Wednesday, February 10, 2010

Challenge Your Neighbor

I think I'm going to try a new exercise in my financial math class tomorrow. We've just finished Chapter 1, which is on simple interest (yes, a whole chapter on simple interest). If you are visualizing how the following project might go, here are some parameters: 45 students (we'll see how many actually show up), 75 minutes. If you've done a project similar to what follows, or even if you haven't, and you have some feedback for me (things to watch out for), I'd love to hear about it (before noon Thursday :)). Below is the assignment I'll be giving my students:


The goal of this project is for you to write your own questions to challenge your classmates, and help review chapter 1 material.

Outline: In groups of 5, you will be given half an hour to create a list of 4 ``interesting'' questions that cover chapter 1 material. The questions must not use formulas or concepts that are not covered in chapter 1. Your questions must not be re-writes of textbook problems, simply obtained by changing numbers or dates. You must be able to solve the problems you create (with the aid of a computer if the algebra is difficult). The 4 questions may all be based around a central scenario.

You will then exchange your list of problems with another group, and, in turn, will be given the problems created by a different group. You will have the remainder of the class period to produce solutions to the problems you have been given.

Specifics: In the first half hour, you must produce 2 papers, both containing the names of all group members. One paper should contain your list of questions. This paper will be given to another group in the second part of this assignment, so should only contain the questions you have written. Questions must be written well enough to understand without further explanation. Your second paper should contain well-written solutions to the problems you have written. To save time, you do not need to copy the text of the questions to this second page.

In the second portion, you must write solutions to the challenge questions you have been given. You may use the paper you have been given. You must write the names of all your group's members on this paper. As it will have two sets of names on it (the problem authors, and the solution authors), insure that the two sets are clearly identified.

Grading: Unless it is clear that a group member is not contributing, all group members will receive the same grade for this assignment. You may earn 2 points for each problem you write, up to 8 points total. Points may be deducted if the problem is not relevant or is poorly written. The write-ups for the problems you author, and the problems you are given, will all be graded out of 3 points.

You will not earn extra points for writing extra problems. You may have points deducted if the problems you author are not distinct from textbook problems.


Mitch said...

I'd say be prepared to float around and help them get started. Writing questions is tough (take this from someone who's trying to write a textbook).

Most of the literature suggests that 3-4 is the optimal group size. Not to say it's absolutely essential. However if you're going up to five, be sure you have a pedagogical reason for it. It's more likely group members will make relatively equal contributions in a slightly smaller group, I believe.

sumidiot said...

@Mitch Ok, awesome, thanks. If I do smaller groups, do you think 4 problems is too ambitious?

sam shah said...

I think the idea is super interesting and I can't wait to hear how it turns out. I have four immediate thoughts.

1. You should elaborate more on what kinds of questions you expect to see. How different from textbook questions must they be. Different scenarios for simple interest, or entirely different types of questions. If the latter...

2. I would be slightly hesitant to try this and ask people to come up with problems that are so unlike textbook problems. I guess it depends on the subject matter and the kinds of students you have. The question that I'd ask myself is: can I easily come up with 10 questions that are very dissimilar textbook problems? If not, then I wouldn't expect students to be able to come up with 4.

[You've got me thinking if I could come up with questions very dissimilar to the ones the textbook has for some of my courses, and I'm coming up dry. Which makes me feel a bit sad about myself, but also shows how limited I am in how I think about my subject matter...]

3. What's the goal of the lesson? If it is to learn the basic material in chapter 1, then I'm not sure it will hit the mark. If it is to take the material from chapter 1 to a new level, where students are forced to think about it in various ways, then it seems like it could definitely succeed.

4. I like that you made each problem worth only 2 points -- so they get 2 points for something solid, 1 point if they didn't really put in much thought/effort, and 0 points if they didn't have the question. Coming up with a more involved rubric for something where students only have a limited amount of time to do it would be hard for both student and teacher.

If you get a chance, and feel so inclined, please report back on what you did, how it went, and if you would change anything for next time. You've got at least one person chomping at the bit.


Mitch said...

I agree with Sam regarding being a little more explicit with what sort of problems you want to see. You can also try to float around and intervene if you see them going down the wrong path.

Regarding group size, I'd say four students can produce four problems reasonably. If you don't have a 0 mod 4 attendance figure, make a group or two have five rather than going down to three.

sumidiot said...

Thanks @Sam, and @Mitch again.

I guess this project might be considered a review to the extent that students should think back to old problems to see what has been done, and what hasn't (always harder to see). I'm not sure how well it'll work as a review either, but I'm also not sure there's that much to review. I could be wrong.

Certainly coming up with strikingly new questions will be difficult. I was just a little annoyed with the book, where each section seemed to have one or two "types" of questions. We've spent most of our class time so far talking about questions I came up with while I was doing the reading (alternate ways to set up calculations, why they give you wrong answers,...), so I'll encourage them to try to think about things like what we've done in class. And I started an example last time and said I thought there were many questions that could be asked from where we finished, so hopefully a few thought about it a little. Also, I figure I can tell them to make some sort of crazy rules a bank might apply to an account.

I will wander around and see how things are going, as they write questions.

I'll definitely report back. Thanks again for your feedback, both of you.

Kate Nowak said...

If I read right, you already did your lesson...

If I commented yesterday, I would have reiterated the warnings that the students might find this more difficult than you expected. Writing original problems _is_ hard. And I wouldn't be shocked if what they did produce turned out to be trivial, or clever rewritings of textbook problems.

I would have suggested maybe giving them a loose scenario to start from. Like, Jenny has some money to invest, and wants to retire eventually. Write four different problems about this scenario, varying which quantities are given and what the solver is asked to find. Expect that the solver will use one of these three equations/formulas in their solution.

Or something like that. Anyway, interested to hear how it went.

sumidiot said...

Hi there @Kate. Thanks for the feedback. I did, indeed, try this in class already today, but no worries. I still like the idea, so more feedback is still good, because I think I might try it, or something similar, again (soonish?).

I agree that writing original problems is hard. Especially when there is one single formula in the whole chapter that all of the problems are based on. Looking back at problems I had written and thought were interesting, I expect one could pick out textbook problems that ask the same thing. I guess the goal is that converting my problems to read like those textbook problems is something new and worthwhile. And hopefully the same can be said for the student-written problems.

Giving them a starting scenario might, indeed, be a good idea. I thought about bringing up the example I finished with in class last time, but didn't. I have not yet looked to see if any students drudged it up out of their notes.

I guess it's getting on toward time to write an actual post about how this went. I think I won't get it online tonight. I'll get my current thoughts written, and then grade projects, and then finish up a post for you all. Should be sometime this weekend.