Alternatives to Traditional Intermediate Algebra
Ian received a Ph.D. in mathematics from U.C. Santa Cruz and then taught mathematics at Mission College for thirty- three years. He was ASCCC President when the associate degree graduation competency was increased to Intermediate Algebra in 2006. He was a member of the ICAS Subcommittee that wrote the 2010 Mathematics Competencies document.
In the December 2012 Rostrum, ASCCC Executive Committee members Beth Smith and Phil Smith (no relation) wrote about issues raised by Fall 2012 Plenary Session resolutions regarding specific developmental mathematics projects. In this article I explore additional related issues and argue that the current University of California (UC) and California State University (CSU) practice regarding Intermediate Algebra as a required prerequisite for transfer level mathematics courses is anomalous, and prevents students from taking alternative preparation courses that could be beneficial for the many who do not intend to be STEM (Science, Technology, Engineering, Mathematics) majors. One solution would be to agree that the transfer status of a mathematics course is determined solely by the level and content of that course and not by any prerequisite. A better solution would be for the academic senates of UC, CSU, and the Community Colleges to create a process whereby alternative courses can be examined and approved as acceptable prerequisites for transfer level mathematics courses.
Currently four distinct conversation strands exist regarding mathematical preparation, all with different premises and conclusions, but in some way converging on Intermediate Algebra.
Strand 1 – Common Core
Common Core is a national K-12 conversation but has the potential for significant impact on higher education in general and the community colleges in particular. Several years ago, projects such as Achieve and the American Diploma Project asked the question “what mathematics skills are necessary in order for K-12 graduates to achieve success in higher education or in ‘high-skill, high-wage’ occupations.” The summary answer was that both colleges and employers felt that “intermediate algebra” was necessary. The subsequent powerful national political coalition of Common Core has since moved to implement this answer. But three significant problems with this brief conclusion can be summarized as follows:
- A close reading of the Common Core standards reveals a careful description of broader mathematical practices and critical thinking with the level and rigor of intermediate algebra but a more diverse content base. Incorrectly narrow summary interpretations of the standards seem to claim that Common Core validates the traditional (300-year-old) intermediate algebra topic list in its entirety1.
- Despite curriculum descriptions in Common Core, we do not yet know how the changes will actually impact K-12 practice until the assessment instruments are complete. Three independent implementations of testing are currently under development [Smarter Balanced, PARCC (Partnership for Assessment of Readiness of College and Careers) and GED (General Educational Development Testing)]. They each seem to be encountering practical difficulties in testing wider mathematical thinking versus rote learning2.
- Common Core documentation also involves a statistical research problem. The methodology section of the 2004 American Diploma Project foundational paper Ready or Not includes the statement “the ETS study found that 84% of those who currently hold highly paid professional jobs had taken Algebra II.” The paper does not provide any additional evidence that the specific topics contained in Algebra II are what led to that success – correlation without causation. In all likelihood the success stories had taken traditional intermediate algebra because they had not been offered any alternative.
Strand 2 – California Community College Associate Degree Requirements
The 2006 Title 5 regulations on associate degrees call for “a mathematics course at the level of the course typically known as Intermediate Algebra (either Intermediate Algebra or another mathematics course at the same level, with the same rigor and with Elementary Algebra as a prerequisite, approved locally).” This language was deliberately designed to make it clear that courses with content different from the traditional topic list are acceptable. Indeed the Academic Senate, in seeking to pass those regulations, promised the Board of Governors that it would actively promote and support alternative courses in California colleges. Much of the Basic Skills Initiative attempted to implement the concept that alternatives were not only acceptable but desirable. The regulations also contained language that permitted the local curriculum committee to approve courses taught by departments other than the math department in order to meet the graduation competency.
Strand 3 – Alternative Pathways
A variety of state and national projects are currently seeking to improve the student success rate for the mathematics basic skills pipeline. These projects encourage students to succeed in transfer level mathematics courses by utilizing a non-traditional preparation pathway (Carnegie, Quantway, Statway, Statpath and a variety of accelerated prerequisite courses). One of these projects was the subject of the Fall 2012 Plenary Session resolutions. In particular, several projects and colleges have evidence demonstrating that students can succeed in the traditional transfer level general statistics course without mastering all the topics of a traditional intermediate algebra course3. Moreover, if one were to use content review to validate a prerequisite of intermediate algebra for statistics, many of those traditional algebra topics would never be identified as necessary for success in statistics. Undoubtedly some of those “unnecessary” topics are useful for general mathematical maturity, but there are significant questions about the validity of the prerequisite and the way it is currently used by UC and CSU.
