heard were wonderful things. I knew there
must be another side to the story, so we set
a meeting with the head of the private
school to get his opinion on the homeschooling craze. I thought he certainly must
have a sense of reason. When we
approached him, he said, and I quote, “I
think homeschooling is the best thing a
parent can do for their child.” He went on to
say that it was not for everyone, but he was
very clear about the fact that he strongly
believed in it.
TOS: Why did you develop your homeschool math courses?
Dr. Callahan: We started homeschooling
our daughters when they were in high
school. Friends would ask us, “What are
you going to do about math?” We would
explain that math was not our concern;
teaching them English and literature
would be a bigger issue for us. They often
would say, “Well, can my son/daughter
come over and you teach them as well?”
We ended up with three years of classroom
instruction in algebra, geometry, algebra 2
with trig, calculus, physics, and biology.
However, it was becoming harder to
manage, so we explored other options for
teaching high school subjects. Thus, the
DVD series was born.
work every problem but still have no understanding of what they are doing or why.
TOS: How did you filter through all the
many math programs and decide which
texts to use for your courses?
Dr. Callahan: It first started as part of my
university job. In engineering, we usually
do not see the students until they are in
their second year, after they have
completed most of their three required
calculus courses. We were trying to determine why most students failed in college
calculus before we even saw them. We
interviewed the staff of the math department at the university, and they explained
that the best students came from one of two
public schools in the area. (Yes, I said
So we went and interviewed these
schools and asked them what they did
differently. The number-one issue was that
they used college-level textbooks! So when
we started homeschooling, it was clear to
us what to do. Our search began by looking
at many of the college textbooks available.
We found the best ones and put them in
front of the homeschool students we were
teaching. Together we determined what
was the best fit.
TOS: The course assignments do not have
the student complete every problem in every
lesson. Will students still learn and retain
information that they are taught if every
problem is not worked?
Dr. Callahan: We get that question a lot! It
seems that the most popular homeschooling
math courses require the student to work
every problem. This almost never happens
in the better high schools or in college.
Math is a toolbox. A toolbox may contain
a hammer, but I do not need to hammer in
thousands of nails to develop my skill with a
hammer. What I need to do is build, and that
requires knowing how to use a hammer and
when to use a hammer. By having students
work every problem, we would be missing
the point; we would be making them
perfect at hammering a nail—only to find
they are using a nail where a screw should
We also liken math to grammar. In
grammar we learn about nouns and verbs
and how to diagram a sentence. But the
point of grammar is to develop a set of tools
we use to read and write. Likewise, math is
the grammar of the universe. Understanding
math allows us to communicate at a much
deeper level of understanding about the
complex things going on in nature. Math is
simply a language that allows us to understand complex things.
At the university level, we prefer to have
students who understand the concepts to
those who have worked all the problems but
who still do not understand the concepts.
Trust me, we see lots of students who can
TOS: What is your math philosophy?
Dr. Callahan: Often—too often—math is
taught in a sterile academic environment
void of meaning or real world applications.
I find that boring, as do most high school
The countries whose students perform
best in math teach more applied math.
Students see math being used as a set of
tools as opposed to doing a study of the math
grammar alone. Unfortunately, many math
programs do not teach applied math. We do.
TOS: How can a parent encourage a child
who is not motivated to study advanced
Dr. Callahan: That is a tough one. You
must motivate him. Learning is not forced
in; it must be drawn out. I think the keys
are to first understand what does motivate
him and then let him take some ownership.
Then, by letting him help choose the
curriculum, we let him become part owner
of his education. After all, we are teaching
lifelong learners, so we need to teach them
to explore and go after education rather
than force it down their throats.
My work at the university is mostly
with seasoned professionals, many of
whom have made careers out of things they
never really loved. They were good enough
to do the work and pass classes, but they
never really had a passion. I would rather
tie into a student’s passion and design a