Recently a student of mine, who tried teaching maths to younger brother, narrated the frustrating experience to me - "its so obvious to me, but he doesn't get it. He just doesn't get it".
This is especially true of Maths. Maths is the ultimate compact way of saying things. Obviously a lot of thought is required to unpack all the thought that is hidden in a simple looking maths statement. A teacher can show what happens when different levers are pulled. But to understand how the Maths-machine works a student has to figure it out for himself/herself. Teacher may use various props to nudge a student to think about the inner working of maths. But for the student, think he must.
Maths demands a lot more "willingness to learn" from a student in that sense. The best kind of maths-teaching is when student does most of the thinking and teacher remains invisible.
Some things can not be taught, but can be only be learned.
Saturday, July 31, 2010
Tuesday, July 6, 2010
Form versus Format
In today's schools many things are over-designed. There are formats for all kind of written works - notes, tests, letters, comprehension etc. Children have to follow these formats else they may lose marks.
No doubt this makes it easy for teachers to detect outliers and non-conformists. And indeed it is easy to catch sloppy children by strictly adhering to various formats and rules. However, this has far-reaching, unintended consequence.
Its become harder for a child to develop a sense of neatness in his or her work. There is a difference between a 'format' and a 'form'. Children quickly learn to mimic the format without developing internal sense of form and proportion. An elegant written work has a form - spacing, margins, tabs for paragraphs and justifications.
Sometimes, when kids ask me how they should write some text or solve a maths sum, I tell them to do it in a way that looks neat - no rules. And hope that they will learn to differentiate between neat work and sloppy work.
While it is easy to learn the format, it takes time and an eye to learn the form. Children wouldn't learn elegance of written work if we don't give space and time to explore.
No doubt this makes it easy for teachers to detect outliers and non-conformists. And indeed it is easy to catch sloppy children by strictly adhering to various formats and rules. However, this has far-reaching, unintended consequence.
Its become harder for a child to develop a sense of neatness in his or her work. There is a difference between a 'format' and a 'form'. Children quickly learn to mimic the format without developing internal sense of form and proportion. An elegant written work has a form - spacing, margins, tabs for paragraphs and justifications.
Sometimes, when kids ask me how they should write some text or solve a maths sum, I tell them to do it in a way that looks neat - no rules. And hope that they will learn to differentiate between neat work and sloppy work.
While it is easy to learn the format, it takes time and an eye to learn the form. Children wouldn't learn elegance of written work if we don't give space and time to explore.
Monday, July 5, 2010
Addicted to Eraser
They hold pencil in one hand and eraser in other hand. This seems a common style of writing these days. No sooner they make a mistake they want to erase and correct it. It may be a factual error, or a compute error, or even a case of bad hand-writing. Erasing your mistakes may seem right thing to do - after all children are conscious of their own mistakes, but it has unwanted consequences.
Firstly, by erasing their mistakes they forget about it and make similar mistakes down the line. Leaving a mistake on the page - there to see - helps in identifying it next time you do it. Secondly, most children are not careful in erasing, as a result their writing only becomes more smudgy. Some times the paper is torn as well. Why can't you simpley draw a clean line across your mistake and leave it there for the future ?
Secondly, this habit seem to undermine their confidence. The line between a 'mistake' and 'not getting it exactly correct' is very thin. For example, ask children to draw freely and they hesitate - unless they can use an eraser now and then. By relying on eraser so much, we seem to have closed the feed-back loop that allows a child to learn from their 'not exactly correct' wanderings.
In our efforts to improve educational quality, somehow we have sent a clear signal of what is correct and acceptable. Children are reacting to it by relying more on erasure. Will they ever learn to get things correct in first place, or draw lines confidently ?
Firstly, by erasing their mistakes they forget about it and make similar mistakes down the line. Leaving a mistake on the page - there to see - helps in identifying it next time you do it. Secondly, most children are not careful in erasing, as a result their writing only becomes more smudgy. Some times the paper is torn as well. Why can't you simpley draw a clean line across your mistake and leave it there for the future ?
Secondly, this habit seem to undermine their confidence. The line between a 'mistake' and 'not getting it exactly correct' is very thin. For example, ask children to draw freely and they hesitate - unless they can use an eraser now and then. By relying on eraser so much, we seem to have closed the feed-back loop that allows a child to learn from their 'not exactly correct' wanderings.
In our efforts to improve educational quality, somehow we have sent a clear signal of what is correct and acceptable. Children are reacting to it by relying more on erasure. Will they ever learn to get things correct in first place, or draw lines confidently ?
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