Work in Progress: Exploring Before Instruction Using an Online GeoGebra Activity in Introductory Engineering Calculus

This work in progress paper will discuss preliminary work on a project, funded by the National Science Foundation, to test for the causal effectiveness of exploratory learning in undergraduate STEM courses. Exploratory learning is an active-learning technique that has been shown to improve students' conceptual understanding and is well suited for STEM education. This method reverses the order of traditional lecture-then practice methods, by having students explore a novel problem prior to instruction. Exploratory learning has been shown to deepen conceptual understanding by activating students' prior knowledge, helping them realize the gaps in their current understanding, and leading them to discover important features of the problems that they might otherwise overlook. These processes increase students' need for sense-making, helping them pay attention to subsequent instruction and integrate the new learning with the exploratory experience (Loibl, Roll, & Rummel, 2017). In our previously completed pilot studies, instruct-first (lecture-then –practice; control) and explore-first (experimental) activities were completed during single, face–to-face class meetings (e.g., citation removed for review). COVID19 has limited our ability to conduct face-to-face activities for large enrollment (100+) classes. Thus, we are conducting preliminary, controlled experiments in an engineering calculus course to compare explore-first versus instruct-first methods using online asynchronous activities. The engineering mathematics course is a first semester introductory calculus course for primarily first-time, full time freshman engineering students. There are 212 students enrolled in the course. To accommodate required reduced density in the classroom a hybrid instructional strategy is being used in the delivery of the course, with much of the course content delivered online. About halfway through the semester, students learn about two-dimensional vectors, including both the geometric and algebraic approaches for addition and subtraction, and the component form of vectors. As part of the online course materials, students will complete an activity in Geogebra that requires them to scale vectors, geometrically add vectors using parallel displacement, and then write a vector as the sum of two other vectors. Students in the traditional, instruct-first condition will first complete the instruction (reading and video), then the activity. Students in the explore-first condition will complete the activity, then the instruction. Thus, the exact same activities are given to students, allowing us to test the causal effectiveness of reversing the placement of the activity. Afterwards, all students will complete an online quiz that has both procedural fluency and conceptual understanding questions. This study will be the first to test the effectiveness of exploratory learning in undergraduate engineering education. This study is also one of only a few to implement exploratory learning methods in an online learning setting. This paper will present the design, methods, and preliminary results from this study, which is currently underway.