Blog of a math teacher

If your IT "department" can't figure out how to do network printing from a Mac laptop to the printer in this room when you've got 3 labs of "supported" Macs, I don't see why anyone would come her to study computer networking.

But fortunately, I didn't actually say it, and after spending time trying to figure out how to find the printer settings in Windows (ugh), I was able to set up a network printer on my laptop just fine.

But come on, you can't set up my computer for printing to the printer for "security" reasons? I'm sorry, but I'd prefer the truth. Of course this is the same group of people who've blocked everything but port 80 on their firewall for "security" reasons. Which really means that you're too stupid to know what FTP, Telnet, ssh, etc. are.

On the plus side, the director of For Profit U really wanted to make nice with me after that encounter with him and the IT guy earlier in the day. But all else aside, my schedule for the fall effectively precludes me from teaching at For Profit U for the foreseeable future and if I can pick up another of couple adjunct classes I won't even be tempted.

This may not be the most beautiful place on earth, but it's the most beautiful place out of the parts of the earth that I've seen. Pictures do not do it justice.

1. Pack for weekend trip
2. Write up lesson plan for Algebra class I won't be at tonight
3. Get to For Profit U by bus
4. Print materials for 4:30 class at For Profit U (and also for Algebra calss I won't be at tonight.

My presence seated at the computer, therefore, is quite indefensible, especially since all of the above must be completed in 3 hours and 12 minutes.

Things that I'm going to need in particular will be anything that will help with order of operations and with operations on fractions. Please use the comments to discuss.

Well, while the pay is about half what I get for community college, they also give me a lot more class time so it balances out (roughly). I'd still be better off financially with a proper summer school appointment, though.

On the other hand, class sizes are a lot smaller. Class sizes range from 7-22 with a median of 14 and a mean of 15.4.

The pre-algebra, with it's workshop format is keeping me active and on my feet. I had one student leave when I told him that he needed to bring his textbook to class. That's not quite what I meant, but oh well.

There is a wealth of publisher-supplied materials available, which I'm going to make a point of employing.

Working from Cain Complex Analysis, Exercise 2.10:

At what points is the function f given by f(z)=x³+i(1-y)³ analytic? Explain.

Since the points where the function has a derivative are two intersecting lines, my assumption is that there is no point where the function is analytic. Am I correct on this or am I making some really basic error?

Update: Hmm, going back over the function, the derivative that Cain gives for (1-y)³ is wrong. I tried it using the chain rule, by evaluating (1-y)³ and doing the derivative of the resulting polynomial and I even went to Quick Math and let their solver do it. And I was right, Cain was wrong: The derivative is -3(1-y)², and not positive three. That and a quick internet search on analytic complex function reveals a definition which doesn't seem to match his. I'm thinking that perhaps I want to work with a different complex analysis book over the summer.

Becky's theory has had me thinking about this and it seems to me that one pedagogical approach that I need to work into my lesson planning for the fall is the question, "Can you think of another example?" This has to preclude the answer "no," of course, but it might spark the creative juices at least a little bit.

Coming up with an example seems to be an essential critical thinking skill.

Puzzling over problem 3 in section 10 of Munkres, I couldn't figure out which of exercises 1 and 2 wouldn't work with the definition provided for B. I began to worry that my answer to problem 1 which I had though was easy was wrong. Then I realized that i needed to look at examples 1 and 2.

For a smart guy, I can be pretty dumb sometimes.

Math classes I took at college A that are still in the catalog: 0/3 (although to be fair, they did switch from quarters to semesters).
Math classes I took at college B that are still in the catalog: 4/7.
Math classes I intend to take this fall that are in the catalog: 3/4.

Math professors I had at college B that are still listed as faculty: 3/6.
Portion of those who are listed as emeriti: 1/3.

Number of math textbooks that I still own from my undergraduate years: 2
Number of math textbooks that I intentionally kept from my undergraduate years: 0

...if student mathematical performance would be greatly improved if 4-8 students spent at least a month each year on factoring integers.

It seems to me that some of the problems my students have, whether it's with fractions, factoring polynomials or simplifying radicals all come down to the idea that they don't have a good sense of factoring. Perhaps I'll drill factoring like arithmetic with my pre-algebra students during the summer school quarter.

