The advice given to me last month was really helpful. Samuel believes that in order to succeed in Maths is only possible if you are a ‘genius’ and this may be due to the fact that I had tried to simplify things too much during class and assumed he had understood certain concepts which he in fact is still unclear about. I still find it difficult to convince him why understanding concepts would make it easier for students to work through a question, I have tried all my best but he simply still cannot see the reason behind this. Samuel really does seem to be stressed from school, but he simply does not act upon it and expects others to fix his problems.
There are a few issues in what you have described above. Probably the most important thing to focus on immediately is demonstrating that rule dependency does not work for maths, so let’s focus on that.
Unfortunately you can’t tell a student this simple truth and expect them believe it – sometimes they will but most of the time a conversation alone will not be enough to change their behaviour. Fortunately your student is in year 11 maths and mature enough that you can speak directly. Regular conversations must take place within tutorials to push the concept of Seeking Understanding. This should not be done as preaching or a speech on your part but rather a consultative conversation. Always get his feedback:
- Do you agree? Why? Why not? How do you know?
An effective approach is to demonstrate the truth of what you are suggesting in practical terms rather than just preaching:
- “The definition of insanity is trying the same thing over and over again but expecting different results” – Einstein said these wise words; explore this with your student. He has been working hard at his maths but yet, real success seems to elude him, why does he think this is happening? Obviously he is doing something wrong in his approach? Many students have gone from failure to extreme success in maths – many of them probably did not work much harder than your student? How can this happen? It’s all in the approach. Either way, if he is not getting results using the current approach it makes sense to try something else? Point this out.
- Here is a useful proverb for your student: “Give a man a fish and you feed him for a day, teach him to fish and you feed him for a lifetime”. Maths is the same, once he understands a concept in depth he will always know it. Otherwise revision will be necessary in extreme quantities. Certainly there must be some concepts that he really does comprehend? Take questions from those topics and ask him to do a few; then contrast this by asking him to try questions from a previous topic where he just memorized the rules. Point out how much easier it is when he understood the content.
- Find out why he thinks you can only succeed in math by being a genius? Why does he believe that his only choice is to memorize rules? Where did these ideas come from? Probably from some friends of his who must also struggle with maths if they give such advice. Ask him if he would go to a dentist to fix his car? He would probably go to a mechanic, not a teeth expert. Same goes for maths. Explain that to fix his maths he must listen to those who succeed in maths (such as a maths tutor).
The goal is to get him to question his faith in rule dependency. With enough of these demonstrations, gradually, he will inevitably be forced to confront his own false beliefs about rule dependency. Then it should be easier to get him on-side.
The ultimate purpose here is to change the student’s focus such they when they look at a question or your explanation their internal dialogue is saying:
- “What does this mean? How can I figure this out? What is this about? How does this make sense? What haven’t I tried yet? Which concept is this related to?”
Their internal dialogue should NOT be saying:
- “What was the rule for this? This was done in class – what was written on the board again? What’s the answer? How can I remember this rule/process?”.