Math 093 Boot Camp

I have made it my goal to put together a functional textbook for Math 093 and have it ready for the Fall 2009 semester. I'm quite disappointed with our current book. It's poorly organized and not well presented. It also does not have nearly as many problems as there should be. I ran a draft outline past Russel today, and he likes what I've put together. Now I need to think through the layout and come to a decision about how I'm going to teach presentation through examples.

The plan is to start by developing a workbook. I'm not going to spend a lot of time working on writing up explanations right now because that's not as important as laying out the problems in the right order, having the right number of them, and other such issues.

If I get far enough in the next month, I might even be able to pilot some of the worksheets in my Math 093 classes next semester. The first two chapters (arithmetic and fractions) are likely going to be the most difficult ones to put together.

To do for/before Spring 2009

1) Presentation matters for Math 093
2) Update images for Interactive Technologies
3) Start work on n-hedral group paper
4) Start outlining a new Math 093 text
5) Timed arithmetic spreadsheet
6) Update homework page template to instruct students to look down if I didn't copy the next assignment to the top
7) Update webpage information

JD Smith Middle School

I had the opportunity over the last month to work with some math teachers at JD Smith Middle School. This sort of fell on my lap at the last minute, but it seemed like a good chance for me to try something new and expand my perspective on education in the region.

During the past few weeks, I visited classrooms and made observations of the individual teachers. I then compiled a short list of topics that I felt were relevant to department as a whole, and then presented my findings to them. I also wrote up a short summary of my thoughts on the individual teachers.

My first point was about the careful use of spoken and written mathematics in the classroom. The teachers were using "solve" as a universal instruction for "do what you're supposed to do." This is fine when the students already know what to do, but the ones who don't know get confused because this one word means many different things in different contexts. I suggested to them that there is a clear distinction between solve, compute, simplify, and other word they might use in the future like factor, reduce, expand, and so forth.

The second topic was to look at arithmetic. Arithmetic is really an exercise in bookkeeping, not anything deep or profound (except the fact that we *can* do bookkeeping, which is truly deep and profound). So I talked about doing addition as "big-to-small" instead of "small-to-big" and explained why it works better once students understand the basics of the place value system.

The third topics was more exploratory, which was the topic of fractions. This is probably the most difficult topic because of the breadth of pictures we use to discuss them. Unfortunately, these pictures are not all compatible with each other. This leads to students being confused because they think about the same picture in different ways. I didn't have a lot to say in this area, but opened the door for them to discuss it among themselves. I hope they are able to go somewhere with it.

Overall, I think it is a net positive given the amount of time spent with them. I intentionally stayed away from pedagogy specific ideas because I'm not a pedagogist. I'm just a pure mathematician, but I think this is a helpful type of "outsider" perspective for them. I'm done with that project for now, but I left the door open to come back and talk to them about a different topic if they choose to invite me back.

Instant Gratification

Henderson College's Graduation Rate Disappointing

I found this to a surprisingly negative and pointless article. I accept that the numbers are bad and need to be better, but the article's shading is clearly tilted against the institution and puts it in an unfairly negative light.

1) "If no more finish over summer, Nevada’s newest public college will report a six-year graduation rate of just less than 16 percent — one-third of what California’s public state colleges achieve." -- This is comparing completely different types of institutions. In CA, it's a number taken (presumably) as an average over many established institutions. Here, we have a small, growing, start-up institution in a state with already very low academic standards.

2) "Some NSC students discover they are interested in majors the college does not offer, Stewart said. Others leave Nevada or transfer to UNLV. “ ... But NSC was not meant to act as a community college, preparing students to pursue an education elsewhere. A 2001 report supporting establishment of the new school said Nevada needed a state college to produce more college graduates." -- If anyone thought they would have a fully-functioning college offering the full selection of degree programs as a 10,000 student campus within 6 years, they were poorly mistaken. We're happy to finally have our first new building up, with plans to move in shortly.

3) Though only 10 students from NSC’s first full-time freshman class had graduated from the college as of spring, the school has conferred 586 degrees since its inception, with many going to transfer students. -- Thanks for putting this down in the 4th to last paragraph. It really helps to lead with "just 10 had graduated from the institution" and close with "by the way, there are almost 600 degrees that have been conferred."

4) "The California State University system graduates more than 45 percent of its freshmen within six years, a higher percentage than UNLV. The system’s newest campus, at Channel Islands, began accepting freshmen in 2003 and graduated 25 percent of them within four years."

Being from CA, I would guess that 90% of those students are coming straight out of high school and into college, and they are almost all full time students, as this is how most Californians do college. This is likely an unfit comparison as Nevada students are returning from perhaps several years of work and are in need of remediation.

Spring 2008 reflections

I don't think I put thoughts in this blog nearly as often as I did in the first semester, but now that the semester is over, I have the time and energy to put a lot of thought into how things went this semester.

First of all, Math 124 went a lot better this time around. I still don't think I connect quite as well with that class as I do with the Math 097 students. It is true that I go into the classes with different mentalities. Since Math 124 is a college level class, I treat them more like how I think college math students should be treated. I do less hand-holding and I let the students work on their own more.

Math 097 went very well this time around. I think I found the right level at which to try to meet the students and the introduction of more worksheets seems to have had the effect of helping the students to understand the material.

The homework cover sheet was a pretty good addition. Some students didn't really take to them, but I'm going to keep using them anyway. I changed them slightly so that they interact with the course content more, so that should be a positive change. I also need to write a more defined homework policy and let the students know much more clearly what I am really expecting from them in the homework.

There were a number of interesting comments that I received on the unofficial evaluations I handed out to the students, and even though the probability of them actually seeing them here is very small, I believe it is a useful exercise to reflect on them, and then to take my thoughts from here and put them into the next syllabus and work them into the class content. (Side comment: I'm always amused by the level contradiction from different students about how things have gone in a class.)

