Your Mission Should You Choose To Accept It: How a Futuristic Narrative Framework Helped to Increase Math Discourse and Engagement in an Online Undergraduate Course

Concurrent Session 8
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Brief Abstract

Using a futuristic video narrative, two professors and a learning design team created a course that challenged students to apply mathematical concepts as a means to save the world. Presenters will highlight the specific design decisions from the perspective of the learning design team and the faculty. 

Presenters

Judy Lewandowski serves as the Director of Learning Design and Curriculum at the University of Notre Dame. In this role, Judy leads a team of designers to work with faculty to create effective courses, programs, and new modalities of learning. Prior to arriving at Notre Dame in 2018, Judy was a professor at Purdue University in the Learning Design and Technology graduate program. Judy has 20 years of experience in teaching and designing courses in higher education. She has held roles as a corporate instructional design consultant, faculty member at Indiana University, outreach coordinator for the Center for Research in Information Assurance and Security (CERIAS) at Purdue University, and as an evaluator for the Department of Education. Judy holds a Ph.D. from Purdue University in Learning Design and Technology.
Kuang-Chen (Kuang) Hsu is a senior. learning designer at Notre Dame Learning (ND Learning) where he works in partnership with faculty to create transformational learning experiences at Notre Dame through research-based strategies, technologies, and modalities. Prior to joining ND Learning, Kuang served as a design director at ABen Tech in Taiwan. He completed his Ph.D. in educational technology at the University of Kansas in 2016.

Extended Abstract

It all started with a story.  Two professors and a learning design team decided to tackle the issue of increasing mathematical discourse and student engagement in online math courses.  Their solution was twofold. First, they created a futuristic video narrative that challenged the students to apply mathematical concepts as a means to save the world. Secondly, they designed a course that offered synchronous conversation opportunities and just-in-time resources to aid in the translation of the language of math.

The Importance of Mathematical Discourse

In 2014, the National Council of Teachers of Mathematics called for the infusion of teaching practices that “facilitate discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments” (NCTM 2014, 23)   Increased mathematical discourse has benefits for both students and instructors (Katt et al, 2018). For students, discourse provides an opportunity to reflect on their own understanding while learning from the perspective of their peers. For instructors, discourse provides a mechanism to assess and extend their students’ mathematical understanding. The unique challenge of this design opportunity was in creating a framework that promoted this type of discourse in an online setting.

Using Novelty to Increase Situational Interest

Motivating students to talk about math can be a challenge in a traditional classroom; this challenge is amplified in an online environment. Inherently, the perception of interest is tied to the individual student, but findings suggest that the selection of content and increased engagement can be linked to the development of situational and individual interests (Hidi & Renninger, 2006).  Students who are intrinsically interested in an activity are more likely than students who are not intrinsically interested to exert effort (Downey and Ainsworth-Darnell, 2002; Miserandino, 1996), and learn at a conceptual level (Ryan, Connell, and Plant, 1990). Intentional course design that includes challenge, choice, novelty, fantasy, and surprise can increase students’ situational interest (Malone and Lepper, 1987).  For this course, the infusion of a novel approach (video narrative) was selected as the main strategy to influence discourse. 

Synchronous Sessions for Discourse

The development of the learning environment also has an impact on the level of discourse.  A learning environment in which concepts and material are presented from a growth mindset can increase the self-efficacy of students and thereby increase their willingness to participate in the discourse (Dweck, 2006).  When mathematical content in a course is framed as an open growth subject, students respond with an increased sense of motivation and perception of interest (Boaler, 2016). For this course, a biweekly synchronous session schedule (two times per week) was built into the course design to allow for discourse between the students and the instructor. The storyline of the video narrative was written to create a problem that could be viewed from multiple perspectives.  This open-ended approach links with the principles of growth mindset: difficult situations can be viewed as opportunities to experiment to find solutions. Breakout rooms were used to provide opportunities for student-student sessions and collaboration tools were used to allow for instructors to offer a conversational approach to the ‘worked’ examples. 

