Assessment through a three facilitator model

Assessment is one of the most challenging task in any form of facilitation and it becomes even more difficult in a workshop model. Workshop offers its own unique challenges and opportunities. Till the interaction with the learner is continuous and comprehensive, even the remedies or steps taken by facilitator will be fruitless. Hence I will discuss a unique model by which, the concept of CCE (Comprehensive and Continuous Evaluation) can be utilised to its optimum.

The approach towards this problem is actually utilising the strength of workshop format of learning. Classroom learning in schools is generally constrained by a single teacher burden with many tasks of facilitating the learning process, evaluating the learner, create a comfortable learning environment and many others. But in workshop model, there is no constraint on the single facilitator. We believe in the 3 facilitator workshop (Lead Facilitator, Support Facilitator, Impact Assessor)  in which there is a division of various roles and responsibilities :

  1. The Lead facilitator is one who is directly involved in content delivery and conceptual understanding of the learner. The complete design, methodology, and delivery is the major responsibility of the Lead Facilitator. 
  2. The Support Facilitator is one who is the walk around person during the session. They are part of the learner surrounding and usually sit with the crowd. Based on the preassessment, they involve with the various group (For more on How to Group Learners) of learners to help them in their specific area of improvements and cognitive development. The support facilitator work as the backbone of the learning process.
  3. The Impact Assessor continuously evaluates and assesses learners behaviour, social and cultural responses. They act as a direct source of information for the support facilitator.

Such a model would solve the challenges of execution of CCE and help in the decision making process as the workshop proceeds from session to session.



Do we educate to be free?

This question does not lose significance ever. This has been asked over and over again and there have been many answers that have given and are still been given. Before we try even  tentatively to answer this, lets try and first be very clear as to why are we even asking this question. Another thing that becomes important is to see, wether the question has rightly been understood. I believe that the two things are not very different. In fact we cannot draw a line which shows that this is relatively more important or that is more important. Our reason for knowing the answer or the seriousness of seeing the question.

The very idea of importance shows a division. The division of what we want and what exists but we don’t want. So lets not create this division and straightaway look at the question itself without denying relevance and attention to the other related things. 

Why do we educate?

And what do we in the first place mean by education. I will not try and point out what has already been said in terms of the instrumental aims and the more spiritual or holistic aims of healthy mind and body and for some healthy soul. 

What I want to point is the way this above answer or enquiry in the first place has created a division. The division between the mind, the body, the soul. Have we really gone into the question deep enough? Do we see that there is actually a division or we have been told innumerable times so our mind has got accustomed to it. So accustomed that now the moment we say something it tries to interpret and create labels to hide the fact that we don’t know. Or conceal and cloud the very perception of what is. Is there actually a division? 

Krishnamurti has tried to answer this in many of his talks or rather discussions. He contends that the division is not real and the thought which operates always from past tries to possess the reality and that which is. So what is it? 

Has our education ever tried to answer this. There have been philosophies, the existentialist, the naturalist, the Platonism,etc. But have we seen this rightly and alertly. All the answers given in this moment will be conditioned. So can we sincerely look at it. Not as professionals, not as academician, the expert, or a reformer, but as an enquirer. As an innocence which is not ignorant. 

Whatever answer we can conceive right now 

will still be within the ambit of thought and the thought is never fresh or authentic. So if we see this, and see it totally, absolutely, then we for the first time see that which is. It cant be expressed or put into words. The words limit the very perception an make and ideology or concept out of it. These concepts though give us some temporary security are not real. So the security also is imagined and hence false. 

We see this in all our relations, with the mother, the brother, the wife, the lover, and at a more glorified stage the world. The very security that we seek is not there and then it disturbs us all the more. The thought is so powerful or apparantly so powerful that it again creates some utopia and gives a false illusion of security. Wether it be the god, the new lover, the new relation, some different place, a new job, a new engagement. But do we who is still the same, the same timid and insecure being see that the basis of the security is always false. Be it external in the form of new relations, people, or be it in the internal convictions and beliefs. 

So how can we be free of it? And is the freedom from this absolute? Can it be absolute? 

