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?

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    $\begingroup$ Just some general comments, not specific to the topic of logs. I have been on many hiring committees and always loved to see some student-centered learning rather than a teaching sample consisting only of passive powerpoint. The instructions don't say how much you have to cover, so don't worry about going really fast or trying to cover too much -- this is a common mistake. If you have handouts or worksheets, send them out in advance. If you want to simulate, e.g., think-pair-share, do it in zoom using breakout rooms. Start with a brief preamble, then go in character and treat them as students. $\endgroup$ – Ben Crowell Jan 22 at 21:46
  • $\begingroup$ Thanks for your comment. I will be sending the worksheet ahead of time. Preferably a topic has a short intro before class, either in reading or in video form, with some accompanying questions; the objective here is not an in-depth intro but just letting the students see the topic before coming into class. This component, usually called flipped classroom, is one I'm not sure how to include in the teaching demo (unless just by explanation.) $\endgroup$ – Nights Jan 24 at 1:05

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.

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    $\begingroup$ And yes, ask someone what the expectations for your job are. In my opinion you are overcomplicating this. Talk to people. $\endgroup$ – Chris Cunningham Jan 22 at 5:30
  • $\begingroup$ Chris, I'm a bit wary of spending 3-5 minutes simulating the pre-classroom reading and/or video. For one thing this could come from a different source than me (the textbook; some video online) and is only meant to prompt them to answer some easy questions and be ware of the topic. The next logistic problem is upon starting the class session I prefer to throw the students right into groups, make them do a short icebreaker, then work on these (preferably IBL) worksheets (and I basically scramble to remind them to work together and I take questions). Maybe 10 minutes later we reconvene to discuss $\endgroup$ – Nights Jan 24 at 0:56
  • $\begingroup$ It's during that class discussion I will, if needed "do the introduction." To a traditional teacher I suppose this is "backwards" or disjointed. But we all know traditional teaching is sort of out. So back to my question of how to translate this stuff, in the optimal way, to a 7-10 teaching demo (of course I will include an explanation of this.) $\endgroup$ – Nights Jan 24 at 0:58
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    $\begingroup$ I guess I didn't explain myself very well, but no one is calling your approach backwards or disjointed. Here is how I would do your 7-10 minute teaching demo. 3-5 minutes: Show them the style of the video presentation you would use, to simulate what the students would watch before class. 0 minutes: Icebreaker. Don't waste the committee's time with this. 4-5 minutes: Hand out the worksheet and talk through the instructions and format with the committee, then switch "out of character" and explain what you would do during this time and the evidence-based reasons for doing so. $\endgroup$ – Chris Cunningham Jan 24 at 18:07
  • $\begingroup$ Chris, this is helpful; I didn't think of presenting the pre-class material that way. I could do this, though in the past I typically direct students to specific parts of the textbook, and/or post an existing video for additional help, and prompt them to answer easy questions ("look at example 1; now answer this easy question.") Do you believe this would be frowned upon versus making a lecture video? In fact my goal with the "flipped class" component was 1. get them to open the text, 2. just 'show' them the topic to be explored in class; nothing much in depth. My experience is limited. $\endgroup$ – Nights Jan 25 at 3:57

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.

  • $\begingroup$ Thanks. I will take this as a starting point to think about, content-wise. Are you doing this currently/recently online? If so what's your approach? General question, I know; frankly I haven't had much "cutting edge" experience with online teaching in the pandemic (I have done online teaching that is very much traditional "here's some videos to watch, then answer some questions.") $\endgroup$ – Nights Jan 22 at 1:48
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    $\begingroup$ My school alternates between full remote and hybrid. I taught logarithms with this approach in full-remote recently. I use a tablet as a virtual white-board and overall treat things like a normal classroom I assign exercises through problem-sets or online systems like Khan Academy, and use break-out rooms to facilitate group work. You could create a small lesson like this as Desmos activity. $\endgroup$ – Carser Jan 22 at 2:23
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    $\begingroup$ Isn't it how logarithms normally introduced? Then you offer one of the classics, like given the initial amount in a bank account and the yearly interest rate, how many years has to pass to reach certain amount. Or the binary search algorithm: how many times one needs to slice a sorted array in half to guarantee finding an element. $\endgroup$ – Rusty Core Jan 22 at 17:34
  • $\begingroup$ @Nights Since when "here are some videos to watch" became traditional? People increasingly question the value of college, because one can read a book like Will Hunting did, or watch a lecture by a renowned MIT professor, free. College becomes an expensive diploma-granting machine, and what is your role? Questions can be asked and answered online, and basic stuff like logarithms is well covered. $\endgroup$ – Rusty Core Jan 22 at 18:13
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    $\begingroup$ @Nights I mean that it is an approach that involves active learning, as you asked, as apposed to just demonstrating it to passive listeners. In prompting them to find solutions to the exponent problems, you are helping them to realize that they have the conceptual understanding to calculate logarithms, they really just need the notation. $\endgroup$ – Carser Jan 24 at 1:55

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).

  • $\begingroup$ Respectfully, I'd suggest that the 'fun' type of in class work doesn't always translate to a formal interview/lesson demo. When I was told I'd be observed, I replied that the particular proposed day was a day we'd test. The next class would offer a look at me in action. And yes, an 80 minute observation shared a mix of fun and even current events. I didn't offer my own answer, but I'd say that "7-10 minutes" is hort, and time to use them wisely. $\endgroup$ – JTP - Apologise to Monica Jan 23 at 16:42

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