I once marked a diagnostic test and found an AS Maths student couldn’t do fractions. Concerned if he had chosen the right course, I asked what he got for his Maths GCSE. He replied A*. This was not uncommon. What seems to be happening is a strong foundation isn’t being built in* some* students. One only has to pick up a GCSE Maths or Physics book form the 80’s and see how watered down it has become over the years. So I ask how should children be taught to count and do basic arithmetic? This might sound like a basic question with a simple answer. However, its a question that I’m asking as I work with my six year old daughter and realise the way she is taught in school may not necessarily be the most suitable one for her. Firstly, I’m actually questioning how much academic work she should be doing at her age, not forgetting Steiner, Finland’s outstanding education system and the Islamic tradition (I’m sure there are many others) encourage children to just play till the age of seven.Sometimes, I wish she would have had another year of just play before being introduced to reading, writing and maths. Being the high spirited, irrational person she is – I wonder which system of Maths will best suite her learning style and mindset. School teaches one way. There are plenty of others as I have discovered over the years. I do believe this is vital as the foundations of a child’s approach to numbers are being made and many of the system below are introduced at a young age. I once taught an autistic girl who had a thing for numbers that faded over the years and she began to rediscover it for some magical reason in my class. Her mother told me ‘she loved numbers and found it fun until they started telling her to use her fingers to count”. I’ve seen my daughter using her fingers and nose!

Firstly, there are websites such as http://www.bbc.co.uk/bitesize/ks1/maths/ which provide a games approach. To me this is very different to a playful approach. A playful approach, for me, involving cards for example, is still rooted in principles of Maths and used in a group can stimulate discussion. Maybe more importantly, there isn’t a loss of awareness which often comes through television and computer screens. Learning Maths using games might work for some students and help put some fun in the classroom at the end of a lesson, but I’m weary of children who* only* learn well through stimulating colorful computer screens which make the material entertaining enough for them to process.

Another, approach is using ‘speed maths’ systems such as Trachtenberg – A Jewish professor who devised this system while in the camps to avoid himself going insane from the torture he was witnessing. This however is limited to multiplication but no doubt is a quick way of doing calculations.

If we go further East, there is the Vedic system of Mathematics which I like. Its based on 16 sutras which can be applied from multiplication to advanced calculations in calculus and cosmology. This is quite an amazing system as it has evolved from an oral tradition and uses both sides of the brain. Its a non-linear system essentially rooted in consciousness. I used the Kenneth Williams ‘Cosmic Computer’ books with a dyslexic student once and it did wonders! What I love about the set is that it makes Mathematics alive by linking numbers to Nature and philosophy. It asks student to investigate, reflect and gives them the space to be creative. I’m not sure how widely used this is in India but they are churning out some of the best computer engineers in the world. There’s a Mahirishi school in Lanchashire set up by a transcendental meditation community which, I believe, uses this system and it’s said they produce outstanding OFSTED results. Short video clip shows children meditating and the effect it has on them. http://www.maharishischool.com/

Finally, in my search, I also found the systems of the far East, namely Kumon and the Chinese/Japanese abacus. To me they might be suitable for a certain mind set of people and it well maybe that repetition and discipline works better for some. I’m not being dismissive of them, however, I feel it just reduces Mathematics to *mere* calculation. The approach reminds me of karate forms in a martial arts class, which has its benefits – discipline being one of them. The clip below illustrates my point perfectly.

Mathematics is much more then calculation. The higher up you study, the more it actually becomes about Nature and Beauty and more dependent on inspiration and creativity. Needless to say many posts can be written about this and the contribution the Islamic civilization has made based on their Qur’anic world view. “Truth is Beauty and Beauty is Truth”. Einstein was certain of his relativity probably for this reason, his equations were just so elegant and so he didn’t feel the need to stay awake at night as astronomers confirmed the bending of light from a distant star. Also, the higher up one goes Mathematics lead to discoveries in Physics as string theory has shown us, and visa versa. So I feel all the more important that Mathematics is taught in this way and students are given room to be creative, investigate and relate the abstracts ideas to the world around them and not to limit it to abstract calculations which are either right or wrong. One of my favorite quotes is “Mathematics is the language of Nature and Physics is its poetry.” Here are others…

“Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.” — Johann Wolfgang von Goethe

“A mathematician is a device for turning coffee into theorems.” — Paul Erdos

“Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more.” — Albert Einstein

“Mathematics is like love; a simple idea, but it can get complicated.”

Thak you for such an interesting post. My daughter is 9, very creative, streets ahead in English and yet finds maths really hard work and cannot seem to keep the concepts in her head. She can quite happily do something in the morning and yet by evening you would think she’d never seen it before. Your article has made me wonder as to whether she just needs a different teaching style – any particular recommendations?

26 June 2012at10pmHi.

I think at her age – I would work on just making it as fun as possible least pressure and try and change her relationship to the subject. One way to do this would be to get a tutor or senior student who she gets along with and can work with her.

