Call for Working Group Participants

Call for Working Group Participants

This working group gathers interested mathematicians and young researchers in math education to discuss proof presentation. Proof and reasoning are fundamental parts of advanced undergraduate mathematics, as well as mathematics in general; and students encounter difficulty with proof and reasoning at all stages. Although much has been written on proof, much of the literature focuses on perceptions of proof and evaluation of proof, that is, how students view and validate proof. There exists comparatively less research on comprehension of proof and presentation of proof, and the relationship between comprehension and presentation.

As part of group activities, we will survey major results on proof in the past 30 years. This literature review serves as a motivation for the focal working group questions:

1. What processes do mathematicians engage in when they plan and deliver an oral presentation of a proof?
2. What processes do mathematicians engage in when they structure a written presentation of a proof?

In engaging with an oral presentation of proof by a mathematician, a student may make a comment that leads the mathematician to spontaneously revise their planned presentation. In contrast, a written proof stands alone: all consideration of the audience takes place before final version of the presentation is laid out in front of its reader. Thus we see oral presentation of a proof as more dynamic than written proof.

1. What features of oral presentation of proof is a student sensitive to, and how does interaction with these features influence her written presentation of proofs and reasoning for related mathematical tasks?
2. What features of written presentation of proof is a student sensitive to, and how does interaction with these features influence her written presentation of proofs and reasoning for related mathematical tasks?

A student who understands to some extent the intuition behind a proof may still not be able to produce an organized, coherent written presentation of the proof. We are interested in interactions that enhance their sensitivity to the subtleties of language associated with communicating mathematical reasoning, and which influence the way students learn how to structure written proof.

In the background of these questions are two central issues of undergraduate mathematics education research: how instructors and students understand and use mathematical reasoning, and ramifications of findings on improving instruction on proof and reasoning. An implicit motivation for the questions is the assumption that presentation and usage of proof or reasoning by its audience are related. The purpose of the working group is to design empirical studies that describe whether or not presentation and production are related, and -- whatever the relationship -- examine the consequences of findings on the teaching and learning of proof.

In the time frame that the working group will have, research of course cannot be completed. Nonetheless, critical ideas for research can be sparked, held, evaluated, and revised. If the working group meets its goals, participants will enter the first day of RUME 2010 with outlines of experimental designs, potential new collaborators, plans of cross-campus collaboration and data-sharing, and focused questions to ask of the many RUME conference participants.

Working Schedule

Start time / End time (duration) / What
9:30am / 10:30am (1:00) / Review of proof research in and around math education.
10:30am / noon (1:30) / Work in small groups on focal questions. Discussions to be informed by a selected, small sample of mathematics tasks and proofs.
noon / 12:35pm (30 minutes) / Large group discussion on questions and issues. that have arisen.
LUNCH
1:35pm / 2pm (25 minutes) / Continue discussion on focal questions, planning for meeting with expert researchers.
2pm / 3pm (1hr) / Small groups discuss proposed experimental designs with topical and methodological experts.
3pm / 4pm (1hr) / Continue discussion on focal questions.
4pm / 4:30 (30 min) / Discussion of questions and issues, plans for RUME, and plans for the year.

How to Participate

Participation Form

To join the working group, please fill out our Participation Form. It should take no more than 15 minutes, and filling out the questions will help us plan the best workshop for you.

If you have any questions, we encourage you to contact us. We look forward to meeting and working with you!

Contact Information

Yvonne Lai
University of Michigan
yxl @ umich. edu / Tim Fukawa-Connelly
University of New Hampshire
tim.fc @ unh. edu

Frequently Asked Questions

Q: What kind of proof presentations did you have in mind discussing in the Working Group? Those given in lecture? Those written by students for homework in response to lecture?

A: We are interested in discussing both kinds of presentations.
We view the proofs given in a class lecture as a central type of oral proof that mathematicians present. Although we would be potentially interested in oral proofs that mathematicians may present to other mathematicians, we would also like to stay as connected to interactions with students as possible in the discussions with the working group. So oral proofs that take place outside the scope of the classroom would be most relevant to the working group if they were somehow compared with oral proofs in the classroom.
We view the written presentation of proofs for homework as (in part) a product of a student's prior interactions with written and oral proofs. We are very interested in how students learn how to produce their presentations: that is, once they have a notion of how the proof might go, how do they commit it to writing?

Q: I am possibly interested in the working group on proof presentation. What are the times for the session(s)? I am looking at making flight arrangements and booking the hotel, and I wasn't sure how the working group might change my travel plans.

A: We hope to see you at the working group!
Our activities will run from approximately 9:30am to 5pm on Thursday, February 25th. We know that many of the participants may have obligations teaching or otherwise, and that flight prices vary by time, so we understand if you can't make it to the entire session. Please don't let partial attendance stop you from coming.
The opening plenary will take place the evening of February 25th and is followed by a reception.