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Slumdog Pythagoras – Minimally Invasive Education

Inspired by Sugata Mitra at the SSAT National Conference I decided to try and ape his ‘minimally invasive education‘ within my own Maths classroom.

In a really tough December week this two hours shone out as a great teaching and learning experience.

Before going any further, please head over to my previous post to read about the inspiration for this lesson.

In a nutshell, Sugata discovered that children can teach themselves with the aid of the Internet.  His hole-in-the-wall experiment inspired the book that inspired the film Slumdog Millionaire.  He has since been investigating how to apply these findings in Western school systems.

I followed some basic rules that Sugata has developed.  I split the students into groups, each with a computer and then gave them a problem to solve.

The rules are simple:

  • Students were told to get into groups of their choice of around 4 children.
  • They had one laptop per group.
  • They could walk around and cheat, looking at what the other groups were doing.
  • They could move groups if they wanted to.
  • No input from me other than some encouragement and praise.

My Year 7 class (11-12 year olds) are an able group who I have done a little group work earlier this year.  I gave them a simple question:

Who was Pythagoras?

And with it, the text (but not diagram) of a typical GCSE question:

A ladder is leaning against a wall.  It is 5 meters long, the base of the ladder is 3.5 meters away from the wall.  How far up the wall does it reach?

At that point, I pretty much put my feet up and left them to it for the next two hours.  The maths involved is traditionally not taught to pupils of this ability for at least another 2 1/2 years.  It would be considered as being about 2-3 National Curriculum levels above their current ability.

To say I was surprised and delighted with the next 90 minutes would be an understatement!

Two groups in particular shone at this task and took very different approaches to reaching the correct solution:

Mathematical Logic: An enthusiastic group of girls split into two pairs, one pair hit Google and quickly found Pythagoras’ Theorem, a diagram of a right angle triangle and the formula a²+b²=c².  The other pair started drawing a scale drawing of the problem and within minutes had a fairly close estimate of the ladder problem.  These girls had done little algebra before, they had certainly not substituted into equations, let alone rearranged them.  However I watched them equate the ladder and wall to the example right angle triangle, substitute in the values I had given them in the problem, and begin a discussion about how to find b².  They correctly deduced that to find the missing value “if they are added together, then we need to subtract the 3.5² from the 5² to find b²”.  Perfect mathematical logic!  They then got a little stuck as they had never come across the concept of a square root before.  Halving their value was the first attempt, but they quickly saw that this was nowhere near the value they had got from their scale drawing.  Dividing by 3 was the next logical step for them (a triangle has 3 sides afterall they declared!), again this didn’t work out close enough to their estimate.  At this point they went back to the Internet and found some examples of solving problems of this nature.  Here they stumbled across the square root sign, quickly understood the concept of a square root and then found the button on their calculators, and next the correct solution to the problem.  Quite amazing!  They produced a poster to show their learning:

Other than a little confusion with square and square root symbols, an impressive effort.

Search and yee shall find: A group of three boys attacked this problem by searching for information using both the laptop and also the resources in the room.  They found out who Pythagoras was thanks to Wikipedia.  But they also started looking through the GCSE Maths books in the room and even found a revision guide.  They found an example question in one of the books that was another leaning ladder question.  They used this to quickly find the answer to the problem that I had set them.  This might not have involved the mathematical deduction that I had watched the girls use, but it was an impressively efficient effort, and is just how I learn things these days.  Search on the Internet, find some examples of what I want to do and adapt these methods.  I put another question on the board, this time finding the hypotenuse of the triangle.  The boys found a great ‘3 quick steps to solving Pythagoras’ from the revision guide and applied this to the problem in no time at all.  They produced this presentation of their learning:

Of all the groups, these two groups developed a good understanding of Pythagoras’ Theorem with no help at all.  Two other groups got there after a little bit of peeking at the work of the first two groups (well within the rules), and two groups did not get very far.  This was down to a lack of teamwork, something we can work on in coming weeks, these pupils are only 11 years old after all.  Overall in the two hours we managed to learn: Pythagoras’ Theorem – done!  Square roots – done!  Substituting & rearranging algebraic equations – well on the way!

I will be interested to see how well this learning is retained.  Sugata Mitra’s work seems to show that months later retention from this form of learning is impressive.  I’ll be delighted if the class can solve a problem next week, and even more so if it’s still there after the Christmas break.

This was such a success I will try it out with all my classes this week.  It’s the last full week of term, always a tricky time to keep the pupils engaged, it seems an ideal time to try out a different way of learning.  I’ll be intrigued to see how this works, particularly with my lower ability Year 8s.  I think the success I had with this trial was in part due to the excellent learning habits that class already had and in the pitch of the question.  It offered just the right amount of challenge, and was relatively easy to search for online.

