There is sometimes a misperception that courses such as quantitative reasoning 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 algebraically intensive pathways that may not meet their needs.
When rigor is narrowly defined as mastery of increasingly complex algebraic skills, people often view non–algebraically intensive courses as less challenging. If, however, 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.
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 in the DCMP Implementation Guide (see Stage 3, Action 8).
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.
A high–quality learning experience incorporates 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.
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 co–requisite 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 course and college–level course in one semester.
Given the preponderance of evidence showing that co–requisite 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.
Supports for underprepared students include co–requisite 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. 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.
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. Continuous improvement can be supported through regular review of data and ongoing professional learning opportunities within the department and with external groups.
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.