Classroom connection for Jan 25, 2025
Content ideas and data for math and statistics classes
Classroom connections are less something you can apply right away and more of me pointing out resources. I believe that there is a lot of amazing math, statistics, and data out there that might be used in math classrooms and is also intriguing to the curious. At the same time, the next time someone asks what math is used for, well, here are a bunch of examples.
Some of these examples may require some effort to be classroom-ready, and some of this has appeared in previous posts. I’m ordering this roughly based on the level of math. Please let me know if you or someone you know uses any of this in the classroom or has a relevant idea (email me at thomas.pfaff@sustainabilitymath.org). Really, leave a comment (if nothing else, your feedback is encouragement for me to keep doing this) or send me an email if these classroom connection posts are useful. Similarly, if you have an opinion or concept that is relevant, please share it in the comments. Please share, like, subscribe, and feel free to comment.
Interpreting confidence intervals
This comes from the article Projected Impact of Replacing Juice With Whole Fruit in Early Care and Education (Feb 2025) in the Journal of Preventative Medicine. The calories are the difference in nutrition by replacing juice with apples. Understandable for students in intro stats courses.
Confidence intervals and hazard ratios in a graph
Another artifact that could be used in an intro stats class is from the article Mortality from external causes in late adolescence and early adulthood by gestational age and sex: a population-based cohort study in four Nordic countries (11/4/2024). There are other graphs in the article that could be used.
Caption: Adjusted hazard ratios (HRs) of external causes of death according to country, sex, and gestational age at birth. Adjusted for age, birth year, birth order, maternal age, and highest parental education at birth. For Swedish data, maternal education at birth was used as paternal education was not available. HRs (squares or diamonds) with 95% confidence intervals (error bands). HRs for gestational age and sex categories with < 5 deaths are not shown. For confidence intervals expanding the range 0.44–4.0, the full interval is not shown, as indicated by arrows. All estimates can be found in Additional file 1: Tables S2–S5. Note that the y-scales are logarithmic
Interpreting regression
The article (with an unfortunate title, as the data really has nothing to do with Trump) The Trump Bump: The Republican Fertility Advantage in 2024 (12/19/2024) provides this and other graphs. The nice thing about this graph is the extra information to have students interpret related to the color of the dots.
Spatial interpolation
For those interested in GIS or environmental stuff, we have Quantification of record-breaking subsidence in California’s San Joaquin Valley (11/19/2024)
Modeling
This might be suitable as a student project or independent study from the paper Walk this way: modeling foraging ant dynamics in multiple food source environments (9/12/2024). The screen shot below will either get your attention or not.
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Comments
Please let me know if you believe I expressed something incorrectly or misinterpreted the data. I'd rather know the truth and understand the world than be correct. I welcome comments and disagreement. We should all be forced to express our opinions and change our minds, but we should also know how to respectfully disagree and move on. Send me article ideas, feedback, or other thoughts at briefedbydata@substack.com.
Bio
I am a tenured mathematics professor at Ithaca College (PhD Math: Stochastic Processes, MS Applied Statistics, MS Math, BS Math, BS Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks “R for College Mathematics and Statistics” and “Applied Calculus with R.” I welcome any collaborations.
I would have a couple issues with the "Confidence intervals and hazard ratio" graph.
Putting confidence intervals side-by-side as they are invites interpretation of whether they overlap or not, which is usually not how you would compare the estimates. (You would look at a confidence interval of the difference of the two quantities, not the difference of the confidence interval.)
Also, the side-by-side dodging when the x-axis has a quantitative meaning is misleading.
Not sure if that's helpful. The graph caught my eye because I remember confidence intervals being one of the hardest concepts to get across during my short stint as a graduate teaching assistant.