Beyond Abacus

  Improving school mathematics 1 Across the world, acquiring a certain level of proficiency in the  3R’s is an integral part of imparting education. Reading, writing and Arithmetic. In India, today, there are over 20 crore (200 million) students who are at the school level of education and who have to study mathematics. So it is essential to look at key dimensions of school mathematics. What is it to know mathematics ? In most cases, the unwritten law is that even if students are able to do some addition, subtraction, multiplication and division they are considered to be good at maths and all are happy. All are also happy if year after year, the Board examination results are good.  However, as a future conscious citizens, teachers, educators, it our responsibility to define what does it mean to know maths as we want the students to be active users of technology, do good in business, agriculture, take informed decisions. All this is not possible in the modern technology dr...

  Some more limitations of the Abacus system In personal capacity I have nothing for or against the Abacus as a business model - in fact it is none of my business .  But as a longtime maths teacher, researcher in mathematics education, educationist, when I see the way the system works and its brutal impact on children tender minds it pains a lot to see how the gullible parents, kids, are misled to spend huge amounts of money, time on this system. Children have tremendous stress and strain to develop, hone, perfect, a skill I have never needed in past 61 years. I ask the readers - have you come across any situation where you had to calculate, say 6759 x 3276 accurately in a fraction of a minute (if not seconds) ? Never. We either estimate roughly or use a calculator. Then why bother tender age kids to learn all these skills ? Make them feel guilty for something which you are forcing them to learn which has no utility in life ? Parents spend a lot of money, time, create hatred f...

  Some limitations of the Abacus system Although a commercially hit business model, the Abacus system has some serious limitations especially in terms of the outcome. That is, promoting limited perspective of mathematics just a computational. In everyday class, in their marketing materials, in their counseling process, in their awards and rewards, in every key function, the ability to calculate fast and accurately is construed to be the sole criteria of appreciation of mathematical ability.  Monotony  After a stage, the computational processes become quite monotonous and boring for the students who leave. Individual differences not catered to. The system is specific end driven and in the heat of the highly competitive environment, the individual struggling to manage gets roughed out or is left to struggle. No connection with life Other than the temporary pleasure of showing off skills publicly and some use in saving time on calculation related one unique answer questions...

  About Abacus  Abacus is an instrument which is used to calculate. In the Roman history there have been different types of Abacus instruments, but the most popular and the one which is used till date is the bid based, linear model. Abacus as an acronym stands for  Abundant Beads  Addition  Calculation Utility System. As a business model A hugely successful business model popular by different names in different regions, like UC Mass Abacus, Master Abacus and so many variants, the Abacus is a training / coaching system to dramatically increase the computational speed of the participants. The stage I is introduction to the instrument, familiarity with the instrument, understanding core processes and at the advanced stage, it claimed to be improving both the right and the left brains. Some also claim to have improved visualisation, imagination, qualities which help them better in academics at a much later stage too. Although claims are many, the ground reality is, ...

                                                             Maxims of Teaching - 2 From Whole to Part A good teacher first gives an overview or the scanorio and then discusses a specific point or scene. The teacher, for example, explains the importance of numbers in life, she explains that we all count so many things, we all exchange money, we all use time in daily life. Then, once the broader concept of, for example, time is clear, then she introduces day, night, hours, minutes, seconds, micro seconds, nano seconds and so on. Psychological to Logical This maxim also helps teachers in interpersonal relations with the students as well as with the parents, besides helping in teaching. The maxim states that the teacher takes the level of discussion from psychological to logical, that is, helps the student theorise or build a theory than...

 

  Maxims of Teaching 1 Overview Maxims of teaching are the broad practices which make your teaching more effective. Good teaching incorporates following ideas. If you apply them in daily life also, in detailing, explaining your ideas in personal conversation also, they will help you Known to unknown A good teacher always begins with a clean slate. She does not assume all the students having all the fundamental clear. This is specifically very useful in teaching adults, like corporate training programs, meetings where the audience does not have same background. This maxim helps in developing common perception for the entire class, group, which helps in facilitating learning. Simple to complex While teaching addition / subtraction of numbers or teaching sentence formation, a good teacher always takes students from simple to complex. Main reason is to avoid the stress and strain caused by early failure. As skill builds up, so does the confidence. Concrete to Abstract As proved by the ...

  Dimensions of Creativity During my Ph. D. working, I wrote a short poem about a creative person Such people are very few Who can see, feel, things, people a new When I look around in search I find such a person in you. Back to Prof. Passi class on Creativity, he explained  Fluency Flexibility  Originality as the three key dimensions of creativity Fluency Idea fluency means how fast and how many relevant ideas someone may produce on that point of discussion. Brainstorming where all participants share ideas and then a decision is reached  https://youtu.be/FkvCBUvH6Zc Flexibility Flexibility refers to the length, width, depth to which you go about the idea. It denotes the key variations in the idea. For example, if you have reply    - +  -  = 55, find two numbers that add upto give 55. All the answers adding two positive integers to get 55 are treated as one category like 1 + 54, 9 + 46 and so on…. However,  using a negative number is a flexib...

