Innovating and modernizing a Linear Algebra class through teaching computational skills

Mariana Silva; Philipp Hieronymi; Matthew West; Nicolas Nytko; Akshit Deshpande; Jer-Chin Chuang; Sascha Hilgenfeldt

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Conference: 2022 ASEE Annual Conference & Exposition
Location: Minneapolis, MN
Publication Date: August 23, 2022
Start Date: June 26, 2022
End Date: June 29, 2022
Conference Session: Incorporating Technology in the Classroom
Page Count: 17
DOI: 10.18260/1-2--40766
Permanent URL: https://peer.asee.org/40766
Download Count: 755

Paper Authors

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Mariana Silva University of Illinois at Urbana - Champaign

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Mariana Silva is a Teaching Associate Professor in the Department of Computer Science at the University of Illinois at Urbana-Champaign. Silva is known for her teaching innovations and educational studies in large-scale assessments and collaborative learning. She has participated in two major overhauls of large courses in the College of Engineering: she played a key role in the re-structure of the three Mechanics courses in the Mechanical Science and Engineering Department, and the creation of the new computational-based linear algebra course, which was fully launched in Summer 2021. Silva research focuses on the use of web-tools for class collaborative activities, and on the development of online learning and assessment tools. Silva is passionate about teaching and improving the classroom experience for both students and instructors.

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Akshit is an undergraduate student at the University of Illinois at Urbana-Champaign studying computer science and applied statistics. He has taught as a course assistant for introductory computer science, computational linear algebra, and numerical methods courses. He is a former software engineer intern at Intuit and Google, and is currently a software engineer intern at Meta.

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Jer-Chin Chuang University of Illinois at Urbana - Champaign

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Abstract

This paper describes design choices and implementation guidelines adopted during three semesters of major innovation and overhaul of a traditional linear algebra course offered to engineering students at a Midwest Public University. The traditional course was redesigned based on innovations anchored by the use of computational tools and modern learning approaches (henceforth we refer to the redesigned course as “computational”). The objectives were (1) to establish a stronger integration of basic programming knowledge into the general engineering curriculum; (2) to introduce computational exercises that solve “real-world” linear algebra problems, emphasizing the importance in connecting fundamental and applied concepts in modern mathematics instruction; and (3) to incorporate collaborative learning activities that motivate students to learn mathematics and promote an environment for them to develop social and communication skills. The linear algebra course was redesigned through a Community of Practice consisting of faculty from Engineering and Mathematics Departments, collaborating closely to design the new curriculum and implement the changes in stages, and with a view to sustainability of the project. In a first step, new computational exercises were created following well established practices for collaborative learning activities, such as POGIL, incorporating scaffolding and exploratory questions, enabling students to work together towards a solution and setting up instructors to work as facilitators during class instead of being mere sources of information. These exercises were created as Jupyter notebooks, combining both Python code and rich text elements such as equations, figures, videos and links. Before implementing the computational exercises at scale in the large linear algebra course, we first assigned these notebooks to students enrolled in an additional 1-hour course limited to 25 students in Spring 2020. Feedback from students and from class observations of the group work allowed us to refine the notebooks for the following semester. The computational linear algebra course was first offered in Fall 2020 with 300 students enrolled, implementing the following design changes: (1) replace 3 lectures per week with 2 lecture hours per week plus 1 hour of computational laboratory; and (2) redesign the worksheets given to students during the 1 hour weekly discussion section to foster group interactions. In addition, the lecture content was offered via asynchronous pre-recorded videos due to COVID-19 restrictions. Both the computational laboratory classes and discussion sections were offered synchronously via Zoom, where students worked together as a team in breakout rooms, and course staff moved around rooms providing assistance when needed. In Fall 2020, the traditional linear algebra course had 500 students enrolled. In Spring 2021, both traditional and computational linear algebra courses (both with enrollments around 450 students) were offered by the same team of instructors, allowing for coordination of all the homework and exam assessments. Based on feedback from the previous semester, the following design changes were made to the computational course: (1) adding auto-graded checkpoints to the Jupyter notebooks, allowing student groups to check their progress without much assistance from course staff; (2) adoption of an online app to facilitate requests for help from the breakout rooms; and (3) assignment of roles to students in each group to facilitate productive collaborations. Preliminary results from student surveys and from evaluations of student performance suggest that (i) students welcome the opportunity to learn computational techniques in this format; (ii) students appreciate the practical relevance of linear algebra more than after having taken the traditional course, and (iii) students’ conceptual knowledge of linear algebra is not compromised by the addition of the computational elements. The project also aims at quantitative comparison of student evaluations with and without exposure to computational tools as well as at conducting longitudinal studies of performance in courses downstream of the computational class.

