Wow! What incredible conversations we had about the first two chapters of *Math Sense: The Look, Sound, and Feel of Effective Math Instruction*, by Christine Moynihan. We’ve got a great professional learning community going here!

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Here’s the reading schedule (use the links to visit any of the posts):

__Aug 19, Chapters 1 & 2____Aug 26, Chapter 3____Sept 2, Chapter 4____Sept 9, Chapter 5____Sept 16, Chapter 6__- Sept 23, Chapter 7

### Chapter 3, The Look of the Lesson: Teachers

*“An essential part of being a teacher is to model what it means to be a mathematical thinker and then facilitate such thinking in students.” *Math Sense (pg. 40)

As I read this chapter, that quote really summed up the role of the teacher in today’s mathematics classroom for me. We’ve been talking a lot about the __Mathematical Practices__ on our campus, and this quote fits perfectly with our focus.

This chapter is about the role of the teacher, and what you might observe the teacher doing in a math class. It includes discussions about differentiating instruction, informal assessment and feedback, addressing common misconceptions, wait time, and communication of lesson goals and objectives. All critical components of effective teaching. With this chapter, we have the opportunity to critically reflect on our practices and set goals for the year. I guess you can tell from the quote I included above what my goal for the year is!

What does it mean to “facilitate mathematical thinking”? It means teaching students the habits that are second nature for mathematicians as they carry out their work. Often times we teach math without teaching students how to go about *doing* math. I love thinking of the mathematical practices as habits, because here is the definition of a habit from Miriam Webster:

an acquired mode of behavior that has become nearly or completely involuntary <got up early from force of *habit*>

Now let’s look at the author’s list of the components for facilitating mathematical thinking:

- use of manipulatives to introduce a concept or to explain mathematical thinking;
- application of a problem-solving heuristic; click here for a
__primary poster__based on George Polya’s process and here for the__intermediate version__ - use of mathematical notation;
- purpose of writing in mathematics;
- use of mathematical vocabulary;
- integration of technology;
- importance of perseverance; and
- gains to be made from mistakes.

So share what your big takeaway was from this chapter. Have you set a goal for the year? What part of this chapter did you really connect with?

So I am behind a bit but still wanted to add my thoughts. I teach Kindergarten so the first month is insanity so now that things are settling down I am back in to my professional reading. Chapter 2 was very appropriate as I was preparing my ALP (annual learning plan) while I was reading chapter 2. Last year much of our focus was on facilitating mathematical thinking and eliciting thought deeper explanations from our students so I very much appreciate the previous comments.

For me there were two sections that struck with me: checking for understanding and identifying student misconceptions. I feel that often these two things go hand it hand. Students may think they are understanding but when we start to ask for deeper explanations and demonstrations we sometimes realize they have some misconceptions of underlying concepts. One of my professional goals for this year is to understand both of these areas a bit clearer. If we can prevent some of the very basic misconceptions in Kindergarten maybe we can prevent later confusion and frustrations. I have already ordered some of the additional resources mentioned in these two sections and look forward to exploring them after I finish reading Math Sense.

It always makes my heart sing to hear Kindergarten teachers talk about how important their role is in developing mathematical ideas! I applaud your commitment to continue improve and evolve your math instruction. I hope you have a wonderful year!

Chapter 3 Thoughts-

As others have mentioned, facilitating mathematical thinking was one of the sections that I zeroed in on. I teach K so using manipulatives is a given, but what can happen in K if a teacher (like me) isn’t careful she can do a lot of the talking using a direct instruction format. Yes, the kids are given plenty of time to explore, but then “the lesson” is taught. My goal for the school year is to work on being a better facilitator, focusing on the language I use and the questions I ask. I really do want to honor who they are right now as mathematical thinkers and help them along to the next step. I want to give them every opportunity to develop a deep understanding of math. I know this is a worn out cliché, but I want to teach the child not the curriculum and it’s just so darn easy to slip into the opposite. I, too, find the magnifications in the book very helpful.

Other things that stood out were identifying student misconceptions, teaching from mistakes, and of course the importance of wait time (ugh! sometimes I’m so bad at this). I bought Bamberger, Oberdorf, and Shultz-Ferrell’s book Math Misconceptions. It’s fascinating.

Lot’s of info to process in this chapter. I’ll be re-reading it often.

You are rocking it, Sandi! I applaud you efforts, and I’m sure your kids will benefit greatly from all the new knowledge you’re acquiring!

I read Van de Walle’s book, Teaching Student-Centered Mathematics this summer also. I am learning a lot and am excited to put it all into practice. (Can you tell that working on my Math instruction was one of my goals for the summer?)

It’s a huge paradigm shift to step back from the “sage on the stage” role. Great goal-setting for the year! That’s what professional development is all about.