Should education which is not only restricted to the spaces like school or college, try and engage one with this. Is this not what we always looking. The eternal and more profound security. The security which does not deny the reality but rather sees it. Sees it totall. In the totality is acceptance which is not imagined or imposed. It comes so naturally that it does leave any footprint. We cant say that i accept. It is just the acceptance. Nobody to accept but just the quality. Is this the true place to start with. 

Can education make us free? 

Not the freedom of movement which is important though, but the freedom from the me. My idiosyncrasies, my idea, my world, my ambitions, my wife. Can we be free of it.

There is no answer as there is no one to answer but just the enquirer, which is also not true. So is it just the enquiry with no content and no subject. 

Is this the true freedom. Lets find out.

Gaps in Learning Mathematics

[dropcap]A[/dropcap]s we become conscious about the teaching and learning of mathematics from the children’s point of view; it proves to be more challenging to make children love or learn mathematics. When we consciously plan something for children, we think of lot of methods and strategies by which they will understand and relate to mathematics. .

We are designing a mathematics workshop for school children of middle grades. We are at the stage of content development. It is easy to say that planning something for children is a simple task; we just need to take books of different authors and pick out certain activities and question from them and articulate it to children. Unfortunately this is a slippery path and a small mistake can lead to failure of the whole content development process. Is the planner actually aware of the needs and level of children? Or there is no need to think about the children for whom we are actually planning. .

The whole process came out to be a learning process for ourselves where the healer is healed. While going through the process of planning for workshop we actually struggle with our own thoughts and concepts; that how can we be helpful to them and make them go through different experience of mathematics? Are they actually able to understand, what we are aiming for? It becomes more important when our primary aim is to make children love and enjoy mathematics at a level when it starts becoming more abstract, boring and a rigid subject. .

The society perceives becoming a teacher is the easiest thing to do, anyone can do that. At the other end, it is difficult for students to relate and develop connections with the most of the subjects. The case with mathematics is even worse. We can easily figure out that teaching mathematics is very easy till that point of time when it sticks to textbooks or solving questions. But what when children deal with real life problems? Children fail in dealing with the shopkeeper or are less fluent in finding an average in the cricket match; still after doing all the math in their notebook. It becomes more challenging to equip children experience mathematics in their day to day life. .

This situation somewhere reflects that mathematics is not what we perceive and do in our textbooks. It is far beyond that. When we think about planning from the perspective of children than we realize the essence or nature of the subject matter; whether it is mathematics, language or history. Schools somewhere fail to provide experiences of different nature of the subject to children and limit them to their notebooks, memorization, tests and marks. .

These practices somewhere develop a gap between children’s real experiences and their knowledge. It is important to align children knowledge and experience and bridge the gap between the two for they will never meet without conscious effort and planing. We need to improve planning, pedagogy, textbook, teacher training courses and many more. There is a need of conscious effort in these directions to become an educators and facilitators for children education. .

Grouping Learners in Math Workshop

Teaching Maths in a workshop model offers great opportunities and constraints for both the facilitator and the participants. Identifying learner behavior is one such challenge and catering to their specific needs is even more challenging. One of the strategies that can be taken by the facilitator is to group learner without them identifying the criteria of grouping. This should be so much embedded into the design of the workshop that it either becomes part of some game or an activity. If such an activity cannot be designed, a pre-assessment can go a long way in grouping students according to their potential. Few Points that needs to be taken care for are:

  • It is possible only in a multi-facilitator workshops.
  • The grouping must change from session to session based on the different types of grouping done. For example, type I grouping can be based on previous knowledge while the other type of grouping can be based on their social behavior.
  • Each group must be mentored in a specific way as per the grouping strategy.


How to Think like a Mathematician?

[dropcap]H[/dropcap]ow do great ideas take form? How does one think and develop great concepts? And above all, how do some people are able to think in an abstract manner while others are not? We have a perception that one needs to be a genius, great scientist or a mathematician to develop great ideas. What we fail to realize is that these geniuses are born and nurtured among us just taking a different path in their growing years. They develop certain ability or a strategy that helps them master any concept. I feel any strategy in a right direction is fruitful given it is practiced for a long enough time. I will try to list here few of them that a learner can adopt and practice to be better at Mathematics. Though the context here is Mathematics but a learner can apply this in any field of understanding and knowledge discovery. .