Citation
Format

Silva, M., & West, M., & Hilgenfeldt, S., & Hieronymi, P., & Nytko, N., & Deshpande, A., & Chuang, J. (2022, August), Innovating and modernizing a Linear Algebra class through teaching computational skills Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--40766

TY  - CPAPER
AB  - This paper describes design choices and implementation guidelines adopted during three semesters of major innovation and overhaul of a traditional linear algebra course offered to engineering students at a Midwest Public University. The traditional course was redesigned based on innovations anchored by the use of computational tools and modern learning approaches (henceforth we refer to the redesigned course as “computational”). The objectives were (1) to establish a stronger integration of basic programming knowledge into the general engineering curriculum; (2) to introduce computational exercises that solve “real-world” linear algebra problems, emphasizing the importance in connecting fundamental and applied concepts in modern mathematics instruction; and (3) to incorporate collaborative learning activities that motivate students to learn mathematics and promote an environment for them to develop social and communication skills. The linear algebra course was redesigned through a Community of Practice consisting of faculty from Engineering and Mathematics Departments, collaborating closely to design the new curriculum and implement the changes in stages, and with a view to sustainability of the project. 
In a first step, new computational exercises were created following well established practices for collaborative learning activities, such as POGIL, incorporating scaffolding and exploratory questions, enabling students to work together towards a solution and setting up instructors to work as facilitators during class instead of being mere sources of information. These exercises were created as Jupyter notebooks, combining both Python code and rich text elements such as equations, figures, videos and links. Before implementing the computational exercises at scale in the large linear algebra course, we first assigned these notebooks to students enrolled in an additional 1-hour course limited to 25 students in Spring 2020. Feedback from students and from class observations of the group work allowed us to refine the notebooks for the following semester. The computational linear algebra course was first offered in Fall 2020 with 300 students enrolled, implementing the following design changes: (1) replace 3 lectures per week with 2 lecture hours per week plus 1 hour of computational laboratory; and (2) redesign the worksheets given to students during the 1 hour weekly discussion section to foster group interactions. In addition, the lecture content was offered via asynchronous pre-recorded videos due to COVID-19 restrictions. Both the computational laboratory classes and discussion sections were offered synchronously via Zoom, where students worked together as a team in breakout rooms, and course staff moved around rooms providing assistance when needed. In Fall 2020, the traditional linear algebra course had 500 students enrolled.
In Spring 2021, both traditional and computational linear algebra courses (both with enrollments around 450 students) were offered by the same team of instructors, allowing for coordination of all the homework and exam assessments. Based on feedback from the previous semester, the following design changes were made to the computational course: (1) adding auto-graded checkpoints to the Jupyter notebooks, allowing student groups to check their progress without much assistance from course staff; (2) adoption of an online app to facilitate requests for help from the breakout rooms; and (3) assignment of roles to students in each group to facilitate productive collaborations. Preliminary results from student surveys and from evaluations of student performance suggest that (i) students welcome the opportunity to learn computational techniques in this format; (ii) students appreciate the practical relevance of linear algebra more than after having taken the traditional course, and (iii) students’ conceptual knowledge of linear algebra is not compromised by the addition of the computational elements. The project also aims at quantitative comparison of student evaluations with and without exposure to computational tools as well as at conducting longitudinal studies of performance in courses downstream of the computational class.

AU  - Mariana Silva
AU  - Matthew West
AU  - Sascha Hilgenfeldt
AU  - Philipp Hieronymi
AU  - Nicolas Nytko
AU  - Akshit Deshpande
AU  - Jer-Chin Chuang
CY  - Minneapolis, MN
DA  - 2022/08/23
PB  - ASEE Conferences
TI  - Innovating and modernizing a Linear Algebra class through teaching computational skills
UR  - https://peer.asee.org/40766
DO  - 10.18260/1-2--40766
ER  -