As students discussed the challenges, linked to a shared narrative example, they were able to engage with their peers and instructors in a way that went beyond a standard asynchronous approach common in online formats.  The novelty of the narrative increased the engagement level of the students in alignment with Boaler’s findings in 2016:

“Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people. Teachers can create such mathematical excitement in classrooms, with any task, by asking students for the different ways they see and can solve tasks and by encouraging discussion of different ways of seeing problems.” (p.59)

Creating Audio Tools to Translate the Language of Mathematics

And, lastly, a major hurdle to increasing discourse in mathematics is linked to the language of math.  Faculty observations led to the conclusion that some students are hindered in participating in classroom conversations simply because they do not know how to speak the language of math.  They hesitate from asking questions or making a statement because they are not sure how to translate a visual image (equations, symbols, etc.) into a verbal statement. Developing the language of a subject (mathematics in this case) requires students to engage in practicing and using its discourse (Duschl and Osborne, 2002, p. 40).  A just-in-time solution to this issue was built into the design of this course. An audio library was developed that offered students a chance to listen to the pronunciation of common mathematical terms and notations. The faculty members read the equations to present the format and nuance of the language of math.

Session Focus

This session will document the design decisions behind the transformation of this course from a traditional lecture to a dynamic and interactive online learning environment for non-math majors.  The presenters will trace this design process including the context, theory, and implementation experiences that shaped the design and discuss unforeseen obstacles and design alterations that arose during this process. Through a Case Study approach, presenters will highlight the design process from the perspective of the learning design team and the faculty.  Specific strategies will be shared including audio tools for increasing mathematical understanding, framing a course for discourse, and the steps involved with developing a dynamic video narrative. Additionally, we will offer insight into opportunities for future iterations and applications.  

Audience Engagement 

To engage the audience, we will integrate interactive elements throughout the presentation.  For example, we will use an interactive strategy to quiz the audience to select the most accurate pronunciation of a Linear Algebraic equation.  After listening to three distinct options, the attendees will use Poll Everywhere to select the correct response. This strategy offers attendees insight into the difficulty that learners can face as they attempt to transition from the written to the verbal language of math.  

Following our presentation, we will offer an opportunity for attendees to contribute responses via PollEverywhere to the following questions.  A follow-up discussion on each will complement the anonymous responses: 

  • This course relies heavily upon a video with professional quality media production.  How could this be replicated in an alternative format?

  • Is it possible to capture the essence of the synchronous session in a different format?  Does anyone have a strategy for replicating the spirit of this discourse in an asynchronous manner?

  • Literacy enables learners to fully participate.  In addition to math, what other subjects or topics might benefit from a clarification of the language / nomenclature?

 

Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey Bass.

Downey, D.B., and Ainsworth-Darnell, J.W. (2002). The search for oppositional culture among black students. American Sociological Review, 67, 156-164.

Duschl, R.A., and Osborne, J. (2002). Supporting and promoting argumentation discourse in science education. Studies in Science Education, 18, 39-72

Malone, T.W., and Lepper, M.R. (1987). Making learning fun: A taxonomy of intrinsic motivations for learning. In R.E. Snow and M.J. Farr (Eds.), Aptitude, learning, and instruction: Cognitive and affective process analysis (vol. 3, pp. 223-253). Hillsdale, NJ: Lawrence Erlbaum Associates.

Miserandino, M. (1996). Children who do well in school: Individual differences in perceived competence and autonomy in above-average children. Journal of Educational Psychology, 88, 203-214.

S. Hidi, K.A. Renninger The four-phase model of interest development Educational Psychologist, 41 (2) (2006), pp. 111-127, 10.1207/s15326985ep4102_4

Ryan, R.M., Connell, J.P., and Plant, R.W. (1990). Emotions in non-directed text learning. Learning and Individual Differences, 2, 1-17.