This is part 4 in a series for educators who want to go from "perfectly adequate"  online instruction to excellence, one step at a time, as we move from a forced migration to online teaching toward a more intentional approach in later semesters. Here's part 1, part 2, and part 3.

So far in this series, I've argued that the first steps we can take toward excellent online teaching are structural, not necessarily technological or pedagogical. Our online teaching is only as effective as the fundamental underlying structure of the course design. In the first three articles, I laid out this basic backbone of a well-designed course:

If your body's backbone isn't aligned with itself properly, every physical movement you make is going to be constrained and painful. So it is with this structural backbone of a course. If course activities are out of alignment with the learning objectives, or the assessments with the activities, then no matter how good we are at the course technology or communicating with students, the limitations of the underlying structure will impose upper limits on the effectiveness of student learning.

# Alignment of materials and tools

The next step in improving online teaching also has to do with alignment:

Step 4: Align the tools and instructional materials used in the course with the learning objectives in the course.

Instructional materials, in the words of the Quality Matters rubric, refers to anything that "provide[s] the information and resources learners need to achieve the stated learning objectives". This includes textbooks, videos, slide decks, websites, and interactive content. It's the source material that students have at their disposal.

Tools, on the other hand, refers to software and other applications, used  to deliver the materials to the students or enable student interaction with the materials or with other students. This includes the LMS itself, discussion boards, chat platforms, computational tools like Jupyter notebooks or Wolfram|Alpha, video hosting services, quizzing or polling tools, even the gradebook.

Selecting materials and tools is often the first step that instructors take. We've all been there; I've followed countless threads on my discipline's discussion boards that start with, I'm teaching Differential Equations in the Fall; anybody have good textbook suggestions for me? And I'm guilty myself of getting enamored with a tool and using it as the starting point for my course, and building the learning objectives around that. Step 4 says that this is backwards; it is an injunction to keep student learning first and pick the tools and materials that serve the learning objectives.

## Aligning learning materials

Aligning materials with objectives just means that the learning materials should be chosen specifically and primarily to help students achieve the objectives in the most direct way possible. So begin by reminding yourself what the learning objectives are, and then pick learning materials that will make the pathway to mastering those objectives as straight and continuous as possible for the students.

There's a subtle detail in this, though: Because well-written learning objectives are about tasks that students do and are anchored in action verbs, materials that are well-aligned with those objectives should invite and promote active learning. All other things being equal, a learning material that encourages students to actively engage with ideas and reflect on that activity is automatically more aligned with clear, measurable learning objectives than one that does not.

Let's try out an example, using the Calculus course I've been describing in the previous posts and the module on derivatives of basic functions. Recall that I set up the following learning objectives for this module:

Correctly use the alternative $dy/dx$ and $d/dx$ notation to take and express derivatives.
Compute derivatives of constant, power, and exponential functions including the function $f(x) = e^x$.
State the Power Rule, Constant Multiple Rule, and the Sum Rule.
Apply the Power, Constant Multiple, and Sum Rules to compute derivatives of combinations of constant, power, and exponential functions, including polynomial functions.
State the derivatives of the sine and cosine functions.
Use the rules of Section 2.1 to compute the exact values of the slopes of tangent lines to the graphs of functions (constant, power, polynomial, exponential, sine, and cosine as well as combinations of these), the rates of change in functions, and the second derivative of functions.

With those objectives in mind, I ask, What materials will provide the clearest and most helpful information and resources for students to achieve these objectives?, and Do those materials invite and promote active learning?

My first thought goes to a textbook. I've taught Calculus many, many times and have seen a lot of Calculus textbooks. I have to say that the vast majority of those books are poorly aligned with my learning objectives, for one of two reasons:

1. The book puts a ton of stress on topics and concepts that are not in my learning objectives list, while failing to sufficiently stress concepts that  are in my learning objectives; or
2. The book doesn't invite or promote active learning as much as I want.

This is the case for some cherished books like the Stewart Calculus textbook and the dozens of other textbooks that are isomorphic to it. For example, Stewart puts a great deal of stress on $\epsilon - \delta$ definitions of limits; but that concept does not appear at all in my course. There is also very little intentional promotion of active learning in the book; it a traditional book that explicates concepts, gives examples, and then gives exercise sets. This doesn't make Stewart a "bad" book; it's just not well aligned with my learning objectives.

