OK. So here is what I think is a simple example of me doing run of the mill reteaching of content, after having assessed student work on the topic and determined that there were specific difficulties that needed to be addressed and that students needed extra practice.

Our pacing schedule had us starting a new topic on energy analysis and resonant frequency with SHM, and we had covered elastic potential energy in the prior week. An online homework problem on springs had been assigned, and here is the one I focused on.

I had quantitative data from the online homework system that this was the problem that students were getting incorrect the most often, and I had qualitative data from student emails and office hours drop-ins that students lacked a solid conceptual / representational approach.

From that, I had evidence that very few students were drawing graphs or diagrams to thinking about the problem, and were instead trying to use the equation U = 1/2 k x^2. Many could not get the correct answer; some could get the correct answer but not understand why it worked.

A common approach was to calculate the answer as 1/2 (250 N/m) (0.006 m -0.001 m)^2, although students were not always consistent about doing at all or doing correctly the unit conversions.

Since we follow a common curriculum and pacing guide across many sections of this course, I decided it was best to invest time at the beginning as a "warm-up" trying to address. I did not have the option of spending the whole day reteaching, and that didn't seem necessary

Also, I teach in a studio class where students meet for 3 hours, so a warm-up taking 20-30 minutes isn't out of the question. I started the warmup by showing students the problem, telling them it was a problem from the HW that I wanted to talk about, and gave some time to orient.

I then asked the following clicker question. Which of these force vs length graph best depicts / matches what is described in this word problem? Importantly, I wrote this question with graphs that have no numerical values.

The question was from a year ago, so I don't recall the exact distribution, but I am fairly sure it was "all over the place". I most likely did a "turn and talk" followed by a revote, and after the revote I most likely asked to hear from someone who "changed their vote".

After getting good arguments for the correct answer (A), I "lectured" a few sentences, re-emphasizeing that this is the approach I have modeled getting started on problems like this. Draw representations, not necessarily with numbers. Now, we need to practice adding quant. info.

I did this next question as a "think-pair-share". I don't think it took long, but gave opportunity to sense-make

Part of my direction instruction was some combination of me and or us constructing a representation like this. I had this slide ready to go. There was likely a LOT to unpack here, more than expected, especially about all the different mm values. What did each mean in words. Why?

This was followed up with another question for "think-pair-share", saying, well part of problem-solving isn't just getting known information onto the representation, it's figuring out new information as well.

Students and I quickly constructed the force values from Hooke's Law, something I had better confidence they understood from both formal and informal assessments. At some point, this was a slide I showed students.

I can't remember the details, but the next goal would have been to get us back to thinking about the problem, what was it asking, have we already figure it out, if not how do we figure that out?

I was probably pretty direct into getting that the question is ask about energy, but the question is what specific energy is it asking us about. I would have been directing us to think about energy stored initially, energy stored, and connecting that back to the discussion

I would have asked students to "recall" how see energy on a graph like this, done a quick reclassifying of that, and then asking the following question.

Here are three possible area shadings. What does each of these represent in words? Which, if any, is related to the question that we have been asked? I probably did a turn and talk

At some point I showed students a slide like this and talked about it some.

I then sent students to finish the problem, letting them choose one of two ways to work it:

1. At a whiteboard as a group, working collaboratively
2. At their table, working alone but checking together

Goal was for every student to be able to do calculation but be able to explain why it made sense. For some, my goal was to connect back to the equation. I know I didn't have this conversation with the whole class, but targeted to those who were primed / could benefit from

I had this slide ready, but as I said I am pretty sure, this was not a whole class discussion, partly due to time, partly due to cognitive load, etc. But it touches upon important connection that some students needed to resolve their confusion / difficulty.

I'm not trying to say this is "exemplary" teaching, nor am I saying that "exemplary" sharing of this teaching event. Nor am I saying that this is what @edmunds_dr was describing. What I am trying to do is put out a concrete example in my own teaching, one that

involves aspect of what @edmunds_dr talked about -- reteaching something based on assessment of student work, that addresses specific difficulties and engages students in practice. I want it to be in the vicinity of those things, so we have concrete objects to talk about.

I am super open and welcome to comments, questions about any aspect of the approach - to more information, clarification, etc. I would also love responses that involve you sharing a reteaching example. I am not interested so much in "this is great", or "this is horrible".