## Tuesday, August 2, 2016

### Reflecting on Practice 2016

In PCMI's Reflecting on Practice class this year, we focused on making connections. Here are some things that made me think and that I would like to try.

### 1. Pre-Assessment

One place that it is important for kids to make connections is when they are introduced to a new concept and they build their understanding from their prior understandings. We talked about alternatives to a written, individual pre-test that were primarily short ways to activate students’ prior knowledge and get a sense of how comfortable they are with the pre-requisite (or co-requisite) skills. For example, this is a WODB that could be done at the start of a unit about linear functions with eighth graders, to see what they remember about proportional relationships and to preview some of the new ideas.

In the past, I have generally not done this type of pre-assessment. I like to start my units with a task that students can use their intuition and prior knowledge to solve, but that introduces a new idea in the unit (for example, solving a contextualized system of equations where the difference between the two situations is very obvious). I like that because I get a sense of the different ways students are approaching the new concept before I have given them any sort of direction. I also like it because it is something that we can repeatedly return to as students start to formalize the new ideas. But I see the value in doing this type of pre-assessment as well, particularly if it is pretty quick and low stress. This prompts a wider range of vocabulary, procedures, and concepts than my one task might.

### 2. Contrasting Cases – from Star and Rittle-Johnson

The goal of this routine is to develop procedural fluency that is flexible. This is a format that is pretty similar to things I have done in my class before, but I like it because it formalizes the process a little more and provides a bank of question options to choose from. Students are first presented with two different methods for solving a problem, where the work is accurately done out. There’s then a sequence of questions, first for understanding, then comparing, then making connections. Finally, students choose which method to use and why for each problem in a handful of similar problems. Here’s an example that we did in class.
And here are the different question options:

This seems most valuable where one method is not always better/more efficient than the other. I think that this could either be done where the original problem is a toss up between the two methods, or the original problem is obvious but the follow-up problems are split.

### 3. Examples and Non-Examples

Another routine I could see using in my class is having a set of examples and non-examples. Having students individually choose one that they know is an example, one that is a non-example and explain why. Then have all of the options up on the board and have students place one color post-it on which one they chose as an example, another color on which one they chose as a non-example.  Then discuss as a class based on where there is the most conflict.

Here’s one we did where we had to determine whether there was enough information to tell if the triangle was isosceles.

### 4. Different types of comparison

This slide, from Day 2 in the third module, summarizes the different types of comparisons that we talked about.

For a lot of reasons, discussions in my class this past year were often about what steps to take to solve a particular problem. I don’t think that this is particularly valuable to students or a good use of discussion time (particularly when it is the only type of discussion happening). This is something that I want to work really hard to change this upcoming year and I think it will be helpful to think about for what type of learning goals might I use each of these types of comparisons.

### 5. Quiz Feedback through Highlighting Mistakes

We watched this teaching channel video where Leah Alcala explains how she gives feedback on tests by highlighting anywhere a student makes a mistake in their solving process. I like this in contrast to what I currently do (check or x next to each problem, with a handful of random comments) because I think that highlighting where the mistake(s) is gives an entry point into revision/correction that many students need. Students who are overwhelmed or stuck when they get back a quiz with just a check or x next to each problem have a place that they can start. I still think, though, that you would need to figure out how to support students who even when they know where the error is don’t know how to fix it because they don’t understand the concept/know the procedure. Having students work in groups to do the corrections is a step toward this, but I think as I am highlighting I would also need to keep track of what the misconceptions are, how many people have them, and whether or not they need to be addressed in the whole class, small group, etc.

### 6. Thinking Classrooms

Peter Liljedahl video-conferenced in to talk to us about thinking classrooms. In his research, he found student behavior depends much more on what’s happening in the rest of the school than what the teacher is doing. He defines what’s happening in the rest of the school as institutional norms: normative behavior we take for granted in our institution’s classrooms. And then he researched the best ways invert the institutional norms because the more opposite teachers were to institutional norms, the more engaged kids were. Here are what he found were the biggest disruptors, where the gear size represents the relative impact.

I am really intrigued by his framework and definitely want to read more of what he has to say here.  My overall PCMI commitment to change in my classroom next year is “Use the whiteboards [which I installed all around my room last year] so that students learn from multiple strategies.”