The third quiz in Proofs Class

This term I am teaching our introduction to proofs class IBL style with some great notes from Coe College.  My twist on the class is to have oral quizzes.  So far each has been a bit different.

1. First quiz, I gave the students a choice of three problems that we had already discussed and let them choose their favorite and present a solution to me in my office.  
2. Second quiz, I choose a longer proof of a proposition from their notes, removed all the punctuation, printed it out on cards with magnets on the back and had the students put the proof in order.  I chose a dandy because half of the proof had two cases and nearly every student wanted to start their proof with the line "there are two cases".
3. Third quiz . . . So, now it is time for the third quiz.  I want to give the students an incorrect proof and have them find (and hopefully correct) the errors.  In this chapter we went over functions and cardinality, so hopefully the proof will have something to do with that.  However, I am drawing a blank.

Here are my basic learning objectives for every quiz which I snagged from a variety of web sites:

A successful student will be able to:

• Determine what is exactly given by the hypothesis of a statement, and what exactly is
• required to be proven.
• Identify and use definitions correctly.
• Grasp the sequence of implications and quanti fications of the statement the student has to
• prove
• Justify a proof passage by citing the correct previously known result
• Identify and distinguish
• conclusions from supporting statements,
• relevant from extraneous material,
• necessary steps from corollaries,
• factual from normative statements,
• logical fallacies in a proof,
• questionable term usages,
• unstated assumptions,
• the purpose of a proof passage or a proposition.
• relate analogies and di fferences among proofs and proof techniques.
• identify the fundamental part of a proof from the technical details and grasp the structure
• of a proof.
• outline the main points of a proof and correlate them.

How Do I Assess This?

This term I am teaching our Foundations of Analysis course to 15 students IBL style.  Third time may be the charm, but I am finding it to be going quite well.  However, I don't want to give them a traditional exam.  So . . .

I am experimenting with oral quizzes.

• Students come to my office in their time.
• They are given a selection of problems to work on that are identical to, or very similar to, ones the class has worked through.  The student chooses a problem.
• They work the problem on the white board in front of me.
• I have them explain their work and why they think what they have done solves the problem.

I have a process rubric that I am still refining that includes things like

- Student identifies and uses definitions correctly.

- Student can justify a proof passage by citing the correct previously known result.

This way, I can correct a student who mis-remembers a definition, but still note that he was able to use all other definitions correctly.

So far, the process is going well and, since it is very similar to how class works, the students are comfortable with the situation and able to perform at their best.