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.

The backlash

It was report-day today. Parents came to collect the term reports. As parents went over the answer-sheets of their child, it was interesting to see the their reaction - shaking of their head in disbelief. Irrespective of whether the child had done well or not, parents typically got upset about the mistakes and marks lost.

A few parents reprimanded child on the spot "See I was telling you". Discussing marks on the result-day makes no sense. In fact it is useless from the child's point of view. It doesn't help the child study better, on the contrary, they are repelled and shamed. It creates a backlash and they just shut the parents out.

When a child hasn't performed well, invariably it is due to lack of understanding or skills or habits. Low marks is only a side-effect of poor study skills. While poor study-skills lead to poor marks, shouting about poor marks doesn't lead to improving study skills. None of the success factors grow by hectoring children on the report-day. To master these skills one needs to make long-term efforts.

A few children had come to me before the report-day. They asked me to tell parents not to scold them about marks. They were down in spirit in anticipation of the report-day. And I agree with them. Parents (and teachers as well) should avoid talking about marks, defuse the anxiety on the report-day.

Did I have any suggestions and advice ? parents would ask me afterwards. Yes, I did. "Instead of discussing marks let us cheer them up and ask, what can we do for the long term".

What did I learn

I was going through my students' note-books. As every teacher knows - there are tonnes corrections to be done. Since I give notes of my own (and not from text book) it involved reading my own words through a mountain of note-books. In one note-book I ran into something different. This boy had scribbled something in the margins every few pages. He is an enthusiastic but disruptive boy, so I was irritated see this mess.

To my surprise, he had written "What did I learn" after every topic and in the narrow margins. He had summarized what he found important after we had finished a topic. That was so sensible, and why had this not occurred to me. What did I learn ? I decided to make this a formal practice for my lessons. After every major topic, I would quickly round-up 'what we learnt' from students and commit them to the notebook. This time, not in the margin but within the notes.

The next day, I celebrated this boy in the class and thanked him for giving me this great idea.

Failing the intent...

Over last two-three years, I have observed a curious thing during the school exams. Usually teacher hands-out the question paper a few minutes ahead of the answer sheets. The idea is, by reading the questions in advance, students can organize their thoughts and plan their answers.

However, as soon as the question paper is given the doubts and questions start coming up. Here is a collections of questions that keep coming up again and again, at every exam. Should we also write the questions ? Should we write entire sentences or only fill-in the blanks ? or can we write only the blanks (!) ? Can we solve questions in any order ? How much should I write for this question ? For match the pairs, do we have to write the pairs or only labels ?

These are questions just related to the format. Then there are questions related to the content, comprehension, spellings, grammar. How much time will I get  ? Can I write on only one side of supplement ? the questions continue almost till the end of the paper. If the subject teacher makes a mistake of visiting the class suddenly new questions appear. Now it become difficult to decide if we are clarifying the doubts or actually giving them clues and answer to the questions ? The boundary becomes blurred.

As a teacher, I find this most irritating and worrying. What is missing here is the ability of students to recognize the intent of the question, the question paper and the examination it self. They are unwilling to (or unable to) guess the intent of the question and answer it. Instead of becoming wise thinkers students act like drones and clerks.

Interestingly, this doesn't mean they have become stickler of rules. When the time comes to collect the answer sheets, despite of several reminders, you will find handful of papers without names, roll-numbers, wrongly stapled supplements, answers written on wrong side in wrong order, forgotten to write the question numbers.

Students are failing en-mass to see the intent of the question (what is the purpose of the question) and act judicially accordingly. It seems, as though they can take-in only a word at time and never see the larger picture.

For some reason, such behaviour comes out most during the exams. However, I suspect, this lack of ability to read deeper intent of questions or comprehension must be wide spread.

What are exams for...

In any subject or for any skill, the abilities of students vary. Some are naturally good, some learn to be good, some struggle to learn and some can never really acquire the skill. This is not abnormal. This is how people (even grown-ups) perform on any skill, craft or trade.

If an exam is given to test an ability and we were to plot how many students did how well, it would follow a Bell-shaped curve. A few students would do very well, majority of students would do ok and a few would have done not so well - making the graph look like a Bell. If you are testing a skill and your exam shows this curve then you should celebrate - because your test was fair to all and balanced.

A balanced test is telling you with confidence that those who are on a lower side of the Bell need your help, those in the middle of the Bell need to understand and work harder and those on the upper side of the Bell should work on advance skills. Everyone need to work towards better.

This is not how most exams look though. Most often teachers think that if majority of students get more than 60-70% marks then they have learnt well and teaching was a success. The trouble is, when everyone gets good marks, you are testing very little. And if you get less than 40% then you have failed. They automatically create two casts - those who pass easily and those who fail bitterly. Such exams say more about the exams themselves (was it easy or hard) than they say about the students (who are good and bad performers). They say very little about who is where on that skill. Exams should not to tools to fail students or even pass them.

A good balanced exam will be one in which students follow a Bell-shaped distribution of performance, with majority getting marks close to 50%. In such an exam, there is no pass or fail. Everyone has passed ! Some need to learn more, some need to work harder and some need a greater challenge.

As a teacher one needs to aware of what an exam is testing. Are we measuring students abilities ? Are the marks artefacts of the way we give exams ? Exams should be used to set a passing bar ? or Should exams evaluate abilities and take remedial actions.

When did you understand fractions...

This is a question I often ask parents and other teachers. Fractions are taught as a chapter in Grade 5. At the end of the year students are given tests on fractions. And they pass with good or bad marks. But this has nothing whatsoever to do with understanding of  fractions.

We really can't say when we understood fractions. Somewhere from age 9 onwards the sense of a "fraction" gradually builds. Some interesting twists in fractions may occur to us many years later. For example, its not easy to realize that 1/5 of something can be greater than 1/3 of something else. Then we see how fractions are also related to percentages and to decimals. This is how any true knowledge is built - gradually and through different experiences. Over time, different aspects of the concept are polished. We make mental and graphic links with related concepts and a deeper understanding is built.

If this is how we learn and learn well, then why are our Tests not designed for this. While learning is a continuous and interactive process, testing is not.The Exams expect that everyone in the class must learn fractions in Grade 5 to the given competence level and prove it by getting passing marks.  Our exams say, you better know this here and now, else you have failed.

This create two bad trends. Firstly, students just learn to operate numbers by given rules and get the correct answers. Getting marks makes them think that they now know fractions. But there is no real understanding happening. Secondly, students who can't grasp the rules fail, nearly fail or barely pass. They have no second chance. In Grade 6 we move onto other Math things, too bad for you.

Our Exams are designed to disrupt the learning process, to encourage learning rules and to disqualify those who can't do it here and now.