IOLA-X: Experiencing Linear Algebra through Inquiry-Oriented Activities
By Jana Talley, DUE Point Co-Editor, Jackson State University
Inquiry-Oriented Linear Algebra Extended (IOLA-X) is the continuation of a collaborative curriculum design project that began over a decade ago. During the first IOLA project (NSF DUE #1245673/1245796/1246083), the instructional design theory of Realistic Mathematics Education (RME), which frames mathematics as a human activity, was employed to develop activities in which students engage in an experientially real task that the instructor can leverage towards a guided reinvention of key ideas. The current team, consisting of several graduate teaching assistants and faculty researchers from a variety of institutions, has developed problem-based instructional tasks for concepts typically introduced through lecture-based approaches in Linear Algebra. In the current project, they are working to increase the amount of IOLA resources available for in-class instruction as well as create and implement a new curriculum research tool known as the Design Research Spiral. The faculty researchers leading IOLA-X shared with us how their materials function as a rich resource for teaching and learning linear algebra in new and innovative ways.
Tell us how IOLA-X extends on the original IOLA project.
In the first IOLA project several members of this team collaborated to develop three units of inquiry-oriented instructional materials for an undergraduate course in Linear Algebra. These materials include tasks that position students to uncover key ideas through their activity rather than apply already formalized concepts to a task. By the end of the current IOLA-X project, we will have task sequences and instructor support materials for each of the following:
a. Vector Operations, Linear In/Dependence, and Span
b. Systems of Equations
c. Matrices as Linear Transformations
d. Determinants
e. Subspaces
f. Eigentheory
g. Least Squares Approximations and Projections
2. Please explain how you chose the content areas and context for the instructional units.
We chose the content areas based on needs identified by experts in mathematics education research, our experience with common topics on course syllabi, and content that education researchers call “experientially real starting points” for students to engage in problem-based instruction.
3. What would you like to share about the development and implementation of your design research spiral that other educational researchers should know?
In addition to the inquiry-oriented tasks, we developed the Design Research Spiral as an innovation in curriculum design research. The spiral consists of 5 phases: (1) initial task sequence design, (2) Paired Teaching Experiments, (3) Classroom Teaching Experiments, (4) Online Working Groups of implementing instructors, and (5) web publication. Each phase is an opportunity to refine the tasks to better support student learning and instructor implementation. We see this process of shifting one’s theoretical and methodological perspective in response to the phenomena under consideration as not only a vital component of broadening our activities from one stage of design to another, but also an effective approach to education research in general.
4. How has the use of IOLA-X materials transformed classroom experiences?
Instructors shared that though they were apprehensive, “students took to it very quickly” and “they seemed to have higher levels of engagement.” Their students are independently internalizing ideas that they generally struggle with. They went on to say that “Even though the material doesn't align with our department wide syllabus, my students do better than average on the common exam.” Additionally, students are choosing to enroll in the IOLA-X sections of their linear algebra course offerings. This has helped the participating instructors become more acquainted with their students. One such instructor emphasized that “I've found the material to just be more fun than traditional lectures…Teaching these units varies my work, and keeps me engaged. I look forward to using IOLA materials for years to come.”
5. Tell us about the team members who have contributed to the development of the IOLA-X project.
The IOLA-X project has benefited from a group of bright, hardworking graduate research assistants (Matt Mauntel, Jessica Smith, Inyoung Lee, Minah Kim, Mark Watford, Zac Bettersworth, Isis Quinlan, Matt Park, and Shelby McCrackin) who developed curricular materials. As evidence of how meaningful our collaborations can be, one former IOLA graduate assistant, Dr. David Plaxco (Clayton State), is now a Co-PI of the IOLA-X project along with Dr. Megan Wawro (Virginia Tech), Dr. Michelle Zandieh (Arizona State), and Dr. Christy Andrews-Larson (Florida State).
6. What would you like to share with instructors who are interested in these materials and would like to access them?
The tools provided through IOLA-X include (a) the inquiry-oriented task sequences, (b) rationales and learning goals for each task sequence, (c) samples of student work, and (d) suggestions for implementation. For students, the plethora of instructional support materials create an environment in which students develop robust conceptual understanding, enhanced interest in mathematics, and a sense of belonging in mathematics classrooms.
The project website (iola.math.vt.edu) already has three full units and some supplemental materials. We are working to add the new units to the website. Any linear algebra instructor is welcome to request an account on iola.math.vt.edu for free access to all IOLA materials, including all the implementation support materials.
Learn more about NSF DUE (#): 1915156
Full Project Name: Collaborative Research: Extending Inquiry-Oriented Linear Algebra
Abstract Link: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915156
Project Contact: Megan Wawro; mwawro@vt.edu