So here's what I got from netflix for my weekend of bachelor life:

• Twelve Angry Men
• Five Easy Pieces
• The Seventh Seal

See a theme? (unintentional, I swear!)

Also in the unintentional coincidence category, all three films have the length 1:36.

This morning a hawk came down and grabbed himself some duckling for breakfast. I had hoped to get a picture, but one of the teens in the apartment complex was apparently very upset and tried to free the duckling, a pointless endeavor as it had no chance of survival after being caught by the hawk, not to mention that hawks have to eat too. It was rather tragic to see the mother duck making distress calls as the hawk killed her child on the bridge above her, but also curiously fascinating, like watching a nature documentary.

I'm beginning to make a start on the hard work of the syllabus. I have three mandated topics: Probability, Statistics and Consumer Mathematics.

I'm thinking that I'd like to use some ideas about mathematical thinking (probably using Kaplan and Kaplan for this) to lead into probability. I'm not sure exactly how to extend statistics and consumer math into other areas of mathematics.

I do think, though, that I'll divide the class into three units using each of these topics as either the culmination or the prolegomenon of our work in that unit.

I'll have some early classes on using tools of the trade: How to read mathematics, how to use a calculator, how to write properly, and then dive into the first unit.

One of the questions haunting me this semester as I taught my math for liberal arts majors class has been the fact that the homework (and consequently the tests) have not really called for much beyond some fairly basic recall and application. Putting this in terms of Bloom's Taxonomy of Knowledge, I don't think that I've gotten much above level three.

A quick review:

1. Knowledge
   Basic recall of subject matter.
2. Comprehension
   Distinguish between different sorts of things, group things, translate knowledge into new context.
3. Application
   Use information, methods, etc. in new situations to solve problems
4. Analysis
   Seeing patterns, identification of components
5. Synthesis
   Use old ideas to generate new ones, generalize from given facts, relate knowledge from several different areas.
6. Evaluation
   Make choices based on reasoned argument, verify value of evidence, compare and discriminate among ideas.

As I plan the semester, I want to make sure that I really ask the students to do more than memorize problem-solving recipes. In fact, I'm thinking that on some tests, I would like to ask them questions that they have never encountered before. My fear is that in the past when I've attempted this, it's resulted in nearly every student not even making the attempt.

My wife is going on a retreat this weekend, so I'll have a weekend of being a bachelor ahead of me. I've reallocated our netflix queue so that I'll have all three films and they should arrive tomorrow or Saturday at the latest. I'm planning on staying up late and having some italian sausage, fried in grease, perhaps with a heavy tomato sauce and some pasta. Or maybe I'll order a pizza. Or perhaps both. I need to make a list of all the foodstuffs that I don't normally get to eat because my life doesn't like them. Ooh, cole slaw or better yet sauerkraut! Mmmm, some polish sausage with sauerkraut, that would be nice. If only I could get bread dumplings here.

I think I'm also going to stay up late.

A Tamalón is a tamale the size of your head. My first attempt turned out a bit weak, but it was still well received. Adapted from Rick Bayless' Mexican Kitchen.

1 teaspoon baking powder
2/3 cup vegetable shortening
1 1/4 cup maseca
1 tablespoon salt
One small bunch chard
One bunch watercress
2/3 cup chicken broth
1 large banana leaf

In an electric mixer, mix the shortening and the baking powder for about 1 minute until well mixed.

Meanwhile, reconstitute the maseca by adding 1 cup of hot water and mixing thoroughly. Add the maseca to the shortening a bit at a time until all is well-mixed.

Coursely chop the chard and watercress then mix in with the dough mixture.

Pour in the chicken broth, continuing to mix.

Spoon the mixture from the mixing bowl into the banana leaf in a form a bit less than a 12 inches long and about 4-5 inches wide. Roll into a big giant tamale and use strips of banana leaf to tie up the leaf.

Place into a bamboo steamer and steam over medium heat for 75-90 minutes.

Place the finished tamalon into a serving dish and cut open the top of the banana leaf to expose the corn dough. If it's a bit gooey still, place in the oven uncovered for about 5-10 minutes.

