I was asked to lead a math session today for district-wide subs to help them better understand the math they’d find in CCSS classrooms. Thinking about how to craft a PD on mathematics for K-12 substitute teachers who work in any classroom from kindergarten to high school PE and everything in between was a challenge. Like many of you, when faced with a teaching topic on which I am stumped, I head to my friends in the blogosphere

Recently, a UC Berkeley undergrad in my math pedagogy course asked if it would be considered plagiarism to use a lesson his girlfriend had taught in his current teaching placement. My reply was that if it was a great lesson that was appropriate for his students, it wouldn’t be plagiarism at all, and was actually what all great teachers do.

So thank you, Robert Kaplinsky, as I very much stole your work today, though I gave you credit all along the way. I am indebted to you for inspiring my session today which somehow left a room full of subs, with VERY diverse experiences, quite excited to teach math this year.

Between being a teacher in my district for a long while and now having been a parent here for a long while, I was surprised to realize how many of the subs in the room I knew. Several of them had subbed for me and many more had subbed for my colleagues and even my son. That made this a lot more fun for us all.

They started by predicting how 8th graders would respond to the question of:

**There are 125 Sheep and 5 Dogs in a Flock. How Old is the Shepherd?**

They then watched this video which is further discussed in this blog post.

Man did I have a captive audience. My favorite comment was from a woman who admitted that she hates math and would never sub in a math class. She said that had she been asked this question, she would do what many of the kids in the video do, write down the numbers and DO something with them. She would assume that though the question made no sense, that it was she who didn’t understand and she doesn’t trust her math abilities. She went on to say, however, that had this question been posed in an English class, she would have been the first to question the teacher saying that it made absolutely no sense. She challenged the group to pose this question to both a group of middle school math students and again in a middle school English class. She was confident that outside of a math classroom, more students would speak up about how the task makes no sense. I found that hypothesis to be brilliant (while also worrisome that she’s right).

Following this conversation we did Robert’s lesson on questioning strategies which is explained in his blog post. In short, teachers were in groups of 3 where one role played a teacher, one a student and one was an observer who wrote down all the questions asked by the teacher. The teacher was given slip of paper with a math problem and knew the solution that the student had gotten. The student was given a slip of paper with the math problem and a specific misconception. The goal of the teacher was to ask questions to determine the misconception of the student.

For example:

**Student**: You are working on ordering decimals from least to greatest. The problem you are currently working on is ordering the decimals 0.52, 0.714, and 0.3. You correctly place them in the order 0.3, 0.52, 0.714. However, the reason you put them in this order is because you look at the number after the decimal like a whole number (3, 52, 714) and do not understand the significance of place value. You are confident you are correct and don’t realize that you only accidentally got the correct answer.

**Teacher: **Your student is working on ordering decimals 0.52, 0.714, and 0.3 from least to greatest. Determine what understanding the student has by asking questions, especially questions that encourage elaborate responses.

I LOVED this activity and the rich conversations it generated. We easily spent 45 min. role playing 3 scenarios and debriefing each one and these teachers had so much to say. We talked a lot about how developing questioning strategies could help a student unearth misconceptions even when the math the student was working on was too complicated for the sub.

However I realized that for this group of teachers, there were so many who feared math, that they couldn’t focus on the misconceptions and instead, for some, could only focus on explaining to each other HOW TO DO the problem. In hindsight, I think I should have modeled the conversation one could have. I could have role played the student and had the whole room of subs role play the teacher asking questions to me. Only I would know the misconception and the group would ask questions to determine where I was confused. I think had we done that for one scenario, these teachers would have been able to let go of their own fears of making math mistakes a bit easier.

What a neat afternoon for me and for them!

I thought the allusion to the English class was interesting. I’m sure the conclusion is right, the English students would have questioned the question, but I’m not sure it is a “fear of math” that discourages that. My reaction was that math is a language just as is English, it just communicated different things. The students are more bold in English classes because they understand the language better and realize the problem is not complete, where in math they are not sure they understand the language and thus are more reluctant to question the question, they rather assume that their inability to solve the prolem is their shortcoming not the shortcoming of the language posing the problem.

The same is true for the other question—ordering the decimals. The “more challenged” ones don’t see .3 as a contraction of .300, just as a non-native English speaker might not see aren’t as a short hand for are not,,,,,,,,,,or an older adult might not know the bro is shorthand for brother which when used for someone who is not actually a biological brother is short hand for “my very good friend and companion of whom I am very fond”

To use math to solve problems you first need to understand it as a language, then you can learn the tools, then the way to decide which tools to use in what order.

Your experience in implementing all of this is very interesting. First, the fact that your district trains subs is awesome. I don’t believe I’ve ever heard of that. I’m glad that the video was a catalyst for breaking open a conversation on teachers’ inner fears.

It also sounds like you did a great job with the Questioning Scenarios activity. Yes, it is always a challenge to not focus on fixing the problem rather than on uncovering the problem. Part of that stems from the fact that normally once you figured out the misconception, you would transition to addressing it. An example does help, but they usually have it figured out by round 2. I’m just glad that the write ups were clear enough that you could implement it.

Thanks for sharing this!

Robert:

Having been a math and technology coach for many years now, and an avid blog reader (though only an occasional blogger myself), this was the first time I have read about a fantastic PD idea from a blog. I really appreciate how you shared PD materials in the same fashion that we often share classroom materials via the blogsphere. I find it much rarer to connect and collaborate online with coaches than I did as a classroom teacher.

No problem! Regarding the collaboration with other coaches, you might appreciate this series of blog posts: http://robertkaplinsky.com/category/math-teacher-specialist-network/ It’s a bit of a DIY coach community. Takes some work but it’s worth it for me.

You made a great point: Institutional memory and social capital are priceless assetts to a coach. Specially in this scenario. Brilliant!

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