Strand 4 – UC and CSU Entrance Requirements
UC and CSU policy – in particular CSU Executive Order 1065 (formerly 1033), which contains the language “courses in subarea B4 shall have an explicit intermediate algebra prerequisite” is being used for a purpose different than success in the subsequent mathematics course. Prior to Executive Order 1033, language allowed campus discretion for alternative courses but that language was eliminated in 2008. The effect of current policy is that students intending to transfer to CSU or UC cannot participate in any of the alternative courses with the same level and rigor as intermediate algebra, but different content – either those described in Strand 2 that were deliberately created by the community colleges for their new graduation requirements or in projects such as those described in Strand 3 that demonstrate successful preparation for transfer courses.
Conclusions for the Academic Senate and the California Mathematics Council, Community Colleges
The wide range of conversations demonstrates that a strong case can be made for the exploration and implementation of alternative preparations for transfer level math courses that differ from the content of the traditional intermediate algebra course. The Academic Senate should be leading the policy area of this exploration and the California Mathematics Council, Community Colleges (CMC3) should be leading the discussion of suitable alternative course content.
Some of the reasons that lead to this conclusion are as follows:
- We certainly cannot argue that the current structure works well. The failure rate of students in the developmental math pipeline should be unacceptable to everyone;
- At present any exploration of alternatives is effectively blocked by UC and CSU General Education Breadth transfer policy. This situation amounts to the use of intermediate algebra as an entrance filter to four year university rather than as a validated prerequisite;
- This blockage has been amply demonstrated by colleges that created alternative courses to satisfy the graduation requirement (such as non-transfer liberal arts math or vocational embedded algebra) only to see them cancelled due to low enrollment because students did not want to rule out the possibility of future enrollment in a transfer level math class;
- Discussion at the Academic Senate Fall 2012 Plenary Session indicated clear interest in determining the viability of alternatives. Unfortunately the specific resolutions seemed to call for endorsement of one specific approach which is not an appropriate action for the Senate;
- Almost simultaneously, in the Academic Senate’s C-ID public vetting process for the general statistics course, an unusually high number (over thirty) of respondents requested an alternative prerequisite. These requests could not be accommodated because of the CSU/UC regulations described in Strand 4;
- In a December 2012 breakout at the CMC3 North conference in Monterey, attendees were surveyed regarding the necessity of traditional intermediate algebra topics for success in three areas: STEM major, 4 year non-STEM major, high-skill, high-wage, non 4 year (results available on request)4. A large number of participating math instructors identified many of the traditional algebra topics as unnecessary for the latter two categories of students and then identified several alternative topics that would be more useful - largely from geometry, trigonometry, logic or statistics. It would be valuable if CMC3 were to conduct a similar survey on a larger scale. At present community colleges cannot successfully offer such an alternative content course because of the CSU/UC regulations described in Strand 4;
- The Academic Senate has an inescapable moral and professional commitment to facilitate alternatives given the very public pledges that it made during the adoption of the new associate degree graduation competencies.
The California Mathematics Council, Community Colleges (CMC3) should conduct a formal conversation with its membership to explore and identify appropriate alternative content to the traditional intermediate algebra topic list. A hidden assumption exists that only the traditional 300-year old topic list can provide mathematical rigor. But both the Common Core mathematical practices and Intersegmental Committee of Academic Senates (ICAS) approaches to mathematics stress the need for integrated, thoughtful use of mathematics in critical thinking and problem solving. Furthermore project evidence already includes courses where students demonstrate success in rigorous alternatives and subsequent success in traditional math transfer courses.
Simultaneously the Academic Senate for California Community Colleges should work with its four year partners to acknowledge the need for and value of alternative content in the mathematical preparation of many university bound students, especially non-STEM majors. This conversation should lead to implementation with the expeditious creation of a mechanism to permit approval of an alternative array of courses that are accepted as prerequisites to transfer level math courses.
We owe it to our students to provide alternative pathways to the successful application of mathematics in their lives and careers.
1. For example, Common Core State Standards Algebra Overview includes the language “understand the relationship between zeros and factors of polynomials” but none of the associated CCSS HAS APR language seems to require the large amount of time most traditional intermediate algebra classes currently spend on learning to factor trinomials with non-unit leading coefficient or “special shapes” such as difference of cubes.
2. Private conversation with GED Testing staff member, May 2013.
3. For example, City College of San Francisco. Math 45.
4. Results of this survey are available upon request to the author of this article.
The articles published in the Rostrum do not necessarily represent the adopted positions of the academic senate. For adopted positions and recommendations, please browse this website.