This is an account of planning and teaching a first lesson with upper primary (age 8-11) on 'shape'. The classroom teacher asked me to plan some lessons on 2D/3D shapes, angles, and so on. I decided to start by looking at polygons.
I explored a few ideas whilst planning, including:
(1) What shapes can you create by making various folds and making one cut? (from SMP Book A).
(2) I had a brief play with some some pin-boards (see video below). I have decided to spend one or two lessons making 12-pin circular geo-boards with the children, and then exploring them.
(3) I plan to explore various ways of classifying triangles, quadrilaterals, and perhaps other polygons. The article 'Classification' by David Fielker (from MT 95, and part of the excellent ATM collection 'Removing the shackles of Euclid') is inspiring; this paper alone has enough ideas to fill a whole series of lessons. I am also planning to spend a couple of lessons exploring classification of quadrilaterals via their diagonals, using Geostrips.
(4) Logo will be a great way of exploring side lengths and angles of polygons, as well as introducing the children to programming.
However, I decided to start with a couple of lessons exploring so-called 'Iso-tiles', which contain copies of the golden triangle and golden gnomon, mostly because me and my partner had most fun playing with them.
Play, record, describe
The aims of the lesson were: (1) play, (2) record, and (3) describe. I created a series of tasks, the first task being free play (inspired by Gattegno's Mathematics Textbook 1, Chapter 1, my favourite first chapter of any maths textbook). I learned from my 'mistake' of not doing this when we started with Cuisenaire rods. Here is what the children created in the very first minutes of play, a lovely mixture of the mathematical and the artistic:
A second (more constrained) task formed the core of the lesson for the majority of the children:
Many children showed a tendency to want to name the shapes, but I encouraged them to really look at each shape and describe them in terms of side lengths, parallel-ness, symmetry, angles... Here are some of their responses (click to view gallery):
There were so many interesting discussions - about parallel-ness, sameness and difference, and symmetry - and so many starting points for further exploration over the next couple of lessons.
It seemed that a few of the children felt over-constrained by the two-triangles task, and decided to work on their own mathematics instead. Here are some examples that might also provide rich starting points for further exploration:
Last week I felt a sense of anxiety while teaching this class, but was not sure why. This week, I came to realise that it may be because I was beginning to wonder if the children were getting much out of the lessons. I had felt a sense of resistance from a number of students, and wondered how the children viewed the lessons. I wondered if I was failing in one of my main aims: to involve these children in different/fun/interesting ways of working on and thinking about mathematics. I have taught mathematics more or less 'successfully' for 14 years, but was not confident that I was providing something useful for this group of children.
It dawned on me then that I don't really know these children, or how they feel about the lessons.
I noticed during this lesson that I have a reticence to approach these students, to sit with them and talk to them while they are working. This is not normally the case with the learners that I have worked with in the past; sitting alongside learners is a crucial way of finding out what they are thinking and feeling. This is partially because I get the sense that these children do not seem that comfortable being approached, perhaps because they are younger and they don't know me very well. I am new to the island, and also don't work full time at the school; I only work with them an hour and a half a week. There is a sense in which I am respecting/reciprocating their reticence.
During this lesson I resolved to (a) overcome my reticence to sit with them, and (b) ask them how they felt about this lesson at the end, something which I always find difficult to do, perhaps because I am generally wary of receiving feedback. Receiving feedback is something I am working at getting better at.
At the end of the lesson, I asked them to write (anonymously) on a post-it whether they had enjoyed the lesson or not and why. Not a very good question perhaps, but here are their responses, transcribed in full:
"I enjoyed this lesson because we played with the tiles."
"I enjoyed it, making shapes."
"Yes, I loved it. Learned a lot."
"I enjoyed it a lot, it was fun and interesting."
"I really liked this lesson because I had fun playing with all of the triangles."
"Yes, because it was fun."
"I enjoyed it a lot because I've never used isotiles before and I enjoyed making shapes."
"I did enjoy it because I like working with shape."
"Yes I did enjoy it."
"Yes I did enjoy it, good fun."
"I enjoyed it because we got to be creative and it was a fun way to learn. I don't normally get to learn like this."
"Fun. Slightly confused about the purposes of exercises. Enjoyable lesson."
"I liked it because I got to cut things out and give them weird names."
"I didn't enjoy. I don't know."
"Yesssss! Because I got to fiddle with shapes and work in a different group, it was a good working together experience."
"I enjoyed the lesson but to make it more fun I would like to be able to choose what partners we had."
"I enjoyed it because I like making shapes."
"I really enjoyed it. I really like fun and enthusiastic teachers, Mr Brown is one."
"I enjoyed it because of the shapes."
I was surprised by this feedback. It is good to know the majority of them are enjoying the lessons. This feedback has allowed me to move forward with more confidence.
It is notable for me that a number of the children described the primary source of their enjoyment to be in making shapes. I have really come to understand the vital importance of working with physical materials since teaching younger (primary) learners. It is something I have carried into my teaching of older learners, right up to higher/A-level.