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.