Professor Jack Nachman was the chairperson during 2002-2010. Click on the graphic at the right for a video of Professor Nachman's statement on succeeding in Oakland University mathematics and statistics courses.
Departmental Policies on Expectations
for a statement on the responsibilities of faculty and students, as well as our grievance procedures.
Expectations — What We Would Like to See Students Bring to College
The National Council of Teachers of Mathematics (NCTM
) lists five "process standards" and five "content standards" that they consider to be the crux of K–12 mathematics education. Within this framework, our department has the following views on what knowledge, skills, and attitudes we would like to see students bring to college. The NCTM is also preparing a "focal points" document at the high school level, to complement their recently released statement at the K–8 level. See their website for more details. In addition, please see the latest curriculum guidelines prepared by the Michigan Department of Education (content expectations
A summary statement is provided at the end of this list.
1. Problem Solving
In our view mathematics is about solving problems, not pushing symbols around. Students need to come to college with the idea that they will be learning to enhance their ability to solve problems using mathematical ways of thinking and mathematical tools, not that a mathematics course consists of memorizing procedures to be performed on demand. Students should be exposed to problems that involve several steps — and even problems that have no clear-cut solutions — not just toy "story problems" that succumb to routine application of formulas. (In fact the routine application of formulas that have not been derived should not be stressed. Every formula should be derived or justified before being used. It is more important to be able to understand a formula than to mechanically apply it.)
The application of critical thinking to developing problem-solving skills should be emphasized. Student should be given specific problem-solving strategies as well (a la Polya's four-step process), such as looking at simpler cases and discerning patterns, drawing pictures, or working backwards; they should never be allowed to say "I don't know how to start." They should be encouraged to reflect on a problem after they have solved it, asking whether the answer obtained makes sense and thinking of ways to go beyond the specifics to generalize their ideas.
Another aspect of problem-solving is to think about mathematics algorithmically, and the study of computer programming is an excellent choice for high school students preparing for college. The computer is an excellent tool when used effectively, and we would encourage high school teachers to spend some time applying such software as spreadsheets, computer algebra systems, statistical software, or interactive geometry programs to nontrivial mathematics problems.
2. Reasoning and Proof
The most important word in learning mathematics is "why", not "how" or "what". Students should, for example, understand why the quadratic formula gives the roots of a quadratic polynomial. They should expect to justify their solutions to problems, not merely to provide answers. They should understand some simple logic (for example, what it means for an "if...then" statement to be false). They should understand the important role of definitions in mathematics and distinguish between definitions, axioms, and theorems. They should understand the role of counterexamples, and the idea that in mathematics we require a convincing argument before accepting something as true, not just some numerical evidence or the word of an authority. Mathematics should be presented to some extent as an experimental science, in which the student or mathematician investigates situations and makes conjectures, but then tries to understand why these conjectures are or are not true.
Currently students come to college thinking that there is no need to communicate ideas in a mathematics class — that what they write down is just