## Friday, August 9, 2019

### Is a bridge needed?

This summer I’ve been tutoring a student taking a one-semester course in College Algebra.  I love working with college students – they have a sense of purpose and I find them eager to get the work done.

What has been particularly interesting to me is the curriculum in the semester course of College Algebra.  Here’s the catalog description:

M 301 (TCCN: MATH 1314). College Algebra.
Subjects include a brief review of elementary algebra; linear, quadratic, exponential, and logarithmic functions; polynomials; systems of linear equations; applications. Three lecture hours a week for one semester. Usually offered only in the summer session. May not be counted toward a degree in mathematics.

Does that curriculum seem familiar?  I’m sure that most of us teach these very things in our Algebra 1 and 2 sequence.  Our college students should be knocking College Algebra out of the park and yet that doesn’t seem to be the case.  In fact some say it is the most failed class in college.

Other observations …
• This course is most often offered in the summer; 4 days a week; 4 weeks.

• It’s fast.  In those four weeks, the course covers several familiar but “big” topics:  basic skills with functions, linear functions, quadratics, other nonlinear functions, piece-wise functions, composition of functions, and systems.

• My student has 20 – 30 problems of homework daily; the problems are not 10, or even 5 or 3 of the same kind.  Typically those 20 problems cover 20 different kinds of math skills within a topic.

• Most often these are skill practice, exercises, very little “problem solving.”

• He has to turn the homework in – daily.

• Part of the homework is graded – the instructor chooses 2 – 4 problems to grade.  The rest are checked for completion.  (By the way, this college teacher takes points off if the paper is not headed correctly, stapled correctly, or if the work is not spaced correctly.)
This course is clearly taught as a review course.  I haven’t sat in on a lecture although I would love to do so.  There isn’t time for the instructor to build understanding, to do much explanation.  There doesn’t appear to be any hands-on activities, no manipulatives, no visual explanations.  It’s all very skill-based.  I can tell from my student’s classwork that the instructor simply works through one example after another.

Now I’m not advocating that we should do the same.  After all, our courses (Algebra 1 & 2) are introducing and building on concepts.  We must use all modalities for teaching abstract ideas.

But what I do wonder is how do we prepare students for the college classroom.  Should we prepare them?  Or is the high school level a level unto itself, and college a level unto itself?  Should there be a bridge?