Building Calculus: Materials

Building Calculus: Materials

It's now under three weeks until Fall semester starts for us, and despite the uncertainties of what's coming, my courses are beginning to come together. (Or, at least it feels that way; I've been wrong about these feelings before.) So far, I've written about the framework and modality for my Calculus course, the learning objectives, the learning activities, the assessments, and the grading system. In the next couple of articles, I'm going to focus on facets of the course that seem mundane but have profound impact on the other components, starting with the instructional materials students will use.

What do I mean by "instructional materials"? Here, and in all the other posts in this series, I'm keeping one eye on the Quality Matters rubric for online courses in higher education. Quality Matters (QM) is an organization that provides training for and evaluation of online and hybrid courses. This includes a certification process in which online/hybrid courses are submitted for review, then a team of reviewers combs through the course using a 42-item rubric in which every aspect of the course β€” from high-level learning objectives to the structure of the course home page β€” is scrutinized. Β The course is scored out of 100 points using this rubric, with each item carrying between 1 and 3 points. There's no partial credit. Courses must have a final score of at least 85 to be QM-certified. According to the QM rubric, instructional materials...

may include but are not limited to textbooks, Open Educational Resources, publisher- or instructor-created materials, slide presentations and interactive content (such as simulations), expert lectures, videos, images, diagrams, and websites.

There's a difference between instructional materials and course technology, which I'll write about next week. Here, we're looking at the raw material we give students to enable their learning, not the mechanism by which we deliver it or enable active learning around it. A video is an instructional material whereas YouTube, for example, is just one of many tech tools to connect students to that material.

Instructional materials and learning objectives

The QM rubric devotes an entire section β€” 12 out of the 100 points β€” to instructional materials, and there are two particular items in the rubric that are 3-point items, which means they are essential standards. These must be satisfied by a course, or else the certification process is halted:

4.1: The instructional materials contribute to the achievement of the stated learning objectives or competencies.
4.2: Β The relationship between the use of instructional materials in the course and completing learning activities is clearly explained.

This partially explains the order in which I've engaged in this building process. We start with the learning objectives, then build the learning activities, then (after assessments and the grading system) select the course materials so that the materials align with the learning objectives and activities.

"Alignment" is an important word in the QM rubric, and it means what it says: arrangement in a straight line, or in a position of agreement. We are to pick our learning materials so that there's a direct line of sight from them back to the learning objectives and to getting the learning activities done.

It's helpful to think about what a misaligned set of materials would look like. For example, if in a Calculus course there were a lesson on related rates problems, and I posted a video of funny cats that has nothing to do with related rates problems, or a video that is about related rates but which is poorly made (bad audio, poor explanations, etc.) then this does not help students complete learning activities involving related rates or to meet any learning objectives about them. Or, if I picked Rudin's blue book for my Calculus class because I like Rudin and wanted to look like a badass to my mathematical colleagues, this would be a bad choice because it from the students' point of view, that book makes no sense and doesn't help them attain my learning objectives for the course. (Unless "write complicated analysis proofs" is a learning objective, in which case I probably need to rethink my objectives.) It does nothing but add extraneous cognitive load. Instructional materials that are aligned properly, are the opposites of these.

Like a lot of other things in online course design, this is exactly opposite of the way I was brought up on how to get a course ready. My habit in the past was to pick the textbook first, then build the course around the book. The QM rubric is saying that this needs to be flipped: once the learning objectives and activities are chosen, you then pick the learning materials that make the most sense relative to them. That might be the textbook you were going to pick anyway; or we move through the book in a different order; or we cut out large chunks of the book; or maybe no textbook at all. The same goes for all the other forms of materials we might use.

Guiding principles for instructional materials

In choosing materials for my courses, I have a lot of choices (which is a luxury/curse that many colleagues elsewhere don't have). So I need to have some principles for guiding those choices:

