dr bob teaching faq
- Why do you call yourself dr bob? Isn't that a bit
- You may call me Dr Jantzen, dr bob or just plain bob or
"professor", depending on what you are comfortable with. I am older than your parents (I was born the same year as Mad Magazine, you do
the math) and probably around your grandparents' age so "bob" may be a bit uncomfortable for you with
society's rules for addressing people, but I don't like to have this
artificial wall of formal address between me and the people with whom I work,
including my students. I prefer "bob" but "dr bob" is sort of a playful
compromise between complete informality and formal address, which keeps us all
grounded in the idea that we should not take each other too
- What is the number one way to do well in bob's course?
- In my course surveys students seem to get the answer: do the homework!
- Why don't you
- Some students ask why I don't collect homework. They
think forcing students to work homework problems would help them learn better.
[Our online homework system now makes this a bit outdated, but
the explanation below is useful.]
But I believe in treating college students as adults who should begin to take
responsibility for their own learning. Each of us has has a different learning
style, but in mathematics, doing problems is the single most important way to
begin to appreciate the concepts and associated algorithms for answering
certain kinds of mathematical questions and to understand the concepts for use
in applications outside the course. I try to select key problems that hit the
important points of each section we cover without overburdening the student
with too many homework problems (this is a very subjective call). By not
requiring that they be handed in, the students can cover them at their own
pace when other obligations reduce available time, as long as they catch up as
soon as possible. It also allows me to answer questions on any homework
problem the next class day that arise when students attempt them as part of
the daily homework assignment, without having to also grade such problems (an
incentive for students to ask that I do as many problems for them as time
permits). However, copying down problem solutions is not a very effective way
to learn, since watching someone else do an activity is very different from
doing it yourself. Requiring problems to be handed in also encourages copying
of problems from other students, which again is of little value in helping a
student learn. It is important once I have discussed a problem that you have
not gotten earlier without help to return to it and try it again without the
notes you may have taken, provided that you have understood the explanation.
It is up to you to dog me until I explain a given problem to your
In a similar way, preparing for tests by looking over already solved problems
or reworking them again is of little value if you are then unable to solve
similar problems that you have not seen before. You can put a lot of effort
into studying this way and yet still not perform well on the test for which
you are preparing for this reason. Trying new problems from a section without
looking back at the book is a good practice for whether you really understand
the concepts without the book in your hand to keep looking back to, and gives
you some confidence that you will be able to handle problems on a quiz or test
that you will not have seen in advance. Tests which ask you to solve problems
that you have already seen but with the numbers slightly changed do not do you
a favor, nor do "practice tests" if they are prepared in this way relative to
the actual tests.
The weekly quizzes, always on sections whose assigned homework problems have
already been discussed a previous day, are a way of me getting feedback from
my students about what they are learning, and in turn gives those students
feedback from me about the kinds of problems I expect them to be able to do on
tests, with published solutions showing them how to organize their work in a
clear way that communicates the process of solving such problems. I try to
give each student as much class time as possible to complete a quiz, allowing
some to continue working while the majority of the class moves on to discuss
new material or homework problems.
Do I need to bring my textbook to class?
[If we have an e-text, this question becomes irrelevant! Bring your laptop!]
If you understood all the homework problems, then no.
If you had trouble with a problem, write enough down about it on your paper
workspace to ask an intelligent question about it without referring to the
book, so that you do not need to bring the book. Normally the book is not
necessary in class apart from referring to homework problems. In our
calculus sequence, we have an e-book, so it is accessible on your laptop, or
even on your smart phone, though inconveniently small.
- Why do you bother telling us about why certain
mathematical results or algorithms work? Why not just tell us what to do to
solve the problems?
- If you expect someone to tell you what to do without understanding it at
all, you are not going to be of much use in the real world where you often
have to figure out things for yourself. It is important to see how the
mathematical foundation we build relies on a series of plausible steps, that
allows us to begin to understand how the mathematics works as we build up the
machinery and how to use it more effectively, as opposed to short term
memorization of recipes for recognizable problem types.
I try to explain key ideas in a general setting that we then use in solving
related problems, for which a "rigorous proof" is not usually required. Often
it is just doing a relatively straightforward computation, one that you would
not have come up with yourself (then again neither did we: mathematics
develops over decades and centuries), but that you should at least be able to
follow. Repeating such derivations is not very useful, but by going through
them once, it takes away some of the mystery of why we do the things we do.
Later in life if you have a challenging job, you will continually be asked to
go beyond what you have learned in college, and that often means reading up a
bit yourself on the technique or ideas that you need to work with and figuring
out how to use them to accomplish your goals. In fact our use of computers
constantly forces us to upgrade or be left behind. Career needs are often
pushing us to do the same. The most important thing you can do in college is "learn
how to learn", which means acquiring the skill to develop enough of an
understanding of new material to be able to use it. The phrase may be a bit
worn out, but the idea is not.
