Travis Kalanick tells us ‘Every problem has a solution. You just have to be creative enough to find it.’ This is true of maths, reasoning is increasingly part of maths exams, yet students find it increasingly more difficult to overcome. Why?
As I discussed last week, maths language is a barrier for many. They know what they are doing in fluency exercises, however, worded problems or the need for explanations leaves them confused and unable to express themselves. This creates frustration, which in turn leads to the belief that they are unable to access this branch of maths. A maths dictionary can really help support this notion and increase confidence in using and understanding maths language.
What is Reasoning?
For many, reasoning is instinctive and as a result it is difficult to explain to others. There are a number of occasions when we may need to use reasoning.
- To select an operation
- To decide what a question is asking us
- To form a plan to answer a question
- When different approaches can be used to answer a question
- When deciding if an answer is correct
This list above is not in any way complete, it is just a set of examples, we reason all the time, everytime we make a choice we have used reasoning. The skill of using what we already know to make a decision in another situation. For example, we know the ingredients list to make a curry to serve 4 people, but, we are having a party and we need to serve 8. Our existing knowledge tells us that we have doubled the number of people eating, so we must double the ingredients. We know what to do, because we can use our knowledge and logic and produce a plan. That is all there is to reasoning.
So what do we do when we reason?
I have thought about how to answer this for such a long time, it really wasn’t easy to explain. In fact, in order to write this I had to use my reasoning skills, hopefully my approach makes sense!
Reasoning can be:
- Assessing a situation
- Selecting a strategy
- Drawing a logical conclusion
- Developing a solution
- Describing a solution
- Reflecting
Let’s start with assessing a situation. This is often a swift process, as the brain determines what it can see. We consider what we can see, what we can make links between. With the curry scenario above, we linked 4 and 8 together, we know the original recipe is not enough, we have to solve that problem. So our assessment of the situation is: I want to cook the curry for 8 people, I only have a list of how to make it for 4 people, this is a problem.
Next I think about what strategy I can use to solve this. I start to think about what I know about the numbers 4 and 8. I know they are in the same times tables. I know that multiplying 4 by 2 will give eight as an answer. My strategy is: I need to double the amount of curry I make.
Next will be applying my logic. I could solve the problem by making two curries. I need two sets of ingredients, pots, pans and spoons. Logical conclusion is: By making the curry twice I will have enough curry to feed everyone.
Developing my solution means I have to decide how to solve the problem. In this case, how I am going to make my two curries. I have decided to make the two curries separately.
Describing my solution means telling someone else what I am doing, so they would be able to do the same. So here goes! I decided that it could be confusing to try and make two curries at once and I know curry can keep warm in a pan. So I will prepare my first curry, by chopping all the veg, preparing the meat and measuring the spices. Then I will follow the recipe to make the curry. When the curry gets to the point it only needs to be stirred now and then I will make my second curry in exactly the same way. Then when they are ready I can serve them to my guests. After my guests leave I will do the washing up.
Reflecting, means deciding if my solution was effective and efficient. In this case my method was effective, I needed to provide curry for 8 people and I achieved that. However, it took me longer than it normally would to make the meal, because I made it twice. This is a reflection, something that I have noticed. Now I need to think about how I could solve this to make the process more efficient if I was to repeat it. Instead of making the curry twice, I could have doubled the amount of each ingredient, then followed the steps of the recipe. This would mean the curry would take roughly the same amount of time as normal to create. I could also use a bigger pan, to make sure there was enough room for all the curry. This would still feed all 8 people and it would be more efficient as I am only doing each step once.
This is how reasoning works. It is being presented with a problem and putting steps in place to solve it using what we know already. We then use our reflection to decide if we could do it better. Sometimes we reflect and decide we were spot on the first time…that is fine too.
Reasoning is easier when you work with others, you each have experiences to share and from them you can develop a better plan to solve your problem. Reasoning allows children to express what they know and why they think it is important, while teaching them the value of listening to the experiences of others. By merging experiences and ideas together children often discover the most efficient strategy sooner and by being able to discuss their ideas their confidence develops. This makes them far more likely to attempt reasoning independently as they have been able to develop their own strategies by experiencing what others would do. This is fundamental to developing strong reasoning skills, for maths and beyond.
If you are interested in developing your child’s reasoning skills, register your interest for our upcoming group maths sessions.