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Adaptations for the COVID era

Engaging underprepared students

First clarify what they are underprepared *for* : not just new emotional challenges, but "how much harder and more demanding college work will be." Transitions are difficult, especially in going from high school writing to college writing. Take the time to list explicitly the old habits they should give up and the new habits they should embrace.

Explain early and often how the skills in your class will be used. If students can see the transferrability of skills they practice in your class, they will dive into their assignments with more enthusiasm and less reluctance.

Model critical thinking. Give students a reading guide listing things they might not know to look for on their own.

Overcoming the inhibitions that keep students from speaking up in class or coming to office hours:

Mandatory participation (quota for each student)
Explicitly point out the value of wrong answers too.
Not answering at all only reinforces a student's acceptance of powerlessness, invisibility.
Be sensitive to some students' expectations that their contributions won't be recognized.
Greeting students individually as they enter the Zoom meeting will help them feel like they belong.
Inviting students to come in pairs makes office hours less intimidating.

The 20-year question

What do you hope students will keep from your class after 20 years (when they're living *their* lives)? Certainly not something so specific as the loan amortization formula, or integration by parts?

The most durable memories are of how a teacher made them *feel*. Therefore, ask yourself whether the activities you have them do in your classroom are likely to result in *changed attitudes*:

A sense of joy and success rather than their opposites.
A growth mindset throughout their lives.
Persistence in the face of challenges.
Ability to work for a longer period of time on a question (Sitzfleisch).

What features can you put into the day-to-day classroom experience to foster these attitudes? The typical student does not witness *teachers* struggling to wrap their heads around complex ideas, even though a real scientist/mathematician doesn't spend most of her time going from success to success. Aim to demonstrate that a problem can be worked on productively even when the route to a solution is not known.

In the same vein, the goal of mathematical discourse should not be to introduce ideas with the same polish as a textbook presentation. Less precise, everyday language is friendlier. If the imprecision of an opening statement leaves room for confusion, all the better! The questions that emerge out of that confusion will illustrate the joy of figuring things out.

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