# Two Things I Am Wondering…

It is an interesting perspective moving out of the classroom into a coaching position. I have had more face-to-face teacher math conversations this year than ever in my career and it is wonderful. This position also lets me take a step back from the daily lesson planning and think about things I see across all of the grade levels. Most times, my thoughts are about the trajectory of mathematical ideas, however over the past couple of weeks I find myself thinking about two things I saw as norms when I taught, but now wonder more about…

1 – Is there a such thing as an addition, subtraction, multiplication or division problem?

I am sure we all can relate to the stories of students struggling with story problems. We see them be successful with Notice/Wonders and 3-Act Math tasks, however when given a story problem some “number grab” and compute without thinking about reasonableness. Why? While I think there are many factors at play here, I have another theory that has led me to question problem types. I could be completely off, but as I look through the curriculum and think about the progression in which I taught in 5th grade, I wonder if there is something to teaching “types of problems” within a unit. For example, in Unit 1, Investigation 1 could be my multiplication lessons while Investigation 2 could be my division lessons. While we don’t explicitly say, “this is how you solve a multiplication problem” and we explore various strategies to make connections between the operations, the header of the activity book pages say things such as, “Division Stories” or “Multiplication Stories.” Also, the majority of the work that week is the specific operation and applications.

From there I began to wonder, is there really a such thing as a specific operation problem? I would think that any division story could also be thought of as a multiplication problem. Do we lead students to think there are certain types of problems even if we make clear all of the strategies to find solutions? I love how CGI talks about problem types and wondering why more curriculum are not set up that way instead of keying students into operation-specific problems?

2 – What makes students attach meaning to a vocabulary word? Do they need to?

Every year in 5th grade, I was confident that all of my students could find area and perimeter of rectangles. However, I was also confident that there would also be a handful of students who could find area and perimeter but didn’t know which was which. After much work with area and perimeter, they would have it by the end of the unit, but did they remember when they got to 6th grade? I am not sure.

Now, seeing all of the work they are doing with this beginning in 3rd grade, and talking to 3rd and 4th grade teachers who are seeing the same thing, I am left wondering why this is? What makes students attach meaning to vocabulary? This question is then followed by the my very next question…when do they have to?

I wonder if students should ever be given a problem where the context would not allow the students to figure out which one, area or perimeter, the problem was asking. For example, if Farmer Brown is buying fencing he would need the perimeter where if he was buying something to cover a piece of ground, it would be area. Should we ever give them just naked perimeter or area problems with no context where knowing the meaning of the word impacted their ability to solve it?

And then, after they do all of this work with both measurements, why do they forget which word is which year after year? I know the teachers do investigations with the work and use the vocabulary daily during the unit, as I did, but students still don’t hold on to it. What makes it become part of their vocabulary? Is it just too long between when they use it? Is it

These are just two things I am wondering about….

# Who is Coaching Who Here?

I am so fortunate to be involved in a wonderful state-wide cohort, MiST (Math Instructional Specialist Team), organized by MSERC and made up of specialists from the University of Delaware, the Delaware Department of Education and districts across the state. This year, one of our foci has been content coaching, looking deeply into the structures that need to be in place and how it can be used to develop lead teachers in our schools. Our latest “homework” for the group was to try content (math) coaching with a teacher in our building.

At my school, we do not have a coaching model in place as of this current school year. However, with our implementation of the CCSS, we are writing a district plan that involves structuring a content coaching model into each of our elementary schools. We are fortunate to have both a math and reading specialist in each elementary school, so we are starting with a foundational structure in place.  I thought it would be great to “try out” a coaching situation with one of the teachers in my building to bring back to MiST and get a feel for how it would work.

I have a wonderfully open 4th grade teacher in my building who is always excited to learn and willing to have me in her classroom and go through this process.  I find one of the more difficult things of coaching is finding that teacher who is open to having someone else in their classroom and sees the value in the learning experience.  I really lucked out with her! We met a week prior to the the day I would be in her classroom to choose the lesson and chat about which area(s) she would like to focus. The lesson we chose was on linear equations and in our pre-conference she wanted to focus on the timing of her launch and how to meet the needs of her “done early” and struggling students during the lesson.  We  planned a day to meet within the next few days to discuss the details of the lesson more thoroughly.

Having never taught this particular lesson before, I read and re-read the lesson, taking notes on the math involved, the launch of the lesson, how to extend and intervene for the students. I really was feeling the pressure to know EVERYTHING about the lesson and be overly prepared for any questions asked of me.  I think I was more nervous about this meeting than she was.

The day we were meeting about the lesson (pre-conference), I got to her room only to find out the plan had completely changed. She had just found out that in another RTI group (where @ 6-8 of her students go) they had already done our planned lesson. Oh No! We had to refocus quickly (45 minutes of planning isn’t much time), so we looked ahead to where she would be in her core math class and chose another lesson.

This was probably the BEST thing that could have happened to me, although at that moment, I found myself starting to get nervous.  I am a planner. I feel as the “math specialist,” I need to have all of the answers to any questions the teacher may ask. Which is so ironic bc with students, I am completely OK with saying “I don’t know that answer, let’s check it out” but with adults, I put pressure on myself.  With this unpredicted switch in lessons, I instantly went from coach to co-learner and it was awesome.  We read through the new lesson, asking questions as we went, learning from each other. I was offering ideas, she was offering ideas and we collaboratively “lived” the lesson for her 45 minutes of planning time. We talked through questions (inspired by Lucy West) such as: What is the math in the lesson? What previous experience have the students had? Who will struggle? Who will be done early and what will they do? What will the share out look like? Would you like me to chime in during the lesson?

She taught the lesson the following day, I filmed it, and it went beautifully! (I will be blogging more about the actual lesson soon).  Her classroom culture and routines were evident from the way the students respectfully disagreed with one another and moved around the room. I was so impressed with her! I cannot even express to everyone the excitement I felt when I left the room. I felt the success of the lesson as if I had taught it myself. Things we had talked about in the pre-conference came out from the students during the class. Things we had not thought about came out from the students. I feel like we had a mutual investment in the lesson, both feeling equal responsibility.  Our post conference is set up for next week, so I will blog about both of our reflections on the lesson and the process….so stay tuned!

It led me to ask myself, what does this coaching structure really look like? Who really coaches who? I would argue that this is really a multidimensional coaching model. I offered insight into “the math” of the lesson, the classroom teacher offered questions and insight into her students’ minds, the students offered comments for us to think about in upcoming lessons. When our district revisits our CCSS implementation plan and structure for coaching, this type of experience is critical in setting up those structures.

So thank you to my MiST peeps for the knowledge, motivation and safe environment to learn and share experiences. Thank you to my amazing 4th grade teacher for being so open to having me in the classroom and willing to learn through this with me. Thank you to the students who teach me something new every day I walk in the building.

Mathematically Yours,

Kristin