Teaching mathematics by visual scaffolding

By | November 27, 2011

Visual scaffolding is a natural support to learning mathematics since most mathematical concepts are first distilled visually i.e. a concept is conceived as having a specific visual beginning, and a defined visual progression. As the concept progresses, numbers are incrementally engaged in translating the visuals into numerical information. The visual connections are designed to make mathematical connections explicit since leaving them implicit is what makes Mathematics appear so “difficult”. When this is done  via dynamic imagery (animation), numerical reasoning is evoked quite easily.

It doesn’t take long before learners grasp the thinking that is going on behind the mathematical operations. It is this thinking that learners start to assimilate. Before long, they develop a mindset, a way of thinking that is mathematical: i.e. cognitively organized, intuitively analytical, meaningful and  purposeful.  They start to think of, and arrange numerical information  in intelligent  patterns, and their personal heuristics start to develop a trajectory in the direction of formal algorithms.

Visual scaffolding approach is drawn from the fundamentals of basic learning theories. Everything we learn is first received by the sensory apparatus (see, hear, touch, etc) before getting converted into “digitized neuro-bytes” of abstract information for deeper and more extended understanding and application.

In Karismath’s, most lessons and exercises have different levels of visual scaffolding. For teaching algebraic expressions for example,

In Part 1 no numbers are used.  Learners use “green peas and red tubes” to engage in trial-and-error approaches to  solve a problem. The concept of an equation is communicated non-numerically.

In Part 2, learners are introduced to a “smarter” way to approach the same problems. Their prior knowledge of equality is all that is needed. The design of the templates (peas and tubes, and their placement) evokes their  “cognitive consensus”  over a simple piece of reasoning: that the removal of the same quantities from the left and right  side of the equation will maintain the numerical balance on both sides. This fact leads to the discovery of a strategy that helps them solve the equation correctly each time, without any trial and error.

In Part 3, the visual processes are simply translated as recordings of what was done visually. That’s all. The numerical representations become formal mathematical garments of processes that were initially common-sensical, processes that were visual and even possible to perform physically.

Karismath displays the power of mathematical thinking in this transition from the concrete and the visual to higher levels of abstraction . Once learners understand this power, it is not difficult for them to get addicted to it.

Those who understand Mathematics this way, from within its inner core of brilliant reasoning, can often get addicted to its power of abstraction.

Which is what Karismath is trying to achieve. Please check out the Karismath Insights video Clips on You Tube in the Karismath Channel link below: http://www.youtube.com/karismath

You can also see the same lessons, with their index, by clicking on the following link:


Many more Karismath Lessons will be uploaded almost weekly, all through this year and the next.

Shad Moarif


About Shad:

Shad, a Harvard graduate, has a background in Science, Psychology, Reading and Mathematics. He has also developed a comprehensive theoretical perspective of his Five Stages of Math Achievement that awaits publication. 

His work has been influenced by his 35 years of teaching Mathematics and Language to children (and adults) with Mathematics and Language-learning difficulties in Asia, Canada, US and the UK. He has conducted numerous teacher-training seminars and workshops at conferences  in the US, Canada, UK, Singapore, Bangladesh, Pakistan and Kenya.

 In 2010 he was the Keynote speaker in  two major conferences (Canada and the US).  Shad was Vice-President, International Dyslexia Association (British Columbia), and also served as a member on IDA (BC)’s Advisory Board, and also on The Aga Khan Academy (Mombasa’s) Steering Committee for Mathematics Teacher Education. 


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3 thoughts on “Teaching mathematics by visual scaffolding

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