Serve with the salsa of your choice.

---

And now we have no more chard left. You can substitute just about anything for the chard and watercress. Meat, other vegetables, have fun. This is a great party/potluck dish.

I've had two e-mails already today asking to know grades. I've decided that there's really no point in responding to them, so I've decided to just delete them without reply.

As if I wasn't trying to do too much already, I'm putting into my summer projects bin: Math article project (which really amounts to writing up my cool new proof of an old theorem and seeing if anyone would actually publish said write-up), non-fiction book project (it's been bumping around for a long time, is about half-written and since the little bar graphs seem to motivate me, I'll use them to keep me on track). Fiction book project (I started this last summer and I'll also let the bar graphs help me along.

Because it shows up in my searches and I get e-mails asking about the tests.

Here's my experience with the CSET:

• I took the English CSET and passed it.
• I didn't take the math CSET because it wasn't required
• I took the (roughly) equivalent test for math in another state
• I've looked over the math questions at the CSET website.

My advice: You need to know your subject matter. A last minute cram isn't likely to help a whole lot. The tests are broad and cover essentially the whole high school curriculum. If, after completing your major and credential coursework you can't pass the tests, you aren't ready to teach.

Seriously.

The math test is comprised of three parts. If you get test anxiety, you can do each part in a separate session.

Some notes:

• Subtest I
  You need to know your field axioms (which you learned in both your math analysis course and your abstract algebra course). You also need to know some basic linear algebra, but not a whole lot more than would be covered in Algebra II and Precalc in high school. Everything else, a good high school senior would be able to do.
• Subtest II
  You need to know the basics of the standard stats and your conic sections. The rest is high school geometry. One hopes that this was emphasized in your program.
• Subtest III
  This is mostly trig and calc. But you're a math major. You can do this right? You probably would have done better on subtest III right after your freshman year of college, but you use calc all the time, so you'll nail this one.

Well I've got my summer school assignment at For Profit U. Five classes. Only two preps though and frankly, I need the money so I'll deal with it. I end up teaching four days a week although Monday is just an hour and a half. Tuesdays and Thursdays go from 4.30 to 10 while Wednesday is 12.30-6. I'm hoping to get textbooks and course outlines later today. With 4 hour weekly classes, I'm going to have to build in some in-class work time to the lesson planning.

Do you know this man?

And you know that there's going to be a film of his story.

Can anyone recommend a good upper-division undergrad logic/set theory text? This was the course that got me to drop out of college the first time around and I'm thinking that I should go back to this material and learn it once and for all.

this is an amazing article. Some of my favorite bits:

When Wiles made the announcement it was celebrated around the world. In Chicago, for instance, mathematicians marched on the streets in euphoric celebration.

From Andrew Wiles' letter to Escultura

Your work is incredible, I read all of it just yesterday and let me tell you I respect you. I am going to review all my ‘proof’ which I am sure is wrong (thanks to you!).

...

Also I’d like to have the address of the guy who let you get a PhD 30 years ago. I’d like to discuss few things with him. . .

And the money quote from Escultura himself:

Two of the axioms of the real number system are false, namely, the trichotomy and completeness axioms (the latter is a variant of the axiom of choice), counter examples to them were constructed by Brouwer and Banach-Tarski, respectively.

I dreamt last night that I was doing observations in my student teaching classroom and ended up helping one of my current community college students with matrix multiplication. He was having a great deal of trouble with the material and was crying in the classroom as I tried to help him remember the procedure.

Psychoanalysts, start your engines.

I've finished up the grades for the weekend class. I need to go to the registrar in person though to correct a grade that should have been an I.

I'm satisfied with the way grades came out and none of my students should have cause to complain about their grade. We'll see if that holds up. Mr D managed to eek out a C for the class.

This will be only the second incomplete I've ever given. The first resulted in the student never taking the final and getting an F after the expiration date of the I. This student is either the unluckiest person alive or a big liar. I didn't accept her offer to see documentation of her latest trauma since there are only four possibilities: If it looks real (but could be real or fake). I say OK, and get on with my day. If it looks fake and is fake, then I'm in the position of either knowingly complying with her lie or having to embarrass her with her poorly executed fraud. And then there's the big cost one: Looks fake, is real. I point out its fakeness and am horrified to discover that it's not fake.

