# PD: A Math Task for Teachers

I’m planning a PD for a group of elementary math teachers that I’ve never met before. This makes things difficult because I don’t know anything about what they know or what their experiences are.

I was told that one of the sessions should be about engaging students in doing mathematics–which is what I think all PD sessions should be about:).  I’m trying to use a math task to engage teachers in doing math before we talk about how to engage students. My goal is to use the task to build some content knowledge around fractions and to have a shared learning experience that we can generalize from. Here’s the task I’m planning on using during the session:

I used the guidelines I posted last time to help me select and modify this task.  Here’s what I was thinking as I planned:

1. The task starts by asking for a prediction or estimate of the final answer:  I added this in because I wanted to get a quick read of the group and to make sure that everyone understood the task. I’m debating about using notice/wonder instead.

2. Knowing the formula is not enough to complete the task: It’s not enough to know the procedure to find equivalent fractions to complete all parts of the task.

3. I can provoke an interesting discussion based on a common misconception. The numbers in the task allow me to pose the following misconception: “The first three situations are equivalent since there is always 1 sandwich fewer than the number of people.”  I’m hoping this will lead to an interesting conversation about why this thinking doesn’t work and what you might do with students that think it does.

4. They have to prove WHY something is true. I like the idea of having them create a poster with convincing evidence that supports their solution. The discussion that comes out of comparing different posters will allow us to discuss what it means to convince or prove in math.  I’m going to encourage using diagrams and I also plan on handing out connecting cubes that they can use to work through the problem.

5. It can be used with students with minor tweaks. The task will need to be modified based on the level of students it’s used with, but I think it could be used across grades 3 to 5.

After we complete the task as a group, I’m planning on using these prompts as a reflection:

• Doing mathematics: Write a about the activity from the perspective of a learner. Think about the learning processes. What helped you as a learner? What helped you sort out the mathematics
• Teaching mathematics: Write about the activity from the perspective of a teacher. How is this activity different than other lessons on fractions? What do you like about it? What are some concerns?

The comments you all left last time were so helpful. You pushed me to think about now about how I will decide what warm up task I’ll use, what type of reflection prompts might be helpful and to keep in mind that some teachers that might be uncomfortable with the content.

I’m excited to hear your feedback on this task and any suggestions on how you might change things before I actually try it out.

# Professional Development: Doing mathematics

This may sound like a no-brainer, but I find it’s really important to engage elementary and middle school math teachers in doing mathematics during professional development. The experience of doing math in a different way than the way it was learned is critical before we talk about how to teach it in a different way than we learned.

It’s hard for me to figure out which tasks to use. I try to find activities that allow teachers to explore a particular mathematical concept in a different way than they may have learned it when they were students. For example, I recently worked with a group of teachers who knew the formula for surface area and volume of a cylinder but never had a chance to unpack why or how it works.

My goal is that through experiencing math this way, teachers will see a benefit to this way of learning–that when we have the experience of seeing why a formula works or how it works, we have a different experience, which leads to a different type of understanding.

I’ve been trying to think about how I select and modify tasks I use with teachers. It’s similar to how I select tasks for student in some ways and different in others. Here’s what I have so far:

1. The task starts by asking for a prediction or estimate of the final answer: This gives everyone an entry point, builds on what they already know, and it allows me to assess where the group is. It’s not always necessary but it helps.
2. Knowing the formula is not enough to complete the task: Because teachers have often memorized formulas or procedures, I need to make sure the task can’t be answered solely by knowing the procedure. I want a task that creates a need to unpack the formula or procedure they already know or apply it in a new way.
3. I can provoke an interesting discussion based on a common misconception. Sometimes someone in the group has the misconception. Sometimes I will bring it up. Either way, this type of discussion allows me to have a conversation about how important it is to anticipate misconception.
4. They have to prove WHY something is true. This allows me to set norms about what it means to convince or prove in math. I can create the shared understanding that we don’t just want to prove something works but that we want to explain why it works.
5. It can be used with students with minor tweaks. At the end of the day, I want teachers to walk away with something they can try out in their classes

I’ll share some of the tasks I’ve modified next time, but I’m curious what else you would add to this list. How do you choose tasks to use in professional development?