Ways to be creative Today we will discuss the four different major ways of being creative. The four P’s as discussed by Prof. Passi are Person Product Process Press or the environment Creative Person means someone who thinks altogether differently, works differently, reacts differently. All artiste, actors, designers, fashion Trend setters, Inventors come under this category.  A very good discussion you can see here  https://youtu.be/5EarvYtrbQo . Try to identify your own qualities and work towards the remaining. Creative Product means a product that is unheard of like the great Indian sagas Ramayan, Bhagwad Geeta, iTune making world of music in your pocket, the theory of relativity, vaccines these are some of the products that never existed before. But have not been replaced since they came on scene. Other, different innovations also are creative products be it mobile, airplane…. Creative Process There some processes which guarantee a creative outcome. Like the Sanskaar or r...

Understanding creativity  As discussed earlier too, right from the B. Ed. stage, I got deeply interested in educational psychology. During our B. Ed. Course too, Prof. B. K. Passi used to take once a week class on educational psychology. His topic of interest, at our level of course, was creativity. In his jovial style, he used to take us to different facets of creativity. Studied in 1981, I still remember the major things learnt in those interesting classes. Of course, later on I worked on them more seriously during my Ph. D. in creativity research area, The Walla’s stages of creative problem solving  Preparation or Seeing the problem. First of all, the creative person sees a problem. He is able to see that there is an issue which needs to be resolved. Like all Inventors, felt difficulty, limitations of what existed and strongly felt the need for a change. The creative person also sees the same issues, problems from an altogether differe...

                                        Pathway to research….. Back to B. Ed. College After doing formal education in sciences. B.Sc. with Physics, Chemistry, Mathematics and Statistics and doing M. Sc. (Statistics), doing B. Ed. was an altogether a different experience. I contested student body elections too this year for the post of President University Teaching Department (UTD) and lost by a very narrow margin. Made many friends on the way, created temporary foes too who also became friends although I never tried nor try now to extract anything tangible out of that friendship. Our friends, leaders that time are today state and national level leaders. The most prominent being Shree Tulsi Silawat, Minister Govt of MP and Shree Kailash Vijayvargiya, BJP Secretary In charge West Bengal. Soon the direct election era ended. Next year I contested again and won President post as well as Univer...

  Mathematics as a science of patterns  As against treating mathematics just as a computational tool, once we start treating mathematics as a  science of recognising, understanding, appreciating and creating patterns a quiet revolution starts happening. Some of the implications are  Teaching becomes wide based The teacher does not just confine to teaching abstract concepts, but she relates concepts to student's daily life experiences. Right angle, for example, does not remain a geometrical concept taught by a teacher, but she makes all her students understand that all buildings in this world are at right angle to the ground.  The students just do not know feet, centimetre conversions mechanically, but can guess / estimate lengths by watching.  Learning becomes fun As the child is taught mathematics through the environment, from his reality, the concepts start developing on their own as the child constructs her reality in an incremental, organic way.  ...

  The importance of definition  I would like to discuss how the policy makers', parent body, school administrators, investors', teachers' perception of what is it to be good at maths ? affects the students and ultimately the workforce, industry, economy in general. 1. Mathematics as a computational tool    This is the current, popular perception of knowing maths. Our classroom teachings, examination system, wide spread tutoring, coaching business all tend to develop, appreciate, the skill of reaching one unique answer as fast as possible. The Abacus or its various versions, as a training tool are classic examples of this. Students are expected to be too good at a skill in past 61 years of life I have not needed. I ask the readers, how often, if at all, you needed to find 5813 x 3876 infraction of a minute and that too accurately ? I bet never. But, just as a ritual, under peer pressure children go year after year to learn something which is first of all not needed at...

  What does it mean to know maths ? Different people have different perception of what does it mean to be good at mathematics ? Some popular perceptions wide spread among school going students, parents and even teachers about what does it mean to be good at maths ? (without being judgemental of one being better than the others, I am just listing) The ability to do long calculations in short time like solving 4538 x 3659 orally in few seconds (or neno seconds) this is the skill taught in the courses running under different names with prefix, suffix Abacus.  The ability to score very high in each and every test, examination The ability to recall, use tables upto 30 or more The ability to create or memorise and reproduce tables of quarters, two thirds etc The ability to tell answers even if the question is just finished (By memorising all questions through practice) I even saw a girl, not good to name publicly, who told the question when I told the answer. Feel free to add more i...

  Overview  Past   36 years I have been a maths classroom teacher by choice.  Childhood and family Born in a Maharashtrian Bramhin family in 1960, with father being a medical doctor, childhood was very blissfully ignorant of the ground realities of the world. Being a government doctor with zero PR activities, I continue the trend, transfer or long posting in tribal areas was a norm. We spent 6 years in Bastar district in early 1970s. One of the most interesting things to recall is we three brothers often used to sit and talk a lot in Hindi. In the presence of parents, we three used to interchangeably toggle Hindi - Marathi. Hindi with brothers, Marathi with parents. In 8th standard, the elder brother school fee was a whopping 30 paise per month, my huge fee was 15 paise per month and the third had to pay nothing in the Government Multi purpose school Bastar. Moving to Indore To reduce the stressful impact of transfers on our studies, in 1976 myself and elder bro...

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...