The shift in the teaching of mathematics, and STEM in general, has been one of leaving behind the classical sage on the stage, through a cognitive analytic perspective, and landing on the foundations of constructivist pedagogy (Abdulwahed, Jaworski and Crawford 2012). Students should be the autonomous center of the learning environment, and the curriculum should be contextualized through authentic, experiential sources based in the real world (Szydlik 2013). The use of real-world examples not only helps students to engage in the curriculum but it also allows for a cross-disciplinary approach to presenting the material (Jackson, Johnson and Blanksby 2014). There also exist issues with student affections toward mathematics curriculum; therefore, there has been much debate on the use of scaffolding and about mitigating for students’ lack of enthusiasm, which may mask deficiencies in knowledge. According to Wilkerson (2015), a solution to a lack of mathematical affection lies in the use of Christian ethics and teachings to scaffold a student’s inner resolve, to support digging deeper, to continue past the desire to quit and to persevere in hope of a greater reward, knowledge and understanding.
At Grand Canyon University, the decided best course of action has been to incorporate integrative practices to transform a discrete general education math requirement into an engaging, collaborative course that scaffolds course, program and mission-critical competencies in a series of culminating learning experiences. The newly modified course combines procedural and conceptual mathematical concepts that focus on the practical application and transferability of learning outcomes (Star 2000). The activities are balanced between procedural and conceptual; students are asked to demonstrate their attainment of procedural complexity and to reflect on the concepts within a real-world example. Through a series of formative and summative assessments, student mastery of the content is checked, reinforced and guided throughout the term, providing actionable and transparent data of their learning.
For all Bachelor of Arts students and the majority of Bachelor of Science students at Grand Canyon University, MAT-144 is the recommended general education mathematics course, with a correspondingly large and diverse demographic. Before the development of this course in January 2014, the general education mathematics curriculum was not intentionally aligned to all outcomes of the university’s mission and its Christian heritage, nor did the curriculum focus on the practical application and transferability of learning outcomes. Although the previous math curriculum supported the “critical thinking” outcome the university determines for students, it was not designed to address the additional mission outcomes of “global citizenship,” “responsible leadership,” and/or “effective communication,” nor did it integrate principles of Christian heritage (Wilkerson 2015). To address these gaps, as well as to bridge quantitative and qualitative performance-based assessment, the curriculum of this foundational course was collaboratively designed to develop student competence in conceptual and procedural mathematics and to better articulate with the university’s mission (Richland, Stigler and Holyoak 2012).
Specifically, the redesigned assignments in this course are aggregative and build on each other; the learning experiences are cross-disciplinary and problem-based (Freeman et al. 2014; Jackson, Johnson and Blanksby 2014). The learning outcomes span across the course curriculum and also across multiple general education and mission-critical competencies. Throughout the course, students actively engage in all aspects of planning an overseas mission trip, demonstrating logic, critical thinking, effective communication, leadership, expense budgeting, inference, hypothesis, sampling, data analysis and so on (Kaus 2014). The use of formative and summative assessments throughout the course inform and determine mastery of the procedural and conceptual objectives. Initial analysis indicates improved student success rates and correspondingly lower withdraw/failure rates for students in the new course compared to the rates of students in the previous general education mathematics course. The layered, cross-competency design of multiple assignments within the course provides the opportunity both for students to demonstrate and for faculty to assess achievement of a broad spectrum of learning outcomes (Race 2014).
The result of this redesign has effectively brought math out of its silo and allowed this general education course to become a hub for interdisciplinary learning and real-life application. The authentic learning experiences embedded in the course provide students with opportunities to demonstrate all course-level competencies while simultaneously and intentionally aligning to multiple general education and mission-critical learning outcomes. The initial success and continued student affection for and satisfaction with this course, combined with the enhanced assessment and learning documentation, have encouraged a further analysis of applying this paradigm to other mathematics and non-mathematics curricula.
Abdulwahed, M., B. Jaworski, and A. Crawford. 2012. Innovative approaches to teaching mathematics in higher education: A review and critique. Nordic Studies in Mathematics Education 17 (2): 49–68.
Freeman, S., S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt, and M. P. Wenderoth. 2014. Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences 111 (23): 8410–8415.
Jackson, D. C., E. D. Johnson, and T. M. Blanksby. 2014. A practitioner’s guide to implementing cross-disciplinary links in a mathematics support program. International Journal of Innovation in Science and Mathematics Education 22 (1): 67–80.
Kaus, C. 2014. Using SoTL to assess the outcomes of teaching statistics through civic engagement. In Doing the scholarship of teaching and learning in mathematics, ed. J. M. Dewar and C. D. Bennett, 99–106. Washington, DC: Mathematical Association of America.
Race, P. 2014. Making learning happen: A guide for post-compulsory education. Thousand Oaks, CA: Sage.
Richland, L. E., J. W. Stigler, and K. J. Holyoak. 2012. Teaching the conceptual structure of mathematics. Educational Psychologist 47 (3): 189–203.
Star, J. R. 2000. On the relationship between knowing and doing in procedural learning. In Proceedings of fourth international conference of the learning sciences, ed. B. Fishman and S. O’Connor-Divelbiss, 80–86. Mahwah, NJ: Lawrence Erlbaum.
Szydlik, S. D. 2013. Beliefs of liberal arts mathematics students regarding the nature of mathematics. Teaching Mathematics and Its Applications 32 (3): 95–111.
Wilkerson, J. B. 2015. Cultivating mathematical affections: The influence of Christian faith on mathematics pedagogy. Perspectives on Science and Christian Faith 67 (2): 111–123.
About the Authors
Sherman Elliott is Dean of the College of Humanities and Social Sciences, Ben VanDerLinden is Assistant Professor of Mathematics, and Judith Eroe is Director of Assessment at Grand Canyon University in Phoenix, Arizona.