# How to make calculus lecture time more interactive?

I taught my first university course last Summer. It was integral calculus that usually has about 200-300+ students during the school year, but my Summer class had only about 35 students. I taught by lecturing during the whole class time. I am teaching again this Summer, but I really want to try something different. The main reason I want to avoid lecturing the whole time is because I thought about my own math education and how I hate sitting through lectures. I actually slept through most of the calculus lectures I attended as an undergrad.

I think that because the Summer courses are a lot smaller, I can try other methods of teaching besides only lecturing.

Here are a list of things I wanted to try this summer for my integral calculus course:

1) Lecturing for short periods and then giving the students a problem about the short lecture and letting them work on it for 5-10 minutes 2) Lecturing most of the time and leaving a period at the end to work on problems 3) Have the students present problems during lecture time

I was wondering if anyone has other suggestions or different ways of making class more interactive that has been successful.

Two suggestions: The first is to try clickers. They work like the voting system in "who wants to be a millionaire?". You can activate students and foster discussions on questions. There is no need for clicker hardware as long as your students have internet access via tablet, smartphone, etc. see PINGO software. The second suggestion is flipped classroom. Students shall prepare at home. You might want to upload videos or hand-out a text, refer to books, whatever. There is no need to come together just for listening to the teacher and reading what he is writing. Your lecture therefore becomes a place for discussions, since the students now are prepared. There are a few mistakes not to be made, e.g. you should not stand at the blackboard trying to lead the discussion. Your students will then wait for you to do something. You rather stay back behind them and only act if real problems arise which the students can't answer. Succesfull experiences were gained naming one student to just moderate what the others say and one more student to simply write on the blackboard everything they say.

More literature on flipped classroom can be found here.

• The paper you linked to by Simelane and Skhosana contains a nice nutshell description in section 2.3 of a good student-centered learning technique originated by Mazur. Mazur originally described the technique without any electronics, and the point of the technique was to get students to talk in small groups about difficult concepts, which testing had shown were not being learned through traditional lecturing. These days many people seem to be focusing on clickers rather than on the technique they support, and using them in a misguided attempt to make classes entertaining, like a game show. – Ben Crowell May 11 '14 at 13:42

You can assign problems for students to work on in class, in pairs.

If students get stuck, you can provide hints.

Here are some challenging possibilities, which can be modified to suit the class:

1. Numerical problems with graphing calculators.

a. Where is the minimum of $f(x)=x^2+e^{\cos(x)}$? How many digits of accuracy can you get for $x$ and for $f(x)$ at that point?

b. What is the area between the axes and the curve $x^2+x^3+y^4+y^5=1$?

b. What is the importance of the number .67449 in statistics? What does this have to do with integrals?