Learning to Learn in Developmental Math Courses Wade Ellis West Valley College (retired) Fall CMC 3 Conference, Monterey, California
Ideas about learning mathematics. This OR That. Wade Ellis
The only way to build strong knowledge about a mathematical skill is by drill and practice with a large set of problems.
OR Students analyze and generalize from a few problems.
The skills of reading math books can only be done by faculty. Thus, the faculty member feels obliged to explain the book through a lecture.
OR Introduce a Reading Methodology. Have students fill out a Reading Log and assess their reading performance.
Group work is not effective. Many students don’t like to work in groups. Also, what students learn in groups has to be retaught be the instructor anyway.
OR Group work with roles for each student that are rotated creates a comfortable learning environment where students feel comfortable analyzing and challenging other students reasoning and developing learning skills.
There are many things that students must memorize (without true understanding) in the math classroom.
OR Students explore why something works when confused rather than memorizing something they don’t understand.
Students can assure the accuracy of their work only by the answers at the back of the book or approval by an instructor because they can’t validate their own work or the work of others.
OR Hold students accountable on problem solutions by validating their own work – i.e., an answer without validation has little value.
There are only right answers. Thus, measuring the quality of a problem solving performance is not valuable or needed.
OR Very seldom is a problem cut and dry. The focus should be on the quality of mathematical reasoning and its application to the context.
When modeling/demonstrating what you want students to do, you can’t have students do it. Student presentations will cause other students to get confused.
OR Students making false moves or errors is fertile ground for collective understanding for all students.