FAQs about Ward’s classes.

Q: What is the most common mistake students make in your courses?

A: I visualize the content of each of my courses as a wall of specially shaped bricks, which must be put in a particular place in a particular order. In each class period, certain bricks are distributed to the students. By participating in class, working on the homework, and asking questions, the students need to get those bricks in place so as to be ready for new bricks that will be forthcoming.

Students often delay getting those bricks in place by procrastinating homework for a couple of days (or more) or by failing to ask questions, for example. Then they end up with a whole bunch of bricks scattered randomly around in their heads. It’s then very hard to go back and systematically get those bricks in the proper places in the proper sequence.

Q: How can students avoid that mistake?

A: They should study the material and the homework before the next class period. Not everything will be perfectly understood at that time, of course, but things are usually well enough in place in order to accept the next bunch of bricks. For the frequent lingering uncertainties, students should ask questions in the next class or in office hours or in a study group. After asking questions they should study the material again and go back to any homework they were unable to do.

I believe in a 3-day learning cycle. Day 1: idea(s) presented and homework assigned. Day 2: homework discussed and students work more on the homework. Day 3: students should understand each homework problem quite well, if not, they should seek immediate help. Of course, cycles overlap. Usually, day 2 of one cycle is also day 1 of the next cycle. It takes persistence to keep up. Get help immediately if you are still confused on Day 3 of the above cycle.

Q: Why do you make so many mistakes, like typos and arithmetic errors, in class? Why do you forget names and conversations?

A: I blame it on all the jobs I had in high school and college that involved contact with lead products. My back-up excuse is old age. Fortunately, there are always alert students who promptly correct my errors in class.

Q: Why do you write so much on the board?

A: First, so that students don’t have to write so much. Writing a lot slows me down so that the students have a little bit of time to think. They should not write everything that I write, except when copying definitions. Otherwise, they should be taking notes, which are abbreviated versions of what is on the board rather than transcriptions of what is on the board. Second, writing on the board allows two senses to be involved and gives two opportunities to catch an idea. Third, if a student’s mind wonders for a moment, the written record allows him/her to see what was missed.

Q: Why don’t you grade all the homework problems?

A: Whenever one is learning, more practice is needed than will be evaluated by an instructor. A music teacher doesn’t listen to and critique every scale his student plays. A tennis coach doesn’t observe every practice serve of her student. Mathematics is no different. One must do a lot more mathematics than the instructor grades.

Q: An entry about you on RateMyProfessors.com says “gives one example, expects you to know how to do the rest. Many classmates agree he didn’t explain much!” Is that true?

A: It’s partly true. I do not (and should not) show how to do every problem on the homework, so that all the student needs to do is mimic my solutions. Instead, I make sure students have the necessary tools to do most of the homework and perhaps show one or two examples, which students will be able to more-or-less mimic to get a start on the homework.

I do not expect the students to know how to do all the problems. Instead, I expect them to be able to figure out how to do many of the problems using the tools provided and the examples in the book. (Class is not the only source of examples, that expensive textbook contains many more!) Next, I expect them to ask about the remaining problems either in a study group, office hours or during the next class period. That provides ample opportunities to eventually understand every problem.

All of that is consistent with a goal I have for each of my classes: Students should be able to use a collection of basic facts to solve problems and make deductions from those facts. That activity is widely applicable outside mathematics.

Q: Sometimes you seem irritated in class. Are you?

A: Yes and no. I am often irritated with myself. I am rarely irritated at students. I do get disappointed in students who do not keep up on their work, who do not ask questions, or who do careless work.

Q: Why do you use graders?

A: It gives the student a “second opinion” on their work. It provides work and experience for advanced students. It gives me extra time to spend with students and on other professional duties.