I asked my student today how she had done in her exams. She said she did well and after a moment added that she had perhaps not done so well in Mathematics. My heart sank.

Literacy and Numeracy are considered the two main pillars of education in India. When children start kindergarten (or even playschool) they are first taught skills to build strong foundations in Language and Mathematics. Subjects like Science and Social Studies are introduced in class three when the child is around 8 years old.

Children at a very young age learn anything provided it is presented to them in a concrete fashion. When a child sees a dog and calls it ‘doggie’ an abstract sound d-o-g-g-i-e becomes concrete. A child is able to form a picture of a four legged animal and learning takes place. However, the goal of mathematics education as mentioned in the position paper of teaching Mathematics of NCERT is that the child should be able to develop problem solving skills and also handle abstractions. How does one teach a subject that is meant to be abstract to children who are not developmentally ready to acquire it in the first place? Piaget’s Theory of Cognitive Development suggests that children from 7-11 years old need to use manipulatives to make the abstract concepts concrete. This stage is aptly called ‘concrete operations stage’. Hands on activities like using chips, counters and little objects to add, subtract, divide and so forth will accelerate learning. 7 to 11 years means class two to class six. Have you seen a class six student use objects or images to learn whole numbers or tests of divisibility?

The class six syllabus of Mathematics of the SSC Board (Maharashtra) includes topics such as ‘Use of Letters in Place of Numbers’, ‘Divisibility’, ‘Order of Operations and Use of Brackets’ which imply that the topics are indeed abstract. The aforementioned position paper suggests that there are several problems in successful mathematical instruction in India ranging from lack of quality teachers, inadequate training of teachers, outdated assessment techniques and in general “a sense of fear and failure regarding mathematics among a majority of children”.  Are children afraid of learning Math before they fail or after, is left unstated. If kids are naturally inclined to learn, I am assuming the fear of learning Math takes place only after one has failed. Failure in my opinion takes place only when students are taught inappropriately.

If Piaget’s Theory was to be implemented in teaching in India (like UK did in 1966) the fourth stage of cognitive development- the formal operations stage (from age 11 years onwards) would mark the beginning of the child’s ability to understand abstractions. At this stage children are ready to understand when a letter (abstract) stands for an entity (concrete). Piaget’s theory of Cognitive Development has been criticized for being very tightly compartmentalized and that learning does not really progress from one stage to another.

The theory of Bruner similarly states that there are three stages of learning, the first stage- the enactive stage which is teaching and learning through the use of concrete items, the iconic stage where learning takes places through icons or images (hence instead of using five chips to add, a child might draw five small circles) and then moves to the symbolic stage where language and symbols are used (e.g. 5 + 5). According to Bruner, for learning to take place, these stages must occur in sequence not necessarily according to age.

I have struggled as a student in Mathematics (I studied in a convent school of the 90s in Mumbai) I hated it since the time I was in class one. I clearly remember a teacher teaching us subtraction making us colour squares in our square-line math notebooks. Iconic when we were supposed to be taught enactive?

Going by Bruner’s Theory, learning takes place when every child masters every stage. Those students who find it hard to grasp a topic at the symbolic stage need to be taught at the iconic even if it means it is for just one student in the class.

Well, it is hard but that’s why there needs to be a better method and thought put into teaching Mathematics if not at the systemic level, then at least at the class level. If we have to implement both the theories, teachers need to make Math concrete for students even if they are at a different stage according to Piaget. Because according to Bruner, what if students have skipped a stage in the progression?

Hence, dear teacher in secondary school- carry to class a box of marbles. Someone might need it to count. And know that it is ok.

There are two activities that I have been engaging in recently: cooking and working on the new school I am building. Every time I cook and try to salvage a dish, I have so many thoughts going in my head related to school building. Just putting some of them together: would love to hear some reflections from you!

1.       Preserve the flavor of every ingredient in the pasta

It is tempting to add numerous ingredients into the pasta. Red and yellow peppers, tomatoes, broccoli, different herbs and spices, cheese, flour and so forth. It is however, important to keep in mind that no matter how much you would like all the flavours to infuse and add to that one taste of your pasta, it is best to let the tomato taste like tomato. A school is often a community of very different people. It is the diversity of every teacher and student, and the skill that they bring that adds to the distinctness of the school. As much as a school leader would like to be fair and treat everyone the same way, it might not be possible. A school leader must make space for differences. Also when a teacher or student is allowed to blossom in his or her uniqueness will the person grow in his or her truest form and be more comfortable achieving what is set out for them. Like Surya Pratap Deka says, we need to respect the plurality of every child.