  1. Use free/open source/OER materials whenever it makes sense. I'm not above having students pay for their books and other resources, but the quality and quantity of free/OER resources (at least in my discipline) these days is so great that it's frankly hard to justify. From a moral standpoint, especially in these days where students are struggling more than ever with finances and employment, it seems wrong to force students to pay for a book (or other materials) when there are free ones that might lack a little polish compared to professionally-published texts but which don't carry a $100+ price tag.
  2. Use a variety of media. There's nothing wrong with just a textbook, but one thing research in online learning has told us is that using multiple sensory channels improves learning and memory. Using instructional materials that involve video, audio, and kinesthetic (for example, interactive computer demos) activities in conjunction with a plain text book would be ideal.
  3. But not too much, because a fundamental principle of the upcoming Fall semester is the same as back in the spring: Keep it simple. It's way too easy to overload students' buffers with instructional materials in many different forms and thereby create decision paralysis. Pick only the best few forms of materials.
  4. Keep them connected to the learning objectives and activities. As the QM rubric suggests, the basic question to ask when I am auditioning a learning material is – Does it help students attain the learning objectives and complete the learning activities? If so, then I can keep thinking about whether it makes sense using the first three criteria above. If not, or if I'm going to need to spend a crazy amount of time remixing it so that it does align, then I should just drop it and move on.

Materials for the Calculus class

Here's a manifest of what I'm including in the Calculus class so far.

  • Textbook: Active Calculus by Matt Boelkins. Full disclosure, Matt is one of my colleagues in the GVSU Math Department and someone with whom I've worked closely for years, including giving some contributions to this book. I'll also say that I broke my own rules here because I always start by assuming I'll use Matt's book, rather than build objectives and activities and work backwards. That's simply because Active Calculus is such a good book, and it's freely available online, and it gets better every year with new additions, and because I know how Matt thinks about Calculus and that he and I think very much the same way about it --- that I know it will align with my learning objectives and activities. In fact many of my class activities are drawn directly from Active Calculus because it's full of activities and they are almost all outstanding. One of my favorite things teaching calculus is being able to send students the link above and tell them, "Here's the book – it's free."
  • Video content: The Calculus playlist at the GVSUMath YouTube channel. Also full disclosure: I authored most of these videos several years ago when I was converting Calculus to a flipped format. They aren't perfect; they are dated, some of them have mistakes, and although we recently fixed this for a large portion of the playlist, most of them are not captioned. But, students seem to get a lot out of them, and they help students attain the learning objectives (at least the lower-level ones that I expect students to complete before class) and I try to make activities that have explicit connections to the videos. Although, this is one thing I need to work on β€” clearly explaining that connection.

Side note: I often get asked by other profs whether it's OK to use those videos in their own classes. Yes, it's OK. They are licensed under a Creative Commons BY-SA 4.0 license, so copy, remix, redistribute, and build upon them as you will β€” but give attribution and don't restrict the license. (Check the license for details.)

  • Slide presentations, assignments, and other documents: Mostly Markdown and LaTeX documents. There's another part of the QM rubric that is all about accessibility, and when I was undergoing training this summer to become a QM peer reviewer I learned a lot about accessible documentation. I used to make my documentation in Google Docs because it was easy to share and archive and I liked giving student the ability to comment on documents. But this time, to address accessibility, I'm keeping these documents very simple by writing them in Markdown or LaTeX (which makes it a lot easier to meet the accessibility standards of the rubric) and then compiling them into different forms. For example the syllabus is written in Markdown, and I'll eventually use Pandoc to convert it into Word, RTF, and PDF formats β€” this way the documents will have a strong, platform-independent structure and will play nicely with assistive tech like screen reading software. (I can then post the Word document as a Google Doc and turn on comments if I want to.) For slide presentations, like this one that we'll do in week 3, at the moment I am using the LaTeX Beamer package to create PDF's of slides with nice mathematical notation and then distributing the PDF's on Blackboard.
  • Interactive content: Desmos Teacher activities. I've used the amazing Desmos online graphing tool for years, and it's become the standard tech tool for calculus for me. But only this summer did I start learning about interactive content that can be made, using Desmos as a platform. Briefly, Desmos Teacher activities allow me to create activities that involve interactive data and graphical tools and then observe student work as they work on them. Here's an example (created by Desmos, not me) that uses card sorting to help students learn about mathematical functions. I am converting a lot of my old Guided Practice assignments β€” formerly posted as text documents and completed using Google Forms β€” into these activities.

I should note that all of these materials listed are free or constructed using free software. Also, it's a variety of media but IMO not overwhelmingly so. And as always I am starting with the learning objectives and working backwards to the materials, not the other way around.

At this point, we're straddling the line between materials and technology since materials and the tech used to deliver them are often inextricable. Choosing tech tools has its own place in the QM rubric and the building process, and I'll write about that next time.

Robert Talbert

Robert Talbert

Mathematics professor who writes and speaks about math, research and practice on teaching and learning, technology, productivity, and higher education.