# Monday 4/3 – Recap of the midterm

### // Before class

• Recover from the midterm, catch up with anything you needed to

### // During class

• Get your midterms back
• Reminder of how to compute your grades
• Work in groups and class discussion to try to get to 100% mastery on all questions on the midterm exam

### // After class

• Read BOTH Section 3.1 (the Mean Value Theorem) and Section 7.5. In Wednesday’s class we will talk about the Mean Value Theorem and about some of the introductory material from Section 7.5, so Wednesday’s Daily Quiz will be something about that.

### // Looking to the final…

Remember that every midterm exam consists of some of the questions that could be asked from the material we covered. This means that, when you study for the final, it won’t be sufficient to only review the questions from the midterms.

To help illustrate this, here are just some of your answers to “What could have been on the exam, but wasn’t?”:

• Graphing Riemann sums
• Integral that is solved with the reverse product rule
• Other sigma notation questions
• Find the general Riemann sum of an approximation and then use sum formulas to compute it
• Approximate an area using the Trapezoid Sum
• Take the limit as n goes to infinity of a Riemann sum
• More questions on proofs that we covered (both geometric and algebraic)
• Upper and Lower Riemann Sums
• Using definite integral formulas to actually calculate a definite integral exactly
• Physics/velocity or data applications that use Riemann Sum approximations
• Questions about what definite integrals calculate
• The Horizontal Asymptote Theorem
• Proving the sum formulas or the other definite integral formulas
• Write an expanded sum in sigma notation, or vice-versa
• State the definition of the definite integral in terms of limits and sigma notation
• Proof that the definite integral of a sum is the sum of definite integrals

# Friday 3/31 – SECOND MIDTERM EXAM

### // Before class

• Study! While somehow also getting lots of rest the night before 🙂

• Rock it

### // After class

• Sleep/rest/relax

# Wednesday 3/29 – Midterm Review

### // Before class

• You should have completed all homework for Sections 7.1–7.4 and be ready to ask any remaining questions about those sections in class

### // During class

• Question time! Ask me anything

### // After class

• Study for the FRIDAY MIDTERM and get lots of sleep the night before!

# Monday 3/27 – More Indefinite Integrals

### // Before class

• You should have completed about 2/3 of the homework for Section 7.4 and be ready to ask questions about the harder questions in class

### // During class

• Daily quiz from a basic Section 7.4 homework problem
• Group work and discussion of the rest of Section 7.4 homework

### // After class

• Complete all remaining homework for Section 7.4 before Wednesday’s class
• Continue with your preparation plan for the MIDTERM ON FRIDAY

# Friday 3/23 – Indefinite Integrals

### // Before class

• You should have finished all homework for Section 7.3, and read Section 7.4

### // During class

• Daily Quiz on the reading from Section 7.4
• Discussion and group work on Section 7.4

### // After class

• Do the homework from Section 7.4. Here is a suggested minimum set of problems; you should do at least 2/3 of these before Monday’s class:
• Thinking Back – all problems
• Concepts – #0, #1, #2, and at least five more from #3–20
• Skills – At least 25 problems from #21–58 and 3 problems from #59–64
• Applications – At least 1 problem from #65–66
• Proofs – At least 2 problems from #67–75

# Wednesday 3/22 – Problems Day

### // Before class

• You should have completed all homework from Section 7.3, except for possibly a few lingering questions to ask in class today

### // During class

• Daily Quiz – One homework problem from Section 7.3 (you can copy it right out of your notebook)
• Questions!

### // After class

• Read Section 7.4 and take notes, to prepare for Friday’s Daily Quiz
• Catch up as needed
• Continue with your plan to study for the Midterm at the end of next week

# Monday 3/20 – More Definite Integrals

### // Before class

• You should have completed about 2/3 of the homework from Section 7.3 and be ready to ask questions about the harder problems in class

### // During class

• Daily quiz on something relatively easy from Section 7.3
• Discussion and group work on Section 7.3

### // After class

• Complete the homework for Section 7.3
• Figure out what you want to ask about during Wedensday’s Problems Day
• Be ready for a possible Homework Quiz on 7.3 during Wednesday’s Problems Day
• Continue with your plans for preparing for the midterm at the end of the month

# Friday, 3/17 – Definite Integrals

### // Before class

• You should have read and taken notes on Section 7.3

### // During class

• Bonus Daily Quiz on one homework problem from Section 7.2 (to reward you for doing homework)
• Daily Quiz on Section 7.3
• Discussion of Section 7.3

### // After class

• Do the homework from Section 7.3. Here is a suggested minimum set of problems; you should do at least 2/3 of these before Monday’s class:
• Thinking Back – all problems
• Concepts – #0, #1, #2, and at least five more from #3–20
• Skills – At least 5 problems from #21–28, 7 from #29–40, 4 from #41–46, and 4 from #47–52
• Applications – At least 1 problem from #53–54
• Proofs – At least 2 problems from #55–62

# Active learning & flipped class? Or “she doesn’t teach, we had to learn it all ourselves”?

It seems like people learn better when they know why the teacher does what they do, so today I’m going to write you this note about why I’m not teaching our calculus class lecture-style.