If you do work with her, keep it short like around 20 min of maths. If it’s morning and evening ask yourself would that be too much? Also, just find what works really. The Vedic Maths by Kenneth Williams is good but I think that’s for year 7. You can always buy some Vedic Maths books, teach yourself and then teach her – make it into a game – One by Vali Nasser is good. Another idea would be to take her yourself to a bookstore like Foyles and ask her to pick a maths book – allowing her choice/decision in this whole process.

Also, reading and watching about science and maths maybe good. Michio Kaku is the clearest author and speaker I know of in this field, I think he’s done some horizon programs.

One more thing – the golden ratio – is amazing- from snail shells, milky way, finger prints to ipods. Ask her to research it – give her a week and see what she comes up with. May be she can write it up (if she’s good at English with diagrams) or make a powerpoint slide to present to you.

I hope Ive been of help.

27 June 2012at10amThe jokes and quotes you featured here crack me up! Growing up in a family of literature lovers makes math seems foreign and intimidating to me. I wish it hadn’t been so. The school’s approach towards the subject didn’t help make the subject more endearing (no offence to my dedicated math teachers!) Perhaps equating mathematics to nature and beauty would have engaged me more. It would have ignited wonder and appreciation for the universe, and ultimately to the One Source. Thank you for this eye-opening post.

27 June 2012at1pmThanks. I really look forward to the day i can take my kids to the Alhambra palace in Granada and have them research its Maths and history. The fact is mathematics is all around us from from binary digits which computers use, radar signals by submarines, to flowers, bees, stars and the motion of planets. “Mathematics is the language with which God has written the universe”. by Galileo Galilei. – This is of course one perspective – The Qur’an offers many more.

27 June 2012at3pmMy immediate reaction to the question ‘How should children be taught to count?’ is to reframe the question as: ‘How should children be taught to do much more than counting? ‘ Mathematics is much more than numeracy. Experts have expressed concern that the teaching of mathematics is increasingly being reduced to nothing but numbers, and that the death of geometry, the study of shape and space, in mathematics education can only be to the detriment of visual and spatial intelligence (e.g. report published in 2000 by the joint Royal Society and Joint Mathematical Council working group. See Times Educational Supplement, 18 January, 2001 – Curriculum Special: Mathematics.) I studied Euclid’s theorems at school at the age of 11, but I doubt very much if this is the case today.

It astonishes me how so few people seem to have any idea of where they are in space. They do not know where they are in relation to the points of the compass, and are unable to use the position of the sun at the time of the day as a rough guide to the cardinal points. The use of SatNavs is another way in which spatial awareness is being eroded (that will be the subject of another post!). I use maps, landmarks, and directional awareness to find my way around, and, to be honest, I’d never use a SatNav. I also use my memory, memorising the route for a complicated journey before I set off, so I don’t need to put pressure on a navigator (isn’t there a book called ‘Mars and Venu’s which is subtitled something like ‘Why Men Can’t Listen and Why Women Can’t Read Maps’? Just a joke, I hasten to add.) Memory is another faculty undervalued in our technology-dependent society. Many of our key cognitive functions are atrophying because of lack of use.

Lack of spatial orientation also has a symbolic significance. If we do not know where we are in space, might it be the case that we also lack a qibla (point of orientation) within? Is not disorientation, both outer and inner, a feature of modern life in many ways. The word ‘orient’ of course also refers also to the East, the direction of prayer in Christian churches, and its root also gives us the word ‘origin’. Orientation means that we facing in the direction which reminds us of our origin, and ultimately that is a point within the centre of the human Heart even if turning to an actual physical qibla may remind us of that point.

Given the pressing need for the revival of geometry in the Mathematics curriculum, and the importance of geometry in Islamic civilization, the best education founded on Islamic principles should be in the forefront of such a revival.

Ibn Khaldun emphasises the educative role of geometry in fashioning the intellect: “Geometry enlightens the intellect and sets one’s mind right…The mind that constantly applies itself to geometry is not likely to fall into error….the person who knows geometry acquires intelligence.” (Ibn Khaldun, Al Muqaddimah, translated by Franz Rosenthal, abridged and edited by N.J. Dawood. London: Routledge and Kegan Paul, London, 1978, p.378. Quoted in Mathematics: The Islamic legacy by Q. Mushtaq and A.L. Tan. Delhi: Noor Publishing House, 1993, p. 68).

It is equally important, however, to emphasise that in the tradition of scientia sacra the educative role of geometry is not solely an intellectual one, but is also a purifying activity which connects the perception of truth with the attainment of goodness. Ibn Khaldun emphasizes the moral as well as the aesthetic dimension of correct proportion and he likens the impact of the science of geometry to the cleansing effect of soap on the garment.