- That said, I try to spend more time actually working problems than
introducing new material, either as part of presenting the new material or in
discussing homework problems on material you have already partially digested
and therefore are in a better position to learn from.
- What is the single most
important thing that can help students who are often confused about
mathematics to get better control of it?
- Being organized in working problems is really important. Documenting your
progress through the problem in clear universally accepted mathematical
notation in as many individual steps as possible helps you reduce your
uncertainty to smaller steps where you can rely on basic rules of algebra or
calculus or the relevant area of mathematics that you are doing. Combining
several steps in a mental calculation and then just writing down the result
will often hide a mental error that will leave no trace in your work and be
difficult to track down later.
Identify an expression you write down by putting an equal sign to its left and
the symbol which explains what it is on the left hand side. If you continue
working with this right hand side expression by altering its form without
changing its value, continue by adding equal signs to the right of each
expression and then returning to a new line where the next equal sign aligns
with the first equal sign on the previous line, and then if you change the
expression by doing a new operation, start a new series of equations, like:
f(x) = 3(x+1)^2 -1 = 3(x^2 + 2x + 1) -1
- = 3x^2 + 6x + 3 -1 = 3x^2+6x+2
f '(x) = 3 (2x) + 6(1) + 0 = 6x+6
= 6(x+1) = 6(x- (-1)) = 0
-> x = -1
The more steps you include, the less chance there is to make an error and the
easier it is to follow the calculation. Part of being able to not be put off
by mathematics is just being organized. When you are not, everything seems
confusing and the path is unclear; if mathematics seems unreasonable, then it
is easy for you to just do unreasonable things with it.
- Why do you get us up to the board to work problems even if we don't know
how to do them all the way through to the end?
- First I always send you to the board with at least one or two other people
to work together in attacking a problem. It is important to see where a
stumbling block occurs in the problem solution so we can all learn from it.
And it forces you to make an attempt to work problems, without which you
cannot really learn. Working together is also very useful since you speak the
same language and can often help each other see something the other cannot.
Even if you do succeed in getting through to the end, we can still all learn
from the way in which you do and present the calculation. We learn from
mistakes. This is a fact of life. There is no shame in making mistakes. The
shame is if we don't try to use them to our advantage.
- Why don't you finish a problem completely in
every detail to the very end sometimes in class?
- Sometimes I will explain how to overcome a hurdle you might have run into
while attempting to solve a problem and then allow you to continue working on
the problem yourself, giving you some guidance in how to proceed. This gives
you an opportunity to continue learning from the same problem, while if I
simply finish it off, it becomes one of those dead problems you saw done but
did not do yourself and accepted it once you saw it explained but then may not
be able to do again when faced with a similar problem. Of course if you still
cannot finish it after trying, you can ask me again and I will complete it.
- Why do you often screw up the arithmetic or
miscopy a number from one step to the next on the white board?
- Like you, when I am not absolutely careful (like when I am talking,
writing, and thinking ahead in lecture mode), I make mistakes in details which
I know how to correct/trouble shoot using common sense and technology as a check.
Having a machine deliver perfect calculations to you in a lecture is a useless role model.
Doing mathematics is just a matter of having a grasp of the ideas and being
organized in how one puts them together. In fact the most important part of
the process of solving a mathematical problem is the flow chart of the steps,
not the individual steps which involve algebra or calculus rules and mechanical
manipulation which depend on the particular functional form of the relationships
being considered. If you understand this flow chart, you can tackle much more
realistic problems with ugly numbers using technology to do the mechanical steps,
unlike the homework problems which usually have relatively simple numbers and algebra
and just give us practice with the ideas.
You should also be able to document this flow chart of the problem
calculation/solution so that it speaks for itself,
giving a self-explanatory summary of each major step and how it flows into the next major step,
as well of as the particular minor mechanical steps which make up each part.
The certainty of human error in mathematical derivations also points out the
role of cross-checking your work and troubleshooting errors. If you solve
any equations, you can check whether they are satisfied. One can also use
technology to follow through the calculations as a check.
- Why should we believe anything you say?
- Well... this is a real problem in our world. Who can you trust? Let's
narrow it down to my expertise. I have been using calculus, differential
equations and linear algebra in solving problems in the physical sciences for
over forty years. I don't just teach the stuff, I use it. My degrees are in theoretical
physics and my perspective when I teach is based on what matters for
applications to physical problems.
- Do you really expect us to read all this
- Like any FAQ, you can read the parts you might be interested in and forget
the rest. We are all busy and no one has the time to read everything we might
benefit from. We have to go with what we think is enough.
last update: 11-jun-2021