content courses providing potential teachers with the mathematical knowledge and skills necessary for an elementary educator.
Technical or vocational mathematics pathways emphasize the knowledge and skills that are necessary to achieve the goals of each program. These pathways vary widely depending on their aim. Programmatic mathematics courses may be designed specifically for programs like welding, fire science, or nursing , to name a few.
Finally, there is a general education mathematics pathway intended to satisfy the college requirement for mathematics in liberal arts, fine arts, and other disciplines. The pathway consists of one course that surveys potentially useful mathematics that students can use in their lives and work. At Rock Valley, the MLCS course leads to this pathway as well as to the traditional STEM pathway. Classes like MLCS and Quantway are designed for students who intend to take a general education mathematics course.
Section 2: Barriers
A number of steps are involved in the development, adoption, and implementation of a new pathway in mathematics. Each step may encounter potential barriers. This section will be broken into three
subsections: departmental, institutional, and state-level barriers.
2.a. Departmental barriers
One of the most commonly recurring barriers to new mathematical pathways at the departmental level is faculty attitude. This theme manifests itself in several ways: trust, philosophy, pride, caution, and conservatism. Other barriers at the departmental level may be related to materials, training, and placement tests.
Trust between the administration and the faculty is critical to the success of a new mathematical pathway (Cappetta). A lack of trust may cause faculty members to hesitate before proposing or implementing a new pathway. A rough push from administration may make people uneasy and less inclined to cooperate (Lontz). In other cases, faculty members may doubt whether a new pathway is actually in the best interests of students, the department, or the institution.
Faculty within a department generally have philosophical views about their discipline and about instruction. These views may prevent them from teaching a course that does not include what they consider to be essential elements of a college education. Their concern is that removing certain topics from a student’s education would be doing them a disservice and could make the institution, as a whole, less credible. Without a critical mass of faculty members whose philosophies are open to creating new pathways, the department may not be able to bring about serious change.
Pride may also be an issue with some faculty members. Interviewees suggested that a change in teaching methods or curriculum could be viewed as a reflection on past and present practices, even as an attack on the methods that they have been using for years. Some people take a call for change as a personal criticism, causing defensiveness and resistance. Adopting new pathways may be seen as an admission of ineffective teaching. Fear of failure may also be a driving factor since faculty who implemented a new pathway could be blamed if the new courses fail to improve student success.
8 Section 2: Barriers
Some departments and faculty members may be generally more cautious about change, and their conservatism may manifest itself in a variety of ways. First, faculty members may fear watering down the curriculum. Secondly, being academics, they demand evidence of the value of new pathways. Other faculty may resist change as a matter of principle, deny existence of a problem, or assert that change is impossible. Numerous interviewees suggested that the lack of comprehensive information on the need for and success of a new pathway constitutes a serious barrier to implementation at their institutions.
While some promising preliminary data was compiled on the success of alternative programs described in this paper, many departments are waiting on thorough long-term data to justify the creation of a new pathway (Almy, Anderko, Pulver, Read).
Aside from individual and department objections, another barrier to implementing a new pathway is the lack of materials available. Inadequate access to books and other instructional materials and resources acts to deter the creation of a new pathway. When the MLCS course was first being implemented at Rock Valley, the instructors created their own materials and distributed copies. Do-it-yourself course materials can make replication of a course within pilot sites or at other institutions difficult. Over time the MLCS instructors published a textbook, which made the process of teaching more manageable (Almy). Similarly, the Concepts of Numbers course mentioned earlier developed a book (Lontz). In both cases the books were authored by the faculty who designed the course.
Training is another important issue. When Barbara Lontz’s Concepts of Numbers course is replicated at another institution, she makes sure to visit the campus to provide training to those who will teach the course (http://www.takepart.com/article/2013/05/23/college-math-crisis). In some of the innovative pathways, the style of teaching differs significantly from the traditional lecture style. Teachers who are new to the discovery approach, for instance, will need support from people who are experienced in the new delivery methods (Almy). Finding teachers who want to teach the new course is also an issue. Most alternative pathways employ innovative pedagogy and cannot be utilized to their full potential without teachers who are willing to adopt new methods.
Lastly, placement exams can present barriers whenever new courses are introduced. To consider, adopt, and implement changes requires an evaluation of prerequisite material for placement into the new courses. Poor placement of students could undermine the whole purpose of an alternative pathway, which emphasizes the need to carefully examine the entire intake process for students (Rambish).
2.b. Institutional barriers
Institutional barriers also present challenges to adopting and implementing new mathematical pathways. These include curriculum committees, degree issues, cost effectiveness, counseling, and mobility.
When considering a new course or pathway for students, committees must study, revise, and eventually accept the alternative. Since mathematics is a prerequisite for many fields, a new pathway may need to be confirmed by multiple curriculum committees (Almy). Agreement among so many departments may be difficult to obtain (Harris). A new pathway also has implications for degree attainment. Separate committees may be involved in the alteration of a degree, a necessary step for a new pathway to be
9 Section 2: Barriers
sustainable. Changing the degree requirements for some programs may take longer than a year (Cappetta). Each of these committees would also investigate the probability that a new pathway may mean that other institutions or accrediting agencies do not recognize that degree or course (Anderko).
