Presenting a New Model to Support the Secondary-Tertiary Transition to College Calculus

Abstract

Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the transition from secondary precalculus or calculus to tertiary calculus. Using the Four Component Instructional Design (4C/ID) model and empirical data from the United States (US) nationally representative FICSMath project, we mapped instructional experiences of students in the transition to theoretical components of the 4C/ID model. From exploratory factor analysis (n=6,140), we found six factors that mapped to the 4C/ID model components and created the new Secondary Precalculus Calculus (SPC) 4C/ID model. In this model, the Learning Task Component represents tasks to engage learners in meaningful problem solving; the Support Component grounds instruction in reasoning and understanding; the Procedure Component integrates group work and graphing calculators to connect concepts to procedures; and the Part-Task Component represents instruction to develop automaticity. The SPC 4C/ID model presents a unique support for precalculus and calculus teachers in the quest of teaching for learning and transfer of learning across the transition.

Investigating effective teaching practices in advanced placement calculus AB: A qualitative exploration of student recounts

“…Participants in this study, for example, recounted transferable benefits from being required to present work and explain their reasoning to others -an activity that would likely not be categorized by students as "standardized preparation" -yet simultaneously seemed to have helped in both preparing for the AP Exam and the rigor of college instruction. More research is needed, however, on how we can prepare secondary calculus students for both the AP Calculus Exam and for tertiary calculus, since these two type of classroom settings and expectations may be vastly different; in addition, future studies should explore how to connect mathematical discourse to increase student performance while supporting the learning of all students (Wade et al, 2018).…”