Posted in Teaching mathematics

What is Universal Design in Learning?

This is a perfectly good knob to use. Grab it, turn it, pull (or push), and the door swings open. So it meets your needs. Or does it? Does it meet ALL your needs, your universal set of needs, needs that arise in different situations, different contexts?

Well,  suppose you are rushing down the corridor in your office building, with a cup of coffee in one hand, the other clutching a folder or file. You are late. You run up to the door and see the same round knob as above. Can you open the door with it when both your hands are “occupied”?

Or would this design do a better job:

Because with this, you can lean down a bit, and push the handle with your elbow. If neither hand is occupied, you still grab, turn, push (or pull) as always. The handle meets your diverse needs, needs that rise in different situations. It has, what we call, a “universal design”.

It took a long time for people to become conscious of needs that go beyond those that are mainstream and taken for granted. Like people using wheelchairs. When they first built houses and office buildings, people used stairs or steps to climb up the building to get to upper floors. This alienated a population of people who were unable to use their legs. They used wheelchairs in hospitals. Maybe a few in their own homes. But by and large, they were kept out of office buildings and even prevented to do social visits. They couldn’t pay their bills, draw their money from banks, or perform any transactions. Or see visit relatives and friends.

It has been only 4 decades that their needs were acknowledged. In the beginning, it was expensive to redesign and rebuild buildings and homes for people with such special needs. So ramps were “attached” on the side of the buildings for such “special” people. Like this:

“We” soon became associated with the “normal” population that could use steps, and  “They” with “those” people who couldn’t.  Handicapped people. Those “poor people” who couldn’t walk. This led to the exclusion of a part of mankind to a lower, somewhat lesser conceptual level where the handicapped felt like outcasts in their own midst. They were made to enter from the side rather than from the front, “like the rest”.  It compromised their self-dignity.

The Inclusion Movement rallied against the tradition of “Exclusion”  for decades. Until the day came when leading architects and designers began envisioning buildings in which various options were made available to negotiate higher floors. Technology, too, came to the rescue. So elevators and escalators took over. No side-entrances for special needs was necessary. ALL needs were human needs. And ALL needs had to be equally respected, equally addressed. Everyone deserved to enter from the front. And if ramps were needed to enter a building, then the ramps would be integrated into the design of the building from its very conception. They would run alongside the steps. All who enter a building should enter as equals. And all buildings and homes should be designed for such “universal access”.

This same idea applies as much to education as to buildings and door-knobs. Learners have different needs. And these may vary among individuals of different ages and genders as much as within anyone’s given lifetime.

Can educational courseware be designed in such a way that they address the needs of (a) gifted learners (b) disadvantaged learners (c) and all learners that fall between these two extreme poles?

I have tried to meet the demands of Universal Design in Learning in the educational courseware I share in Karismath Insights Videos.

I suggest you read my two other posts on What is visual mediation? and Teaching mathematics by visual scaffolding to fully appreciate the theory behind the videos.

Shad Moarif
Founder-Developer
Karismath

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.

Posted in Algebra, Math videos

Teaching mathematics by visual scaffolding

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:

http://www.dyscalculia.org/experts/karismath/see-lessons

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

Shad Moarif
Founder-Developer
Karismath

 

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.