Do you have any more suggestions as to how I can help my year 12 student to get into good problem-solving habits, he does not like the self-questioning process?
It is hard to answer your question because of the lack of specificity. What specifically is wrong with his problem solving skills? Is it that he simply doesn’t get what to do a lot of the time and gets stuck? Or does it seem to you that he has the right knowledge and could have answered most of the problem questions but for some reason he left them to go through with you?
Problem solving ability can for our purposes be looked at as two general pillars:
THE SKILL of problem solving is really all about globalising a problem and then breaking it down. Go through this process again and again when you get stuck in the problem until you arrive at a solution. A student must learn to:
1. Decipher the meaning of the question and understand what the problem wants (chunk up)
2. Break it down and decide on at least the next step by putting pen to paper and doing some working out (chunk down)
3. Realign with the meaning of the question to understand where they are up to in the process and then continue once again (chunk up then chunk down)
This is the general gist of the problem solving process. Strong problem solvers do this naturally. Consciously or not, problem solvers go through their own version of the Self Questioning process:
1. What does the question want?
2. What am I given?
3. What do I know about this?
4. What haven’t I used yet?
5. What else do I need to do? Anything? Let me at least back-check first…. etc
While your student may be reluctant to consciously go through this process because it is “lame” or whatever, he must already do this to some extent with the questions that he gets correct. You should explain this process to him and see if you can find some common ground. Try to find how he naturally does this and point it out when you see it – hopefully this will connect some dots. At the very least – when he gets stuck with problems probe him with these questions rather than giving him the answer.
THE PSYCHOLOGICAL PART: Has your student ever left a question for you to help him with but upon looking at it you knew that the question was not even close to beyond his skill? This is a really common experience, especially with students who are accustomed to being “bad at math”. As a student improves in maths they must break through or at least stretch various psychological barriers if they are to improve further. One such barrier is learning when to give up and when not to give up.
The nature of problem solving (real problem solving – not easy questions in the guise of challenge) is that a student is not supposed to know how to do it straight away. They are supposed to figure it out by “playing” with the maths. It is this very “playing” that stretches problem solving capacity.
Not only must students feel that It’s OK To Be Wrong, but that it’s ok to be wrong again and again until you figure it out. This is where lots of developing students fall short. They don’t really appreciate this truth and come to believe that a question is beyond them when it is not.
If this happens with your student, start to break the pattern. Sometimes, you may even blatantly refuse to answer a question – especially if it was a really easy one. Instead probe him through it using self questioning techniques to demonstrate to him that he was capable of answering it on his own. Over time the goal is to stretch his expectations of himself and condition him to “play” with the math when he gets stuck.
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