Math

Here's an interesting article that compares the stagnant math scores on the NAEP with the ever-increasing GPAs for students coming out of high school. How do we fix the education system? I have a hunch that it will take strategies entirely different than the ones currently being suggested.

During my Saturday review session for the first M408K exam, I used the doc cam, and then scanned the notes, so that you can compare them with your own, or review them if you didn't take notes, or didn't attend

This article discusses the fact that the part of your brain where you worry about math is the same part of the brain where you actually do math, so you can't do both at the same time with any success.

Here's the schedule of review sessions for Exam Number 3. Of note, mine will be led by Dr. Gilbert.

• Thursday, 4/27, 5pm-7pm, ECJ 1.202, Carrie McGraw
• Thursday, 4/27, 6:30pm-8:30pm, RLm 5.104, Darice Chang
• Friday, 4/28, 11am-1pm, GAR 215, Moses Kim
• Friday, 4/28, 4pm-6pm, RLM 5.104, Grant Lakeland
• Friday, 4/28, 5pm-7pm, BUR 108, Ricaardo Conceicao
• Sunday, 4/30, 7pm-9pm, RLM 6.104, Mark Rothlisberger

My review for the second exam will be in RLM 6.104 on Sunday (March 26) from 7:00-9:00. I'm sorry for the late notice.

Instead of 3:30-4:30, my office hours today will be from 4:00-5:00.

Harry Potter days are coming to TA sessions. Learn more tomorrow.

I'm helping to raise funds for the Austin-area Crop Walk. If you're interested in making a donation to this organization, which is dedicated to eradicating hunger both locally and worldwide, please see me.

Apologies for the lateness of this list, but here's a list of topics that I expect might be on the exam, and some supplemental problems to look at. As a disclaimer, this is my personal understanding and list of topics; I have no information about what actually will and will not appear on the test; I am judging solely based on information that is also available to you, as students. Trust yourself before you trust me. Remember, the professors who write the homework problems and quizzes are the same people who write the exams, and they can be notoriously tricky.

• Homework 1:
  Antiderivatives (general and particular)
  Graphical interpretation
  Physical modelling
  pp.305-306 #1-43, especially 11, 15, 16, 32, 34, 35, 41-43
• Homework 2:
  Riemann Sums
  Estimating integrals with finite Riemann sums
  Converting between Riemann sums and integrals
  Areas and Integrals (e.g. absolute values of integrals)
  Properties of integrals (e.g. linearity)
  Fundamental theorem of Calculus (two flavors)
  p. 324 #2-5; p.337-8 #17-20, 36; p. 348 #7-11, 19-31
• Homework 3:
  Graphical interpretation of definite integrals
  Areas between curves
  Substitution (a.k.a. u-substitution)
  p. 366 #7-52; pp. 380-1 #1-25
• Homework 4:
  Volumes with given cross-sectional area
  Integrals with exp and ln
  pp. 391-92 #1-18, 51-59; p. 367 #67-82
• Homework 5:
  Integration by parts
  Inverse trigonometric functions
  Trigonometric integrals and substitution (not on exam)
  p. 485 #59-70, p. 516 #1-36

I haven't read this yet, but the summary looks interesting. Although not strictly mathematical, the content suggests that we aren't good at reasoning logically with our conscious minds

Here's a list of which TA is leading which review session for the upcoming exam:

• Thursday, 2/16, 5-7pm, RLM 5.104, Ricardo Conceicao
• Friday, 2/17, 11am-1pm, Garrison 313, Moses Kim
• Friday, 2/17, 4-6pm, RLM 5.104, Grant Lakeland
• Sunday, 2/19, 7-9pm, RLM 4.102, Mark Rothlisberger
• Monday, 2/20, 5-7pm, BUR 108, Darice Chang
• Monday, 2/20, 7-9pm, RLM 5.104, Carrie McGraw

I really have only one question to ask about this article, which addresses severe gaps in literacy and quantitative skills of students about to graduate college: What is going on? Okay, maybe I have two or three questions, for instance: did they ask the wrong questions and give the wrong tests when doing their research? A brief examination of our society leads me to think that it's possible to believe results like these; however, I could also believe that they fall into the third category in Disraeli's venerable quote. What do you think? Will I be able to help students in a calculus class actually increase their thinking skills, so that when Pew does a follow-up study in two years, the results will be better?

I recently read this article from BusinessWeek, about how better mathematical models of business (specificially consumer-oriented business) are changing and will continue to change the way the world works. Thus it behooves us to have a deeper and better understanding of mathematical concepts. This is the fruition of ideas expressed in a great movie from more than a decade ago:

Cosmo: There's a war out there, old friend. A world war. And it's not about who's got the most bullets. It's about who controls the information. What we see and hear, how we work, what we think... it's all about the information!

Cosmo: The world isn't run by weapons anymore, or energy, or money. It's run by little ones and zeroes, little bits of data. It's all just electrons.

This semester, I'll be the TA for Dr. Gilbert's M408L class. I may post information on this web page, but never anything of a critical nature. Instead, that will always be found on the actual course webpage. As a service for those of you who use iCal or Thunderbird, you can subscribe to a calendar for this class. Right now, it's pretty basic, and just has all of the class meeting times (for lecture, discussion, and office hours) blocked out. I may add more helpful information. If you can think of anything you would like to see on the calendar, let me know. To subscribe in iCal, select the "Subscribe" option in the "Calendar" menu, and enter the following URL:
http://webspace.utexas.edu/mpr245/www/Teaching.ics
If you're using Thunderbird (or some other application), I'm confident that you can figure out how to do the equivalent operation in that program.

If you're looking for material that was here last semester (Hi, 427K students!), here is an archived copy.