"D" is for DONE

OK, I finished Math 112, college algebra.

Believe it or not, I enjoyed the class and am glad I took it. I got my first "D" in about 40 years, but that is fine (good for humility and when my students complain about getting a "B" I can just smile inside).

I guess I bombed the final. If I had gotten a "C" in the final, my grade for the course would have also been a "C". Didn't happen. I thought I had done an adequate job "reverse engineering" enough of the multiple choice questions, but it didn't happen.

Still, I feel good about how much I did learn. I am confident that I could have gotten 100% on the final if it were an open book test. I couldn't say that back in August when I signed up for that first Pima College class. It was all Chinese to me back then. And a reason I feel good about that is that no one remembers any of this stuff anyway. Most people can't. Plus, when it really matters, I think it's irresponsible to rely on your memory for stuff anyway.

I was talking with my cousin Joel who is a senior engineer and project manager at Boeing in L.A. When I rattled off some of the stuff we were going through in Math 112, he said he couldn't do any of that stuff by memory. I'm OK with knowing the language and having enough knowledge to go through a book or some documentation if I need to solve a problem. Or, even more important, be able to intelligently interview someone who does use all this stuff.

I'll have more reflections in a future post, but for now I want to share with you a letter I wrote to Prof. Reyes about the class and my current (still evolving) thoughts about math education. I sent this letter by email earlier today:

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Dear Steve,

I want to thank you for a good class and tell you how impressed I was with you as a teacher.

Over the years, I have taken a lot of classes at this university and have rarely experienced a teacher as prepared, organized, and professionalas you. You are really impressive and a credit to the Math Department and the whole university.

Even though, in my case, algebra didn’t click as well as I would have liked, having been in your class this semester has made me a better teacher and has made me appreciate math even more. At the same time, going through Math 112 has allowed me to think a lot about education in general and math education in particular.

I hope you will allow me to share some thoughts that are intended in a positive way to stimulate some discussion if you ever serve on curriculum development committees that consider these things. (And, of course given my grade in the course, you might just dismiss my impressions as those of a disgruntled student. However, there is a difference between a poor student and a disgruntled student. I am not disgruntled. I am grateful for the opportunity to have been exposed to the many new things I learned in your class).

Fairness

I really believe that the course was more than fair to students.

Any student willing to put in the time should be able to pass this course at either the A or B level. The necessary skills are simply mechanical and learning them is a matter of concentrated repetition. The handouts were well done and the way you walked the class through the problems was straight forward.

One of the hardest things for my own journalism students to grasp is how much work it takes to do anything really well. I stress that over and over and when I bring speakers into my classroom, they also stress that. Some of the students begin to absorb that eventually.

Textbook/workbook/web assign

I believe the textbook was weak. There are better tools for learning available, some currently being used at Pima College. I hope someone would look into other options such as the Bittinger series that includes extensive online support, CDs, online video instruction, and hundreds of online exercises. I found WebAssign to be a fairly useless learning tool. It may be an adequate assessment tool for you and the other instructors. For many students, it was unfortunate and disheartening that they were led to buy the workbook and answer book and those were not used. It is not that much of an issue for me, but for many students every $20 or $40 matters a lot. Having students purchase materials that don’t necessarily advance their educational goals signals that the faculty really isn’t “on their side.” Not a good thing.

On Math Education (my son disagrees with me about most of what follows)

I ran into an old friend of mine who is in the UA’s nursing Ph.D. program. We spoke about classes and her program generally. And I told her about my taking math 112. She was supportive and asked what kind of things I was learning. I went through the litany of kinds of new things we were getting into and when I got to dividing polynomial functions she finally stopped me, somewhat incredulous, and asked, “Don’t they have machines that do those things these days?”

She then went on to tell me about some of the sophisticated statistical modeling she was getting into and about how she and her cohort were being taught to use all of the most recent tools to solve problems. “Why aren’t they doing that with you?” she asked me.

I think she has a point.