# How do we evaluate our coaching work?

The school year is wrapping up for me. Like most of you, the end of the year is a time of reflection for me. I’m thinking about the professional development and coaching work and I did this year and what revisions I want to make for next year.

In doing this, I started thinking about how I could assess myself. If I were working with students, I would give a final exam or project that allows students to demonstrate what they have learned all year.

But the last thing I want to do is add more work onto teachers’ already packed schedules. Plus I’m not sure what a final exam or project looks like for teachers. At the same time, I need their feedback in order to improve my practice for next year.

So I started thinking about what data I already collected that I can look at. Here’s what I have:

• My notes from visiting classrooms throughout the year
• My notes from my meetings with teachers individually and in teams
• Their observations from principals and other feedback principals gave me
• Emails from teachers
• Students work they’ve shared
• Exit tickets from PD
• Surveys
• Mid-year reflections

This gives me some rich data about how their thinking and teaching has changed throughout the year. But I also wanted to send out an anonymous survey just to get some direct feedback on my work with them.

I’m working on a draft of the questions I’m going to send out next week. Probably through survey monkey unless any of you have a better platform you’ve used.

Here are the questions from my initial brainstorming.

General questions:

• In what ways do you feel that you grew as a mathematics teacher this year?
• How have your beliefs on student learning changed? On teaching mathematics?
• What types of support did you receive from Nicora this year?
• In what ways did the professional development and coaching offered this year by Nicora impact your teaching and/or your students?
• What types of support would be helpful during the days Nicora is with us next year?
• What topics would you like additional professional development on?
• If someone else wanted Nicora to work with their school…what would you say in the way of recommendation? Why?

Questions specific to lesson study

• What is one word you would use to describe lesson study?
• What have you learned or what have you thought about differently as a result of our lesson study work? Try to be as specific as possible.
• What have you tried out in your classroom because of our work in lesson study (outside of the lesson we planned together)?

I’d love your feedback and any other questions you use!

# Professional Development: Why does it go wrong?

I sat in one of the worst PDs ever this week.

It didn’t build on what those of us in the room knew. It didn’t engage us in conversations or activities that were relevant. It shared products and not processes. At times, it treated us like we were no different that the children we teach. I’m sure many of you have sat in similar ones.

Most likely, the people giving the workshop had good intentions. Some of them were probably effective at teaching children math. But they were completely ineffective at teaching teachers.

I’ve come to realize that we don’t do a good job of providing the people who give PD with the right tools to facilitate teacher learning. They have to make it up as they go.

When I started doing professional development, I had no idea what I was doing. So I started reading a bit of the research out there about what makes for good PD.   This classic by Ball and Cohen was a good start.

Using what we already know about effective PD as guidance, I started making lesson plans for each PD session I did.

Over the years, I developed a list of questions that help guide my planning:

• What is the objective of the workshop?
• What should teachers know or be able to do at the end that they didn’t know before?
• What is the motivation for teachers to be interested in this topic?
• What prior knowledge and experiences do the group of teachers I am working with bring to the sessions?
• How can I build on these experiences?
• What is the best task sequence that meets the teachers where they are and helps them develop new understandings?
• What activities facilitate teacher learning?
• How do I engage teachers in productive struggle so that they construct their own understanding of the topic?
• How will I know if participants met the objective? What assessments will I use throughout?
• How will I differentiate the lesson for different learners? What interventions will I use? What enrichment will I provide?

This doesn’t look all that different than the questions I ask when I teach kids math. However, the answers are.

I’m still working on what theories to use to help me answer these questions. I’m spending some time looking through the research to help me with this.

Even if we don’t have all the answers, the effective PDs I go to are a result of someone carefully thinking through a lot of these questions.   The ineffective ones could be improved a great deal by thinking more carefully about them.

What do you think? How do you plan PD?