JMM 2008

The Joint Math Meetings for 2008 (San Diego) just finished, and so it's time to start sorting through my notes to figure out what they mean.

Class related:

• Minute Paper - I've seen this used and discussed many times, but maybe I'll actually give it a try. The basic idea is to give the student one minute at the end of class to write down what he thinks were the main points for the day. This forces the student to reflect on the day's work before it gets lost.
• Algebra for Dummies - This book exists (as well as others that present themselves in the same way), but the question is what they try to do to make the math more understandable (and whether it works). Part of me thinks that anyone motivated enough to buy such a book will be the type of person willing to put in the work to learn, whereas not all of the students in my classes will be like that. I tend to believe that the personal motivation plays a huge role in education. However, it might be worth my time to look at that book to see what it says.
• Math Labs - It would be nice if I could get students to do self-directed labs (like science labs) by giving them a handout with some instructions to follow and some mathematical things to compute. The problem for pulling this off right now is that I have no idea what topics would be good to pursue in this way. One example for a higher level class (like number theory) is the "McNugget Problem" (boxes of 6, 9, and 20 -- for what n can you get exactly n nuggets?)
• Technology - I've always kept my distance from using technology in the classroom because the students won't be able to use them on tests or anything. However, I can see some time-related shortcuts with graphing where it would be nice to be able to generate several graphs quickly and have students make observations to get the ideas behind the graphs before we actually go through the details. I need to find an internet resource that will allow this (Sage?)
• Pretests - I need to give my Algebra students a pretest so that they can get a better measure of "progress" throughout the quarter.
• Handouts - I haven't made much use of handouts, but maybe I should go back to that. I made these my first year or two as a TA and the response was strongly positive.
• Hiding grades - I went to talk where someone did a study on student improvement when you didn't tell them their grades, but only made comments. I don't know if this works at the level of developmental algebra because the students may not be mature enough (mathematically speaking) to make sense of it.
• Grading - I had an interesting thought about how I can grade my students. I still don't really like the idea of percentage grading. So perhaps I can make competence grading by passing a series of "Levels." For example, a level 1 arithmetic computation would be something like 45 + 24. Then a level 2 arithmetic computation would be something like 6 - 4 * 5^2 (introducing PEMDAS). Then a level 3 arithmetic computation would be something like 5 * 2^2 / 4 + 3 * 8 (a complicated string of PEMDAS where the only way they would get it right is if they knew how to completely break it down). There would be similar levels for other ideas, such as solving linear equations, graphing, and so forth. Then their final grade would be a measure of how many topics for which they were able to show a high enough level of competence. This still needs to be worked out in greater detail.
• Colors - Maybe I can use black/red for positive negative numbers at the beginning of class to highlight the difference between the minus sign as a binary operation (5 - 2) and as a unitary(?) operation (-2)
• Spoken/written mathematics - This wasn't from the conference, but it was something I've been thinking about. I think I need to make my students write "five minus two" and "negative two" because their words and their written math often say different things (and sometimes the ideas in their heads are different from both of those!).
  

Other ideas:

• Placement Exams - I want to look over the placement exams to see what they are testing and how they are graded.
• NSHS Math Students - I don't know who the bright high school math students are, but we should probably be actively looking for them and encouraging them in some way. We could try to get students to take the AHSME or something like that.
• Other math students in the area - Can we make a presentation to math clubs and that sort of thing at other schools? Will this be a helpful endeavor for advertising? (It would help if we had a math major to offer them!)
• Putnam - There was an interesting-looking book titled "Putnam and Beyond" that I might want to buy
• Minicourse - I went to a minicourse on Departmental Self Reviews. At this point, I'm going to treat it as background information for me to have as I start looking forward into where the department is going. But there is one thing that I thought would be helpful, which is to get a list of who taught which classes for the past few years to see what the teaching distribution has been and learn more about our part time instructors.
• Articles - "The Way We Think" (Fanconnier? and ??), "Where Mathematics Comes From" (Lakoff and Nunez)
  

Miscellaneous:

• Webpage - I need to update my CV and webpage
• LaTex - "More Math to LaTeX" looked like a good reference. Also, I want to see if I can learn how to make hyperlinks in LaTeX.
• Mathematics of Poker Class - Given the current budget situation, this probably won't happen. But it would be fun if it did.

MDTP San Diego Conference 2007

MDTP stands for "Mathematics Diagnostic Testing Project". I attended the conference without really knowing (or caring) what MDTP actually does. I went because I was interested in learning about teaching and expanding my ideas about teaching.

The first talk I attended was given by Jeff Rabin (UCSD). I've met him a couple times on an inter-personal level and I took his course mathematical methods course my first year here. He opened by introducing the following problem:

Give an example of two triangles that have 5 congruent parts but are not congruent triangles.

He gave everyone about 10 minutes to work on it. I think I got it at around 7-8 minutes. More important than actually obtaining the answer was the intellectual process that one takes to get from the question to the answer. I can write down an answer and (if you're mathematically inclined) it will take mere seconds for you to conclude that it is a valid example. However, the point was to notice the thought patterns involved in working out a problem like this. There were two important features in play:

1. I did not know the answer ahead of time. I only knew that an answer existed. (Alternatively, the question could be phrased "If possible, give an example..." This would create an interesting situation in a classroom setting with more time for interactions.)
2. I did not know the specific tools required in order to obtain the result. However, the fact that we were talking about incongruent triangles gave enough of a hint as to where to start.

This is the essence of problem-solving. Finding and justifying answers to questions whose answers and method of solution were not previously known to the problem solver. I actually don't remember what else he had to say, but this was already useful information to me. I would like to keep this in mind as I plan problem sets for students in my classes. Of course, there is also the necessity for having exercises (straight-forward computations, questions where the method of solution is actually known in advance -- perhaps given in lecture at some point).

The plenary session was given by Guershon Harel. I met with him once when I was thinking about post-grad school jobs and ways to perhaps transition into math education instead of researching in pure math. He talked was titled "Thinking in Terms of Ways of Thinking." He talked specifically about DNR-based instruction (Click here to read a short paper on it), I would like to find some way of having math students (especially those not going into math) to evaluate themselves and how they think about things. I do like to emphasize that there are different skills in mathematics, which is something I talked about in the Teaching Statement I used when I was applying for jobs. My ideas were not nearly as refined and technical as his, which is perfectly fine by me.