2.       Check the core of the cake or the base of the pizza

A cake might look done from the outside and a pizza might be ready from the top however its only until you check the core of the cake do you realize it is yet uncooked or that base of the pizza is burnt! Things might not be as they seem. A school leader needs to check the core of the school- systems need to be put in place to listen to every teacher, every student and every parent. No formal systems might be necessary- just a walk out of the office during class hours and break times to speak to children and really listen is worthwhile. Asking a child in a class how he or she has solved a sum can show if what the school has planned at the top reaches the child in the way it has been envisioned. Kiran Bir Sethi uses her kids’ feedback as an extremely important tool for the design of her school.

3.       Use the vinegar if the lime is not enough

It takes a lot of expertise and research to use vinegar in a dish. Its strong taste can make or break the dish. It is easier to use lime. One can never go wrong with it. Sometimes, however, the dish needs vinegar no matter how potentially harsh it might be. Similarly, it is tough to be a little strong with stakeholders- it is simpler to use sweeter words and means. However, sometimes, it is not enough- our kids’ learning time is limited and if a teacher needs to be told a little strongly that she needs to change her ways, it needs to be done. While talking to one of the school leaders of Success Prep in New Orleans, the school leader told me that they ask teachers to leave if the teacher is not making a meaningful difference in children’s learning. It is hard, he said, but the teacher who was asked to leave felt grateful for it, as he knew he should have left long ago, but didn’t have the courage to take the step. The school leader, actually, helped him.

4.       See the recipe book or call out to your mum

When you don’t know what they mean when the onion has to turn golden brown- call your mum. She knows. And she will tell you that the onion is far from turning golden brown- it’s burnt! It always helps to have someone tell you what to do when you really do not know. That’s why we have school coaches, team members and friends. It is ok to ask.

5.       Stick to the plan

When the omelette sticks to the pan, it is tempting to stir it vigorously and change it to scrambled eggs- and tell everyone that you changed your mind about making an omelette. It then does not taste like an omelette nor does it taste like scrambled eggs. It is also tempting to change course- a curriculum, pedagogy or a plan mid way because of the uncertainty of what the end product is going to look like. It is tough to wait for 5 years to see if what we did or are doing is right- what if it is wrong? I am not against reflection and course correction, but sometimes it is necessary to keep the faith. Adequate research and the best of execution will bring out the best results, even if it takes time. Mr Rohit Dhankar, Founder of Digantar- India, says that it is best to look out for best practices and learn continuously, as innovations take place every day. But it is imperative that one stops after one truly believes one has found the way and then make sure to pursue that path diligently.

6.       Check each ingredient before it goes into the pan

Only after the salad is ready sometimes, I realize that the cucumber was bitter. And then I need to add some lime to deaden the bitterness, and more cucumber to balance it or then add vinegar. The salad remains bitter. A less bitter, but bitter nonetheless. You get the drift? Every person who joins the team is important. Settle only for the best. Every process, training programme and method is important- choose it with care.

7.       Tea leaves give out the flavor only when in hot water

Along with the flavor, they also give out a beautiful colour and fragrance. Some people surprise us with their true potential only in times of crisis. Some people show tremendous grace under pressure. The best way to bring out the best in people could be to invest in them a huge responsibility that even they might think they are incapable of carrying out- it will bring out wonderful surprises. Like Purvi Vora’s teachers creating the curriculum that was then implemented in several schools of the foundation.

8.       Pickles take time but then add that amazing zing to the meal

It is an effort to make pickles- cut the raw mango or beet, put some salt, some other spice, make sure it is good- even then for some time, the raw mango or beet will be insipid. And then you doubt if the salt was right or was the spice too less. But one day when you taste it, you will know that it turned out amazing. It is the only thing you need to finish an entire bowl of rice! Some members on the team take time to gel with others and even with you. Let them take their time- as they are going to blossom soon. Similarly, with children- once they bloom, oh, there is no stopping them!

9.       Some things are best eaten cold or a day later

You will burn your tongue if you sip the coffee or bite into that red hot sandwich. Molten chocolate cake fresh out of the oven is just a name- it needs to cool slightly before being eaten. When things go wrong and someone has goofed up, the issues need to be resolved some time later. When emotions are flying and tempers are flaring is not the best time to make decisions. Let things cool- it clears things a bit. Reaction is different from response.

10.   You need to toss, turn, press, check, stir, chop and serve

Despite everything right in the pan- the cook has to do the cooking. She cannot go watch TV or take a nap. The cook needs to stand there, by the pan, watching, smelling, and checking to see if everything is going on smoothly. To increase the flame or decrease it, to stir and shake things up a bit. The school leader has to take initiative, lead and get things done.

