Rethinking how we teach math to nonmajors
For too many students, math does not make sense. Many who proceed to college have struggled with math concepts most of their lives, and have consistently underperformed in this subject area. Regrettably, they have adopted a sense of inadequacy as a reflection of their ability to learn. This has been a real source of frustration for math teachers. How can these teachers see gains in math concept mastery if students are resigned to failure? We, the authors, faced this at our own institution and devised a remedial math solution that is working.
Students enrolled at the University of Mount Olive are required to take college math; yet, a significant portion of them was not even performing at a high school level. Automatically placing these students in a college-level math course was setting them up for inevitable failure, and reinforcing their perceived inability to understand the material. These repeated missteps, coupled with deficient computational skills, contributed to their further inability to perform in other courses which required knowledge of basic math. These courses affected most majors across the curriculum including sciences, education, psychology, criminal justice, business, accounting, music, recreation and leisure studies, business and finance. As a result, many students inevitably withdraw from the university.
The Math Department of the University of Mount Olive in cooperation with the Academic Resource Center for Excellence in Teaching and Learning (ARC) decided to examine this trend. What was evident was that the majority of the students did, in fact, display the cognitive ability to reason and compute abstract concepts; however, they tended to not participate fully in math activities. They would disengage. If students had the potential to perform, why did their class participation and test performance not reflect these abilities? What we both realized was that a revolutionary approach to math instruction was necessary, one that emphasized strongly both the Affective and Cognitive Domains (critical thinking) of Bloom’s Taxonomy to encourage meaningful learning (Anderson, Krathwohl and Bloom 2001).
We redesigned the remedial math course to break the pattern of traditional math instruction. We implemented both flipped classroom techniques, in which instruction took place at home using teacher-created interactive lessons and videos (Tucker 2012), as well as data driven and differentiated instruction that took into account differences in how students learn and each student’s mastery for each unit as well as the overall strengths and weaknesses of the class (Dixon, et al. 2014). Formative and summative assessments allowed for frequent “checks for knowledge” and were incorporated throughout the teaching process, allowing instructors to monitor the progress of each student and the overall comprehension of the class. In particular, assessments were integrated into the at-home lessons. Students remained engaged and focused, and as their confidence increased, so did their participation. This afforded us to have a clearer and more accurate view of each student’s ability; thus, our learning objectives were dynamic and more relevant to their actual learning gaps.
Based upon their pretest scores, students were divided into three levels: high, medium, and low. Additionally, they were monitored closely in their groups by an embedded peer supplemental instructor, trained by the ARC and the professor. This direct access to peer support created a “no stake” learning environment. In this environment, to improve retention of the material, students completed low-stakes assignments (Wiklund-Hörnqvist, Jonsson and Nyberg 2013). As an added measure to monitor student concerns and participation, these peer instructors, who attended each class, met weekly with the professors offering valuable insights into the student’s participation and concerns.
Now that the course was divided into manageable segments, student learning objectives were easily assessed. Lectures were recorded and posted online, enabling students to familiarize themselves with the upcoming topic prior to class. This also gave them the ability to revisit the instruction. Class time was then dedicated to activities that emphasized the analyzing, evaluating, and creating tiers of Bloom’s Taxonomy of Cognitive Learning Domains. These activities were hands-on, real-life, problem-based learning activities emphasizing applications in students’ areas of academic interest. The literature demonstrates that this is one of the most effective ways to teach students to produce meaningful learning. Collaborative learning activities encouraged all the group members to participate. Rather than assessing the students in “high stake” exams twice a semester, smaller and more focused exams were used frequently, each building on prior knowledge.
At the conclusion of the course, we were able to demonstrate that the learning outcomes were substantial and students consistently demonstrated a deeper understanding of math in general. Furthermore, when they went on to enroll in the required college math course, for the first time in the history, these students outperformed their counterparts.
Professors Watson and Stone-Hernandez will be speaking at ICTCM 2017. Register today and join your colleagues either in Chicago or virtually to discuss many mathematics topics.
About the Authors
Dr. Robert Watson is an associate professor of mathematics at University of Mount Olive. He has taught a wide variety of mathematics courses at UMO since August 2010. He graduated from North Carolina State University in May 2010 with his Ph.D. in mathematics, concentrating on Lie Algebra and symbolic computation. Today he has expanded his interests to include instructional technology as applied to general education collegiate mathematics courses. He has presented twice on topics in this area at past ICTCM meetings—in 2015 and 2016.
Dr. Regina Stone-Hernandez is director of the Academic Resource Center, which provides free comprehensive academic support to the teaching and learning of University of Mount Olive students. As director, Dr. Stone-Hernandez oversees all of the ARC’s functions, and plans/implements individual interventions when needed. She is a current Education department professor, and is involved in many academic committees and programs. Dr. Stone-Hernandez is also the co-curricular chair of the Education Department.
Anderson, Lorin W, David R Krathwohl, and Benjamin Samuel Bloom. A Taxonomy for Learning, Teaching, and Assessing: A revision of Bloom’s Taxonomy of Educational Objectives. Longman, 2001.
Dixon, Felicia A, Nina Yssel, John M McConnell, and Travis Hardin. “Differentiated Instruction, Professional Development, and Teacher Efficacy.” Journal for the Education of the Gifted, 2014: 111-127.
Tamborin, Christopher R, Changhwan Kim, and Arthur Sakamoto. “Education and Lifetime Earnings in the United States.” Demography, 2015: 1383-1407.
Tucker, Bill. “The Flipped Classroom.” Education Next, 2012.
Wiklund-Hörnqvist, Carola, Bert Jonsson, and Lars Nyberg. “Strengthening concept learning by repeated testing.” Scandinavian Journal of Psychology, 2013: 10-16.