1. Algebra at Different Levels Sheldon Gordon gordonsp@farmingdale.edu

2. Enrollment in Algebra Courses In the year 2000 at four year colleges and universities: 219,000 students were enrolled in “remedial” courses. This represents about 13.5% of the total mathematics enrollment.

3. Enrollment in Algebra Courses In the year 2000 at two year colleges : 763,000 students took “remedial” courses. Of these, 292,000 took elementary algebra, 255,000 took intermediate algebra. These two groups represent 40% of the total mathematics enrollment. The remainder took arithmetic and college algebra courses. All told, remediation accounted for 55% of all math enrollment.

4. Two Year Colleges – Two Extremes Many faculty at two year colleges are among the strongest proponents of very traditional algebra preparations. Most of the reform efforts at the developmental algebra level have come from two year college faculty.

5. Philosophy At One Two Year College “Every student from elementary algebra on up must be viewed as a potential candidate for a master's degree in pure mathematics.” This is a rather extreme position, but is indicative of an attitude among many Two Year College faculty

6. Master’s Degrees in Mathematics In 2002, P There were 482,000 master’s degrees P Of these, 3487 were in mathematics This is 7 tenths of one percent!

7. Associates Degrees in Mathematics In 2002, P There were 595,000 associate degrees P Of these, 685 were in mathematics This is one-tenth of one percent!

8. Why the Extremes? 1. One of the overwhelming curricular issues in the two year colleges is the worry over the transferability of courses. This concern can drive the focus on trying to build very strong manipulative skills, whether or not they are needed by any of the students.

9. Why the Extremes? 2. Many two year college faculty worry about the image that their graduates project about the strength of the program they came through when they transfer to a four year college or university. Seemingly weak algebraic skills is thus perceived as reflecting very poorly on the quality of the math program at the two year college.

10. Why the Extremes? 3.The typical teaching load at a two year college is 15 hours and is often higher. This leaves little time or energy to rethink courses and so tends to keep the status quo intact.

11. Why the Extremes? 4. The bulk of the developmental instruction at the two year colleges is now borne by part-time faculty. They tend to worry about how the department views their performance and one way to prove how effective they are is to train their students in algebraic skills.

12. Why the Extremes? 5.There is typically minimal in the way of institutional funding for professional development. Consequently, many faculty and whole departments are not acquainted with changing curricula or do not have the financial support needed to implement major curricular change.

13. Why the Extremes? At the other extreme, two year college faculty tend to be far more directly involved in teaching developmental courses than in four year colleges and universities. As such, they are much more aware of the issues involved in the mathematical education of these students and so many have taken the lead in changing the focus of these courses.

14. Why the Extremes? Among the most influential and widely used reform texts for developmental algebra are: 1. Darrell Abney, Kathy Mowers & Lillie Crowley 2. Maricopa Math Consortium: Allan Jacobs, et al 3. Mercedes McGowan and Phil Demarois 4. Consortium for Foundational Mathematics (Ernie Danforth, et al)

15. Features of these Reform Courses 1.Focus on conceptual understanding as being at least as important as manipulative skill. 2.Emphasis on functions and their uses. 3.Extensive use of non-routine problems, not just template problems whose solutions can be memorized and regurgitated. 4.Mathematical modeling and realistic applications 5. Focus on real-world data to motivate the mathematical ideas and methods. 6. New mathematical topics – such as data analysis, difference equations, etc. 7. Routine use of technology.

16. The Differences with Four Year Schools At four year colleges, there is nothing to prove, there is no expectation that remedial algebra students will become math majors there are fewer reasons to want to develop a high level of manipulative skills there may be more flexibility in terms of adopting a reform curriculum if anyone cares enough

17. What Makes Algebra Hard Easy? Motivation Attitude Maturity Mommie can’t post a test with anything less than an A on the refrigerator!