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This is Emily Grainger, Year 4 teacher from Bungaree Primary School, with my second blog post for the year. You can read my first one here.
This experience has taught me so many things. The most important I have found is the value of talk and discussion in mathematics lessons. Over the year, my students’ confidence in contributing to class discussions has skyrocketed. They are so keen to share their ideas, hypothesises, and reasoning. The value that these discussions have added to my lessons is immeasurable.
Example: Why is 386 bigger than 368? This might seem like a very simple question, with a simple answer ‘It’s a bigger number.’ But I have pushed the students to justify their answer with more sophisticated language. If I ask my students this question now, they will say “386 is bigger because the 8 in the tens place is larger than the 6 in the tens place in 368.” It has been a huge learning curve for me to place more ownership on the students to explain their thinking. The students need to question what they already know and link it to new understandings.
To foster a positive culture around class discussions, I focused on simple discussions around ‘agree’ or ‘disagree.’ Through this we were able to target the discussion on why they agreed or disagreed. It was great to see how I was able to create web of discussion that links the students. It made students more comfortable sharing their ideas as they were able to springboard off a peers idea, or simply share whether they agreed or disagreed. Students are now familiar with this idea and are able to justify their response – “I respectfully disagree because…” or “I agree because…”
I am working on varying my use of ‘Talk Moves’ in my teaching practise. While ‘turn and talk’ has been a strategy I have always used (pair-share), I am learning how to use it more effectively in my discussions. The question needs to be specific, targeted, and able to be shared easily between the two students. I have found that when I plan specific questions for a pair-share or ‘turn and talk’ my students get more out of the discussion. The students are more engaged in the discussion, and the mathematical concept becomes more visible to students. The ‘turn and talk’ is a ‘safe’ strategy for the discussion. It allows students who struggle to access complex ideas to feel ‘safe’ in a discussion with a peer.
For my class, I find that using ‘wait time’ allows for my less confident students to mull over the ideas for longer. They are then more equipped to answer questions when I call on a ‘non-volunteer.’ My focus is now on further utilising the ‘revising’ talk move to continue to challenge my students.
Problem Solving Question: Jane is making a Number Tower with 1, 2, 3, 4 and 5 on the bottom row. Jane thinks that to make the largest total at the top, you need to put the largest number (5) as the first number on the bottom row. Find proof to defend (agree with) or challenge (disagree with) her?
Our discussion for this question was very effective as students of all abilities were able to share their findings. Most students were able to explain that the five had to go in the middle position as it is ‘used the most.’ The discussion was then focused on this idea of ‘using’ the 5 the most. After a turn and talk we were able to derive that when we say ‘using’ the 5 we mean it is ‘added’ the most. In one students’ work there was arrows from the ‘5’ going up the pyramid to demonstrate this idea. If I was to do this discussion again, I would have used this diagram to reinforce the main idea.
During our number tower discussion, I was able to use turn and talk questions to draw out the mathematical concept. Once we focused on the idea of ‘using 5’ multiple times I had the students turn and talk to each other about what they meant by ‘using 5.’ Most students weren’t able to answer this question – yet. After we had looked at the number tower again and talked through the addition of the 5 multiple times, I asked the question again as a turn and talk. This time, the discussion was much more lively and multiple students were able to provide an answer. I learnt from this experience the importance of an ‘accessible’ turn and talk question in order to keep the discussion going.
Problem Solving Question: Matthew has agreed to work for his Mum over the holidays. Matthew will get $1 for the first day he works, but for each day he works from then on, his pay will be doubled. How much money is he paid on day 7?
The discussion for this question was exciting as we were able to ‘create’ the matching number sentence as a group. Once all the groups had presented their strategies, I asked the class “What does the number sentence look like for this question?” They all had a go at writing it on their individual whiteboards. The term ‘number sentence’ was unfamiliar to many of the students. Two of my students came up with – 1 x 2 x 2 x 2 x 2 x 2 x 2 x 2. I wrote this on the board and gave the students time to have a look at the numbers and what they ‘represented’ (another unfamiliar term).
Underneath the 1 I wrote ‘Day 1,’ as a hint to the students. We discussed how the 1 represents day 1 – because Matthew was paid $1 for the first day of work. I then had the students turn and talk to discuss where I would find ‘Day 2’ in the equation. Some students replied with ‘2 x 2,’ but were respectfully challenged by their peers. We agreed to box in the ‘x2’ to represent Day 2. I handed the rest of the equation to the students to determine what the rest of the equation represented.
By the point we got to ‘Day 5’ I asked the students who had written the original number sentence, if they would like to revise their thinking. They had noticed through this group diagram that they had added an additional x2 as they assumed they needed to multiply 7 times. This was one of the most rewarding discussions I got out of the problem solving this year. It was so pleasing to see students of all abilities recognising the elements of the number sentence and how they linked to the worded problem.
I look forward to all the ways I can challenge my current and future classes through deep and investigative discussions. Talking through maths has proven invaluable for students of all abilities.