"Math mini-modules" to support and focus quantitative class activities

Megan Kelly, Arrupe College, Loyola University Chicago

I frequently ask students to work with numbers during class in one way or another. I have often operated under the assumption that students are skilled with the basic mathematical operations I ask them to do and mainly need instruction regarding how those operations are connected to the science content at hand, or perhaps about technical skills like using spreadsheet software. My goal for students was to master the disciplinary content at hand, by using the relevant mathematical skills. Recently, I realized that improving fluency with numbers that describe the physical world could stand on its own as an incredibly important goal for my class. Simultaneously, I realized that my assumption of students' comfort with mathematical operations is frequently an erroneous one.

I have a new goal of identifying quantitative skills that students will be able to use in their communities and their lives, and giving as much importance to those skills as I do to disciplinary content. For example, I used to think that teaching unit conversions, dimensional analysis, and significant figures in introductory, non-majors coursework was a tedious and unproductive way to spend class time, based on my experience as a student of learning those skills in a vacuum, disconnected from the disciplinary content of the courses in which I learned them. So, for the 3 years I've been teaching this course, I have neglected those topics.

I changed my mind this year when I answered for the umpteenth time the question, "how many decimal places should I keep?" I believe that teaching significant figures will improve students' skills with measurement (important for the second course in the sequence) and perhaps estimation. Teaching significant figures will necessitate teaching scientific notation. Teaching scientific notation should allow for productive discussions of scale. I also believe teaching scientific notation will open up teaching unit conversions, which I expect to improve student skills with simple mathematical modeling. Teaching unit conversions in a structured way should decrease the amount of time I spend coaching students with them during activities that use simple unit conversions, and should dovetail nicely with teaching dimensional analysis.
To improve student success with quantitative tasks, I hope to develop a series of math mini-modules that can be inserted into many content areas. For example, I often use the HHMI Biointeractive activity on coral bleaching around the globe (https://www.hhmi.org/biointeractive/coral-reefs-and-global-warming). Students examine sea surface temperature over the maximum monthly mean at coral sites around the world, and estimate the number of degree heating weeks (cumulative degree-weeks above the maximum monthly mean in a season) by finding the area under the curve. This term, instead of asking students to do the activity on Excel and visually count the "boxes" that form a degree-week, I gave a short, interactive presentation on Riemann sums, gave the students printed copies of the graphs, and asked them to count the degree-week boxes uses pen and paper. Students finished this activity much more successfully than in previous terms, leaving time for a deeper conversation about global patterns of coral bleaching.
I hope to create similar "math mini-modules" covering additional quantitative reasoning skills, in a way that be applied to a variety of disciplinary content. For example, a mini-module on scientific notation could support course content related to measuring distance. In fact, a recently published case at NCCSTS on the metric system and skin cells would be an excellent fit for such a mini-module in an introductory biology class. Additionally, I would like to locate and examine datasets from urban environments for potential classroom use, as I expect that working with local data would be compelling for students. I also believe that working with local datasets could help students view their city or neighborhood as being part of the environment.

Downloadable version of this essay

Megan Kelly EDDIE workshop essay (Microsoft Word 2007 (.docx) 15kB May2 19)
Riemann sum mini-module (PowerPoint 2007 (.pptx) 148kB May2 19)