(Written in January, 2024)
My first experience of teaching Mathematics happened with my younger sister in the year 1973. She was appearing for her 11th public examinations and I was in 2nd year of B.Sc. (Mathematics) then. The experience was fulfilling for both of us.
Then when my children were in schools, I kept in touch with their school Mathematics to the extent of teaching a few problems. As my father was a school teacher and I was a beneficiary of his teaching, his psychological approach to children and interactive style of teaching embraced me. While solving a Math problem I will stand as a facilitator only. I will give comparisons, contrasts and analogies and the learner has to come forward with steps. Aiming to understand the concepts clearly is more important than aiming to score higher marks, I would insist to my children.
I remember well the scene of teaching Math to my son. The air would range from storm to breeze. Fortunately, the storm would precede rather than coming in the end. Initially he used to stand in the diametrically opposite corner of the hall, to be of maximum distance from my sofa! Step by step, his willingness to listen and cooperate would increase and the distance would decrease. After sometime I would find him sitting next to me. I was pleasantly surprised when my colleague and friend Rama reminisced my Mathematics encounters with my children long after my children completed their schooling like this – “It is difficult being Lalitha’s children. They had to work out the full Mathematics question paper in home after each examination”.
Now I do peep into the Math notebooks of my grandchildren whenever an opportunity arises and offer to teach them. Actually, I had the pleasure of teaching them on a few occasions too. But what I hear generally from parents is that nowadays schools do not encourage teaching of Mathematics by parents as what they teach in school is new Math which is vastly different from traditional Math and that the teaching methods also have changed. I gather that this is the general universal view across the nations. But what surprises me is that I consider Mathematics problem solving as breaking it into tiny little steps which is bound to be unique in its bottommost split. The process of prime factorisation may be a better analogy to understand what I say.
So, I browsed the internet to understand what NCERT says in our country and what the schools in USA say there regarding teaching Mathematics. Vast materials regarding new Math and its teaching methods surfaced. The concept of new method of teaching Math has emerged as early as 2005 it seems.
The preface of the 159 page National Curriculum Framework, 2005, (NCF, 2005) (https://ncert.nic.in/pdf/nc-framework/nf2005-english.pdf ) starts with NCERT’s proposals on what to teach our children and how, regarding major subjects like language, Mathematics and Science. The word Mathematics comes 85 times in the writeup. Section 3.2, between pages 61 and 64, covers proposals for Mathematics. Sense of fear and failure regarding Mathematics for majority of the children has been highlighted. Vision for School Mathematics and curriculum for various stages right from pre-primary up to higher secondary have been presented. The goal is narrated as enhancing the child’s resources to think and reason, to visualise and handle abstractions, to formulate and solve problems. The framework envisions children learning to enjoy mathematics rather than fear it.
National Education Policy, 2020 also aims at reorienting and revamping all aspects of curriculum and pedagogy, vide https://www.education.gov.in/shikshakparv/docs/background_note_NCF.pdf and https://ncert.nic.in/pdf/nep//NEP_2020.pdf).
Went through a couple of research articles, viz
and
https://www.researchgate.net/publication/320385212_COMPARISON_OF_NEW_MATHEMATICS_TEACHING_METHODS_WITH_TRADITIONAL_METHOD by Mr. Abdolreza Lessani, Ms. Aida Suraya and Ms. Kamariah Abu Bakar
on new methods of teaching Mathematics which enumerate them as problem solving, experimental learning, discovery learning, inquiry based etc which are all said to be student centred learning vis-a-vis the traditional method which is said to be of teacher centred learning. Also new method of learning is said to have shifted from earlier content-based learning (which contains more of lectures and expects students to memorise mathematical rules) to experience based learning to make learning more interesting.
The buzzwords of pedagogic reform, experimental learning, critical thinking, exploratory skills, optimizing learning based on cognitive development etc are seen in many places in the above materials. It is observed that axioms and definitions, if at all, should come in the end, after the children are able to abstract themselves. The main goal of teaching Mathematics has been highlighted as Mathematisation (ability to think logically, formulate and handle abstractions) rather than ‘knowledge’ of mathematics (formal and mechanical procedures). Coming to the pupil-teacher’s ratio, the affiliation rules for CBSE schools stipulate that the same should not exceed 30:1, vide
Now coming to understand what the schools in USA are telling about new Math and modern teaching methods, the article by Ms. Barbara Armijo, vide the link
https://www.usnews.com/education/k12/articles/understanding-the-new-math-your-children-are-learning
amply explains them. We observe that ‘Common Core Math Standards’ arrived there in the year 2010. The article highlights the emergence of New Math language and some phrases like “friendly numbers”, “making 10s”, “landmark numbers” and “decomposing” are given as examples and the relevant approaches are explained. Teachers nationwide have modified their methods in order to apply the federal standards to traditional mathematical practices. Students are asked to collaborate, work with their peers and discuss situations. The article asserts that the days of parents having had a basic grasp of how to help their children with math homework are gone with the arrival of ‘Common Core Math Standards’.
Regarding student strength in USA classes, the link https://www.learner.com/blog/student-to-teacher-ratio-in-high-schools says that there is no student-teacher ratio requirement at the federal level and that these codes are established by the state, county or local educational systems. Some States like Florida are said to have the requirement at 25:1, some States like Maine are having it at 11:1 and some States like New York do not specify a ratio cap for public schools, says the author.
Thus, it is observed that there is a paradigm change in pedagogy in the last decade. I still believe that a parent confident of teaching Mathematics to his / her child can refer to the current textbook and teach accordingly. Those supplementation efforts will be fruitful, as NCF, 2005 itself (vide page 62) asserts that when children learn a variety of approaches over time, their toolkit becomes richer and they also learn which approach is the best rather than simply believing that Mathematics is an exact science. Also, parents can groom the skills of listening, focusing and application in their children. They can impress upon the children the importance of not wasting the time and the need to discharge one’s duty well at each stage of life. For this they can quote maxims or from literature. Even film songs with good messages can become handy for the purpose. Recognizing a child at the right and genuine moments will boost his / her self-confidence and will improve the performance.
Mirror of Times 