Tuesday, April 24, 2007

Math 25 Changes

This term I am teaching Math 25 for the first time. This is a class about group-work activities involving practical math.

Ideally, the class gets through three activities each week. There are seven weeks of "core" activities required by the different academic majors that use Math 25 as a graduation requirement or prerequisite.
  • Week 1: Percent Review, Restaurant Tax and Tips, RCMP Licensing Percents
  • Week 2: Checking Accounts, Budgeting, Mortgages and Annuity Tables
  • Week 3: Simple and Compound Interest, Charge Options
  • Week 4: Retirement Planning (and Midterm #1)
  • Week 5: Health Formulas
  • Week 6: Payroll, Employee Taxes
  • Week 7: Floor Plans and Scale Drawings, Markup, Discount
Three subsequent class days are for assessment. There is a second midterm. There is a math "skills test" during Week 9 that looks a lot like a Math 20 midterm. A big portfolio focusing on an out-of-class project is due after once class day devote to letting students finish it up in class.

The other class sessions are for "instructor discretion" activities. In other words, past instructors have composed a collection of activities and each term whomever is teaching the class picks 3-5 of these, makes up their own, or lets students pick which to do. (The last day of class is usually set aside for review before the final exam.)

Due to the needs of the different majors making use of Math 25, some aspects of the class cannot be changed. Students are supposed to be learning how to apply mathematical problem-solving techniques to situations they have not seen before. So the class must focus on group-work about real-life activities. The instructor may not lead students by the hand through these activities by presenting similar problems to mimic or by answering so many student questions that step-by-step answers are provided. Neither may activities be grouped by which mathematical techniques apply to them.

(These requirements are understandably unpopular with many students. It would be much easier for them if we went through all of the "percent of percent" activities together, with lots of example problems to mimic and step-by-step guidance. But students would leave the class have gained little helpful experience in problem-solving.)

Four weeks into the class, it is clear that the following changes would be helpful. I am still tweaking the details of each for fine tuning, and soliciting student feedback on these ideas and other suggestions...
  • The "skills test" should happen at the end of Week 2 or the beginning of Week 3, in addition to happening at the end of the term, with students being graded on their highest score. An early version would encourage students who did not master the Math 20 material to visit office hours early in the term for help. Students who had mastered Math 20 material could do well the first time and have the option of skipping the test in Week 9 when they have a lot of work due in their other classes.
  • Probably once (but maybe twice) there should be a class day devoted to remedial review of Math 20 material. Students who did not need this would not attend this class and instead do an out-of-class activity. This activity, representing 1 of 20 class days, would be worth 5% of the overall grade, which would be a 5% that the students receiving the remedial help would be forfeiting. But those students are not aiming for an A+ anyway, and an entire class focused on their needs would help a lot more than 5% over the course of the term.
  • The next time I teach math 25 I will probably not do any of the established "instructor discretion" activities. Instead, I will push back the "core" activities two weeks, so these do not begin until Week 3. This would provide time at the start of the term to carefully develop the skills students have learned in Math 20 into a real "toolbox" of techniques with which to approach real-world math problems. For example, the concept of "percent of percent" occurs in multiple activities (RCMP Licensing, Compound Interest, Retirement Planning, Markup, Discount), but currently in a way that appears haphazard and confusing to many students; if that concept was solidifed before a bunch of activities were presented then the students would be better prepared to see these activities as using something from their "toolbox" instead of each being an isolated task needing its own procedure to solve it. Problem-solving approaches are themselves a valuable "toolbox tool" needed in this class, which could also be taught during the first two weeks.
Unrelated to the class itself, this term more students than before are having trouble with LCC's Moodle website. There is not much I can do if the web browser on their computer at home is set to not download certain file types. But over the summer I should definitely use a college computer with Camtasia to record an "introduction to Moodle for students" screen-capture movie with voice narration.