Quantitative Reasoning at the Baccalaureate Level: How We Arrived at This Moment and the Need for Further Dialog among All Faculty
In September, the California State University Academic Senate passed Resolution AS-3230-15, Establishing a Task Force on the Requirements of CSU General Education Mathematics/ Quantitative Reasoning (B4) Credit, calling for a task force comprised of many CSU faculty, including discipline experts, and representatives from the community colleges including the California Acceleration Project and the Academic Senate. The charge of the task force is to review and evaluate aspects of the CSU general education requirement for quantitative reasoning. The current standard is written in CSU Executive Order 1100 and requires an intermediate algebra prerequisite to any course satisfying general education area B4.
A Brief History of Quantitative Reasoning Requirements
From 2003 to 2005, the Academic Senate for California Community Colleges debated raising the graduation requirement for quantitative reasoning from the established elementary algebra standard in Title 5. This proposed change was partially in response to increased graduation requirements and the implementation of standardized exit tests for high school students and the pending adoption by the California Department of Education standards that effectively made elementary algebra the high school graduation requirement. At the Spring 2005 Plenary Session, the ASCCC adopted a position that Title 5 should be amended to require intermediate algebra as the local graduation standard for the associate degree – one level higher than the high school requirement. In 2006, the Board of Governors expressed reluctance to adopt the recommendation of the ASCCC, and the ASCCC promised that it would actively encourage discipline experts to consider and support alternative courses to the traditional intermediate algebra that would satisfy the graduation requirement. The Title 5 language that was finally adopted reads as follows:
Title 5 § 55063:
Competency in mathematics shall be demonstrated by obtaining a satisfactory grade in 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), or by examination;
The competency requirements for written expression and mathematics may also be met by obtaining a satisfactory grade in courses in English and mathematics taught in or on behalf of other departments and which, as determined by the local governing board, require entrance skills at a level equivalent to those necessary for Freshman Composition and Intermediate Algebra respectively.
Experimentation with Basic Skills Mathematics
Since the graduation requirement was changed, numerous efforts have attempted to address basic skills attainment, the length of time students spend in remediation, and the equity disparity in skill attainment and placement. The Basic Skills categorical funding given to community colleges impact these issues through specifically designed programs and services. Many colleges now offer a variety of remediation efforts from Summer Bridge models prior to assessment to compressed class offerings that accelerate time-to-completion to learning cohorts specifically directed toward disparately impacted populations. One of the major issues with offering alternative pathways has been the CSU and UC requirement that intermediate algebra be a prerequisite to transfer level courses in math and science such as statistics.
Two projects that offer alternative math pathways are Statway, established through the Carnegie Foundation, and the California Acceleration Project (CAP), supported by the California Community College Success Network (3CSN). These models are under consideration or at various levels of implementation at a number of California community colleges.
In 2010, the General Education Advisory Committee (GEAC) for the CSU Chancellor’s Office approved a pilot study for five community college districts to use a Statway model. In addition, several CSU mathematics departments were also experimenting with a Statway model for students requiring remediation. Explicit approval was required because Statway attempts to address remediation content and baccalaureate graduation requirement content in statistics concurrently in a year-long sequence, as opposed to the traditional path which is generally a year-and-a-half long sequence. This model does not include the explicit intermediate algebra prerequisite per CSU Executive Order 1100.
The CAP is a different pathway from the Statway model. Students take a one-semester course designed to prepare them for statistics. This one-semester course has no prerequisite requirement and is not equivalent to intermediate algebra. Therefore, students must use the challenge process to meet the intermediate algebra prerequisite, as permitted by Title 5, in order to take the standard statistics course.
One concern expressed about both models is that students are tracked very early into pathways that prohibit exploration of majors in science, technology, engineering, and mathematics. The other concern impacting CSU mathematics departments was that the project relies on small class sizes in a cohort model and may not be scalable to larger class sizes.
In 2014, the Carnegie Foundation presented an update to GEAC, but the data set of completers through baccalaureate attainment was small. The question of student success in upper division general education and non-STEM upper division major requirements seemed positive but was inconclusive due to the limited number of students completing since the 2010 waiver was granted. The waiver to existing districts was extended for one year.
Also in 2014, the American Mathematics Association for Two-Year Colleges (AMATYC) passed a resolution Position Statement of the American Mathematical Association of Two-year Colleges that states Prerequisite courses other than intermediate algebra can adequately prepare students for courses of study that do not lead to calculus. This statement has been interpreted in a variety of ways by different groups but seems to indicate that intermediate algebra is not necessarily required to complete courses commonly offered as baccalaureate level general education in the area of CSU-GE Breadth Area B4, like statistics or ideas of mathematics.
Current Status of CSU General Education Quantitative Reasoning Requirement
In September 2015, GEAC met again to address the question of the Statway waiver for the five participating districts. The data of completers was more robust and the data from the community colleges seemed to be sufficient to state that time spent in remediation and equity disparities were both positively impacted with this project. In addition, more data was presented about graduation and upper division success in non-STEM fields.
The CSU Math Council, however, brought a consensus view of the CSU discipline faculty that the project was not successful for a variety of reasons. The two concerns from before the pilot began were reiterated. Their larger concern seemed to arise from a study of students who engaged in traditional remediation and Statway remediation against a baseline comparison of the Entry Level Mathematics (ELM) requirements of the CSU system. The ELM has a mixture of elementary algebra, basic geometry, and arithmetic questions, and this standard is lower than intermediate algebra. Students in the Statway cohort did not demonstrate mastery of the CSU entry requirements compared to students in other remediation efforts. Thus, the CSU Math Council’s contention is that students in the Statway cohort do not meet the requirements for entrance to the CSU, let alone graduation requirements in CSU-GE Breadth Area B4. The Math Council representative asked if this level of quantitative reasoning is acceptable. If so, then EO1100 must be modified; if not, then Statway does not comply with the current standard.
This information led to a serious discussion about what is expected of students in possession of a baccalaureate degree in terms of quantitative reasoning skills. GEAC recommended to the Academic Senate for CSU that this question needed to be answered and should involve intersegmental dialog. Later in September, Resolution AS-3230-15, Establishing a Task Force on the Requirements of CSU General Education Mathematics/ Quantitative Reasoning (B4) Credit, was passed.
While the GEAC meeting was contentious and strong feelings remain around these issues, the fundamental question of what defines baccalaureate level quantitative reasoning is important. As this task force moves forward, the community colleges need to be ready to participate in the dialog. Recent discussions have taken place during breakout sessions at the Spring 2015 plenary session and the 2015 Curriculum Institute regarding the requirements for math for students in the California community college system at both the associate degree level and for those that plan to transfer to a CSU or UC. This dialog should include the California Mathematics Council for Community Colleges (CMC3).
Much work has been done, but clearly more remains to do. This dialog may seem like a concern for the discipline experts in mathematics, and it is; however, it is also a dialog in which all faculty should be prepared to engage. General education and what it means for any student earning a degree is the purview of the faculty of the entire institution or, in this case, the systems at large.
Resources to Inform Further Discussion
A comprehensive summary of the work of GEAC, the CSU Math Council, and Statway can be found in the meeting notes for the September 2015 GEAC meeting at: http://www.calstate.edu/app/GEAC/documents/2015/sept-2015/06-Statway-presentation.pdf
The CSU Academic Senate Resolution and supporting documentation, including the guiding notes for general education, can be found at:
The California Acceleration Project website is: http://cap.3csn.org/teaching/teaching-pre-statistics-courses/
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