10 Top Tips for Effective Reasoning
It used to be the trend that children would practice a mathematical skill then, when they were fluent, their extra challenge was a reasoning question. Often reasoning was only for the more able pupils. Thankfully, with the extensive research carried out into effective teaching and learning in maths, that trend has died a death! We know that reasoning is one of the core principles of teaching for mastery which should be woven through the lesson. I see reasoning as the golden thread of a good maths lesson, tying everything together and securing the loose ends. With this in mind, I would like to share some of the strategies I use to develop effective reasoning skills.
1. Give children opportunities to reason in every lesson.
The more children practice reasoning, the better they get. In my experience, and often to my frustration, children tend to listen to each other much more than they would listen to an adult. When children are empowered to explain the how’s and why’s of their maths and unpick a concept for themselves, learning is more memorable and it sticks! With this in mind, children should be given opportunities to reason in every maths lesson.
2. Start at the beginning – it is a very good place to start!
Children should be prepared to reason about their learning from the start of the lesson. I often start a lesson with a picture or series of pictures and ask children what is the same and what is different? Here, the children do not need prior knowledge of a concept, they are reasoning using their own common sense and observational skills. Going back to my golden thread analogy, you wouldn’t start sewing a hem in the middle because you would miss out. I like to see reasoning in the same way.
3. Draw out the learning objective and success criteria
Building on my previous point, discover the maths together then ask children what the learning objective is today. What concept have we been looking at? What did you notice? What skills did we use today? Let’s write the objective together. What do we need to remember this lesson in order to be successful? Write the success criteria where appropriate. Remember that your role as an excellent maths teacher is to facilitate learning – not to disseminate knowledge. Children should be allowed to explore and reason about mathematical concepts, developing their own objectives and success criteria with a little help from their ‘guide on the side’ – that’s you!
4. Encourage Collaboration and Talk
Set a precedent in your maths lessons that all children are active participants – there is no space for passive learning. Everyone is expected to talk, collaborate and be part of each other’s journey in maths. In my year mixed KS1 class, everyone is given a partner. All children are expected to talk each other through their reasoning then share back to the class. I mostly stopped hands up questioning in maths so that all children had opportunities to practice verbal reasoning and it has paid dividends.
5. Make Mistakes
Make deliberate mistakes based on common misconceptions. If you are new to the profession, White Rose Hub small steps planning includes common misconceptions for each objective. I often make a mistake then wait to see if children can identify it and unpick the part of my mathematical thinking that went wrong. This involves children working back through a problem. It could be that some of the children had the same misconception and can now understand the reason behind it. If the children do not see that there is a mistake and a tumbleweed moment ensues, I usually model the reasoning then try again.
6. STEM Sentences
As touched upon earlier, reasoning is a skill that gets better with practice. We can support children to reason verbally using STEM sentences. A stem sentence is a sentence or sentence opener that the children learn by rote but change depending on their reasoning. I have worked with colleagues who display the STEM sentences for the week on their maths working wall. I have also met colleagues who use reasoning STEM sentence fans which give children a starting point for their reasoning. I tend to write my STEM sentence at the bottom of my powerpoint slides and the children now know where to look.
7. Can you show me a different way?
If children are quick to answer could they show you that they are correct in a different way or draw a model to show that they are correct.
8. Why?
Always have the words ‘why?’ and ‘How do you know’ on the tip of your tongue.
9. Scaffolding
Reasoning can be challenging for some children but when teaching for mastery, we all work at the same level with different levels of support and scaffolding. One way I encourage children who are struggling to reason is by giving models or images that support. I sometimes give one that supports their reasoning and one that does not. They can select the model or picture to talk about or just show it. STEM sentences can also reduce cognitive load and allow children to share their reasoning in a simpler way.
10. Vocabulary
Share vocabulary and model using that vocabulary throughout the lesson. Only accept answers (for the most part) in full sentences. An example of this is when asking 7+4, do not simply accept 11 as an answer. Prompt children to say the full sentence e.g. 7 + 4 = 11 altogether and I know this because 7 +3 = 10 and 1 more is 11. This not only develops their speaking skills, but their mathematical reasoning.
I hope you have found my 10 tips helpful. Mathematical reasoning is something that our school have really worked on and developed over the last four years and I am proud to say that it has had a notable impact on attainment in maths. I would love to hear back from you– please tweet me @Miss_J_Petch. Happy reasoning!
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