With that in mind, this week I will try the following:

  • Year 7 (NC Level 5-6):  Independent Probability: How do you find the probability of two independent events happening? What is the probability of winning the lottery?  What is the problem of getting 5 out of 6 balls in the lottery?
  • Year 8 (NC Level 3-4):  nth Term of Sequences: How do you find the 100th number in a sequence?  Present with a sequence problem from diagrams e.g. matchsticks and ask for the 100th term.
  • Year 10 (GCSE Grades E-D):  Sine Rule: How do you find the area of a scalene triangle? Present with triangle to find area of.
  • Year 11 (GCSE Grades D-C): Transforming Graphs: What is the equation of this graph? (Transformed sine wave – pupils have not come across sine waves before)

What do you think?  Are these suitable questions?  Have you tried anything similar in your classroom?  Will you try this method of enquiry based learning now?  I’d be really interested to here your views and experiences.

As this is a fairly hands-off form of teaching I may try and live-tweet the lessons – we’ll see how things go.

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  1. Great outcome;I was lucky to see Prof Sugata Mitra the other week and was very impressed with his work and pleased to see his techniques being put into practice.
    I teach in a FE college and would like to try this with my students, but my feeling is that it may not be as successful with older students? however after reading your blog I will be giving it a go this Monday, (I think it may be a bit of a shock to their system).

  2. Thanks!

    Yeah, I’m not so sure how well this will go with my older pupils, but this last full week of term seems like a perfect time to try, and I’ll egg them on by pointing out that Y7 taught themselves Pythagoras!

  3. Absolutely insprirational stuff!!!! I’m going to point my Year6 pupils in thus direction and see if they’re up for a challenge!!

    Just superb!

  4. Conrats of your trial.

    Having just had a pretty poor outcome to a research task with a generally low ability Year 7 ICT group, I’m going to roll out an experiment using Mitra’s ideas across 3 year groups to see what happens. As mixed ability groups I’m going to set the groups in some classes and not in others.

    The key is whether the level of research is better or anything is remembered at all!

  5. Daniel,
    I sent this post to Sugata who is co-chairing the 2011 ALT Conference – http://www.alt.ac.uk/altc2011/. Sugata replied “Thanks Seb, it’s just fabulous!”. I said, in a shooting-from-the-hip way “What we now need to do is to crowd-source the “small group questions” for the whole of the national curriculum.” to which S replied “Absolutely!”. Obviously more easily said than done, but if I can help in any way I would be glad to do so, and one possible place to do some small scale “prototyping” might be on the ALT wiki at http://wiki.alt.ac.uk/.
    Seb Schmoller

    1. Awesome – many thanks Seb!

      Crowd-sourcing the questions sounds a great idea. With such a hands-off approach it all comes down to the questions, when I spoke briefly with Sugata at the conference he pointed out all the skill was in the questions. I’d be interested if he’s written up any research on what type of questions work best, and also what age of pupils have been trialled so far?

      Wiki is a good idea, I’ve been crowd-sourcing something else completely unrelated today and wonder if we could also use Google Moderator to do so, voting up the best questions? http://www.google.com/moderator/#16/e=457ca – I like the voting part of the site, seems ideal for this type of thing.

  6. I really enjoyed all this – a good case for discussion.

    Now I am often told that I take things too seriously, so forgive the rest of this response, but instead I hope you will be pleased with the depth of reaction your experiment has inspired!

    No mention of ‘suspending the curriculum’ nor ’21st century skills’, but a mention of ‘enquiry-based learning’ at the end.

    I found interesting the creative development of the means of finding square roots, but even more exciting the rejection of false concepts by comparison with empirical data (scale drawing) – these seem to be excellent learning habits. Often it is the teacher’s role to say “wrong”, not “what’s wrong about that”, for lack of time and impatience rather than poor pedagogy. If year 7 can operate with team dialogue at this level, there is real hope!

    I found it exciting that the groups had taken the trouble to create aesthetically pleasing presentations.

    There is an oblique reference to the ‘get there on your own’ individualistic culture that dominates in secondary in this quote from the blog:
    “Two other groups got there after a little bit of peeking at the work of the first two groups (well within the rules)”

    I think it is vital to explore why two groups did not get very far and to know how they felt about spending 90 minutes getting nowhere – perhaps maths as usual, but not so boring?
    “This was down to a lack of teamwork, something we can work on in coming weeks, these pupils are only 11 years old after all.”

    I think that teamwork in school is always going to be difficult amidst a culture of individual endeavour is best, how did those who did work effectively as teams overcome this barrier? Year 7 may have just been through a primary education that gave them more time to pursue inquiries and less emphasis on individualism – older students may have been weaned off this progressive thinking!

    “… this is a fairly hands-off form of teaching …”
    So what did Dan do apart from observe and enjoy? What interventions if any, what effect?

    I doubt that all the skill (for the teacher) is in the questions and indeed I think you should be working towards the students formulating the questions. Getting this wrong and experiencing the consequences is important to develop a sense of effective questioning. Perhaps the skill is in offering a range of good and bad questions and encouraging evaluation and selection by the students? How many other ways could you have framed the same Pythagoras inquiry and what would be the poor examples? The example you gave, although all in text, nevertheless combined an open question and a closed question with relatively straightforward visual, concrete imagery – an excellent combination I think.

