Welcome to Week Two

Equations (MAT090)

Weekly Content - Equations

This week we'll be moving squarely into algebra material. Specifically, we'll be reviewing the properties and techniques for solving equations with one variable. We'll look at some methods for working with expressions that have exponents but the only equations we'll be solving at this point will have exponents of 1. For example 3(x + 1) = 2.

Weekly Motivation

"In mathematics, you don't understand things. You just get used to them."
-- John von Neumann [1]

von Neumann's comment sums up the frustration that I think a lot of students experience but it also points toward a solution. I can't overemphasize that mathematics has to be something that you do. To get good at it or, as von Neumann put it, "to get used to it", you have to spend as much time as you can doing it. I remember when I was an undergraduate taking third semester calculus, I literally did every problem in the textbook. In the context of this class, you should spend as much time as you possible can doing problems from the textbook and asking questions about the ones that you don't understand.

[1] Reply to Felix T. Smith who had said "I'm afraid I don't understand the method of characteristics." - as quoted in The Dancing Wu Li Masters: An Overview of the New Physics (1984) by Gary Zukav footnote on page 208.

Class Notes - Discussions

Week one's grades will be posted today (Monday), including the grades for the discussion. Keep in mind that I'm looking for detail in your discussion posts. A vague or open-ended statement like, "Carpenters use math." is not what I'm looking for. Your answer should give specific concepts, formulas or calculations that they use. An A level response would also have a specific example that illustrates your point. A one sentence answer will rarely be sufficient.

Improving Your Grade - Metacognition

One of the most important things students at this level need to learn is what educators referred to as metacognition. This refers to understanding how you learn and managing the process of learning. At this point, your week one grades should give you an idea of whether or not your approach to learning the material in this class is going to be effective. If you aren't satisfied with your grade then you should review what you did last week in terms of studying and look for ways that you can make improvements. Here are a few suggestions for you to think about:

  1. Talk It Out. If you find you have trouble understanding a passage or example from the textbook, try reading it out loud to yourself. Even if you do understand something, it can still be beneficial to explain it to yourself out loud. Talking to yourself may sound a little strange at first but Chi, et al. (1994) showed that students who explicitly verbalized their understanding of material not only learned the material better but developed a deeper understanding of it.
  2. Take Notes. In the ground-based classes that many students are used to, you spend a significant part of any lecture taking notes. For many students this subconsciously becomes an important part of the learning experience. Obviously, we don't have a lecture in this class but you can get the same effect by taking notes from the textbook as if it were a lecture. I've personally used this technique when I'm taking online classes.
  3. Use the Available Materials. Be sure that you're using the supplemental materials that I post each week as well as the materials that are availalbe on the MML website. With that said, I wouldn't necessarily start there or even read through all of the file. This week's sections cover a wide variety of topics. So much that the notes I've attached runs over 20 pages. I don't suggest that you try to read all of them. Instead, start by reading through the textbook and identify areas that aren't clear or where you'd like to see more examples. Then open up the notes that I've attached here and look up those areas in it to get a different perspective on them.
  4. Recap. If you struggle through a problem and final get to the right answer. Go back and write out the correct answer from the beginning without all of the missteps and corrections. This will help you to see the clean solution without any distractions.
  5. Tutoring/Live Sessions. Some people need to hear problems solved by someone else or they need to walk through them with someone else. If you feel that's the case with you then you should try accessing the tutoring service that the University provides access to or attending one of the Supplemental Instruction sessions. You can find information on accessing those sessions at the bottom of the Week 2 area.

Now, I'm not suggesting that anyone should do all of those things. Instead, you should evaluate what you're doing so far, think about which of my suggestions sound like they would be beneficial to you then integrate them into your weekly routine. If you'd like to talk over what you're doing and what changes you should be make, I'll be glad to do that with you. You can reach me by phone during my office hours or on Skype most afternoons and evenings.

Chi, M., de Leeuw, N., Chiu, M., & LaVancher, C. (1994). Cognitive science. Educational Studies in Mathematics, 18, 439-477.