"I do not think quizzes you be a part of attendence." The same student also wrote "I like participation credit for [the] test." This is the type of comment that I feel deserve little attention. I know that Jason gives credit for attendence (he also has 'detention' where he forces students to show up to the tutoring center for specified periods of time to make up for missed classes), but it seems like extra paperwork to me. This is a college level course in which the emphasis is on learning content. What part of that description implies that credit should be given for simply showing up? It's very much like a work environment. Do you expect to get paid simply because you show up for work, and not because you actually perform your job competently?

"Quizzes should be at the beginning of class." Over the course of the last year, I have started to agree more and more with this, and will probably implement it during the summer session. This will also be used to make sure class actually starts close to 'on time' and only punish the students who show up late to class.

"Too much homework." No student actually used that phrase this time around, but a couple students commented on it. Students who say this are usually the ones who aren't very good at math, and they often spend far too much time on their homework because they spend all their time being lost and making zero progress. These also tend to be the students who don't come to office hours or ask questions to get help. Even though students will probably make this comment as long as I'm teaching math, unless the response is overwhelmingly stating that the assignments are too long, I will tend not to give much weight to these comments. (There was another comment from another student: "The amount actually helped me to learn the material." That's the whole point of the homework!)

I had a spot on the evaluation where I ask the students to write themselves a short note to themselves at the beginning of the semester. I find this quite amusing and I will definitely have to talk about this on the first day of class for the upcoming semesters. I added my own comments in parentheses:

• "Do your homework." (This was the most frequent comment)
• "Stop slacking!" (Do I need to say more?)
• "Do not miss any classes, you will get behind."
  
• "Be prepared for the quizzes." (If you spend the 5 minutes before class glancing over the homework, the quizzes will be significantly easier because the ideas will all be fresh in your head.)
• "Don't take this class if you are taking other hard classes." (Straight-forward, reasonable advice. Math classes take up a lot of time if you're not as natural with it, and this is worth considering at the start of the semester.)

Math 373 was a fun class this semester. With such a small class, I handled it very differently. I left a significant chunk of time in class to doing numerical explorations as these are really key in number theory. A lot of the results came out of 'playing' with the numbers, so that's how I tried to approach it.

90% Failure

Here are a couple articles from the local paper:

Math Tests Carry Shock Factor

Preliminary Math Test Failure Rates

Basically, 90% of the high school students are failing middle school algebra. There seems to be some controversy about how those tests were administered, but 90% is simply too large to be merely a statistical outlier. As a department, we agree that this is pathetic and that we want to do something about it, but we have no plans yet (we also have no funds -- but there's some work being done on that side). Our plan is to address this issue at the middle school level because we think high school is too late. Elementary school level would be better for getting students interested in math in general, but we don't think it will have as much of a lasting effect. I think we're going to target some middle school teachers, but this has to be thought out more carefully.

NSC on TV

I hope I got the link right...

NSC 5 Year Anniversary

You're not doing math

I had an interesting conversation with a student after class today. The essence of the conversation was that he did not receive full credit on a problem on his exam even though he arrived at the right answer. My reason for not giving him full credit was that he did not demonstrate how he arrived at his answer and that the work that he showed did not make sense.

The problem gives some relationships between various angles of a triangle and asks the students to compute the angles. This student's first step was to divide 180 by 3 because "there are three sides on a triangle." Now, it happens to turn out that one of the angles of the triangle is 60 degrees, but the fact that 180/3 = 60 has no bearing on this. Nevertheless, the student continued to insist that this makes perfect sense.

Upon further attempts to argue with me, he reached the point where he declared that I'm not giving him credit because he "did not do it [my] way." To this, my response at the time was that he did not receive credit because he did not demonstrate how his calculations give him the correct answer.

Afterwards, I decided that I had the option of taking the much more confrontational route, which is the "what makes you an expert in math?" route. Am I not the teacher in the class, the one who is being paid to determine what is and what is not math? Did I not spend 9 years of my life studying math? And yet he believes what he is doing is, in fact, math. And because he thinks it's math, I should therefore defer to his understanding of math? How absurd. Does this happen in other fields? Do physics students try to convince their physics professors that they know physics better? That doesn't make sense (but I'm perfectly willing to believe it happens).

Whether this second option is any better doesn't seem like a good debate. Obviously, it's more edifying to me to simply pull rank to shut him down, but it does little for the student besides pulling further into the grave he has dug himself by being unteachable. My basic conclusion is that I really don't care what this student thinks. He's wrong and he's unwilling to admit it. So how can you work with such a student?

I offered him a challenge: I changed the numbers slightly and challenged him to show me how dividing 180 by 3 is a correct first step towards arriving at the answer. If he can do that he will get back his two points on the test. I changed the numbers so that the answer will end up with fractions, so he's not going to accidentally stumble across the right answer. I gave him until next class to come up with something, so it should be interesting to see what he says. Part of me thinks that he's simply going to walk away from the class, which is perfectly fine by me.

There's a principle in play here that is part of Gershon Harel's formulation of learning mathematics. It is the "necessity principle" (if I'm remembering right). A mathematical concept will be accepted as true by a student until he discovers that it is necessarily false. Necessarily false means that the two ideas are inherently contradictory and so one must eliminate one of them in order to maintain a logically coherent understanding. The purpose of the challenge is to force the student into a position where he is unable to solve a problem using his random techniques. Until he realizes that his toolbox is insufficient for the task at hand, he will never look to new tools. So now I just sit back and wait to see what he comes up with.

Money issues

This is a news clip about the impending budget issues. This is one of those things that I didn't ever really think I would have to think about, but here it comes anyway:

Link to the clip

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.