    I also think that the broad range of interventions you make to foster the habits of inquiry-based learning are the critical teacher skill, including the rules and the ‘permission’ you gave.

    An exciting read – thanks Dan.

  7. Well take 2 today didn’t go quite as well!

    Lessons learned:

    2 hours minimum (did 1 hour per class today to be finished later in week – not ideal)
    Pupils do need motivating, encouraging. If you’re tired and ill this doesn’t work so well.
    Choosing own groups may not work for all classes especially if they are not well versed in group work.

    You live and learn. I’ll report back later in the week when hopefully I’ll have got rid of this awful cold and will be able to enthuse the pupils a little more!

  8. Many thanks for the in-depth reply Richard, it’s much appreciated!

    There was a deliberate lack of ‘suspending the curriculum’, I see this as a way of teaching the current curriculum (although I did jump a year or two ahead!). 21st Century Skills would be an apt term to use for the skills involved.

    You’re right, this approach did give me more time to engage the pupils in conversations about the errors they were making, and I’m aware that I will have helped them in the right direction with these conversations.

    Today’s further experiments with older groups definitely showed me that this comes more naturally to groups closer to Primary age. Although I developed a stinking head-cold today that limited my interaction with the pupils. Less questioning, less encouragement (Sugata has done work looking at the ‘grandma’ model of simply offering encouragement and praise to keep pupils motivated).

    An open and a closed question do seem to make a nice pair to instigate this process. I’ll report back later in the week after the other classes have had a fair crack of the whip.

    Thanks again for the comments, I’m glad I could inspire such thought 🙂

  9. I find that one of the most insightful comments in this blog post is the one that quoted Sugata Mitra who ‘pointed out all the skill was in the questions’.

    It made me think of the poem by Rudyard Kipling from his Elephant’s Child story in his Just So Stories book:

    I keep six honest serving-men
    (They taught me all I knew);
    Their names are What and Why and When
    And How and Where and Who.
    I send them over land and sea,
    I send them east and west;
    But after they have worked for me,
    I give them all a rest.

    I let them rest from nine till five,
    For I am busy then,
    As well as breakfast, lunch, and tea,
    For they are hungry men.
    But different folk have different views;
    I know a person small
    She keeps ten million serving-men,
    Who get no rest at all!
    She sends em abroad on her own affairs,
    From the second she opens her eyes
    One million Hows, Two million Wheres,
    And seven million Whys!

    1. Wow! Thank you. Would be really interested to here how this work is going in your NE projects? Any findings of successes and failures, ages of pupils etc.. Also key to this being successful seems to be the questions that you ask of the pupils, both as the main task, and as you walk around encouraging. Would be really interested to here of successes and failures with the questioning.

  10. Well seeing as this exact lesson went so well I’m going to use the same question with my 14/15 year olds next week for my observation lesson. They’re not as well trained as the Y7s in independent group work, and we’ll only have an hour to complete, but I think it’s worth the risk. I’m confident it will either be Outstanding or Inadequate so fingers crossed!

  11. Your Pythagoras lesson sounded fantastic, but because I feel that the enthusiasm online about Sugata Mitra is a bit over the top and feeds into a dangerously uncritical approach to hi-tech bling, I was more interested in your comment about the need to motivate (rather than just pose the question, boot up the laptops, and then step to the side). Sugata has said some ridiculously dismissive things about teachers – things that assume that motivation is just not an issue. He ignores, for instance, the way his hole in the wall project surreptitiously fed off a very dubious source of motivation that wasn’t innate in the children. The monitor resembled a TV. The kids new about TV. Their society instituted TV in such a way that it acquired a halo (see Walter Benjamin on the halo). Anything that resembled TV shared in that halo. That gets the hole project going.

    Society gives shiny HD touch-screen hi-tech a massive halo. I imagine most early lessons that use the new tech piggyback that. Society doesn’t give things like poetry a halo. If we believe poetry matters, and matters so much that all children should be exposed to it, we need to work quite hard to make poetry seem important and worth exploring.

    Poetry is also not about the processing of information, so it is not easy to get a creative poetry session going with a question along the lines of those used in your Pythagoras lesson.

    This ties in with another worry about SM: The education he seems to focus on is all about the processing of information, not about the acquisition of values and the critical reflection upon those values. Knowledge remains a mere tool, not something that reshapes the ends of human existence. The ends are assumed to be unproblematically given. It is no accident that the slumdog is shown pursuing the crudest end of the society around him: wealth. When society promotes ends as crude as this perhaps there is a role for education in suggesting higher ends or alternative ends or values that call into question the ends promoted by the military-industrial-PR complex. Was there a chance that from the hole in the wall we could have had a slumdog poet?

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