Designing Dual Modeling Task Sequences to Build Functional Analysis Learning Trajectories for Engineering and Mathematical Sciences Education

This research-to-practice paper investigated the development of Functional Analysis Learning Trajectories (FALT) within the undergraduate courses for engineers including Calculus, Differential Equations, Communications Theory, Control Systems and Electromagnetism. Focusing on the local instructional practices, manifestations of functional analysis ideas are tracked along these courses. Corresponding concept maps are collaboratively within and across courses to portray the relevant connections for engineering mathematics education. These trajectories help engineering and mathematics instructors to collectively design, implement, refine task sequences to improve students' preparedness for upper-level math-heavy courses in engineering, connecting mathematics to their disciplines. Here we utilized collaborative concept mapping as a research heuristics to build curricular innovations with functional analysis learning trajectories across courses, hierarchically arranging, integrating, and conceptually connecting instructional tasks. Through sequences of dual stance learning tasks, students are given opportunities to take multiple stances in a learning task from the perspectives of engineers and mathematical scientists. A higher stance on mathematics was supported to be developed by comparing and connecting alternative disciplinary perspectives and practices with the dual modeling tasks and reflecting on the cross-cutting ideas along the learning trajectory. Here we present the collaborative design and analysis of concept maps along functional analysis learning trajectories for undergraduates. This research builds an interdisciplinary scholarship of teaching/learning mathematics across disciplines among engineering and math faculty. This work helps foster reflection and collaboration on their teaching practices to design and implement instructional tasks to build coherent mathematical perspectives across disciplines. It exemplifies how to design a research-based practices to build cross-curricular innovations. Concept maps within courses are presented and discussed here to build mathematical connections and functional analysis learning trajectories for engineering and applied mathematics education.