Students in one of the courses I teach produce an online publication called Border Beat. It is viewed by people in all 50 states and (so far) 30 different countries. It has won national and regional awards.

The students learn and use several state of the art video, audio, and photo editing programs in addition to the content management system that controls the site. I don’t take a minute of their time to lecture about the underlying code. It simply doesn’t matter. It helps if they know about five HTML tags, but that’s all.

What does matter is that they can visualize how they want to present a multimedia story to the world and use the tools available to them (Final Cut Pro, Photoshop, Audacity, Joomla, Dreamweaver, etc.) to get it done.

What does this have to do with math 112?

In my blog about my math adventure, I posted this about two weeks ago: “A Kino Bay neighbor, an engineer, told me, ‘Math is a tool. Nothing more,nothing less.’

I didn't want to believe him. I wanted math to be poetry. If it was poetry, I didn't get to see it. I saw tools. I think my neighbor was right.”

Although I don’t have survey data to support this assertion, it seems to me that math 112 will be the last math course many of these students will take for the rest of their lives. If that is the case, I think we are doing them a disservice by focusing on the underlying mechanics rather than the actual use of math as a tool that can solve problems. It seems that apart from the mental calisthenics (that might be useful for people like me who are pushing 60) there is no reason to ask a 19 year old to take the time to learn (for a semester) how to derive square roots or divide polynomials manually. As my friend said, “There are machines that do that these days.”

The idea that math departments across the country refuse to allow lower level math students to use any tool available to solve problems feels a little nutty. I really don’t get it. No matter what math education theorists might say, it doesn’t seem intuitive that working through the underlying math is a necessary precondition to be able to use applications on Matlab or even pre-programmed handheld calculators. When I went through my MBA, students spent useful time learning how to use tools from the still great HP 12C business calculator to fancy forecasting software.

Today, there just isn’t enough time to learn it all.

If we had taken the time to learn how to manipulate logs by hand, we never would have been exposed to the many ways to solve real problems using today’s technology.

In my world (journalism education) we spend time talking about how necessary it is for students to know grammar. We are even discussing requiring a one-unit class in grammar. There are faculty members who insist that a student needs to know the mechanics of "adverb clause devices" and "subordination by appositives" and "choosing modifiers after sense verbs" before they can be a credible journalist.

Well, it turns out, that simply isn’t true in real life, or even the classroom.

A person’s ear for English is in tune or it’s not. A reporter is curious or she’s not. The person values the truth or they don’t. The reporter can feel empathy or not. When a junior wrote a story about a 20 year old man who was suffering emotionally because the young woman who he impregnated choose to have an abortion rather than let him raise the child, it really didn’t matter whether she could on a test, differentiate between “reflexive, intensive, demonstrative, and possessive pronouns.”

On the other hand . . .My son Seth, who has taught pre-calc/trig, at University High all year points out to me that my assumptions are wrong – he says that many of my classmates will go on in math and they absolutely do need to know what’s going on from a math point of view. He also says that there is no way that an individual could be even an accountant, much less an engineer or scientist, without being completely comfortable with logs and functions and the rest. He also kinda accused me of being “elitist” by assuming that most students have the opportunity to take college level math in high school. He says that is not the case, and the UA is right to provide students with the kind of math that allows them to continue rather than assume that it is “terminal” course.

In any event, I am so happy that I had the chance to take your class and will always value the time I put into it and be grateful for the time and energy that I know you devoted.

As I mentioned in class, please don’t take my grade as a reflection on your teaching at all. I think you are an excellent teacher and I’m glad I lucked out and landed in your section.

Best wishes to you and good luck where ever your future takes you. I hope to see you around and just visit some day.

Sincerely,

Jay M. Rochlin, Ph.D.
Assistant Professor of Practice
School of Journalism
University of Arizona

Final Monday

I can't make myself study for Monday's final.

It is scheduled for Monday between 8 a.m. and 10 a.m., but I hit the wall two weeks ago.

