Monday, April 22, 2013

Teaching/Learning Mathematics



There are two components to learning mathematics: learning skills and learning conceptual thinking.

Skills are learned through practice and drill. The fact that you understand the concept of parallel parking does not mean you can actually do it. You have to practice and practice and practice some more until you can do it. Once a skill is mastered, you never lose it; you may need some refresher practice after a long time of not using it, but that is all. Think bike riding. Skills are relatively easy to teach.

Conceptual thinking is a completely different thing.

The sequence of math classes from primary school through college form a continuum. At the lower levels, it is mostly about learning skills. At the advanced levels, it is mostly about conceptual thinking. In between, it is a mixture of both.

Monday, April 1, 2013

Resurrecting California’s Public Universities

So, I pick up the Sunday Review section of the New York Times and there on the editorial page is an editorial with the above title.
Quoting from the editorial:
"The same California State Legislature that cut the higher education budget to ribbons, while spending ever larger sums on prisons, now proposes to magically set things right by requiring public colleges and universities to offer more online courses. The problem is that online courses as generally configured are not broadly useful. They work well for highly skilled, highly motivated students but are potentially disastrous for large numbers of struggling students who lack basic competencies and require remedial education. These courses would be a questionable fit for first-time freshmen in the 23-campus California State University system, more than 60 percent of whom need remedial instruction in math, English or both.
"The story of how the state’s fabled higher education system got to this point is told in a troubling analysis by the Public Policy Institute of California, a nonpartisan think tank."
For a variety of reasons, our state legislature is reflecting society at large in trying for the quick fix to every problem that presents itself. This NYTimes editorial and others need to be understood as not antagonistic to online classes in general, but rather against using them in the wrong setting. To the extent MOOCs in mathematics have been successful, they are successful in the more advanced classes where students are already skilled in the basics and are organized, disciplined and motivated.

Online classes at the community college level can be a tremendous aid for the many students with family and job responsibilities who find it difficult to regularly attend on ground classes. However, they are not suited for students missing any of the above mentioned characteristics. The legislature, if it continues to pursue this short-sighted course will only hasten the long slow slide of California's higher education system from the envy of the world to just another state education system fallen on hard times.  In my opinion.