So it was really more trouble than it was worth to look at her documentation. Realistically, she'll probably end up with a D at best if she actually follows through with the class, and I'm not going to lose any sleep no matter what.

After getting a plea for something that will get his grade up to a C (besides studying for the final) from a student, I've decided I'm not sending any e-mails to students this weekend.

As for Mr D, well, Easy Grade Pro informs me that he has lost 7.5% of his grade purely by not turning in a significant fraction of the homework. Given that homework counts for 10% of the homework, that's a VERY significant fraction of the homework.

Of course to turn in the homework he would have had to come to class... and that also appears to have been a bit of a challenge for him. I have no qualms about giving him a D. It's the grade that he's worked very hard to earn.

I got info on the last of the textbooks that I'll need for this fall (for the classes I'm taking). It's the same text that I used on a previous pass through the material, although a later edition. I should be able to get through textbook season without spending more than $70 (for four graduate math classes no less).

I'm doing a little dance.

So this morning I decided to get my exercise by taking a 15 minute swim in the community swimming pool. About 10 minutes into the swim, I noticed that some of the ducks that live on the pond in the community had entered the pool deck, but it seemed that they had sufficient fear of people to not get in the water with me. A few laps later, I looked up and discovered mama duck and 2 adolescents in the pool with me.

Silly ducks, my people eat your people.

The posts below are two of the recipes I've come up with which use the chard. I've got one more bunch still, so I'm going to use Rick Bayless' recipe for tamalon de acelgas to use up what's left.

Olive oil
1 medium bunch of chard
1 small white onion
1 15 oz container ricotta cheese
2 eggs
2 medium zucchini
1 package dry lasagna noodles
2 jars pasta sauce
water
1 cup grated romano cheese

Preheat oven to 375F
Grease the bottom and sides of a 9x12 baking dish.
Remove the stems from the chard and coursely chop the leaves. Puree the leaves in a food processor. Coursely chop the stems.
Chop the onion finely
Beat 2 eggs into the ricotta cheese, then mix in the chard leaves and stems and onion
Chop the zucchini into 1/4 inch dice.
Pour 1/4 cup water and 1/4 cup pasta sauce into the bottom of the dish.
Make a layer of pasta noodles across the pasta sauce and water.
Add a layer of the cheese mixture, then a layer of zucchini, then a layer of pasta sauce.
Repeat the layering until you've run out of noodles (generally 3 layers). Cover the top with pasta sauce then the grated romano cheese.
Cover the baking dish with foil and bake for 60-75 minutes.
Let cool before serving.

This makes 12-16 servings. But everyone will have seconds so realistically you'll serve 6 with it.

Sorry, no pictures. Ingredients based on what was in the fridge at the moment:

1 medium bunch chard
1 medium kohlrabi
2 cups brocolli florets
Half an onion
1 clove garlic
5 Eggs
1 15 Oz container ricotta cheese
Some olive oil

Pre-heat oven to 350F.
Lightly grease a 9 inch glass pie dish.
Remove the stems from the chard, coursely chop, then puree in a food processor.
Grate the kohlrabi.
Chop the onion.
Mince the garlic.
Sautee the kohlrabi, onion, brocolli and garlic over medium heat in a large skillet until tender.
Beat the eggs, then mix in the ricotta cheese.
Add the sauteed vegetables and mix thoroughly.
Add the chard and mix thoroughly.
Pour the mixture into the glass pie dish, place the pie dish on a baking sheet and bake in the oven for 45-50 minutes.
Let the quiche cool for ten minutes before serving.

The recipe I started from claimed that this would make eight servings. Realistically, if this is a main dish, it's about 3-4 servings.