I completely understand what you mean when you say you end up doing a lot of talking. I also do! So I guess I should add to my list of goal is allow the students to explore more to get the answer instead of saying this is how we find the sum of and addition problem. I agree with you wanting to teach the students and not the curriculum, but it’s so easy to do the opposite.

Great reflections can be found in these comments thus far! A few of my reactions:

~ Yes, I know that while something always sounds good in theory, it is far more difficult to put our good intentions into practice. Starting a math class with a whole-class lesson (a relatively short one) and then breaking the class into smaller groups WILL give you a much better chance at catching student misconceptions and helping students to deepen their understanding. If you can start the year that way — and give yourself permission not to have everything go “perfectly” — you will more likely be able to sustain your drive toward that goal — and succeed!!

~ And yes — specific feedback will yield far greater results. Dawn shared that she has recorded herself to determine how often she uses the over-used “nice work” and “good job” and then challenged herself to be more specific — the sign of a reflective and active practitioner!!

~ Hurray for the comment about using manipulatives for the older grades — collectively they really are tools “to support” and to help students “deepen their understanding”!!!

It seems that shifting to a role of facilitator of mathematical thinking was a big ah-ha for many of us! I’m excited by the idea of how classrooms will be impacted this year by this new thinking.

“An essential part of being a teacher is to model what it means to be a mathematical thinker and then facilitate such thinking in students.” Math Sense (pg. 40)

That same quote really got me thinking. When we teach writing we do think a-louds, we talk through the process but when it comes to math it’s becomes of a here is how you do it now go do it. I have always tried to get the kids to think mathematically, explain their thinking of how they got to the answer, but what I realized is that I might not model that the way I should.

My goal this year, and right now in theory it works wonderfully, is to start with a whole group lesson and then break in to smaller groups, which will allow for me to differentiate my instruction, provide the necessary feedback, and address any misconceptions that arise. Like I said in theory it all works out great so we shall see how it goes.

Megan

Great connection to how we teach reading and writing, Megan! I will echo what Christine said, stick with your theory and it will become reality. Working with kiddos in small groups is THE way to go!

I just got home from a course I am taking for my math specialist degree. As I looked back at what I read from Chapter 3, it was like reading a summary of what we just talked about in my numbers and operations course and the standards for mathematical practice.

For me, the highlight of Chapter 3 was the Magnification section for Facilitating Mathematical Thinking. As I read through Ms. Lin and Julio’s journey to verbalize his understanding of multiplying fractions my mind was blown.

“Okay, let’s start with the statement that the hexagon is equal to one whole. Any thoughts from there?” (Math Sense pg 42)

I feel like many teachers stop using manipulatives in math after kindergarten. Then we wonder why they so many students struggle with fractions. I am definitely inspired to use my manipulatives as a better tool to support my students and deepen their understanding of math concepts.

Yes, Lori, I think fractions represent probably the best example of why manipulatives should be used in the intermediate grades. It’s such an abstract concept. I’m also struck when I see teachers trying to remediate skills without manipulatives. If a kiddo doesn’t understand the concept behind, for example, subtraction with regrouping, giving him a page of abstract problems to attempt isn’t moving his understanding along any.

In my role, I don’t usually give written feedback, but I need to be more explicit when I am giving verbal feedback to students. In the past I have recorded myself to see how often I use phrases like, “nice work” or “good job.” Then I challenge myself to think of more specific feedback I could have given. It’s an area where I need to continue working.

I love the idea of taking pictures as part of feedback! I understood the written feedback to be for students, not necessarily parents, so I think oral feedback for Kinders is absolutely appropriate. Keeping in mind, as you mentioned, that it should be specific, productive, and respectful.

I also teach Kindergarten and find feedback difficult. We are a play based program so often there is not a product that I can write feedback on. I use oral feedback frequently I feel that the three areas mentioned in chapter 3 can still be used (specific, productive and respectful). I do often take pictures of their work and mathematical exploration that I share with parents and maybe I can add written feedback on these for parents and students to review together.

It’s so important that we’re specific with our feedback. Dawn, I love that you videotaped yourself. As a math coach, that’s something I’d like to do more of for my teachers. It’s a powerful thing seeing yourself in action!

More thoughts on feedback – I’m taking an online class through Stanford, taught by Jo Boaler. She talks about the importance of saying, “I’m giving you this feedback because I believe in you.” She cited research that students who heard “because I believe in you,” made greater progress.

sorry that should be giving, not given!

I teach kindergarten so given the students written feedback on their paper isn’t something I do often because they can’t read it, if I do, it’s more for the parents. I say “good job” or “well done” more than I should too. After reading this chapter my goal would be to be more specific in saying I notice how you… and let them know exactly what it is that they did do well.

Until recently, it never occurred to me to write much more than, “well done” or “neater please” on student papers. I think it is important for the students and parents both to understand what it is we like about their work or why their work needs to be neater. It is a good way for us to communicate to the students about their individual needs or strengths without doing it in the middle of the classroom.