What Galileo discovered

I never thought a simple pendulum could generate so much excitement. We are studying estimation and measurements. One of the things that I wanted children to understand is the concept of 'per second'. So we decided to look at simple pendulum. Each group made a simple pendulum of different lengths using thread and stone.

The story goes that, Galileo was attending the church one Sunday and he noticed the swinging chandeliers. Using his own pulse, Galileo measured the oscillations. He found that oscillations can be used to keep exact time (which was useful for making clocks) and oscillations don't depend on the weight (which may have led him to the famous Pisa experiment). Would you want to discover what Galileo found out ? I asked, and the students got in to a frenzy.

Each group counted the number of oscillations in 10-20 seconds to find out its period (the number of oscillations per second). We did 5 measurements to get average and accurate period. They now know that more number of observations when averaged give accurate measurement. Tomorrow we will be tabulating all the lengths and periods and find out what the data tells us. What surprised me was the amount of excitement this generated. 

This confirms my hunch that children like to step into the shoes of Galileo, Newton, Darwin or Faraday. We should teach science as it was done by these great people. The way they found things for the first time !

Express yourself

It can be safely said that if you can't express it you haven't understood it. This, rather obvious fact, is grossly overlooked in classes today. The flow of information from teachers mouth to students hands and then to teachers eyes and ears is tightly controlled. The subject is broken into concepts and concepts into bullet points. You read these points, students write them and in exams they give back those points to you. This has hardly any space for students' expression.

It is not surprising that students are high on marks and low on understanding. The fault is not theirs but ours - we have left no spacein class for them to express what they think. This is a great loss because the process of expressing (call it explaining) is a powerful tool to promote understanding. A good explanation can tell us what we know and what we don't know. When a child tries to explain things, he/she is having an internal argument. If the child is correct then you will find a new and original explanation. If the explanation is wrong then you have greater chance to find out where the confusion is, either way you learn.

If you want to promote original thinking and true understanding then it is crucial that we spare time in our classes for students to talk. We should let them explain what they think in their own words. Expressing your thoughts verbally is a powerful tool to drive understanding.

Rigged

Are exams suppose to evaluate how well you have learned ? Then, by this standard, almost all exams are rigged. Over time we have somehow come to deceive ourselves. There is a simple test to tell us if we are truly testing childrens abilities. I need to explain.

For any test you give find the distribution of the marks children have got. You can do this by counting the number of children who got marks between 0-20, 20-40, 40-60, 60-80 and 80-100. Now plot the number students against marks between 0-100. If the test is fare and balanced you should get a curve that looks like the following.

If you were to plot the distribution of height of students in your class, you will also get the same Bell-shaped curve. How is it that such widely different things give you same curve ? Well, many things in life follow this curve because there is a range of competencies (or heights). But they are not totally random, they stay close to average competency or the average height.

In this Bell-curve you will have majority of students getting close to 50%, some are getting less and some are getting more than 60%. The average marks should be close to 50%. In such exam it should be easy to get above 30% and difficult to get above 70%. It would test everyone in class - those who are slow to learn and those who are fast to learn.

When the distribution of any measurement doesn't follow the Bell-curve, it may have many reasons. But the two most likely reasons are - either our class (or sample) was not balanced with a range of students, or our test was not balanced with a range of questions.

I bet that for most of the exams the Bell-curve is not balanced and centred at 50%. Most children get above 60%, many are close to 80% and a only a few get bellow 30%. The Bell-curve is considerably distorted and shifted to far right. The shifted and distorted curve is telling us that we are making it far easy for under-performers and we are dumbing down high-achievers. We are moving most of the class into average performance zone. This means that we are not differentiating under-performers and high-achievers well.

This is not surprising given that none of us, parents, teachers or students, want to take any risk. We want students to do well and move onto the next grade. Marks are usually like a barrier to cross. Once you are over it, you go to the next grade. Our exams reflect these desires. Exams act like a filter to promote students and not to evaluate competencies. We aren't treating marks as indicators of performance, but only as licence to get to the next grade.

However, this is perpetuating a larger tragedy. When the distribution is not Bell-shaped and centred at 50%, we failing to identify under-achievers and their deficiencies. We are also failing to recognize the true high potential of high-performers.

So next time you look at marks, as a teacher or a parent, ask for the distribution plot, Does it look like a balanced Bell-curve ? and ponder !

Compared to what ?

Can someone tell me how bad a hand writing should be before it can be called illegible ? Typically, when a teacher corrects a note book or an answer sheet, a badly written answer sheet can take twice as long to correct. As the hand writing degrades, teachers struggle to understand what is written. After all, the marks are to be given for the content alone – who cares if teacher takes twice as long in grading that paper. Most teachers evolve strategy to deal with badly written papers – they either correct them up-front or keep them pending till the end. 

Many urban schools have taken their eyes off the art of writing. We teach writing alphabets, then words and then cursive writing. Thereafter we do not enforce writing – it’s not in the syllabus. For many children down-hill journey starts from here. They adopt bad postures and use jell-pens. As the pressure to write lot and fast builds their hand writing degrades.

By the time children reach secondary school their hand-writing ranges from good (for a few) to ok, readable, bad and unreadable (for many). Badly written notes, illegible answer-sheets, poorly drawn diagrams now result in poor academic performance. But it’s too late.

It's hard to say when a teacher should give-up. However its easy to get consensus on a good hand writing. This is why we need to establish writing standards in schools. These standards help us, students and teachers, realize that one needs to be close to the standards. In absence of any such guidelines, we are on a slippery slope leading to illegibility.

Adopt fairly broad standards for good writing, push students to conform to them though not strictly. Instead of not having standards, not promoting it and then suffering from a range of illegible writings.