There is sometimes a misperception that courses, such as quantitative reasoning, in non-algebraically intensive pathways are less rigorous than traditional College Algebra/Pre-Calculus courses. In order for math pathways to become the normative practice, this perception must be addressed up front with open discussions about the meaning of rigor. If this issue is not addressed, some pathways will be viewed as less desirable and students will continue to enroll in an algebraically intensive pathway that does not meet their needs.
Math departments can address this issue with discussions about what they want students to know and be able to do after their terminal math course. These discussions should be informed by relevant readings and research. When rigor is narrowly defined as mastery of increasingly complex algebraic skills, people inevitably view non-algebraically intensive courses as less challenging. However, if the definition of rigor is expanded to include deep conceptual understanding, reasoning, and problem solving, then people will recognize the rigor inherent in well-designed quantitative reasoning and statistics courses.
This type of discussion among faculty can help a department build a common understanding of the rigor that should be represented in all math courses that may have a great effect on the design of courses. In particular, this can influence the approach to quantitative reasoning courses . Many systems have courses that fall under the various labels of Math for Liberal Arts or Contemporary Math. These courses are often general survey courses in which individual faculty have great latitude to select topics and content; these courses also tend to vary greatly in expectations for students. Quantitative reasoning courses should have rigorous learning outcomes that allow for customization of context.
In addition, an expanded understanding of rigor can--and should--impact the design of algebraically intensive courses to move beyond a focus on algebraic manipulation. Aligning pathways to programs of study creates an opportunity to redesign the traditional College Algebra pathway to aim towards better preparing students for calculus and algebraically intensive programs.
A number of resources to support the design of all math pathways are provided on the Take Action page.
Rich Geist from Angelina College describes how his students in a course aligned with the Dana Center Mathematics Pathways Model learned to take responsibility for their own learning.
Effective math pathways provide students with a high-quality, coherent, and consistent learning experience. Such pathways support students to grow as mathematical learners and as communicators, problem solvers, and independent learners. This is true whether a “pathway” for a particular student is a single course or a sequence of courses.
A high-quality learning experience extends beyond a narrow definition of instructional practices focused on mathematics content to include strategies that support the “whole learner.” Examples include intentionally building a classroom culture that helps students develop a sense of belonging and mindsets that increase perseverance and skills as independent learners.
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Growing evidence demonstrates that more students are successful in completing a college-level mathematics course when they enter directly into the course and are provided with appropriate supports as compared to traditional developmental sequences. The models for corequisite supports vary widely and include concurrent enrollment in a developmental course, concurrent enrollment in a lab or other type of learning support, and back-to-back “compressed” courses in which a student completes a developmental and college-level course in one semester.
There are students who are not successful in a one-semester model. We do not yet know how to identify these students, but it does appear that standardized test scores alone are not enough. Tennessee Board of Regents found that ACT scores did not predict success in a one-semester corequisite math course ( click link for reportview full resourceDownloadFile). In fact, students earning ACT scores of 13 to 19 are more likely to earn college math credit in a one-semester model than in a traditional developmental course sequence.
Given the preponderance of evidence showing that corequisite models benefit students, we encourage institutions to make a one-semester model the default for most underprepared students and to gather data to learn more about the students who are not successful. Decisions to place students into longer sequences should be made based on data that the intervention is likely to increase the number of students who earn college-level mathematics credit. When longer sequences are used, strategies for continuous enrollment in mathematics course sequencesview full resourceDownloadFile should be employed to minimize the impact of attrition between terms.
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Supports for underprepared students include corequisite courses taken concurrently with the college-level course, stand-alone courses, and modularized, self-paced programs. In all cases, these supports should first prioritize content that will prepare the students for success in the college-level course in their pathway.
A second priority is content that students are likely to use in their careers or in their day-to-day lives. For example, exponential models or unit analysis skills are not necessarily prerequisite skills for Introductory Statistics. However, exponential models are important in understanding many critical applications in modern life, including compound interest and population growth. Nursing and other allied health students, who are increasingly taking statistics, need unit analysis for their jobs. It is important to ensure that students have the opportunity to learn these additional skills and concepts. It is equally important to set a high bar for inclusion of content to avoid the “mile wide, inch deep” syndrome of covering so much content that students are not able to develop deep understanding.
We strongly advise against using developmental courses or other supports to try to “remediate” all gaps in mathematical learning.
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Most mathematics faculty welcome the opportunity to improve instructional practice, curricular tools, and support services for students. Engaging in this type of continuous improvement requires an institutional and departmental culture that creates a safe environment to talk critically and openly about the successes and challenges of teaching. This can be supported through regular review of data and on-going professional learning opportunities within the department and with external groups.
Faculty describe the value of professional learning and their experiences in a Dana Center workshop.
Higher education has long operated on the assumption that students are best served by having the freedom to choose from a wide variety of options, but growing evidence indicates that students benefit from a more structured experience with a small number of clearly defined choices. Many colleges and universities have begun implementing guided or structured pathways.
One of the tenets of guided pathways is that faculty should identify the most appropriate courses to meet general education requirements for programs of study. Often non-mathematically intensive programs allow students to select from a number of different mathematics courses. Consequently, a large number of students take College Algebra, not because the content meets their needs but because the course is the most familiar and is perceived as allowing greater flexibility.
Identifying a single, clear recommendation does not have to restrict all other alternatives. Institutions can create processes for students to opt out when another option is appropriate.
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