Our mentors were so right to tell us not to expect results immediately. Not only were the children learning a whole new way of participating in a maths lesson but so were we as teachers learning new "talk moves", how to write engaging questions, how to scaffold but not lead discussions, teach the norms and know how to ask open ended questions and to try and engage all learners when some did not wish to be engaged or did not have the necessary maths knowledge to help their group even with simple counting on materials.
By the end of Term 2, I was already seeing a change in the maths thinking of some children. They were beginning to ask "rote" questions and they were prepared to be patient and work with a small group, following group norms and having some good discussions. Not every maths lesson was successful but I could see that there were more successful lessons than unsuccessful. Some children were able to give an answer to a problem but they found it hard to make their reasoning "visible" to others. Explanations were often a simple "because..." with no real logical answer. A sort of "I know so why don't you not know as well."
Terms 3 and 4 still left me trying to engage my reluctant learners and worrying how these children would gain number knowledge. The mentors said that children would gradually become more engaged and that they would "learn on the job" and this is exactly what did happen. When I used the JAM test at the end of term 4 I was pleasantly surprised to formally assess their knowledge. I had seen children extend their number knowledge, quickly count in 2s and 5s and share things equally when solving problems but to be able to look back at previous results and see just how much progress was made was satisfying.
|A snap shot of priority learners to show their increase in Add/sub and number Id.|
|Term 1 and 2 participation|
|Term 3 and 4 Participation|
For those children who can use the norms and listen to other children's reasoning (not arguments) then persuade others that there might be another way of looking at the problem it is great to see the progress they have made. In a recent problem I had a picture of a pattern built using Duplo blocks. The challenge was to guess how many blocks were used without counting the blocks one by one. I thought they might be able to find two solutions but they surprised in finding seven solutions before we ran out of time. These included being able to see that some of the solutions were repeated addition, groups of 10, symmetry of groups, multiplication (groups of) and the commutative law. Given time to work collaboratively through this problem they were able to see different possibilities and share their thinking to help others see another possibility. The debriefing at the end also helped others see the possibilities.
All this also shows the development of the children's language. They try to give logical explanations and use mathematical terminology to be more precise in their descriptions of what they have found not just give a vague wave of the hand over a drawing. They are encourage to ask questions (although many are still what I call "rote" questions because they find difficulty in framing a question and building their reasoning skills). The norms of having a discussion with one person talking and the other group members listening and giving others time to think, has flowed through to other areas of classroom discussions. I will certainly be introducing the norms early on in maths next year to get DMiC maths off to a flying start as well as using it in class discussions in other areas to show that this is the way we have a discussion.
Using the maths wall as a warm up each day has helped children learn shapes and to think about why I have grouped certain shapes together. It is no longer enough to say a vague "because..." but they are trying to explain their thinking using every day language such as "four corners" or "one long side". Fractions, before and after, subitizing of numbers, tens and ones, counting in 2s, 5s and tens all help show maths and the language it uses is all part of our life and is not something too difficult and to be avoided at all costs.
It is exciting to come to the end of the first year and to realise how the expectation that everyone contributes and encourages others in DMiC maths has helped in the acquisition of language.