A variety of pathways are available for students to meet state and institutional math requirements, although choices tend to be limited within each institution. This section begins with a discussion of developmental courses, which provide a foundation for study in college-level pathways, and proceeds to describe typical college pathways.
1.a. Developmental level
Students’ readiness for college-level math is usually determined by testing. At NIU, a majority of incoming students take the Math Placement Exam, a locally devised assessment. NIU and local colleges also use the Compass, Accuplacer, and other test scores to determine placement. Students who are not adequately prepared are recommended for developmental course(s) before proceeding to the college-level math pathway of their choice.
At most northern Illinois institutions, the components of developmental math courses are organized sequentially: arithmetic, elementary algebra, intermediate algebra, and geometry, depending on students’ entry level knowledge and skills. These developmental courses prepare students for college algebra and are most often geared toward an eventual study of calculus, which is the status quo route to majors in the STEM fields (science, technology, engineering, and mathematics). This pathway is strongly rooted in higher education, and plenty of instructional materials are available.
4 Section 1: Available pathways
Challenges to the status quo in both developmental math and the calculus track have emerged due to the retention rates of students who complete developmental courses, the high attrition rate of students in college-level math courses, and the questions about the appropriateness of calculus in the humanities and other fields. Recently, What Does it Really Mean to be College and Work Ready, a publication of the National Center on Education and the Economy, stated that only 5% of American workers use calculus in their jobs and do not need to master the courses in the calculus track.
Kathleen Almy and Heather Foes at Rock Valley College have developed alternative developmental courses. Math Literacy for College Students (MLCS) is a 3- to 6-credit hour course that uses what Almy and Foes call the discovery teaching style. To qualify for this course, students must earn a passing score on a placement test, receive a specific ACT score, or pass a pre-algebra course. While the content of MLCS is intended to be unique from high school mathematics, the level is approximately the same as beginning algebra. The discovery teaching style focuses on learning mathematics through problem solving, critical thinking, and communication of mathematics. The concepts of numeracy, proportional reasoning, algebraic reasoning, and functions are addressed while using statistics and geometry as recurring themes. The Illinois geometry requirement is satisfied by this course. Upon completing the course, students are prepared to enter a college-level statistics course, a general education mathematics course, or an intermediate-level algebra course that leads toward STEM majors. Teaching materials for MLCS are available through Pearson and include a book, online resources, and teacher training aids. The authors are working with several publishers to produce both online and print resources for similar courses (Almy, http://www.slideshare.net/kathleenalmy/mlcs-packet-almy-foes-2012). Initial sample sizes are small, but pass rates range from 55-70%, and MLCS students pass intermediate algebra at a higher rate than do beginning algebra students in traditional courses
(http://www.niu.edu/collegereadiness/links/Developmental_Math_Pathways_Presentation). Long term tracking is underway.
Modular pathways offer another alternative for students at Rock Valley College. The modules are eight-week courses, offered continuously so that students who fail one module have the opportunity to retake it in the next eight-week period and may continue on through the next eight-week module after that. Students begin the modular pathway at a point based on results of a placement test, ACT score, or by passing pre-algebra, which is also offered in a modular format. Conceptually, offering mathematics in modules prevents students from moving on to more difficult material before they have mastered prerequisite ideas. The pace is slower so that students won’t fall behind. The geometry requirement is not met in this pathway, so students must complete a separate geometry class unless they met the geometry requirement in high school. Under the traditional model, students at Rock Valley College passed algebra courses with an A, B, or C 48% of the time. In contrast, since 2009 students in the modular pathway have passed at an overall rate of 69%, with 55-70% passing part 1 modules and 60-80% passing part 2 modules (http://www.slideshare.net/kathleenalmy/rvc-developmental-math-model-packet-2013).
Rock Valley also offers accelerated pathways, a seemingly opposite concept from modular pathways.
Accelerated options may combine beginning and intermediate algebra into a one-semester course of six credit hours. Students entering such courses may need a higher placement score than students going
5 Section 1: Available pathways
into beginning algebra. This pathway does not usually satisfy the geometry requirement. The overall intent of this course is to get better-prepared students into college-level mathematics quicker than their counterparts. At Rock Valley College, the pass rate (A,B,C) for traditional algebra courses was 48%, while the pass rate for students in the combined algebra accelerated path attained a pass rate of 71% since 2009 (http://www.slideshare.net/kathleenalmy/rvc-developmental-math-model-packet-2013). These numbers may demonstrate a bias, since students enrolled in accelerated pathways may, as a group, be better prepared for an algebra course than those in the modular pathways.