Yesterday I tried to spend some time going over study aids and practice tests. Pretty futile. I have learned more algebra than I thought I could, but I've also forgotten a lot already. I suppose it could come back if I put in the time. But my mind and my motivation seem to have moved on already.

On Wednesday, Prof. Reyes handed out individual stats letting students know where they are in terms of points. Before the final, I'm teetering between a C and a D. If I do well on the final I get a C. If I do poorly (likely) I'll get a D.

Before a student can be admitted to the School of Journalism they must pass this math course or a similar one with a B or better. Friday night at a School awards ceremony I was given the incredible honor of being named "Teacher of the Year" for our J-school. I was (am) grateful and honored and somewhat embarrassed, but still couldn't help but think for a moment how curious it is that I get to be an award winning professor in the School but wouldn't be accepted into the program as a sophomore.

The math test is multiple choice. I should have absorbed enough to be able to get through at least part of the test by reverse engineering it. We'll see.

I feel for the kids who have to pass this course. There is a lot to learn and if they were good at it they wouldn't be in this class in the first place. They would have had this as sophomores or juniors in high school. At the same time, if they are willing to take the time, there isn't much of an excuse not to pass. Between the study guides and the in-class handouts, the whole final is there. And, I am convinced that it's not a matter of brains, it's a matter of reps. If a student puts in the time, he or she can pass this class with an A or a B. But, as I'm demonstrating myself, putting in the time is easier said than done. There is almost always something better to do than solve math problems for practice.

For example, I rode my bike to the top of Mt. Lemmon with about 2oo other crazies on Friday. Way better than sitting at my dining room table figuring out functions.

My own journalism students don't get it about how much work it takes to do anything really well. But I imagine they all have things they'd rather be doing also. I hope my assignments for them are things they think are worth their time. Last night I saw Ira Glass at the UA Centennial Hall. One of the things he spoke about was how incredible difficult it was to find people to feature on This American Life. The producers might talk to 50 people and begin working on stories and interviews with 10 or more and complete all the work on five just to come up with the two or three that are actually broadcast. And, if you don't put in the time, it just won't be all that good.

So this phase of my math adventure is about to end and the results, at least measurable results, won't be that good. And I wonder whether that is OK.

My friend Keith (who does just about everything well) was being a good friend and feeling bad for me for my poor performance. For him, to do something (anything!) less than excellent is to fail. He was concerned that I might be depressed or unhappy as a result of probably getting a D in algebra. I don't know whether he believed me when I told him that I was fine with it. I enjoyed the ride and it was worth it and the grade I received or even the level of excellence I attained, really didn't matter to me. The process was worth it and I'm glad I did it. And even if I fail math, they're not going to take away my Ph.D. or fire me from my teaching job and Gail and Seth will still love me.

At the same time, Keith did make me think about whether I should be more concerned about doing well for the sake of doing well. My yoga teacher quoted a teaching that said, "How you do anything is how you do everything." I don't think I believe that, but it makes me think anyway.

Keith didn't ride to the top of Mt. Lemmon on Friday, partly because he didn't believe he was in shape or the right frame of mind to do well. I did ride to the top and had a great experience even though I was one of the last guys up the mountain and one of the last guys down.

Anyway, the algebra final is Monday and I've enjoyed the ride.

I'll report back.

A Success and a Failure

Since my last post I've had two quizzes. I passed one with a much higher grade than I expected, 79 out of 100. The other, which I took yesterday, I know I failed.

I hit the wall at logs.

I can't tell for sure whether it is simply my own lack of capacity or the failure to put in the time, but manipulating logarithms is simply not clicking for me. I'm finding that a little sad because I remember in 7th grade, when I was a potential math wiz, I was excited to learn how to multiply and divide using logs.

In any event, I can feel that my two-semester romance with algebra is coming to an end. Every time I try to make myself try to study for the May 11 final, I find something more important that has to get done -- grade my own students' papers, review Border Beat stories, start to learn Joomla for next semester. Or, even better, take a bike ride to train for BTC or RAGBRAI.