I've modified the flylady routine so that I spread the weekly home blessing over the week (I made a list of 25 tasks to be done weekly and a chart to indicate when I last did them). I call the home blessing part of my daily routine. But I've let the kitchen go to seed a bit and two of the tasks for today were: Wipe down the kitchen counters (this was actually also yesterday's zone mission), and clean out the fridge. These have ended up taking most of the day as the counters were full of clutter and the fridge really needed a thorough cleaning (as in take everything out of the fridge including the shelves and take soap and water to the lot of it). The good news is that I have no dirty dishes, no clutter on the counters and a fridge which looks great. But now it's time to make dinner.

I was thinking that one of the questions that often gets left unsaid is, "What is the purpose of this problem?" I think that there's generally a bit more purposefulness in higher-level texts than lower level texts, but every question should have some objective. It might be, "practice a skill that was covered in this section" which is pretty typical of a high school textbook math question. I had tried once in the past to have questions whose purpose was to lead students to a discovery, and I think that one of the reasons that I failed was that I failed to make explicit what the point of the question was. I think that I will have to make a point of doing this as a part of how I teach the liberal arts math class in the fall. I also can see it being a useful skill in looking at the problems as I work through my (growing) list of math textbooks to work through this summer.

I've decided to keep a post which I can use as a central repository for my summer syllabus work. I'll link all the later posts to this one and link to this one from the sidebar. So here are the things that I need to do (this list will be updated periodically):

• Formally declare the course objective
• Determine the major questions of the course
• Break down the questions into smaller topics
• Plan 31 classes
• Create course packet (handouts, guides for student presentations, homework assignments)
• Create beamer presentations for classes (not necessary for every class)
• Make new course website

Further posts:

• Overarching questions: What is the purpose of this problem? (12 May)
• Overarching questions: Bloom's Taxonomy (19 May)
• Course overview: The big picture (19 May)
• Lesson Planning: Can you find another example? (23 May)

I'll be teaching at For Profit College over the summer. As many as 6-8 classes! Put they're once-a-week classes with 9 meetings each, and while I might have as many as 3 preps, I'm going to aim for 2.

From student:

I'm worried that I won't be passing the class with a "C".  This is the last 
class I need in order to transfer to  Mid-Level University in the Fall. I've 
been at Community College for four years and I was excited about 
finally transfering, but now I'm streesed and it seems like I won't be 
transfering any time soon.  I've been going to the Math tutoring center 
at SAC to study and for extra help, but I haven't been doing well at all 
on the tests.  I'm going to fix up my math project and study a harder, 
but I still feel nervous.  I hope I make it.

To student:

I hope you do to. Leaving class early those past few times did not really 
help a whole lot. 

My wife and I signed up for the local CSA produce service. It's been fun (and we're eating a lot more salad because of all the greens that have been coming in). The one thing that has mystified us is the vast quantities of Chard that we get (usually a 12 oz bunch each week), none of which we're using. Chard recipes are welcome in the comments. And Kohlrabi too.

Reading Royden 2.2, I find the "Axiom of Archimedes" followed by a proof of said axiom. Huh? Royden admits that it's not of Archimedes, but here is the confirmation of my other problem with that statement.

Or was. I think I've reached a fatigure point for planning for tomorrow's class, so I'm thinking that I'll put aside the lap top and focus on cleaning and cooking for a while.

The blogroll is gone for the moment. I've only updated the index, so it will live on in the archives, but I've decided that since it was created when I was teaching high school, it doesn't really reflect my new peers. Not sure how to divide up the new blogroll or who exactly will go in it.

And there's a pretty little chart on the right side showing my current progress on my summer projects.

But I've got all the MW class's tests and homework graded and a bit less than half of a beamer presentation with Wednesday's homework answers finished.

Everyone else is working out there summer plans, so I figure I ought to as well. Classes start up again August 22nd. That means that this summer I have a total of 110 days (starting now) to do everything that I'd like to do. I got an app in last night for a last minute summer school opening at one of those schools that advertise on TV, and assuming that they like what they see (and based on the job listing, their expectations are low), I should have that. But beyond that, I've got the following on my to-do list:

• Math. Another blogger set a goal of 8 hours a day doing math. Maybe I should set the same goal.
  • Royden Real Analysis. I have 100.5 sections to go. If I do a section a day, I'll be done with the whole book before fall.
  • Munkres Topology. 76 sections to go. Same plan as for Royden.
  • Cain Complex Analysis. I have 10 chapters to go. I suppose a chapter a week is a reasonable objective.
  • Write new syllabus/course plan for liberal arts math class.
• Cleaning/organizing the house.
  • Clear off my to-do list on the white board. There are only about 10 items there, I should be able to do one a day and clear this out quickly.
  • Have the whole apartment at least reasonably presentable.
• Music
  • Finish up the recording/mixing for my old band's CD. This may require some travel.
  • Get at least four songs completed/recorded with the new band.
  • Learn at least one solo piece on bass.
  • Teach my self saxophone
• General (from my long-term to do)
  • Read at least one book per week from the top 100 novels list
  • Watch at least one film per week from the top 250 films list

Yeah, that should keep me busy this summer. I should get back to Royden and/or Ulysses and/or music practice. Or maybe cleaning or grading.

I'm getting a late start on my plan to do the homework for the grad courses that I'm (not) taking this semester. And early on, I hit a snag. Exercise 1 in chapter 2: Prove that 1 in P (P being the set of positive numbers). It looks to me like Royden's axioms for the positive numbers are incomplete:

• B1. (x,y in P) => x+y in P
• B2. (x,y in P) => xy in P
• B3. (x in P) => -x not in P
• B4. (x in R) => (x=0) or (x in P) or (-x in P)

The notation is a bit sloppy already with B4 (I would write "either" after the implication). But it seems to be the case that these axioms also apply for P being the set of negative real numbers. I'll have to dig up the argument for (-1)(-1)=1 from the Art of the Infinite and see if this helps. It's always these trivial problems at the beginning of the book which trip me up... Update (5/3): Aha, I worked it through and it seems that part of the proof that 1 in P required me to show that the product of two negative numbers is a positive number. That then allowed me to use the contrapositive of B2 to show that if xy not in P that exactly one of x and y is not in P. From there, I could take the fact that given x in P, 1(-x)=-x requires 1 in P. I guess it's questions like this that separate the math majors from the English majors.

I decided to check to see how I'm doing on seeing the IMDB top 250 movies. It's a bit of a moving target, so films at the bottom of the list change often. But as of today, I've seen a total of 120/250 or 48% of the films. We have one of the films I've not yet seen ("Lawrence of Arabia") out from Netflix so I'll show some real progress (to 121/250) soon. I'd need to see 16.25 movies per month to finish this to-do by the end of the year. I figure, though, that I can probably hit 55% by summer's end.

Currently reading Ulysses which will bring me from 37% to 38%. To finish this task by year's end would require reading 9.125 books per month. Possible, but unlikely. I'm going to aim for 55% by summer's end.

Newly added to the to-do list: Visit all 50 states, all Mexican states, all Canadian provinces, a couple long-distance swims, a triathlon and publishing academic articles in two unrelated disciplines. For this summer, I'm going to write up my novel proof of a standard theorem and check with some faculty friends about whether this is something anyone would publish. I figure if nothing else, it might go to Math Teacher or perhaps some MAA journal.

I spent yesterday at my old college. Not actually the one that I graduated from, but the one that I dropped out of. I went to my actual alma mater reunion 5 years ago. I knew one person from my graduating class. She insisted that I come to the class dinner then she blew it off. That was kind of the end of my AAM alumni stuff. But yesterday was a lot of fun. I saw the old school, talked with the old math department chair (who did remember that I didn't actually graduate). Heard an amusing tale of someone who ended up having to do a bonus year on campus to graduate because he hadn't met a 1-class on campus grad requirement, took the extra semester, but then pulled his GPA down so he had to do another semester to bring it back up, played some croquet, drank some wine, ate some food. Curiously, I got some encouragement from one of the profs at dinner that after I finish my PhD, I should make an effort to teach at NAAM, as they need good math people. That would be nice (and I'd never have to teach anything lower than Calc if I did). I also realized talking with him, that none of what I told him about my teaching philosophy made it into my cover letter or other printed materials for my application packets. All of the ideas and energy which mark me as a really good teacher are absent from my paper packaging. Perhaps I should drink some wine and tape myself talking about this sort of thing.