This emphasis on both the intellectual and moral dimensions of geometry echoes the words of Plato: “There is a faculty in the mind of each of us which these (geometrical) studies purify and rekindle after it has been ruined and blinded by other pursuits, though it is more worth preserving than any eye since it is the only organ by which we perceive the truth.” And again, “[Geometry] has the effect of making it easier to see the form of the good. And that, we say, is the tendency of everything which compels the mind to turn to the region of ultimate blessedness which it must spurn no effort to see.” (See Erwin Panofsky, Meaning in the Visual Arts. London: Penguin, 1970, p. 120).

The educational impoverishment in the over-emphasis on numeracy and the abandonment of geometry is also reflected in the decline of concrete observation and practical experimentation in the school curriculum. Ten years ago, a report on science teaching at GCSE level drawn up by Dr. Ian Gibson, Chairman of the House of Commons Science and Technology Committee, described the shepherding of pupils through GCSE practicals as a set of “recipe-like steps” which had very little to do with the process of scientific exploration. At that time, GCSE, assessment of investigation was dominated by just three experiments: measuring the resistance of a wire, the rates of chemical reaction and the rate of osmosis in a potato, which is “a bit like reducing the teaching of performance in music to three standard scales on a recorder. Any teacher with even half an understanding of science knows that this approach …bears as much relation to science as painting by numbers does to art.” (Warwick Mansell, “Attack on science ‘by numbers’”, reporting Jonathan Osborne, Professor of Science Education at King’s College London, Times Educational Supplement, 2 January 2004). I suspect that, if anything, the situation is worse today.

Another report on science teaching in mainstream schools has found much of science teaching “boring, pointless and stultifying” with far too much weight given to facts and content. Few opportunities were given for experimentation, little connection was made with topical modern developments and controversial issues, let alone with that sense of wonder and mystery which authentic science evokes. The scientific method itself was rarely taught, and the limitations of science hardly ever addressed.

Given the enormous contribution of Islamic civilization to the development of empiricism and the scientific method in the West, it might be expected that an educational system based on Islamic principles would be in the forefront of reviving a culture of observation and experimentation which is in decline in British schools.

The focus on numeracy in the educational system is the result of the reduction of education to a merely functional process designed to serve economic growth. Its aim is to churn out a legion of useful slaves for offices, shops and other commercial contexts, much like the Victorian system geared to churning out an army of ledger clerks to adminster the empire. The fact that it’s not even working properly at that level (mathematics attainment in the UK is dire) does not seem to deter the policy makers.

To follow up some of Saqib’s excellent suggestions, I recommend the book ‘A Beginner’s Guide to Constructing the Universe’ by Michael S Schneider. See http://www.amazon.co.uk/A-Beginners-Guide-Constructing-Universe/dp/0060926716

This page also gives links to related books on sacred geometry, the golden section, and the like.

7 July 2012at8amDearest Jeremy,

Thank you for such wonderful enlightening comment. I agree. Just to put the title in context, this post came about after seeing my daughter struggle with her Maths homework (KS1/foundation) and I began wondering if the system of using fingers or number lines was really best suited for the way her brain is wired.

Working in post-16, I get to see both the GCSE-retake and A-level Maths students who have made it, i.e the end result. The Cosmic Calculator books by Kenneth Williams do precisely that. There is beautiful balance between geometry, calculation based on vedic principles and investigation. I do feel pedagogy is another very important area for how Maths and Physics (maybe other subjects too) can be explored to allow for creative thinking, given by their very nature they involve problem solving and are essentially inspired by Nature. When I was in year 9, I had the wonderful opportunity of being taught by an amazing Maths teacher, a Polish Cambridge graduate, called Mr Jastrazembski. We would discuss things from marriage to time-travel and black-holes. Anyway, one day, he decided to give me a year 11 problem, involving pyramids, to keep me busy. I hadn’t learned trigonometry at the time. I didn’t even know what was needed to solve the problem. He would mentor just through brief comments and clues every now and then. Over the course of a few weeks, i was able to teach myself the topic and went on to show how the numerical properties of a pyramid carry mystical dimension to them. He ended up sending my work to a friend of his who worked geometry and the Sacred and in return sent me a signed book- the handwriting did appear suspicious and I still wonder if he signed it himself! Anyway, that was my introduction to Vygotsky’s zone of proximal development. By giving a student a problem just beyond their current level or knowledge, an open ended one, it gives them space not just to learn and explore, but for creativity to flow through. I always detested the university system at undergrad level for not having an open-module in which a particular topic could be explored in depth.

I’ve also recently come across a newly published book by Watkins bookstore, called the Hidden Geomtery of Life, the science and spirituality of nature – which looks at everything from music, dark matter to individual being. At some point, would like to explore Rene Geonon work on the symbolism of calculus. Maybe just as seeing Shakespeare’s plays in the light of Sacred art as Martin Lings suggests, Mathematics in its very language as well as it geometry, can too be explored in that light.

Warmest

Saqib

7 July 2012at9amDear Jeremy and Saqib

Thank you both for your informative and constructive answers – they have given me a guideline as I have (despite having studied Maths at A-level!) been rather at sea as to how to help her.

7 July 2012at10pm