# Why We Need Two Teachers in Every Classroom…

This job takes two brains to handle the thoughts of these students.

In class on Friday, one student made the comment that he didn’t really like adding fractions on the clock because it could only be used for certain fractions.  When I asked him to expand on that, he explained he could only do halves, 3rd, 4ths, 6ths, 12ths and 60ths easily and what if he wanted to do other fractions like 1/8 or 1/24?  He said he couldn’t do that without breaking the minutes up.  I am excited at this comment especially because this student is one whose parents have taken him to Kumon math for years for “extra help” and he is most comfortable memorizing procedures over thinking about the math. He thinks changing to “common denominators by multiplying the numerator and denominator by the same number” is faster and easier than this clock.

Upon reflection, I think it is interesting that he stayed with fractions of the fractions we were working…why not pull out 1/9 or 1/11? But my first train of thought in the moment was changing the whole. I wanted to see if he could put the clock in terms of a whole day, 24 hours, 2 rotations around the clock being the whole instead of one. That way 8ths and 24ths would be more apparent.

So I asked him if he could think of a way we could change the clock to do 1/8 or 1/24 without breaking up minutes? His first reaction was no, so I said “That is interesting because there are 24 hours in a day, so I feel like this should work.” Possibly leading him too much but at that point I could see the glazed look in some of the students eyes and I felt like I was losing the class’ attention. I told him that during math workshop that day he could chat with me about it or he could take that thought and work with some more for Monday.  He said he wanted to think about it over the weekend…I think mainly because he didn’t want to miss the Math Workshop activities, so we will see what he has for me tomorrow.

After school, I am recapping this lesson for Nancy and saying how difficult I thought it would be for them to grasp two rotations of the clock as the whole for the 24 hours that would allow for 8ths and 24ths more easily.  After listening to me ramble for about 5 minutes about this idea, she casually says, “What about military time?” UMMMmmm…DUH. Where was she during that class period??  This job really does take two brains.

So needless to say, I have amended my lesson for tomorrow. I am handing them this military clock and letting them talk about what fractions we can work with easily that are the same as our first clock and which one’s are different. Design addition equations we can solve with this clock that we couldn’t do on the other clock without breaking minutes.

Don’t get me wrong, I still want to get to changing the whole on our original clock, but I think after working with this clock, it may be more accessible for more of the students. I will post later to update on this lesson to show how it went…but good or bad, the questions and thinking that led to this lesson are so worth it!

-Kristin

# Meaningful Math Conversations…

I am a true believer that content coaching is a necessity in the improvement and sustainability of math instruction, however we all know that finding time to even use the restroom during the course of the school day is close to impossible! So how do we find time for these important conversations to happen and more importantly, we need to be fortunate enough to have a position in our school that does just that, coach.

Last week, my class was working on finding fraction/percent equivalents using a 10 x 10 grid.  They did great with the fourths and eighths, but then we hit 1/3!  As I walked around and talked to the students, I saw a range of strategies: shading one out of every 3 squares, shading one out of every 3 rows, then squares, and some just knew that three 33’s was as close as they could get with whole numbers and had just shaded 33. No matter which strategy they chose, the “leftover box” was leaving many perplexed.

After quite a bit of struggling with what to do with this leftover box and some happy to just settle at 1/3 = 33%, Nancy (our math specialist, former 3rd grade teacher, and partner in crime with all things math) came into the room.  She helped me by chatting with a group about their thoughts on what do with this 100th box. Class, unfortunately, had to wrap up to go to lunch, and I wasn’t comfortable that some students had had sufficient time to think about it, so I left the class with that leftover box as food for thought that night.

Over lunch, Nancy and I were talking about what she had heard from the students and she made the statement, “It is amazing how they don’t make connections to all of the sharing brownie work we did in 3rd grade when trying to count off by 3’s in the grid..” For those who use Investigations, you will  know the exact lessons to which she is referencing, for those who don’t you can probably infer the context 🙂 We discussed the difference of the contexts for students, the array work they do in 4th grade and then tried to figure how to make that connection for my afternoon class. Tall job for the 15 minutes left of lunch, AKA speed eating.

I typically start my class with some type of number talk, so we sketched out a number talk that focused on the brownie problems of years past. Lunch ended and when the class came in the classroom, they headed to the carpet for a number talk.

I did the following sequence of problems, sharing strategies as we went:

How can four people share one brownie?

How can four people share 6 brownies?

How can four people share a pan of 21 brownies?

They did an amazing job and were very confident in their strategies and I definitely put them into a “fraction state of mind.” We then went into finding our percentages and even the strategies for finding the percents equivalent to fourths and eighths seemed smoother and then when we hit 1/3 and that leftover box was much less mysterious.  There were still a few who struggled but I definitely could see more perseverance and entry points at problem solving. They seemed to make a connection to the brownie problems at the beginning of the lesson.

This entire rambling of my thoughts really boils down to one thought….Improving instruction is about finding time to have those meaningful math conversations. Had I not had that conversation with Nancy and changed my number talk for the second group, the lesson was going to have the same fate as the first.  That conversation helped me make math connections that I could then make my students. Would I have loved to have more time to think out this lesson and retry it the next day, of course, but did Nancy and I improve it…absolutely!

~Kristin

# 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