short teaching demo on logs; but by someone who uses active learning

Question

I am to give the following for an interview:

"a short 7–10-minute teaching demonstration on logarithms. Please consider this as your first 10 minutes of introducing logarithms as if you have not previously mentioned the word to this class. Treat this as closely to what you would do during an in-person classroom course. Assume that you are teaching to a typical audience of community college students enrolled in a College Algebra class, who may not have previously encountered logarithms."

Now the caveat. In my previous jobs I use a bit of flipped classroom- having the students read a bit or watch a short video and answer several questions- prior to coming into class. This introduces the topic if only vaguely. Once in class, after a short icebreaker with their peers, they jump into group worksheets which (hopefully) motivate the topic and bring the students through the topic with a series of (inquiry-based learning) questions. The active worksheet is the focus of the class. When I call attention to the front of the room (when we reconvene for full class discussion), which is done intermittingly, it is to give some answers to problems, summarize, prompt students to do work on the board or ask additional questions. In other words I try to minimize the old fashioned "talking at them" and I've eliminated powerpoint slides for example (this is based on student feedback.)

Can anyone give me advice on how to reconcile this with the interview as mentioned above? Logistically do I try to tell the committee ahead of time? Do I prepare a 7-10 minute presentation the old fashioned way and then tell them how it'll actually go down in my active learning class?

Right now I am planning to prepare the active learning inquiry-based worksheet as I would for this class topic, and I will explain to the committee that students will preferably have already seen a bit of an intro before physically coming into class. But I will give the 7-10 minute introduction, with the active learning caveat in mind, as if logs require this special 7-10 minute introduction before students jump into the worksheet. Can anyone comment on this strategy?

To further complicate all this of course, I am assuming my job would start Fall semester and that the expectation is for in-person classes. If that happens, and if students are still distanced within the class, this leads into a whole other problem about how to do active work under these conditions.

So more sub-questions: can I ask the committee outright what the expectation is by Fall and whether there will always be an online component regardless? Do I approach all this as if I need to have separate teaching strategies for both in-person (distanced or not) and online, permanently?

Answer 1

Explain what you explained here to start the interview. Do a 3-5 minute intro that introduces logarithms the way your video would introduce it. Then spend the rest of the time doing whatever else you would do in class.

Bring the activity with you. Hand it out to the committee.

Basically I don't see any reason to do anything other than give a faithful representation of what you would actually do in the job, just like for any interview.

If the place you are interviewing is any good, then the committee is made up of mostly educators, and this will be a good task for an interview: it tests your ability to follow instructions from administration, keep track of time, and concisely explain tricky topics.

Answer 2

I introduce logarithms as answering the question "to what power do I raise this base to get this result?" Ideally I would review exponents beforehand, but 7 minutes is no time at all. Presumably these students will be familiar with exponents, so you can pose problems like $$2^{x}=32$$ $$3^{x}=27$$ $$4^{x}=16$$ Then you can introduce the $\log$ notation. It is always nice when you can build the concept first and then offer notation to support the concept. I would introduce the notation by translating the first examples , i.e., $$2^{x}=32 \iff \log_{2}(32)=x$$ $$3^{x}=27 \iff \log_{3}(27)=x$$ $$4^{x}=16 \iff \log_{4}(16)=x$$ Obviously there is more to cover, and you should go over vocabulary as you introduce the notation, but this is how I teach logarithms in 7 minutes and require the students to do most of the explaining. The only thing you would be explicitly telling them is the notation.

Answer 3

I introduce logarithms via a number guessing game. I wrote a run-of-the-mill Python program to do this. It asks for an integer, $n>1$, and the class has to guess the random integer between 1 and $n$. Each time they do not get the answer right, a message lets them know if the number is higher or lower.

After a couple of rounds, I ask them what they think the maximum number of needed guesses should be. By this time, many students pick up on how they can cut the number of options in half at each step. However, it often isn't easy for them to articulate that into a mathematical answer.

Before I tell them the answer, I introduce logarithms as the inverse of the exponential function and how they are used to find unknown exponent values. After a couple of examples of rewriting exponential form to logarithmic form, we revisit the guessing game. By this time, students suspect the maximum number of guesses has something to do with logarithms.

We discuss the "cut in half" pattern and many students jump to $\log_2(n)$, although I do hear a few base one-halfs too. Luckily it doesn't take long for students to see that the logarithm can not have a base of 1/2 in this game.

After looking at a few more examples, including when $n=1$ and when $n$ is a power of 2, the class eventually comes to the conclusion that the answer must be $\log_2(n)+1$, rounded down to the nearest integer (I don't cover floor and ceiling functions when talking about families of functions; however, I mention them here).