I used to lecture in my calculus classes. Every day, all class period. I think my lectures were pretty good and in fact one of the things I do outside of teaching is that I get invited a lot of places to give talks, and they seem to go pretty well. It was fun, actually, teaching class with lectures. And it was easy; lectures are completely predictable and very easy to prepare for. It was how I was taught so it seemed like the right way to teach. But some years ago, the mathematical community started thinking seriously about finding better ways to teach than straight lecturing, and as a result I tried “flipping” my classes, and never looked back.

Part of what “flipping” means (also called “Active Learning” or “Inquiry-Based Learning”, depending on how you do it and who you talk to) is that students do the easier parts of the reading before class, so that during class we can focus on clearing up more challenging questions and having students work together on problems in small groups. It turns out that hands-on active learning can be much more effective than passive lecture-watching; here’s an article from Science about it:

Of course, you know all about active learning because we’re doing it in class right now. And you might think that it is frustrating, difficult, or even awful. I know that you might think this because when I switched to active learning strategies about ten years ago, my student evaluations took a nose dive. I used to get all “Excellents” and suddenly I was getting a lot of really mixed reviews. This situation is pretty common with active learning; for example, read this article from Vitae:

The funny thing is, the most common complaint I got from unhappy students was that they would say “We had to learn everything ourselves, she didn’t teach us!”  This was usually followed by comments that implied I wasn’t doing the “work” of teaching/lecturing, but was instead making the students do all the “work” themselves in class.

Here’s why that’s funny: Because lecturing is SO EASY, while teaching an unpredicatable class in which you try to help six groups doing work on different blackboards come to a meaningful place and then somehow turn that into something to wrap up at the board for the class is not! As a teacher, it takes way more work and preparation to figure out what students’ groups should work on, how to handle random tangents and misunderstandings on the fly, and even how to make the basic logistics of the class work out. It’s also a lot more fun, so I’m not complaining; but I want you all to know that pulling off “students teaching themselves” is a hard trick, not a sign of laziness on the teacher’s part. In fact, on the very few class days here and there when I ended up spending most of the class lecturing, it’s actually because I couldn’t figure out how to make that day’s topic more “active” so I reverted to the tried-and-true lecture style for that lesson!

But none of that really matters, because the important thing is this: With active learning, I can help students every day in real time with their work and give them instant feedback. The students are learning MORE. Fewer students fall through the cracks and get left behind. And students learn how to DO things and TALK about things instead of just passively watching a lecture. They learn how to struggle and fight and actually figure things out, which is a much more permanent type of learning than the typical watch-repeat-forget cycle of passive learning. They learn how to learn things on their own rather than wait to be told. Yeah, how to “learn it all themselves”, even.

I don’t really care how high my evaluations are, but I do care about what people learn in my class, so to me the switch to active learning was a massive improvement. Nobody likes diets or budgets or walking up stairs but all of those things are good for you too, even if they cause people to complain. And again, I’m not the only one that thinks active learning might be worth a shot; here’s one more article, from The Conversation:

Of course, our calculus class is also frustrating, difficult, and yes, even awful for students simply because calculus is hard, and learning it is difficult however it happens. I just wanted you all to know that we aren’t just messing around in class or wasting our time; the time you spend confused, frustrated, and stuck on problems (and then, hopefully, getting unstuck) is extremely valuable, even though it can be difficult. Good luck and let me know if you need any help or advice!

# Wednesday 3/15 – Problems Day

### // Before class

• You should be done with all of the homework from Section 7.2, and have completed the Spring Break assignment playlist from the Khan Academy.

### // During class

• Homework Quiz on 7.1, 7.2, and Khan Academy playlist
• Question time

### // After class

• Take care of any remaining issues with the first part of Chapter 7, and start considering how you are going to study for the second midterm exam that we are having the end of the month.
• Read and take notes on Section 7.3 to be ready for the Daily Quiz
• NEW THING: I will also give a second Daily Quiz on Friday. It will consist of one homework problem from Section 7.2.