Posts Tagged ‘Recreation’
“This paper describes a lesson taught to Judy’s Y2 class in a rural Hertfordshire primary school. It shows how meaningful mathematics can be made accessible to young children and, importantly, how fundamental issues of variant and invariant properties might be developed. An important component of this understanding is the position to term relationship – the relationship (or rule) between the position, n, of a number in a sequence and the number itself. In short, it is our view that young children, when given appropriate opportunities, can operate at levels substantially higher than the curriculum would indicate was likely.”
The teacher in this case made an animal, a dog, using linking cubes. The general shape was expanded upon to make two larger animals in a ‘family’ of three dogs.
“We discussed the dogs we had made. My questions and prompts were intended to alert them to an awareness of those elements of the dogs that remained constant (invariant) and those that changed. In respect of those elements that changed the intention was to encourage their understanding as to the systematic, and therefore predictable, nature of that change.”
The key to the children’s understanding seems to be labelling each of the parts of the dog, head, legs, shoulders, body and bottom. Once they could apply these labels to each of the three dogs, they could see how the animal was made up. They then used this knowledge to predict the make up of the fourth dog.
After this, they applied their knowledge to their own animals – working out the 4th and 10th members of the family. Some did this in tables, some did this in sentences, but they all could do it regardless of their mathematical abilities. Some were making generalised statements linking the term in the sequence to the body parts. All good stuff and remarkable when you consider that these children are in Year 2…
Reference:

Andrews, P., Sayers, J. (2003) ‘Algebraic Infants’ Mathematics Teaching, Vol. 182, pp. 1822
On Thursday I followed up Wednesday’s work outside by taking it a step further.
My Year 6 pupils were asked to create mini versions of our large circle using wool and paper plates. I had precut the plates to have a range of evenly distributed and more random slots around the edges. Pupils were then asked to secure the string by sliding it into the slot once, looping it at the back, then sliding it down the same slot.
They were invited to invent their own rules to create a pattern (such as missing every other slot, or missing two slots to go down the third). Finally, they were requested to photograph the resulting patterns, a selection of which, representative of all ability groups, are shown below.
As you can see the potential for discussion about shapes is huge. There are a range of polygons, angles, regular and irregular shapes all visible. Also, with ones that haven’t quite worked, we can look at the reasons why. Interestingly, the plates with evenly distributed slots were far easier for them to use then the irregular patterned ones.
Yes, I could have followed the outdoor work up on paper with predrawn circles and dots around the edge as suggested, but I thought that this related to what was done outside, was a little more fun and – important in this world of changing curricula – helped to develop handeye coordination skills.
Many boxes were ticked here and all sorts of interesting conversations were had with the children about their predictions for the shapes they would produce and about the ones they created.
Next week, I work with Year 3 children along very similar lines. I haven’t worked with Year 3 for about three years now and so I’m not too sure what to expect as the main differences in outcome – language will clearly be different, especially with it being so early in the school year. As for what else will be different, I’m waiting to find out!
I’m not entirely happy with the way yesterday went. For a start, we didn’t manage to fit in everything I had originally expected, which stops me from trying out all three activities with the small group as planned. Also, the group had grown by two to thirteen, making it a little on the large side to do much meaningful investigative work with the string.
Positives:
 They all enjoyed a slightly different way of working.
 They all appeared to be engaged throughout both activities.
 They all gave a range of input into discussions – the outdoor environment, while far from perfect at my school – encouraged a freer feel.
 It flew by. The fifty minutes scheduled for a Wednesday numeracy lesson honestly only felt like fifteen minutes.
Negatives or interesting outcomes:
 My highest of high flyers really struggled with the secret construction – more on that later.
 A feeling that more should have got done – did everyone make progress in that lesson? It’s hard to tell. Maybe my pacing was off.
 The larger group number made it difficult to get the most from the outdoor activity.
My fabulous mathematician, the sort of child anyone would want in their lesson as a human calculator, confirmed my long help suspicions – that his mathematical talent lays mainly with number and most other aspects of the subject are weaker for him.
For instance, in the opening task, the secret construction, he failed to notice that the colours his partner was using were the backs of the magnetic pieces, therefore all black. I’ve recreated the shape they had to make and the outcome he instructed.
He used all the correct pieces, just back to front. Also, when discussing the shapes made with string, he was adamant that that a turn between two sides would be around 70° when it was an obtuse angle – something we had been discussing only he day before.
A mixed one this so far…
I am developing these ideas further today with Year 6 and have a session planned to work with some Year 3 children next week along similar lines.