I'm glad to took these two courses and don't regret any of the time I put into studying. I've learned a lot about algebra and lots of other things.

Here are some thoughts I have about the enterprise:

Learning math at this level is a function of time and practice, not brains. It's all mechanical. You learn the steps and do them. Some people can learn the steps faster than others, but ultimately, it's just steps. I don't know yet whether that changes the higher you go in math.

Even though Steve Reyes, my teacher, is very good, except for the use of calculators, it feels like the the University of Arizona classroom experience is much like what it would have been in 1955 or 1963. I was disappointed that the UA is not taking advantage of some of the wonderful computer video and animation teaching tools that are available, tools that Pima College does provide for their students.

A Kino Bay neighbor, an engineer, told me, "Math is a tool. Nothing more, nothing less." I didn't want to believe him. I wanted math to be poetry. If it was poetry, I didn't get to see it. I saw tools. I think my neighbor was right.

Fantasizing about the Math book for Journalists was fun. But it didn't meet any one of my three criteria for taking on that kind of a project. If I were to commit to writing a book it would need to satisfy one (more is better, but at least one) of the following conditions: 1) It would be amusing and fun as a project for its own sake, like making a painting that you'll never sell; 2) It would do some good for other people, satisfy a need, or help make the world a better place; or 3) It would make a lot of money, or at least some. The Math book for Journalists didn't pass.

My plan is to take the final, but not to put too much time into studying for it. Then I will make what, for the time being, will be a final entry in this blog, and then move into whatever I want to put energy into next.

But right now, I need to read the final stories that my students in my feature writing class wrote.

The Adventure Winding Down (I think)

Dear Steve,

(who, according to Justin, is a skinny kid from Cambridge who is "acquiring a bunch of science credits from Columbia via their post-back program.")

Thanks for reading my blog and sorry I haven't posted for awhile. Whats going on is that I hate blogs that are mainly whining. I like blogs, like WPM, that tell real stories about real people and real things and stuff that happen in real places. I thought my math adventure might be like that, but so far, for me at least, it hasn't.

I'm still enjoying learning new things, but haven't figured out how to write about them. Like, how would you tell Justin how cool it is to create an exponential function that will let you create a graph of a catenary. Or how slick "e", the Euler number is?

My teacher is still very good. No complaints at all. What I think I was looking for was something like "the aesthetics of math" or just, as trite and unrealistic as it sounds, some kind of truth and beauty. Well, not yet. Most likely, maybe never.

There are about four more weeks left in the semester. There is a test this Friday and the final around May 9. I'm likely going to get a passing grade for the class, but that never mattered, but it is nice. I'm probably not going to take the next class, trig, because my own teaching load is cranking back up next school year and I want to do a better job for my students. Also, there are too many other things to learn.

I imagine these couple of algebra classes I have taken have been good mental calisthenics. Plus I really "get it" about how compound interest and half-lives work, but I can't honestly say the the end result was worth the investment in time I have made so far. On the other hand, the process probably was worth it. Like going on a great bike ride. The finish is fine, but the ride through beautiful mountains and along rivers with changing leaves is what it is really all about.

One way I can tell I am winding down is that I am sitting here typing rather than diving into inverse functions. Another part of the reason I haven't posted was because if I had some "math time" I would want to study rather than write this blog.

One thing that I have learned is that learning math takes time. Lots of time. Just like music or writing or sports or anything. I tell my own students that they can't possible write a good story on their first try and easily. Pros can't, so why should they be able to. I can tell I haven't put in nearly enough time, even though Seth can't believe how much time I do put in. I still would like to try calculus and have a feel for it. But that's not going to happen yet. I certainly have a lot of respect and admiration for people who can do this stuff. But I still wonder whether they see "larger" things that I can't, or if they put in the time to learn the mechanics. You probably have a better feel for that than I do.

I can tell that I'm rambling but I did want to post again. Right now I need to switch focus and learn how to "find the inverse of a function with a restricted domain."