Math is often used as a gatekeeper, “it has been used to stratify students, affording privilege to some and limiting opportunities for others (Martin et al., 2010, p. 14). These types of courses serve not merely as academic milestones but as critical junctures where varying backgrounds, preparedness levels, and educational goals converge. In environments such as developmental, remedial, or pre-college mathematics classrooms, the challenge intensifies as educators strive to meet the needs of students from diverse backgrounds, often marginalized in the realm of mathematics education. My aim is to reduce or even remove a barrier that persists for those who are already trying to have their relearning of math getting in the way of their already full lives.
I use the term developmental where remedial has been used in the past in a similar way. I prefer developmental and refrain from using remedial in either sense with the idea that it could imply there is something wrong with the student to be remedied. However, I do like the reclamation of the word usage by Bahr “Thus, remediation is, by definition, a ‘‘remedy’’ intended to restore opportunity to those who otherwise may be relegated to meager wages, poor working conditions, and other consequences of socioeconomic marginalization” (2008) because it gives power back the student. In this context, ‘developmental courses’ refer to foundational educational programs designed to equip students with essential skills and competencies, as mandated by an educational authority. These competencies are prerequisites for enrolling in gatekeeper courses that are advanced courses identified as pivotal requirements for ensuring that students can effectively participate in society and excel in their chosen fields by said authority. Thus, I want this course to be a means to remedy student’s past barriers as a free and open resource to all.
This course, once fully developed, would be useful for all people who want to build their mathematical competencies to a level that will help them better function of their own volition within our society. This course can also be used as a refresher course for those who are going into a College Algebra course to better prepare themselves or it could be used as a practice to re-enforce points where they struggle. One of the major tenets of this project is that it is free and accessible to anyone.
Developmental mathematics for adults. What my course is intending to do is prepare those from no background to be ready and able to take the mathematics portion of the GED/HISET1. The GED/HISET is a test that can give high school equivalency but there are few supports for those who are studying independently. This also is the transition point to college mathematics and will serve those heading into or re-entering college mathematics.
The learners would be adults who have been through compulsory education and are seeking to rebuild and re-engage with mathematics. This could be a pre-requisite course for college mathematics, and this could be a GED/HISET math preparatory class. Among all undergraduates who take any developmental courses, they take an average of 2.6 courses and has been estimated to be a total direct cost of 7 billion dollars to students (Scott-Clayton et al., 2014, p. 371). This trend is exacerbated for first-generation students, English as Second Language students, Black students, American Indian/Alaska native, and Latino students, who are disproportionately placed in developmental courses and less likely to complete them (Hodara, 2019, p. 1; Uretsky et al., 2021 p. 7). These courses serve as financial inhibitors, academic barriers, and they have an opportunity cost when many institutions do not offer credit for completing these courses. I hope that a free and open course that is self paced (but designed for 16 weeks) will provide some alleviation from barrier to entry.
Basic Math Operations
- Addition, Subtraction, Multiplication and division using a calculator
- Fractions, decimals, percentages, roots, and exponents
Geometry
- Use formulas related to shapes and objects (not memorizing)
- Be able to calculate surface area, radius, and diameter using given formulas of mathematical objects
Algebra
- Determine the value of a variable in an equation. Also understand how to write a formula with a variable based on a word problem
Graphs and Functions
- Read and analyze information in graphs and charts
- Understand common ways data is organized and use tables
- Understand concepts of median, mean, mode, range, probability, and statistics
Ideally, mathematically none. However, there will be a need for a level of literacy needed, such as an 8th grade reading level.
- Website to host class (or learning management software such as Canvas)
- Video lessons
- Including in video quizzing
- Practice Problem Sets
- Discussion Boards or Forum Component
- Video hosting for student work (possibly)
- Curriculum Guides
The focus of this will be on rebuilding upon previous knowledge that the student already must engage with topics they have seen before. They will have some concept of some of the mathematical ideas present in this course. Where students who encounter ideas they ‘met-before’ influence relearning by either supporting or hindering it, depending on the context. (McGowen & Tall, 2010). What I hope that this class can do is take the students’ ideas and have them test those preconceived notions, keep the ones that work for them already, and challenge the ones that don’t so they can build more fruitful operation-ability. How this manifests itself are still a bit nebulous but here are two considerations.
- In the structure there will be videos for the students to watch which will have pause points with questions for them to answer. At the end of the video the number correct will determine the next course of action available to the student. Whether that is continuing on in the curriculum or sent to another video where alternative methods are shown that they are either more familiar with or will find better illustrate their natural thinking.
- Another idea is to have them teach their methods as well. How interactive this is with other students or myself is to be determined. At the base level it would involve them taking the time to create a script (or some other deliverable, such as a video) walking through a problem of their own creation with their own reasoning. This is called Problem Posing within mathematics education. And through problem posing students can and will respond in ways that reflect their personal commitments and values (Silver, 1994, p. 26). What this could mean is that that product can then be used by the next student in line as a reference or for critique, then they create their own for the next student, and so on. This would keep the course evergreen and center the student voice.
I also want to build this class in a manner that is self-sustaining with those who are interested can join at any time of their convenience outside of the university timeline. So those who are preparing for college or finished their high school equivalency can use this anytime. I also hope that this ends up being a free resource for anyone to join.
Email me at [email protected] about the course. It is currently being built via canvas and I can add people for testing and looking it over.
Bahr, P. R. (2008). Does Mathematics Remediation Work?: A Comparative Analysis of Academic Attainment among Community College Students. Research in Higher Education, 49(5), 420–450. https://doi.org/10.1007/s11162-008-9089-4
Hodara, M. (2019). Understanding the developmental mathematics student population: Findings from a nationally representative sample of first‐time college entrants.
Martin, Danny Bernard, Maisie L. Gholson, and Jacqueline Leonard. “Mathematics as Gatekeeper: Power and Privilege in the Production of Knowledge.” Journal of Urban Mathematics Education 3, no. 2 (December 8, 2010). https://doi.org/10.21423/jume-v3i2a95.
McGowen, M. A., & Tall, D. O. (2010). Metaphor or met-before? The effects of previous experience on practice and theory of learning mathematics. The Journal of Mathematical Behavior, 29(3), 169-179.
Scott-Clayton, J., Crosta, P. M., & Belfield, C. R. (2014). Improving the Targeting of Treatment: Evidence From College Remediation. Educational Evaluation and Policy Analysis, 36(3), 371–393. https://doi.org/10.3102/0162373713517935
Silver, E. A. (1994). On mathematical problem posing. For the learning of mathematics, 14(1), 19-28.
Uretsky, M. C., Shipe, S. L., & Henneberger, A. K. (2021). Upstream Predictors of the Need for Developmental Education among First-year Community College Students. Community College Journal of Research and Practice, 45(2), 139–153. https://doi.org/10.1080/10668926.2019.1655501