Beyond Abacus

A new leaf…… Answers to the question number 7 Quiz are given in the pic below  I am very glad to share that in pursuing the ways to maths teaching - learning more student - teacher - parent friendly, I have been repeatedly asked my daughter Snehal Moghe, now Mrs. Prabhune, to link Artificial Intelligence gaming and other features to enrich learning experiences of the students.  She will be joining us to share her expertise for teachers to use AI Principles  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 80859...

  You know maths - Properties of Parallel lines Background Today we will discuss some properties of Parallel lines The figure below has 7 distinct diagrams numbered one to seven.  Although many academicians do not like the idea of denoting angles by numbers, I find it very convenient to explain without going into naming angles in terms of vertex, arms. I have also used a,b etc to show different angles. Figure 1 line l is parallel to m and m is parallel to l. This is called symmetry property. Figure 2 Line p is parallel to q, p is also parallel to r, so q is parallel to r. This is called transitivity. Figure 3 line m is parallel to n, p crossing them is called thetransversal. The angles shown as 1 and 2 are called corresponding angles. Because each is above the line. If both angles are below the line, they too are corresponding angles. They are equal. Figure 4 Line l is parallel to m, q is the transversal. Angles 1 and 2 are called alternate interior angles because they are on ...

  You know maths - Parallel lines  Background  In continuity of the framework You know maths , today I would like to discuss the concept, examples and non examples of parallel lines, spaces, surfaces, planes in daily life, sciences and so on. Parallel means which do not meet at any point. In school mathematics, we use this term for two or more lines which never meet. It means, however you extend them on both sides, there is no point at which they will cross or meet each other. There are many properties of parallel lines with reference to various angles between them and the transversal (a line crossing or cutting them at different points). About them we will discuss in a separate post. Examples of parallel lines lines drawn in a notebook, lines drawn on a graph sheet, printed lines in a book, opposite sides of a parallelogram / rhombus / rectangle / square,  Parallel lines / surfaces in life opposite sides of a notebook, door frames, bars in a window, legs of a study...

  Evaluating MOCPA questions Background Now that we know what is MOCPA in mathematics education, the next important question is how to evaluate them. Evaluating means measuring and giving professional assessment, including reporting of the results of the measurements. As the MOCPA questions create a large number of correct answers, it is essential that the teacher evaluates them very carefully. The teacher can evaluate them for  Fluency Large number of relevant answers. Means, in the a + b = 50 question, the student gives a large number of relevant answers. Flexibility The student shows variation in answers. Like, in the a + b = 50 question, the student uses positive, negative, integers, also uses decimals, fractions to get different values of a and b. Originality The answer given by the student is way too different from others’ answers. Like, the student draws a unique triangle and names it, say, P, D, Z Making attempting the solving interesting / challenging The teacher ca...

  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...

  An overview of 100 blogs  Background The 100 blog journey has been quite interesting. Quite broadly, the blog journey can be categorised into  Defining what is knowing maths  Major dimensions of education like the Guilford Model, Individual differences, Bloom's taxonomy…..were discussed How to be creative, what creativity is etc have been my Ph. D. research areas, so many blog posts have been posted. Creating math teachers…..it was realised by me that the existing number of teachers are not enough and that led to my conceptualising Individual Franchise Plan. You know maths…. series has been started by me in which I am trying to make maths interesting for all. I am going to restart the series 300+ worksheets is another initiative in which I have decided to create unique, different, types of worksheets….this will allow also be continued Some unique terms In this long journey since the award of my Ph. D. in Education 1997, I have been working to redefine mathematics e...

  Tending to the 100th daily post Answers to Forming expressions quiz  3+t, 2. 7+y, 3. p+5, 4. a+b, 5. m-2, 6. m - 8, 7 5n, 8 3q, 9. X /2, 10. a/b, 11. c-d, 12. d^2, 13. nx or xn, 14. r/5, 15. r^3, 16. 6c, 17. √b, 18. b >3, 19. c>d, 20. 5<n, 21. x<y, 22. 2p>q, 23. m^4, 24. k(d^3), 25. √d, 26. √(bc), 27. √(h^2+d^2), 28. d^6, 29. (a + b) - (x + y), 30. (y + z) t  Dear Readers, What started out of an effort to regulate my writing habits and share my thoughts on mathematics education, today is one short of being the 100th daily blog post published at 8 am. God has been kind enough to keep me and my family, ailing mother at 84, in His care to be able to maintain the routine. I further seek His blessings and your good wishes too to continue the effort.  Just as a recall of the journey, I will be sharing screenshots of the blog post titles Some more blog titles I will be sharing tomorrow as conclusive sharing of the journey. Thanks for reading, commenting an...

  Forming expressions Background  As shared in Maths language interface , it is very important to understand and use the relationship between mathematics and language. The sheet below has many statements which need to be translated / converted into equivalent mathematical statements. Try your luck and we see answers tomorrow 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

  Guilford Model of Structure of Intellect Background - As it happens with most significant changes, J. P. Guilford was not formally a psychologist who worked in the field of defining a unique model of intellect. He was the first to define a three dimensional model of intellect. In simple words, he said that whatever entered your senses is content, then it is processed in your brain as operations , finally it comes out in the form of products as shown in the diagram below:- The 5 x 6 x 5 = 150 cells for what is technically known as the factors of intellects. The intellect ranges from the lowest, that is cognition of visual units to the highest level that is evaluation of behavioral implications. To illustrate, a very young baby only understands touch, face etc the highest level is like the supreme court evaluating, interpreting the constitutional provisions.  Guilford Model and mathematics education The Guilford Model can be used for practically all purposes in mathematics e...