Implementing such a course or pathway would be ultimately damaging to both the program and the institution.
In an increasingly competitive environment, institutions must consider whether new courses will be viable and profitable over the long term. Consideration must be given to questions like “Is this going to make students successful, and in turn, the institution?” (Read). If a course ends up costing the school more than is gained, then it likely will not remain. Factors that impact cost effectiveness include enrollment, student success, and student retention as well as new equipment and materials, flexibility, and marketing.
Marketing may be necessary for new courses to be successful. Advisors are a primary resource for students making course selections and represent an important point of contact in the success of new classes. Both advisors and students need to know when a new pathway exists, and if it will help them achieve their goals quickly and efficiently. Advisors need to have accurate information about the course design and training necessary to make the appropriate suggestions to the students (Hergert, Rambish).
Rodger Hergert offered an example that illustrates the advising problem. A group of nursing students who needed college algebra as a prerequisite for chemistry were placed in the MLCS course, which must be followed with intermediate algebra before taking college algebra (Hergert). While some of the students may have wanted to take the MLCS course (there is a bridge between MLCS and college
algebra so there is no “backward movement” in the student’s pathway), taking all three courses may not have been appropriate for all of the students.
When students’ goals change, as they often do, will those students need to start a whole new pathway to achieve their goals? The issues of both vertical and horizontal mobility need to be addressed when designing or implementing alternative pathways. Vertical mobility relates to how easy it is to finish a single pathway. For instance, one statistics course is more vertically mobile than the business pathway, which includes a minimum of two courses. Horizontal mobility refers to how easily one switches pathways. Changing majors or focus within a major poses the biggest challenge for students. Under the traditional model, such changes can cause significant setbacks to a student’s progress toward program completion. Consideration should be given to pathways that reduce the impact of these setbacks.
(Read). The MLCS pathway was designed so that students moving into the STEM or another pathway would not have go back to beginning algebra, since the MLCS course takes its place and thus reduces time lost in the transition (Almy).
2.c. State-level barriers
Barriers to new mathematical pathways extend all the way to the state level. Challenges exist with the Illinois Community College Board (ICCB), the Illinois Board of Higher Education (IBHE), and the Illinois Articulation Initiative (IAI). The Illinois State Board of Education’s (ISBE) K-12 policies may also act as barriers to innovation, especially the lack of a fourth-year high school mathematics requirement and the complex approval processes for teacher certification.
10 Section 2: Barriers
The ICCB approves new courses or programs (including degrees or transfer programs) at community colleges (Pulver). Colleges must submit to ICCB staff a request for any new course or program or for revision to an existing course or program before they offer the course or program to their students.
While approval is needed for content, ICCB does not examine the delivery method of the course, leaving such decisions to the institution. Requests for changes or additions to programs and degrees must be approved by board decision (Durham). Kathleen Almy described the process as less difficult than some of the other needed approvals due to state-level support from ICCB for alternative math pathways.
Board approval may take more time depending on the people on that board and their work load (Durham).
The IBHE’s high standards and hard line on policy changes can also act a barrier. Illinois is one of two states with a geometry requirement; for instance, a student must take geometry and intermediate algebra prior to taking statistics. In California, the other state with a geometry requirement, students need take only intermediate algebra. Rules at this granular level can make innovation more difficult (Almy, Read). The IBHE, in conjunction with the Illinois State Board of Education (ISBE), is also
committed to aligning developmental courses with the Common Core State Standards. This additional layer of requirements may be considered a barrier by others, although the state agencies expect that the Common Core will result in marked improvement to students' preparation for college math.
The Illinois Articulation Initiative (IAI) is the system that determines which courses in Illinois are transferable across postsecondary institutions. Currently 111 institutions are members of the IAI (http://www.itransfer.org/IAI/participating.aspx?section=faculty&subsection=school). While the initiative makes transfers easier for students, IAI can also act as a hindrance to innovation (Almy, Cappetta, Harris, Hergert, Rambish). The process for courses to be reviewed is time consuming, and the extra regulations may prevent or deter a transformation in education or even meaningful adjustments.
Kathleen Almy recalled that her experience with state articulation for the MLCS course took three years (Almy).
Graduation requirements, another state policy issue, also affect alternative math pathways. Illinois does not currently require students to take a fourth year of mathematics in order to graduate from high school (Harris, Schaid). As a result, some students go nearly two years (or more in some cases) between high school and college math courses. Since math knowledge and skills evaporate quickly, students who take a "math vacation" are underprepared and out of practice when they arrive at college, impacting both placement and overall aptitude in mathematics. Students who were once prepared to enter a pathway at a certain level may find themselves lacking the skills necessary to succeed at that level.
Development courses and bridge programs help to fill the gap that this policy allows to develop.
Lastly, teacher preparation and certification may also present barriers to adopting new mathematical pathways. ISBE must confirm any alteration made to a teacher certification program. (Wolfskill). Adding alternative pathways affects teacher preparation programs in two ways. First, students entering teacher preparation programs may arrive via different mathematical pathways, bringing different skills with them. Secondly, teacher preparation programs will need to train teacher candidates to teach concepts included in new pathways and the pedagogical methods required by those courses.