Wednesday, November 16, 2011

Nuts and Bolts: Assessment of Presentations

IBL courses deserve assessments that match what students are asked to do in class.  In most full IBL courses, presentations form a significant portion of the grade.  Grading breakdowns could be something like this:

30% Presentations
30% Final Exam
20% Midterm
10% Written work
10% Portfolio

In this post I'll focus on presentations, and discuss the other items in future posts.  Student presentations are one of the key components of an IBL course.  Students should present their work to their classmates to be vetted for correctness and clarity.  This process by itself is immensely valuable.  In fact, it lies at the heart of IBL.  Students work on hard problems at home.  They bring back their findings, get feedback and repeat, until a problem is solved.

Assessing presentations can take on many forms.  One way is to use a point scale.  Here's a rubric which can be adjusted to suit the style of an instructor.
10 Completely correct and clear
8 or 9 minor technical issues, but the proof is correct
5, 6 or 7 Proof is incorrect, has a significant gap(s)

Points don't tell the whole story.  Instructors should have in mind the overall qualities they want from students.  Below is a general guideline that can be adapted to match your own criteria and your institution's.  Students should be encouraged and rewarded for their intellectual contributions to the class.  Generally students should present regularly and also participate meaningfully in discussions in groups and in class.  Students who are able to prove major theorems and present regularly in class should earn an A for presentations.  They are capable of doing original (to them) mathematics.   Students who present regularly, but none of the harder problems typically earn a B for presentations.  Students who show up to class regularly and present only occasionally earn a C for presentations.  Students who miss a significant number of classes and/or do not present more than once typically would earn a D or F for their presentation grade.

*Some instructors also include some bonuses for creativity and ingenuity.  When a student does something that you have not seen before that shows real creative thinking, it should be rewarded in some way.  I take notes in class and write comments and jot down the creative idea.

The main message is that students have an incentive to

  • Show up to class having worked on problems
  • Participate and discuss mathematical ideas
  • Prove theorems on their own
  • Contribute to their own and their classmate's intellectual development
Are these not the qualities we want from our students?  Aligning incentives in positive ways to what society values in people is a something we should strive for.  Assessment is not merely a way to determine grades -- it's also a tool to encourage students to be young mathematicians!