11.   Check the water

Water washes of the spices, cools the temperature of the dish and generally does what water does- waters things down. It might not harm to add a little water to the soup to feed more people, but after a point, the soup might not remain soup. As much as quantity is important, one needs to keep an eye on quality. In a country like India, of course we need a hundred schools- but not at the cost of the quality of impact.

12.   Keep calm

The greatest chefs suggest that one needs to keep calm when the dish is not going right. Panic will add to errors in judgment and the dish is sure to fail. Most often cooks give up cooking when they begin to panic. Similar to points 5, 8 and 9- calmness helps. 

13.   Add the secret ingredient

In India it is rumoured that every mother, every wife and also every great chef uses that one special ingredient in the dish- it is called love. It is considered more important than salt. If there is no love in what one is doing, the ‘school’ is sure to not have any flavor.

                                                                                    (First written for Synergies- Teach For All)

I have been walking into different school principal’s offices on several occasions. A principal’s office offers insight into what the school stands for. Sports, elocution, academic success, success in social service are all on display through the scores of trophies or certificates. The office might have a lot of paper, books and also sometimes a computer. I am prepared for all of these- but the one thing that really takes me back is the presence of an electronic surveillance system.

Let me explain for those of you who have not been into a principal’s office recently. The surveillance system consists of a huge screen that is divided into smaller portions that broadcasts what is going on in classrooms. The screen (which is generally a high end television) is mostly switched on and gives the principal a snapshot of what is going on in the classrooms. There are small CCTV cameras fixed in every classroom including the library, laboratories, and school playgrounds and even at the entrance gates. These cameras create a feeling of being constantly watched hence deter any misbehavior on the part of the students, school staff and in general, any visitor.

These systems make me wonder what is going to come next. Air conditioners are passé and since I have never studied or taught in a high end school I am not sure if I will be able to predict the trend.

Surveillance is everywhere nowadays. The US government’s watch on countries has created outrage and a general feeling of distrust among those who are being monitored.

I studied in a school around a decade ago and at the time there were no such fancy gadgets. This meant that students were not caught red handed doing anything- making noise, bullying, or distracting the class. Teachers were free too- they hit and pinched when it got tough and apologized to discourage the matter from being escalated. No principal had footage of the past seven days to refer to in case anyone complained and nobody probably ever felt the need to refer to it anyway. There are some benefits of using such technology in the schools- children, authorities and everyone else involved are safer even if only psychologically.

There are some places that need to have such surveillance systems like those which are characterized by anonymity, aloofness, huge numbers and impersonality. Public transport systems, malls and high security zones call for such monitoring. If a person is not going to be identified, is not part of an identifiable relationship, and does not have any emotional bonds with the place, damaging behaviours can occur.

Research has shown that surveillance can create feelings of distrust, conformity and mediocrity. Imagine a classroom that has CCTV cameras installed full of students misbehaving. Would a student have the courage to stand out, therefore making herself more visible, and make the rest calm down? Solomon Asch’s studies on conformity have shown how people are doubtful of their ‘correct’ behavior in the presence of those who are ‘wrong’. It is easier to get punished together. Being constantly watched also increases stress. As teachers we have surely observed students who stop writing their answers when they are being watched (studies show that stress interferes with recall). We clearly make more typos when someone is watching over our shoulders what we are typing, don’t we?

These thoughts are triggered every time I see such systems in places like schools that are supposed to have a feeling of community and togetherness. Have schools become so large that school principals are unable to observe instructions everywhere? If our school leaders do not interact with nor visit students do they have a clear idea of how the child is achieving? Are huge populations (especially in a country like India) valid excuses to start schools where a child is not known by name? Are our teachers those who need to be monitored or to be equal partners in building the school? Do our teachers own the school and its systems or do they view it as an impersonal entity? The questions are endless.

I have had the privilege of working in schools and visiting several where every child is known by name (and the names of their siblings, their parents, the parents’ professions, the marks that they have been getting in different subjects and sometimes even what they eat for breakfast!) Such schools exist. But can all schools becomes places where learning is a collaborative process and where everyone takes ownership of the school to the extent that nobody bats an eyelid if the study areas need to be swept or books in the library need to be dusted and there is not one person whose job it is to get that done?

When schools become impersonal and very large to be able to humanly manage, we begin relying on machines and technology. This is then what is scary, we are creating a generation of students who psychologically feel constricted in their thoughts and behaviors on account of being watched every single time.

While we are creating ‘disciplined’ children we might be creating imprisoned adults.