In this article, Palme notes that teachers and textbook
companies are struggling with the development of school tasks that resemble out
of school situations. He criticizes traditional math word problems in lacking
realism and not being authentic. For example, a question involving an elevator
and a number of people does not take into account that people arrive at
different times, and the elevator would not always leave full. Palme attempts
to build a framework that will allow people to judge whether problems are real
and authentic.
In particular, he focuses on the inherent requirement in
problem solving to accept different interpretations of the problem and methods
of coming to solutions. He states, “The students must believe that their
solutions are going to be judged according to the requirements of the real life
situation and not have to think about what different requirements the teacher
might have.” In theory, this seems
logical to me, yet I question how it would work in practice for two reasons: 1)
if students over-simplify a problem, or always focus on simpler strategies such
as guess and check, they may miss learning important math concepts; 2)
Assessment becomes very complicated – it would be difficult to fairy assess the
validity of different solutions.
For my question, I will focus on a dilemma I recently had:
Recently, we had a question on a pre-calc 11 midterm where
students were given the perimeter and area of a rectangle and asked to find the
dimensions. The intent was that students would solve the perimeter equation for
one variable, substitute the expression into the area equation, then expand and
solve a quadratic equation. The question was worth 3 marks, and many students
who had partially correct students got part-marks on the question.
A few students used guess and check methods, and since this
is a valid strategy, I gave them full marks if they provided the correct solution. One student tried a guess and
check strategy, and came up with an answer that was close but not exactly the
solution – I gave him zero marks. He argued that he had partially completed a
legitimate strategy that other students received full marks for, and thus
should receive part marks.
Thoughts?
Hi David, I have experienced a similar dilemma in my class as well. Students programming robots often choose to resort to the guess and check method. One reason for its popularity is due to the nature of robotics – students want to see results quickly. However, this doesn’t agree with our goals, which are to motivate learning through engaging activities. I wouldn’t justify the usage of guess-and-check in homework, but I think it’s a valid strategy for test taking. However, I would make it clear that a high-stake criteria (all or nothing) will be used for guess-and-check method in accordance to its inherent weaknesses.
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ReplyDeleteHi David, I agree that accepting different interpretations of the problem and methods of coming to solutions may result in assessment getting complicated - this is also a thought I'm trying to reconcile after reading my article. As such, to balance practical constraints, problem-solving in its authentic sense may perhaps be better applied not on everyday homework tasks, but perhaps in a topical or termly assignment that pulls a few topics together instead?
ReplyDeleteThanks for sharing your in-class dilemma, sounds like something that could happen in every classroom! I'll need to clarify what guess-and-check means in this scenario - does it mean that the student guesses at the answer in the trial-and-error sort of way, and then checks back to see if that answer works as a solution for the question? I would say there is a need to know why the student only got close to the correct answer using guess-and-check - was it a calculation error, or was it a misapplication of logic, etc? Broadly speaking , my two cents' is that partial marks makes sense only if the teacher deems that accurate student understanding of the process is displayed, despite not getting the correct answer in the end.