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Mathematics and Life 101 MOCPA Core of Innovation in mathematics education

 MOCPA Core of Innovation in mathematics education


Background During my Ph. D. work I studied the theories of  Constructivism, Guilford Model of Structure of Intellect and I realised that just drilling, practicing, the same types of questions is not going to make anyone better at maths. In parallel development, the trend of prestigious selection exams was also changing. The over emphasis on long, fast, calculations to reach one unique answer fast was being replaced by questions having multiple options as correct answers. Also, estimate, approximation, was also enough to reach that answer. 


With my Ph. D. Supervisor Prof. B. K. Passi, I thought of using the notion of divergent production as defined in the Guilford Model to enhance the mathematical competence of the students. Thus, the notion of MOCPA (More than One Correct Possible Answers) came into being. It was further enhanced to mean More than One Correct Possible Approaches also. Specifically in geometrical proofs there are many correct ways a rider can be proved. 


Limitations of one unique answer questions Some of the limitations of one unique answer questions are 


  1. They favour the students already good at maths, thus discourage the students working on them at their pace. With the right answer out, the teacher proceeds ahead.

  2. Do not recognise, encourage, individual differences.

  3. Due to rigid nature of the questions, they do not generate the desire among all students to at least attempt the questions.

  4. They do not help develop higher order thinking skills 


MOCPA Very technically speaking, the MOCPA questions increase the degree of freedom to answer. They give structural scope for improvement, to work at one’s own pace.

Let's see two MOCPA questions 


  1. For what values a and b will the equation a + b = 50 be true ?

  2. Make a triangle, name its vertices.


Answers - 


  1. Even the readers, however educated, would be surprised if I tell that question 1 can have even 1000 correct answers or 10,000 also for that matter. 


This is so because we can first of all add as usual 0 + 50, 1+49, …….then 50+0,49+1, …….. Then we can have negative integers like -1 + 51, -2+52 etc...then we can have fractions, decimals etc.


Now, once you give such a question to the class and declare more than 100 answers are possible, find as many as you can…..all work to their best capacity. The teacher role here is that of a facilitator, one who will move around and encourage each student to do her best. Teachers may ask all to share their answers without being judgemental or appreciating only those doing a lot of answers. The variety of answers is also very important.


  1. Here again, the students should be encouraged to draw different types of triangles. Like, each side is different, the triangle is facing downward, sideways, the vertices are not necessarily named in alphabetic sequence….


Evaluation MOCPA questions need to be evaluated differently, about which I will write soon.


Free Support In case you are stuck with some current or past sheet or concept and wish to clear your doubts, I will be publicly available on 


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Premium support  Individual, one on one, support for learning / revising / doubts clearing available on a case to case basis. Starting from 500/- per consultation, different services can be availed by contacting 8085906962 for appointment (5 pm to 8 pm Monday to Friday)


Dr Prakash Moghe

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drpnmoghe@gmail.com





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