Wednesday, July 22, 2015

Reflection on Practice - Part I

Our second class of the day at PCMI was Reflections on Practice, where we focused on formative assessment. My favorite thing about this class is that it has left me with a lot of questions. Many of these questions don’t have quick and easy answers, but instead will shape the choices I make about how I structure my classroom. Going in to next school year, I will do my best to think through as many of these questions as I can and make instructional decisions based on this thinking. But I imagine that some of these questions I will revisit and revise my answers to for a long time yet to come. It’s the act of thinking through the answers, rather than the answers themselves, that will make me a better teacher.

Throughout reflections on practice, we looked at a lot of research surrounding formative assessment. Here are the ideas that stuck out most to me and the questions that they make me ask. I will do a whole separate post for my take-aways and questions based on our class's video conference with Dylan William.

1. Evaluative vs. Interpretive vs. Generative Listening
This was a framework for types of listening, and really types of teaching, that we analyzed various classroom videos with. With evaluative listening, the teacher comes into the class with a plan for the path that the class will take to reach the instructional goal. If the student responses are what the teacher expects, then the teacher can easily continue with the plan. If student responses are not what the teacher expects, the teacher will simply say the idea him/herself and continue on with the plan. Somewhat opposite to this is generative listening, where the teacher has a goal but uses student work and understanding in order to choose the path for how to get to the goal. In the middle is interpretive listening, which I am the least clear on. I believe with interpretive listening, the teacher comes in with a goal and a path to get to the goal. The teacher is interested in surfacing student thinking and using that to help students along the predetermined path.

Throughout the whole course, we did not explicitly place more value on some types of listening than others. However it was implied that generative listening was preferable to evaluative listening. On the surface, this certainly fits with my teacher training and own educational values. I strongly believe that students will be more invested and understand better if the math that they are doing is connected to and based on their own thinking. But I also think it is much more complicated than saying that teachers should only ever do generative listening. I think that there is a place for being evaluative or interpretative. For example, if I have a group doing a card matching, I might be evaluative and tell them that 6 out of 8 of their matches are correct and to identify and fix the mistakes. That is not always the instructional move that I would make in that situation, but it is one I have made and would make again if I could tell that the group understood the big idea and had either made a careless error or needed to focus in on nuance. 

Therefore, I am left with the following questions:
- What is the purpose of each type of listening?
- In what situation would I be trying to achieve that purpose?
- Based on the previous two questions, is there an ideal balance between the three types of listening?
- What are the common pitfalls in executing each of these type of listening? How do I make sure that I am actually achieving the purpose that I would like?

2. Hinge Questions (See Dylan William’s explanation here)
Hinge questions are in a category of moves where the teacher assesses the whole class and then makes an instructional decision about what to do next based on the assessment. However there are some particular characteristics of hinge questions that increase the efficacy of this process:
- kids should not be able to get the question right for the wrong reason
- the whole class answers the question in only a couple of minutes
- all responses are assessed in under a minute
- the teacher is ready and able to change the lesson based on the assessment

I make instructional decisions all the time based on a formal or informal assessment of the whole class. For example, I will use exit tickets in partnership with informal observation to make decisions about what I will do the next day in class. When I grade homework, I check one pre-selected question for accuracy. This is a question that I have written to be a mid-level question that addresses the main objective from the previous day. Based on responses to that question, I may then decide if we are going to go over the question, if I want to clarify something before we start the day’s lesson, if I am going to check in with particular students during the day, or many other responses. Here’s how I see hinge questions as slightly different from what I already do: it is done in the middle of class and the decision about what to do next is even faster. Due to this the teacher not only has to craft a really efficient question, but also plan in advance the possible directions the class could go and the threshold of understanding for each direction.

This leaves me with the following questions:
- How can I plan and structure lessons in order to have maximum flexibility within the lesson to react and change course depending on how it is going?
- If students are struggling to grasp an idea at a time when I expect them to have grasped it, in what situations is it necessary to react immediately and in what situations can I wait until the next day to address this? How does the percent of students who are struggling with the idea affect the required reaction time?

3. Jo Boaler’s Norms:
We also looked at these positive classroom norms from Jo Boaler:
- everyone can learn math to the highest levels
- mistakes are valuable
- questions are really important
- math is about creativity and making sense
- math is about connections and communicating
- math class is about learning not performing
- depth is more important than speed

These norms align strongly with my own values and math education philosophy. But in the current popularity and push towards growth mindset, I feel like much of the focus is on the language that we use in talking about these ideas. While I think language is extremely important, I want to spend more time making sure that my actions actually match the language that I am adopting. While I believe all of these things, the ways that I structure my class do not always reflect my beliefs. And students pick up on that. For example, it doesn’t matter how many times a teacher says that mistakes make your brain grow if the student work or ideas that the teacher highlights are always mistake-less.

So here are my questions:
- Which of Jo Boaler's norms are most important to me? Are there other values that I have about math learning that are not represented here?
- What structures do I have in place that reflect my values?
- What structures do I have in place that are at odds with my values?
- What changes can I make in my classroom structures in order to better align with my values?

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