13 Jun

Multi-Stage Problem Solving

One of my students has a habit of challenging herself by attempting tough questions, but is unable to complete them and as a result gets demoralised. To fix this,  I usually break up these tougher questions into parts to make them doable. However, in doing so she’ll be unable to answer different questions (say doing a question on area, then volume and then surface area) and not use previously solved parts to help her with the current question. At this point, I believe it’s either a problem of her not reading the question properly or she isn’t practiced enough with doing various questions all together. Usually the solution would be to set tedious amounts of easy questions, but I don’t want to further lower her morale by giving her questions that she believes are too easy. So I’m not sure what to do in this situation.

 

  • It sounds like she is having trouble globalising all the parts of the question or getting back on track once any given part of the question has been completed. The main question she needs to ask herself (or you can ask her) is “what does the question want me to do?”. This question should be re-asked throughout the problem, if she is able to answer it for herself that should really help her put the multiple parts of the question into perspective.

 

  • Rereading the problem, properly, from the beginning, should also help when she gets stuck about what to do next. It is ok and sometimes necessary to do this several times throughout a question.

 

  • It may also be a matter of attitude and confidence. Many students who are developing their skills expect to just know what to do all the time if they have studied it. They think that getting stuck means they can’t do the question which of course is not the case. Getting stuck and then figuring out what to do is a central skill in math; it requires struggle and effort and thought. As soon as a student understands that its supposed to be this way their ego won’t hurt as much and the sustained confidence will help in problem solving.
    • Consider how long she actually spends on the question before saying “i give up”? How hard does she actually strain her brain before putting it in the “too hard” basket?
    • While every student is different, really successful problem solvers can spend up to 30min on one question, moving back and forth until they make progress and solve the problem. Obviously this takes confidence so that the student must believe that the problem is solvable and they have the capability of solving it. Hence it is worth sticking with it even if it takes 30min because they know eventually they will get it – for some students its a matter of pride to finish it on their own.

 

  • When she is stuck get her to write stuff down. Anything that she thinks is relevant; the general formulae, the data in the question etc. Often putting this on paper helps to trigger other relevant thoughts.

 

  • Instead of breaking the question up into parts for her, start trying to talk her through that process without telling her what to do. Use the self questioning process and probe her throughout the question. It may take  a really long time but at least then you will be able to say “see, with enough effort you could do the question – i didn’t actually give you a single piece of information”
    • eventually this will build her confidence and make her comfortable with the problem solving process and the “getting stuck” experience.

 

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