced me to stay involved with the Xth grade math for one slot in the week. I was pleasantly surprised when one of the teachers asked me to take geometry for them. I wondered if it was because I drew so much in algebra classes. He said because the students four it very dry. Whatever the reason, I accepted the offer this became my Math connection with the kids (I also have one slot for electronics)
Public (state board) examinations are conducted for the children of the Xth grade. These examinations are taken seriously and decide if you will be allowed to pursue science, commerce or arts (usually in that order). The questions in Mathematics are picked up as is from the exercises in the book (apparently, verbatim).
Accordingly the present teaching methodology is that the teachers parse the text and peel off any proofs, theory to boil the lesson down to a set of formulae. They sometimes put some context to the formulae (what will be given and what will be asked) and then proceed to solve all the problems in the exercises. The teacher may even try to give some time for the 'brilliant' students to solve the exercises, but soon the teacher relents and solves the exercise on the board for the benefit of all children. At the time the teacher solves the problem the children are expected to pay attention and not copy (yet). Copying happens soon after, often exceptionally well.
I went through the geometry text and realized that it had 'theory' and proofs. The teachers are a little squeamish about proofs, the children freeze on the same. Each theorem has corollaries, converse theorems and builds on what is done before. I was going to enjoy myself and the children are going to be blank, unless,...
No comments:
Post a Comment