Arithmetic - We have to change our thinking!

“Arithmetic is an outdated life skill like swordplay or horse riding.” Sugata Mitra

In his book Beyond the Hole in the Wall Mitra makes the alarming point about the future of maths education.

At the supermarket. you can't tell if the cashier knows arithmetic or not. Your groceries are scanned electronically and prices tallied automatically. Yet the cashier probably still performs his work capably. Arithmetic is an outdated life skill, like swordplay or horse riding. Four hundred years ago, these were vital skills; today they are relics of a bygone world and primarily enjoyed as sports.

Not many educators would argue that our role continues to be one where will fill our empty vessels with knowledge, yet a high proportion of our maths education seems to continue to be just that.

Conrad Wolfram puts it beautifully in this Ted Talk

He breaks down maths education into 4 parts:

*Posing the right questions

*Real world ------> Math Formulation


*Maths Formulation -----> Real World, verification

He then suggests that we stop wasting 80% of our students time on Step 3 (calculation) and instead use computers for this. This means that our students can spend more time on the more important steps (1, 2 and 4)
Wolfram argues:

People confuse ... the order of the invention of the tools with the order in which they should use them for teaching. So just because paper was invented before computers, it doesn't necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics.
He goes on to further argue:
it's very important to get computers in exams. And then we can ask questions, real questions, questions like, what's the best life insurance policy to get? -- real questions that people have in their everyday lives. And you see, this isn't some dumbed-down model here. This is an actual model where we can be asked to optimize what happens
Then he leaves us with a challenge:

So I want to see a completely renewed, changed math curriculum built from the ground up, based on computers being there, computers that are now ubiquitous almost. Calculating machines are everywhere and will be completely everywhere in a small number of years. Now I'm not even sure if we should brand the subject as math, but what I am sure is it's the mainstream subject of the future. Let's go for it, and while we're about it, let's have a bit of fun...
'''This fits in very well with the MIE approach. '''

Let children explore mathematical concepts for themselves in a highly connected environment.

This year we have been trying this concept out (in addition to the more traditional maths programme). We have a thing called 'Problem Posing Maths' where children are required to seek out and ask ''questions'' - as opposed to barking ''answers'' (we have calculating machines for that).
For example, when teaching perimeter we deliberately give them ambiguous information. Traditionally children are given textbook questions like this which requires them only to calculate:
Whereas our approach looks more like this:
This way the kids have to ask and research the questions:

  • How do I measure a rectangle?
  • How do I calculate perimeter?
  • How do I calculate area?
  • How many cms in the base?
  • How many cms is the height?
  • How do I know the information I have is correct?

The calculation is therefore a small part of the activity - the problem posing is the real maths and the maths that they will do in their everyday lives. It really wouldn't matter if they used a calculator because the learning is in the problem posing...
Too often we do the learning for the kids and leave them only with something that a simple machine can do.
This will be the focus of my session at ICOT

5 Year Olds, iMovie, and SOLEs


May 2012
Remoteness was first addressed by Mitra in a geographical sense. For example (in the context of Delhi) he found that the further schools are from the city, the lower the educational outcomes. He then went on to discover that remoteness was not just a developing nation problem but happening in all countries across the globe. Even in developed nations there continues to be areas where there are clusters of 'under-achievement'. When it comes to access to, and knowledge of, digital resources this is often referred to as The Digital Divide.
Like remoteness, the digital divide can lurk anywhere. It is often assumed that the higher the decile, ranking the more access children have to knowledge and digital literacies. However this is an incorrect assumption - there are many cases where children in decile 10 schools can have very limited access to eLearning and, at the same time, many decile 1 schools have exceptional eLearning programmes and opportunities.
It can also be the case that there are digital divides within schools. For example, there are many teachers who bring old devices in from home, encourage students to use their personal eLearning devices (often their smartphones), beg borrow and acquire older computers from wherever they can, and basically do anything they possibly can to increase the computer to student ratio. Yet, in the class next door, there could well be only one classroom computer sitting on the teachers desk while their Tela laptop remains at home and is lucky if it is used once a week for facebook and trademe.
Just as Sugata Mitra has said, the most important factor to increasing learning is very much down to the individual teacher. Too often a student's digital literacy experience is limited by what their teacher can do. How often do we hear "I can't do eLearning unless I get adequate PD first".
Enter Minimally Invasive Education. Today a couple of exceptional junior school teachers and myself pooled all our iMacs together to see if we could encourage our 5 year-olds to gather in SOLES (Self-Organised Learning Environments) and teach themselves how to use iMovie.
Within less than an hour they were creating projects, dragging photos into iMovie, adding sound effects, adding titles, adding transitions, and recording their own voice-overs. They were self-teaching, they were exploring, they were empowered. The topic of their inquiry this term is Beauty and Joy. As an outsider looking in I was overjoyed and it certainly was a beautiful thing!

Where to next?

From a lecture in Bombay (May 2012) Mitra outlines his research on Remoteness, The Hole in the Wall Experiments, and the Granny Cloud. He shows how the children in his experiments were able to Self Organize their learning and reemphasizes the importance of connections and working together in groups. When Mitra talks of children learning on their own, he means in the absence of adults (not in isolation). It is crucial that children work in groups and these are often refereed to as Self Organized Learning Environments (SOLES). As stated in a previous post Mitra discusses that his research has shown that the future of education requires the following skills: Reading and Comprehension, Search and Synthesis, A system of belief. He goes on to outline his new research: If children can self-organise their learning, can they then self-learn these fundamental skills? In other words: Can children in remote areas teach themselves to read in SOLEs? This is the new and exciting next step in his research where he will be investigating this very thing. Can we open up a whole new world of opportunity for our remote learners? We can only wait and see. Sugata Mitra's full lecture here:



Over the next few months I will be exploring the notion of Assessment with Jo Fothergill. We will be arguing that assessment needs to be:

  • flexible
  • self organised
  • owned by the children and the communities that they live in
  • less Eurocentric

We will be looking specifically at children in remote areas and we will be looking at the effects that Eurocentric assessment tools and pedagogies have on our remote learners.
And while you are waiting watch this!