The state of Oregon is adjusting curricula for Math 95 – Intermediate Algebra, a non-college-level course and Math 105 – Contemporary Algebra, a college-level course that “surveys various practical areas of mathematics.” I forwarded these thoughts to those working on the new curricula.
Please consider the following issues as you choose topics for Math 105 and a prerequisite Math 95-like course. To be clear what follows is my personal opinion not that of my department or institution (SOU).
- There are two main purposes for requiring successful completion of Math 95 (or proof of equivalent knowledge by a placement test or SAT Math score) before a student is allowed to take a college-level math course. One is that the requirement indicates that the student has the requisite mathematical knowledge to handle the math in a college-level course. The other, and just as important or more so, is to insure that a college graduate has certain mathematical skills and knowledge that we call “high school algebra” whether or not they are deployed in some college-level math courses. The Math 95 requirement presumes that the student has knowledge of the content of Math 60 and Math 65 which themselves contain important concepts that every high school graduate should know, for instance, the concepts of linearity and linear functions.
- The content of a typical Math 95 course does not represent current trends in high school mathematics education or modern mathematical applications or advances in technology. For instance concepts of probability and statistics are being introduced in the K-12 curriculum but are not commonly covered in a typical Math 95 text. Hopefully we can look forward to the day when high school students come to college understanding basic statistical concepts. There are modern mathematical tools that do not fall into the function, graph, algebraic formula paradigm of the typical Math 95 class. Modern citizens should be aware of mathematical modeling tools like graphs of the vertex and edge variety and matrices for instance. They should also be able to do system thinking (feedback loops, etc.) which can be taught from a mathematical point of view. There is no question that some topics in Math 95 are arcane and unnecessary even for calculus students. The chapter on roots could be greatly simplified if rational exponents would be the dominant notation. Practically, a series of complicated algebraic simplifications is best done with readily available computer algebra systems and add nothing to the teaching or testing of important calculus concepts.
- A Math 105 curriculum and the Math 95 prerequisite should be informed by the quantitative literacy goals of a university. Our quantitative literacy goals here at SOU are that students “Demonstrate the knowledge required to effectively formulate and use mathematical models and procedures to address abstract and applied problems.” The AACU defines it as “Quantitative Literacy (QL) – also known as Numeracy or Quantitative Reasoning (QR) – is a “habit of mind,” competency, and comfort in working with numerical data. Individuals with strong QL skills possess the ability to reason and solve quantitative problems from a wide array of authentic contexts and everyday life situations. They understand and can create sophisticated arguments supported by quantitative evidence and they can clearly communicate those arguments in a variety of formats (using words, tables, graphs, mathematical equations, etc., as appropriate).” I have called the latter, “The Nearly Impossible Dream.” We need to be moving away from the thinking that a single college-level course makes a person quantitatively literate at least in terms of university goals. About Math 95 we need to be asking what knowledge and skills will allow students to effectively participate in quantitative literacy across the curriculum. Since Math 105 is often taken instead of Math 243, a statistics class, we need to ask what topics covered in a statistics class are essential knowledge for a college graduate. Sample variability must be one such concept. This means that Math 105 needs to contain a substantial statistics component. Another question when designing a Math 105 course needs to be considered. What does it mean for a class to be college-level? At the college-level the methods of mathematical justification should be used. For instance when considering annuities, a common Math 105 topic, geometric series should be understood at least in concept.
In sum, changes to Math 95 and Math 105 need to be considered as they affect the quantitative literacy goals of the universities. We need to move away from the thinking that a math college-level course is a hurdle that once jumped can be forgotten.