Omaha, Thursday, Feb 22, 2024
Fostering Mathematical Exploration and Conjecture in Linear Algebra Using Digital Worksheets
Organizers: Ryan Peffer: ryan.peffer@wsu.edu, Judi McDonald: jmcdonald1@wsu.edu, Sepideh Stewart: sepidehstewart@ou.edu
Linear algebra is a subject rich with opportunities for students to engage with novice-accessible proof and formal mathematics that might otherwise be new to them. We wish to develop a core community rooted in mathematical practices of observation, conjecture, and proof. In this workshop, we will leverage technology for the purpose of facilitating experimentation with linear algebraic objects, particularly matrices. Going beyond purely visual ideas and references in 2D and 3D space requires a more algebraic treatment and understanding of these objects. The overall goals include: (a) illustrate using rectangular arrays as a visual source of intuition and insight; (b) implement a set of digital linear algebra worksheets to place student cognitive load on linear algebraic ideas; and (c) collaborate with participants to create strategies and refinements for the design and implementation of digital worksheets and how to assess student thought processes. We will employ an adaptation of Tall’s three worlds of mathematics as a theoretical framework for our workshop.
Please bring a device with the Wolfram Digital Player installed, available for free at https://www.wolfram.com/player/
Schedule for Working Group
| Timeline | Activities | Working Format/Responsible Person |
| 15 min | Introduction | The organizers will give a brief overview of their research. Participants will introduce themselves. |
| 20 min | Talk | Ryan Peffer – 5 years of use of technology in RUME proceedings |
| 35 min | Talk + Group Discussion | Judi McDonald +Sepideh Stewart The embodied world of linear algebraAudience feedback/questions on previous ideas and open discussion |
| 30 min | Group Activity | Give attendees a Mathematica worksheet to experience an array-focused linear algebraic embodied world to observe patterns and make conjectures |
| 15 min | Break | |
| 30 min | Demonstration + Talk | Ryan Peffer + Judi McDonald – demonstrate and discuss worksheet activity (what did you experience? why did we create these, our experiences, some potentials and criticisms) |
| 30 min | Open Discussion | Sepideh Stewart- What technologies are participants using in the classroom? What ideas/thought processes are those technologies engaging? |
| 10 min | Break | |
| 30 min | Open Discussion | Judi McDonald – Retaining knowledge What linear algebra foundations do students need in order to be prepared for interacting (understanding, using, developing codes, etc.) with modern applications, subsequent Math or other classes? |
| 15 min | Closing Remarks | Closing remarks and future works, come to research talk by Ryan Peffer for linear algebra student perspective on digital worksheets |
