I was trained at Keele university by some fantastic mathematicians. They were able to direct investigations of even the most simple of concepts through to degree level maths. To this day I am still attempting to repeat this process, I am sure they had the advantage as we were all on a course to learn how to teach maths, so all able at the subject and confident in our abilities.
When trying to repeat this in the classroom in my first few years of teaching it felt like every little hurdle became a mountain. I learnt that I was trying to control the lesson too much, and that the students needed to be trained how to explore the problem.
In this mini series of articles I hope to help you understand the training process, this can be explored from either end of the scale. I will give no answers, they are for you to find. What I will give is the first stepping stone in the process. As students get more confident they need this step less and less.
Before you rush off to try investigative teaching or learning, you need to understand how to ask the questions. Never answer one as a teacher, even in the observational pressure situations a leading question can give away an answer too easily. Force them to think, be confident to walk away. Of course you can explain your motive for doing this or you may get an angry parent telling your boss that you do not help their little angel enough.
To train them to think a sequence of starters lets you get a foothold. Try starters that are multiple choice, 4 numbers such as 4 9 15 27. Ask for the odd one out, ask for a special one. Look how far you can take the questioning, think about how the students can break the numbers down. It is really interesting to do this as you see lots of different perspectives, and some increasingly strange answers at times as you move down through the sets.
Consider when you question a student;
When trying to repeat this in the classroom in my first few years of teaching it felt like every little hurdle became a mountain. I learnt that I was trying to control the lesson too much, and that the students needed to be trained how to explore the problem.
In this mini series of articles I hope to help you understand the training process, this can be explored from either end of the scale. I will give no answers, they are for you to find. What I will give is the first stepping stone in the process. As students get more confident they need this step less and less.
Before you rush off to try investigative teaching or learning, you need to understand how to ask the questions. Never answer one as a teacher, even in the observational pressure situations a leading question can give away an answer too easily. Force them to think, be confident to walk away. Of course you can explain your motive for doing this or you may get an angry parent telling your boss that you do not help their little angel enough.
To train them to think a sequence of starters lets you get a foothold. Try starters that are multiple choice, 4 numbers such as 4 9 15 27. Ask for the odd one out, ask for a special one. Look how far you can take the questioning, think about how the students can break the numbers down. It is really interesting to do this as you see lots of different perspectives, and some increasingly strange answers at times as you move down through the sets.
Consider when you question a student;
- Are you leading them to the answer intentionally?
- Are they simply looking for reassurance as is often the case?
- Do they know how to start the problem?
- Do they need to be led or pushed towards the solution?
A recent lesson observation feedback made me think if I was leading them too much when perhaps I should have started with a couple of more simple questions. It was equation of the line with a middle ability set, I asked "x is 2, what is 3x..........take 4". Perhaps I should have recognised they needed a quick recap on substitution which they have not done for at least 6 months, with a summer holiday in between. My intention in this style of questioning was to get the students to see the stepping stones simply, even if they can follow each instruction I give it does not mean they can solve this themselves yet. My questions led directly to the answer without them committing any thought to the process. The lesson was graded as good but I know it could have been a lot better, for once the feedback really made me think.
A lot of what I have written and will write is open for debate, if we knew the answers then everyone would find maths easy as we would be able to do our jobs perfectly. There are no perfect methods for teaching maths as everyone thinks differently, this is what makes our job so fascinating.
Take this as an introduction to a set of articles that will explore different skills, no doubt I will edit it to make it clearer in the long run. Try different approaches as starters or mini breaks in a lesson to train them to think for themselves. An investigation does not have to last for a full lesson, it has taken me a long time to realise this! It can be a 5 minute discussion or a mini project over a sequence of lessons while you as the teacher build up the required skills.
I hope you find this of some use.
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