Skip to main content

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 


Zoom ID 9615446314

Password 555628

Time 6 pm to 6.30 pm 

Monday to Friday


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

8085906062, 7489447223

drpnmoghe@gmail.com





Comments

Post a Comment

Popular posts from this blog

My Journey as a Maths Teacher – Part 2

  🧒 From Grade 3 to Guiding Future Teachers It gives me immense pleasure to be of some help to my younger mathematics teaching colleagues like Shruti Goel, Laly, Preeti Garg, Misha Nambiar, Rajendra Paliwal , and many others—across subjects and across schools. But things weren’t always this way. 📘 The Indore Phase – Simplicity, Struggle, and Silent Growth After leaving Mumbai in 1988, I served as a school teacher at Choithram School, Indore , till 1992. I even taught Grades 3 to 5 in a single session . Yet, the spirit was always high. I loved taking classes, creating activity sheets, and even wrote articles I mailed to U.S. education journals —long before emails were common. If there was one shortcoming I admit, it was in checking large stacks of answer books. I often rationalised, “I’m a creative person, so it’s okay.” In hindsight, it wasn’t—but the honesty helped me grow. 🔄 The Decade of Churn (1988–1997) It was a whirlwind decade. Imagine this combination: Ph.D. ...
Post a Comment
Read more

Mathematics and Life 1 Introduction to the article series by Beyond Abacus

Purpose of the series is to explain various basic mathematics concepts in simple language connecting concepts to examples from life,business, science, day to day life. It will be our special emphasise to develop what Dr. Prakash Moghe calls the math - language interface. That is, showing similarity between the words used in daily language and mathematics like point, ray, interest and so on......     Audience This series of posts is for everyone who wants to understand, learn, revise, apply maths concepts, formulae, and wants to develop Problem Solving Approach, critical thinking, design thinking, and mathematical thinking. Agewise , from age 6 to the time one wants to learn / revise / teach basic maths will find these posts useful in their own ways. Frequency of posts At least one post a day has been planned. Length of posts Each post will be self content, so will be long enough to elaborate the point and short enough to keep the reader engaged. The reach Each post wil...
13 comments
Read more

Mathematics and Life 87 You know maths worksheet - 3

  You know maths worksheet - 3 Answers to You know maths worksheet 2 True  2. True 3. True 4. True 5. True 6. True 7. True This was just a very basic revision of geometry terminology. Since geometry is unfortunately neglected across the nation and across the curriculum too, I have designed just a concept brushing, easy going test. Today we will discuss some questions which are a mix of basic arithmetic and basic reasoning ability A leap year comes in 4 years. True / False My friend said I have a one acre plot. Seeing me confused he elaborated, it is nearly 45,000 sq ft. Was she right ? I went shopping and saw an item labelled 2000/-. I also read it had a discount of 10% for the festive season and an additional 10% discount on that purchase as it was their Foundation day. I paid 1600/-. Was I right ? A purchased one thing in 100/-. He sold it to B for 125/-, who sold it to C for 150/-. Who made more profit A or B ? Why ? Or both made the same profit ? Five men can complete a wo...
1 comment
Read more