My main conclusion is that I am going to have the saddest wish list for Christmas ever seen, but all of very valuable items for the classroom!
Novel Mathematics
The session began with the use of playing cards, totalling them, arranging them into sums, then moving onto magic squares (though this was led by first getting rows, then columns, adding up to the same number).
Other ideas for playing cards were also given (see ATM).
Next was a fantastic way to visual fractions. By folding a piece of paper one way to make a wardrobe, then the other way to make thirds, we formed twelfths of the shape (lines were drawn on with pen). The task evolved as follows:
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| Dividing a single sheet up into fractions to use in equivalent fractions and fraction manipulation |
- hold up 1/3
- hold up 1/4
- what is 1/3 + 1/4 ? (can see immediately from counting without being taught method)
- continue with subtraction
- what is 1/3 of 3/4? - take 3/4 size and fold it into 3
- division: using a 'division arm', count how many twelfths on top over how many underneath - interesting to show that division can still be done by first going to equivalent fractions
- repeat with 3 x 5 grid
- finally lead on to finding a method
- generalise algebraically
What does an art student take with them?
- a portfolio
What does a maths student take with them?
- a result
This lead us onto thinking about using written work - getting students to write about what they have learnt and the process that they went through is a far clearer way of gauging their mathematical understanding than a simple test. It was also suggested that children, occasionally, need to stand up at the front and give a very short presentation on something about mathematics. And idea for this presentation could be: "where is the mathematics in..."
Criteria for Assessing Written Work
- communication - steps taken
- extension of the task - and doing that extension
- mathematical understanding
- mathematical vocabulary
- working systematically
A lot of the emphasis of this session was on the culture of the classroom.
A key thing to come out of this was "being able to deal with stuckness." Teaching the students how to approach a problem was key to life and exams. When Mike was told by a student, "I'm stuck," he replied:
"Hi Stuck, I'm Mr. Ollerton, nice to meet you."Other activities using algebra involved looking at Fibonacci's sequence, choosing any two numbers as starting points. We then gave our partner the starting and the ending digit of a 5-box Fibonacci sequence and were challenged to find the missing numbers - a self-differentiating task as it can be tackled either by trial and error or by algebra. This can then be further extended to 7-box, 9-box etc and finding the middle value.
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| Geoboards. Made from 12mm x 160mm x 160mm MDF and escutcheon pins. |
- vectors
- gradients and equations
- co-ordinates
- symmetry
- reflection and rotation
- shapes and their properties
- area and perimeter
- trigonometry
- Pythagoras
As a way to establish prior knowledge, paired work was suggested, e.g. write down everything you know about the number 6, then go round class writing all ideas up on the board.
With all of these "rich tasks" it seems the most important thing is:
Another activity was using a "decimal grid" and the variety of tasks that could lead on from there, seen around the outside in blue. It was particularly noted that joining up 'isovalues' gave the gradient of the line."everyone can participate if the starting point is simple enough"
The final activity was to look at angles and algebra - essential making two crease lines on a piece of paper, drawing over them, then following the tasks on the sheet below.
Handouts on Ofsted criteria for Outstanding Teachers can be found here.
