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Reasoning, Problem Solving and Justification – A Classroom Journey

Hilary shows how her students have developed the skills and enjoyment of reasoning, problem solving and justification.

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Hi Everyone,

It’s me again – Hilary Campbell, Year 2 classroom teacher at Eaton Primary School with an update on how my students and I are going in the Champions of Maths program. If you want to read my first blog instalment again, it’s here.

I’m pleased to report that we are truly amazing most of the time! My students have developed and are still developing strong maths skills. All my students are demonstrating greater confidence in their own abilities, maturity when facing challenges, interacting with each other and are more curious about mathematics. Winner, winner chicken dinner!

Image 1-l Kye, Mark and Connor were given a problem solving task that asked “Create numbers where the ones digit is 9. What is the largest/smallest number?” Their findings to the initial question are in the red circle. From there they started wondering about how that would work for the tens position and the hundreds position so they just kept on going. Mark started experimenting with keeping a 6 in the ones position and the hundreds position. They excitedly compared and shared what they had found. They even complimented each other’s work and asked each other’s opinion. Very cool!

We are still problem solving on a regular basis. Now that the process has been embedded the students are collaborating more effectively as well as not getting caught up with petty issues such as who gets which colour whiteboard marker. Just a quick note on that: I don’t hand out the whiteboard markers until each group has had some discussion time and are satisfied, they understand the problem and have an idea or direction to work on.

Our new focus is mathematical reasoning. Now this has been a revelation! The children very quickly embraced the idea of justifying their answers and in fact they enjoy explaining their ideas. We started with simple warm up activities.

Image 2 A fascinating observation I have made is that when the students see this up on the interactive whiteboard I can see them searching and scanning looking for relationships, patterns and commonalities. I have found reasoning warmups to be a good way of introducing and practising mathematical vocabulary. Different student responses to this type of activity have been: 4 is a different colour so it doesn’t belong, 9 is odd so it doesn’t belong, 16 is greater than 15 and all the others are less than 15 so 16 doesn’t belong. When we use stimulus pictures as a reasoning warm up I hear terms like array, diagonal, groups of, pattern, perimeter and so on.

As our skills improve the children are relying less on drawing pictures and more on writing numbers and groups of numbers to arrive at their answers. Obviously they are all unique individuals and are learning at their own pace but when they are scaffolded within a collaborative team usually everyone has something to offer and joins in willingly. I am constantly delighted by the questions that the seemingly least likely students come up with. They may not understand everything that’s going on but they are in the right neighbourhood.

One of the first full on reasoning activities we worked on came from – what a godsend this site is! As it was our first big task outside of warm ups, I was expecting the children would solve the problem without looking for those patterns and relationships as they do with our reasoning warm ups. Wrong – ish! There was definitely a lot of problem solving but once I asked them to explain and justify their answer they did. Now we are well down our reasoning task pathway the students are expecting to justify their ideas and are disappointed if they don’t get to. Pretty much they are justifying and explaining automatically most of the time.

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The confidence, maturity and understanding that my students are demonstrating towards all areas of maths I credit to our involvement with the Alcoa Champions of Maths Program. It’s been the best professional learning I’ve done.

Image 6-l After a skip counting activity last week I asked an early finisher to use the Turn and Learn board to show skip counting by 3’s. Half way down the board another student joined him. He realised there was problem because the pattern he could see earlier on the board was not repeating. I was so impressed to hear these boys discussing the problem and talking about what they needed to do to fix it. The initial student ended up realising where he had gone wrong and explained it to the the second boy. His solution to the problem was to locate the last position where the pattern was evident and work forward from there. The second student offered an alternate solution of starting again which they discussed then both agreed the first solution was the best. This whole interaction was spontaneous and required nothing from me. Happy teacher!

We are currently working on the Number Tower activity from the reSolve website. I was nervous that this task was too hard for my students. It’s a Year 3 activity and my students are Year 2. They have really taken to it without too much fuss or effort. Currently we are working in pairs. I haven’t needed to adjust the task at all but I have asked a few pairs if the use of a calculator would help. Some said no. Jutt and Lachy were working together on a number tower on Thursday. Our Associate Principal paid us a visit and while she was there I asked if anyone would like to explain to Mrs Cook what we were doing. Jutt and Lachy were very keen and did a great job describing what the task was and what they had noticed. The next day Lachy arrived at school with a folded piece of paper in his hand. I asked if he had something he wanted to share and lo and behold – Lachy had been creating number towers at home for fun. How cool’s that?

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Find out more about the Alcoa Maths Enrichment Program or read the next article.


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