What is pingpong homework?

This is open-ended hwk I use for discovery or where adaption to the individual student's pace is appropriate. You may hand in incomplete solutions, *provided* your solution shows a qualified attempt. A clear explanation of the difficulty you are stumbling over or stuck with is a good place to stop in a qualified attempt.

I'll return graded solutions with full score, if (close to) perfect; incomplete solutions will be returned with indvidual help and comments that should lead you to the next step. You may then return them on the next occasion, using the ideas so acquired to improve or complete the solution. This will still be for full credit when complete.

As appropriate on the individual occasion, there may be a number of pingpong steps.

How do I get a *poor* grade on pingpong hwk?

By turning in something blatantly wrong where you could have been expected to know that this can't be true. That ends the pingpong or leads to a discount on scores. Not every mistake or glitch will end the pingpong or lead to a discount.

Acknowledging ignorance is therefore superior to not recognizing ignorance and instead ascertaining some statement just to poke in the dark for partial credit. After all, the purpose is to help you learn, not to test you on previously learned material.

So much effort for only one single hwk credit?

Mere hwk credit cannot appropriately reward you for nutritious hwk (and pingpong hwk is meant to fall in the nutritious category). But really working through pingpong problems conscientiously will deepen your understanding of the material.

The real reward is two-fold: you'll collect a time refund when preparing for exams (in particular the comprehensive final), because you'll grasp the gist of the material more quickly. You'll retain knowledge longer (for use in this or in subsequent classes). And your deeper understanding will show up in better exam scores. (Actually, that's a three-fold reward; which shows that mathematicians come in three kinds: those that can count, and those that can't).

I cannot offer a formal effectiveness study on this matter (with control group and significantly large cohorts etc.) but my honest belief is that a thorough effort in pingpong problems is worth half a letter grade in the end; `A' students may do it with less effort (and there is no formal A+ grade left for them anyway); `B' and `C+' students gain insight worth half a letter grade. Students at the borderline C/D and below (who typically operate on principles different from those required for pingpong homework) will be forced to `get wet' instead of training swimming movements on dry land: and this is worth the distinction between C and D.

I'm available for individual office discussion, in particular on pingpong homework. This also builds up my own understanding of your difficulties. Which is the final answer to the question in the header: I am matching your effort.

Jochen Denzler --- denzler@math.utk.edu
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