Category Archives: Learning and teaching

Webtools for math teaching

This semester I’m using Gradescope for homework and exam grading. It is working relatively well, although not perfectly. This enables us to reuse feedback, makes it easy for me to review regrade requests, and gives us access to all student work in the course.

For our discussion board, we’re using Piazza, mainly because it’s easy to type in the math via their built in Latex.

Online homework, via Webwork, forms a portion of each homework assignment. These are mainly exercise type questions so that students can receive immediate feedback on whether they are applying procedures properly.

I am curious to take a look at iMathAS at some point. Webwork has a nice bank of questions from the text our course is aligned with, and there is some convenience to that, but it seems worth checking out other options.

Reading “Student learning objectives and mathematics teaching”

I am working to write learning objectives for multivariable calculus this Fall. This article helped distinguish between overarching goals (that students are able to fit the math in the course into a greater understanding of math and of the world) and the learning objectives, of what I hope students will be able to do mathematically after taking the course.

Thinking about goals reminded me that, as in all classes, learning to learn within a disciplinary setting is a goal I think is important. In addition, specifically for multivariable, there is a real potential to start seeing the world through the lens of the course. Thinking about wind as a vector field, about falling leaves via flux, and about everyday shapes via the functions and parameterizations of the course is a possibility. The article also brought up history as a possible goal. I have not actively worked to situate the math we learn within the history of mathematical problem solving, but it is something I would like to learn more about in the longer term.

Reading “Statistics Done Wrong”

While discussing course design for our mathematical modeling course in the Spring, my colleague recommended paging through Statistics Done Wrong. I find the book’s description of the p-value useful: “A p value is … a measure of how surprised you should be if there is no actual difference between the groups, but you got data suggesting there is. … I can get a tiny p value by either measuring a huge effect – ‘this medicine makes people live four times longer’ – or by measuring a tiny effect with great certainty.”

The author explains statistical power via a coin-flipping example. Given some number of coin-flips…

Random – to look up: hedonic treadmill.

Reading “Mental Maps and Learning Objectives: The FAST-SLO Algorithm For Creating Student Learning Objectives”

This article is focused on a method for writing student learning objectives for a course (SLOs). I find writing learning objectives challenging when working alone. They can be written at so many different levels of detail. Almost every example or question in a textbook has an implicit objective associated with it, so writing objectives can end up being a very long process. Finding more overarching, higher level, objectives seems important to be able to do because of how easy it is to lose sight of the big picture amongst reams of specific objectives.

According to the authors of the article (and other articles they cite) teachers often general learning objectives in real-time, while teaching. To aid pre-planning, they outline a technique for generating SLOs. Some notes on the SLOs: if students meet them, they should be able to solve multivariable problems at the level of the course, similarly to the way a more trained-mathematician would.

In the FAST-SLO method, I will first list a bunch of thoughts, ideas, concepts, and topics that I associate with some topic in the course. This is all about massive idea generation. I will also try to map these so that they are getting connected up. After creating the “FAST” via this thought-generation phase, I will be creating just a few SLOs.