When we start learning anything or try to grasp a concept, it is important to start using the first principle (The first principle approach is to start at the beginning of the concept. You clear your basics; understand it and build subsequent ideas upon it.) As soon as the bas concept is clear the next important thing in learning anything especially Mathematics is to doubt. You should not just accept anything as given rather doubt it to your level of understand by putting forth contrary examples or situations. Test it yourself approach is the best for clearing your own concepts and understanding. It is a two-way approach; one it tests the truth and falsity of the statement given and also helps you grasp the concept thoroughly. .


Thinking about the problem is necessary inorder to make new connections. Try to spend as much time as possible with the problem. As soon as you start to doubt; give your mind some time to absorb the content and ideas. When we think too hard on a problem and then give our mind some space to make connections among discreet ideas it results in a much better understanding of the problem at hand. .


When we reach conclusions, it is important to start writing. Many of us believe that we can do this or achieve that but fail to give it a concrete form. The best is to start writing down all the ideas and try to make a mind map. Once we have written all the ideas and conclusion; the next step is to organize it and try to make logical connections among the ideas that we have written down. You will realize that seemingly discreet ideas suddenly start making wonderful connections and relationship. This might not lead you to ultimate answer but will surely take you forward with the work. .


It is easy to reach conclusions but difficult to verify it and say in absolute terms. So test it out with examples and relate it with other subject areas. It will help you to understand a concept thoroughly not just broadly. You will be yourself surpirsed to discover the constituent of your own thories and conclusions. Such a process will help to keep the undesired results out and further improve our results. If your conclusions seem correct, you’ll move forward and using your own theory, you can build your own examples and problems. .


All the vague ideas and conclusions that have been verified; tested with examples and improved must be written in general ideas annd theories. It is important to build a theory so that a logical sequence to your understanding of the problem can be identified. It will also give other readers a clear path to follow which ultimately they should also doubt to keep up the spirit of mathematics. Once the theory is ready; the hardest and the most critical step is to formulate your theory and prove it.  It requires tremendous amount of effort and some prior mathematical knowledge to formulate a proof. Once you have formulated a proof the work is done and you can repeat the process to DOUBT. .



Is Mathematics innate?

I gave choice to my niece of around 1 year that she could select one of the 2 packets of chocolates. One hand had 2 and the other one had 4. She was able to observe and choose the packet with more chocolates. Also, whenever given a choice she always chose toys or objects which were relatively bigger from each other. The case of my niece is not unique and the root to our perception of something big or more has been critical to our evolution. Humans were a hunter-gatherer society and it was necessary for survival to be able to identify trees bearing more fruit than the ones that bore less. The situations like this and many other throughout our evolution helped us develop a sense of number.

We never taught my niece counting or numbers or any other mathematical concept. How could we? She was only 1 year of age. These experiences show that there is something innate about the way we perceive and view numbers. And what does innate mean in mathematical understanding? Innate is the ability that the child is born with or which is present in the child from birth to understand the world and make a choice using the mathematics senses(he) is born with.

Noam Chomsky, a linguist put forth the idea of Language Acquisition Device which is hypothetically present in human beings when they are born. And research has shown that when human beings are born they have this device which helps them acquire the language that is spoken around them.  Similar to this, there is some research that shows that children also do respond to mathematical clues given to them in earlier ages. For instance, when a toddler is shown some objects say; 2 pencils and then after that, a pencil is added, toddlers are more likely to respond differently and this shows that there is some innate knowledge that children have when they are born.

To better understand, if we talk about animals, they also have some mathematical sense when they are born. Like a horse cub who is lost in the forest can easily identify the appropriate way if there is 1 tiger on his left and 4-5 on his right. He would either find another way or choose the way with one tiger as the horse cub has this innate ability to differentiate 4 or more from 1.

Mathematics is innate in humans as well as in animals, but that doesn’t mean that they are fully equipped with mathematics. They just have a sense of mathematics and that too is a part of their unconscious self.