Much better aligned with these learning objectives are books that might not have the gravitas of a classic Stewart Calculus book but where I find a friendlier reception for my learning objectives. The Hughes-Hallett Calculus book is one such example. The book I currently use is my colleague Matt Boelkins' Active Calculus text, which is clearly written, infused with active learning, and fits my learning objectives extremely well. Also it's completely free, which has its own significant set of benefits.

With my calculus class, since so many of the learning objectives are about computing things, I'd want video content providing guided demonstration of computational techniques and visualizations of concepts. Several years ago I built a a YouTube playlist of the kinds of things that my students needed, and I still use it along with anything else I might find on YouTube that seems to be helpful.

Often I will supplement the book and video content with spot-requests from students; for example if students are having trouble remembering the values of sine and cosine at the major angles, I might give them a unit circle chart to use.

Here are some examples of poorly-aligned materials that I might, but shouldn't, choose:

• Any of the textbooks I mentioned above that don't hit my learning objectives directly or don't promote or invite active learning.
• Giving something like Steven Strogatz' Infinite Powers book, or even parts of it, as an assigned reading. Let me be clear: Steven's book is really great and well-written --- but it's not a great fit for my  learning objectives. We have to beware of the trap of adding More Stuff into a course, online or otherwise, just because we like the Stuff. Does this Stuff provide the information and resources learners need to achieve the stated learning objectives or competencies? If you can't say without hesitation that it does, leave it out, or make it optional. Online courses have to stay lean and simple or we risk losing students. (You could add a learning objective, like "Describe applications of calculus to contemporary problems", and suddenly Steven's book could be a really good choice. But this might become another case of adding More Stuff into the course, so weigh that option carefully. "More" is not necessarily more.)

## Aligning course tools

Course tools should similarly support learning objectives and not be introduced or used for their own sake. There should be a clear connection between the tool and the learning objectives, along with clear instructions on how to use the tool and clear explanations of how the tool should be used to achieve the learning objectives. And just like materials, tools should invite and support active learning.

Oh, how I am guilty of violating this in the past. I love tech tools and have a very difficult time restraining myself from using my classes as a beta-testing environment for interesting technology. I used to get student comments at the end of the semester complaining that I use "too many websites" in the class and my thought would be What a bunch of Luddites. But later I realized that students had a point. When I roll out a bunch of tools with no clear purpose or connection to the learning objectives given, even just a handful is "too many" because the tools add to the students' cognitive load rather than subtract from it, which is what a tool is supposed to do.

I tend today to keep tools to an absolute minimum, and choose carefully for tools that are useful and are easily accessible. These include:

• The course LMS, which is almost not a choice at all but a must-have. I've tried minimizing my use of an LMS in the past and shifting most of the LMS functionality over into Slack, with decidedly mixed results. I've come to realize it's better to use one tool that students are familiar with, even if it kind of sucks, than use two that don't suck.
• The exception to the previous point is discussion board tools, which suck so badly on our LMS that I consider them unusuable. So recently I've farmed out all online class discussion and group work to CampusWire, which blends the orderliness of a threaded discussion board with the spontaneity of a chat program.
• Wolfram|Alpha for all symbolic computation (a big part of the learning objectives) and Desmos for graphical work.
• Polling software to do peer instruction, because this is really effective for working with conceptual objectives, and because students like it. PollEverywhere has been my go-to because of its excellent LaTeX integration for math typesetting.

My students also do a lot of written work, and I don't specify a tool for this. I have some tutorials set up for how to use Google Docs for typesetting mathematics and some links on the LMS for how to use Word. Anything else is up to the students.

In the past I'd also used tools like FlipGrid, hypothes.is, Perusall, Turning Point clicker devices (kind of a non-starter for online classes), and many many others. And I may use these again if -- and only if -- my learning objectives call for it.

But you can generate a lot of bad examples of tool use simply by imagining situations where the tool is used for its own sake, or without a clearly-described connection to the learning objectives, or without clear instructions on how to use the tool to achieve the learning objectives. In  fact, I do not provide clear instructions on how to get the most out of CampusWire to achieve the learning objectives in the course; this is something I'll need to improve for the Fall.

Once Step 4 is completed, we will have a course where the learning objectives are clear and measurable and always in view, no matter what part of the course the learners are thinking about at the moment. That helps learners keep perspective and understand the "why" behind what they are doing, and that makes the course powerfully effective.

Next time we'll step away from learning objectives and think about the infrastructure of the course: The calendar, syllabus, LMS and other core tools and materials, and how to build these for maximum value for learners.