Two other pathways, Quantway and Statway, were engineered by the Carnegie Foundation for the Advancement of Teaching with leadership from Dr. Uri Triesman of the Charles A. Dana Center at the University of Texas. Quantitative literacy and statistics are being promoted by advocates as alternatives to both developmental math courses and to the curricular emphasis represented by the traditional calculus track. Quantway leads students into a general education mathematics course through mastery of quantitative reasoning. Statway is a two-semester pathway that satisfies a college-level statistics requirement while remediating developmental math concepts. These pathways have materials available and are being implemented across the country. In spring of 2012, 56% of all students enrolled in
Quantway received a C or better, compared to a baseline 21% success rate along a traditional year-long pathway. Students enrolled in Statway passed the two semesters 51% of the time, as compared with 15% on the traditional pathway. To truly understand these numbers, especially the baseline used for comparative pass rates, one must refer to the following document:
(http://www.carnegiefoundation.org/sites/default/files/CCP_Descriptive_Report_Year_1.pdf). . While not a complete pathway, another developmental course with successful results is Concepts of Numbers. Pioneered by Barbara Lontz at Montgomery County Community College in Blue Bell
Pennsylvania, the course reorganizes a classic pre-algebra course and utilizes the discovery approach. It divides units by concepts like adding, subtracting, multiplying, and dividing versus whole numbers, integers, and fractions. In Illinois, Triton Community College and Kankakee Community College are offering Concepts of Numbers as a replacement or an alternative to pre-algebra. Materials published by Pearson are available for this course. The results of its implementation have been impressive, with a 61% pass rate compared to the 35% for the traditional pre-algebra course (Lontz).
A final alternative is to eliminate developmental mathematics altogether. Complete College America makes this argument in Remediation: Higher Education's Bridge to Nowhere (2012). Citing evidence that students who pass developmental (remedial) courses do not perform as well in college credit courses as do similarly ill-prepared students who start in college-level courses in the first place. In fact, only 9.5% of students who enter at the developmental level graduate from two-year colleges within three years. At four-year colleges, only 35% of students who enter at the developmental-level graduate within six years.
Bridge to Nowhere (page 9) recommends three alternatives that have succeeded in the United States:
• Place students with few academic deficiencies into redesigned first-year courses with built-in support, just-in-time tutoring, self-paced computer labs, targeted help for individuals, and required extra time in the classroom or the lab.
6 Section 1: Available pathways
• Lengthen redesigned full-credit courses with full support to two semesters for less than well-prepared students.
• Provide high-quality career certificates with embedded remediation and adult basic skills, including mathematics for students with significant academic needs.
Career- or major-centric pathways can be devised at any level with specific courses focused on the mathematical material necessary to achieving the goals of the program. This design could result in a myriad of new courses. A similar approach could be taken to creating courses linked to majors which may require less mathematics, such as fine arts or humanities. Going a step further, the National Center for Education and the Economy argues that the only mathematics necessary for a general education is similar to the math taught in middle school. The following resource states that the content taught by math departments is disconnected from the needs of students, another reason to eliminate
developmental courses.
(http://www.ncee.org/wpcontent/uploads/2013/05/NCEE_MathReport_May20131.pdf).
1.b. College level
As mentioned previously, traditional developmental and general education courses are designed to prepare students for the calculus pathway. This pathway usually is designed as follows:
- College Algebra
- Trigonometry or Pre-calculus - Calculus I
- Calculus II
After taking this sequence of courses, students have many options for additional mathematics courses.
This pathway serves as a gateway for most STEM majors. It is considered to have more complex material and includes more courses than other pathways.
The STEM pathway also leads to business majors, which are usually designed as follows:
- College algebra
- Business calculus and/or finite mathematics
- Statistics, which is sometimes redesigned to address business concepts
Business mathematics courses may cover more concepts, but less theory and more application.
Statistics offers another pathway, which can be considerably shorter and is used by a number of majors.
This pathway often consists of one basic statistics course. Usually, this path can be completed after the standard STEM pathway. Students taking developmental MLCS, Quantway, or Statway courses can shorten the route to statistics or quantitative literacy, since requirements are streamlined with the intent of moving students through their programs faster.
A fourth option for students who have completed the traditional STEM pathway is math for elementary education majors. This consists of one or two classes designed to prepare elementary education majors to teach mathematics. These are not necessarily methods courses. Rather, they are intended to be