In a post he published yesterday, John Golden offered two geometric problems he had included in a math final for his preservice math teachers. Please visit his post and take a crack at his problems.

What I really liked about these problems was how open they were. The first problem, giving a circle geometry diagram, challenges John’s students to “Figure out some of the missing information in the diagram”. The second problem, also giving a diagram — this one of a series of lines, segmented only by the diagram edge, asks students to “Find more angles”.

At first, I thought this was a rather vague way to offer problems, particularly on a final exam where marks are summative and presumably weighted more. Then, I gave it some thought. I am not sure what John had in mind, but having questions which ask for “some” or “more” answers leaves the onus of how much work the student does and what weight the problem has on a test on the student. A way to assign a mark to such questions is to make “Each correct answer worth one mark”. Then all one has to do is make the test worth out of so-many maximum marks (less the total possible to get), order the questions so the “big” ones come first and voila … one has a test that the student weighs.

But what about students who answer only some questions thoroughly and skip others? One could make each question worth a minimum amount of marks, or make all questions equally difficult or multi-outcomed. There are likely other ways to ensure all outcomes are covered by the student.

It is an idea, one that just occurred to me as I read John’s post. What I really like about it is that it is truly open. The student cannot prejudge how much a question is worth and allocate effort accordingly. The grade the student gets is tied to the value the student, not the teacher, applies to each question.

What do you think? Do we herd our children with our judgement of worth? Should we be teaching them to do this intrinsically?

Oh, and by the way, my next post will show my solutions to John’s questions.

### Like this:

Like Loading...

*Related*

Pingback: Math: My Solutions to mathhombre’s Problems « Digital Substitute

Excellent job publishing Math: Let Students Earn Their Weight, Digital Substitute. I would like to read more on this subject.

Quite a few of my posts question (or at least reflect on) aspects of teaching and learning that we take for granted, or offer ideas that I previously did not consider and I think others might be intrigued by.

Do I think creating assignments, projects, problems, questions or tests with student-weighing aspects to them is a good idea? I am not sure. I think yes, when balanced with traditional, weighed-to-reflect-amount-of-anticipated-work questions and problems. I also think no, when used solely; some structure serves as guide posts for our students and us. It really depends on the context, the outcome(s), the expectation we have of our students, and our comfort level.

I do think students would benefit from recurring exposure to some questions like these. I think giving them such questions signals a certain trust in and expectation from them. And I think that builds confident, even playful, students and citizens.