Welcome to our book study! The book I’ve chosen this time around is * Math Sense: The Look, Sound, and Feel of Effective Math Instruction*, by Christine Moynihan. I know many of us are in back-to-school mode, and this is a wonderful book to read as you plan your mathematics classroom. I hope this will be a very collaborative book study, with lots of great comments and discussion.

*This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.*

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 1, What is Mathematics?

The book starts out with what seems like a simple question…what is mathematics? Which of the comments in the first paragraph did you most connect with? While I did a lot of head bobbing on all of them, for me it was this quote:

*“Further, you likely believe that teaching mathematics makes a difference in how your students view mathematics and how they view themselves as mathematical learners.”*

Let’s face it, math gets a bad rap. It’s socially acceptable to be “bad at math”. Parents too often tell their children, “Don’t worry, I was bad at math, too.” I think it’s so critically important that we work to overcome that stigma. Math is fun! Especially elementary math. It is a wondrous puzzle waiting to be solved, and who doesn’t like puzzles?

Be sure to add a comment discussing your thoughts on the question!

## Chapter 2, The Look of the Landscape

This chapter introduces us to the format of the rest of the book. Each chapter describes components of effective math instruction–how it looks (Chapter 2-4), feels (Chapter 5), and sounds (Chapter 6). For each component, the author tells what it is, why it’s important, and where or when you might encounter it. Finally, there is a ‘magnification’ of the component–a glimpse into the classroom where you will see student work and hear student voices. It’s a great organization and a very engaging read.

Go into a person’s house, and you immediately see clues about what the people living in the house value. You might see pictures of family members and pets, a large flat-screen TV, high-quality pots and pans, or books scattered around. And all of those items would be a window into what that family values. The same goes for your classroom! If a visitor enters your room, what do they see that tells them you value math?

The chapter contains ten elements that the author says “convey the high regard mathematics occupies and its meaningful role in your classroom.” The list includes tools that should be present (number lines, hundred chart, manipulatives, daily schedule), classroom arrangement considerations (designated mathematics areas, multiple instructional settings), and instructional strategies (mathematics word wall, mathematics literature collection, technology). The final component is one that I feel is often underutilized–student work samples. A long list of authentic examples of work samples is provided, but I really like the explanation of why displaying student work samples is important. Here’s the list of reasons from the book:

The purposes of posted student work are

- to make a clear statement about the importance of their work in mathematics,
- to serve as a source of pride for students in their completed work,
- to demonstrate multiple solutions to the same problem and sometimes even multiple correct solutions,
- to provide a model for other students in mathematical communication, representation, and reasoning.

So my challenge this new school year will be to engage my teachers in conversations about the importance of student work samples and to work closely with them to ensure our mathematicians’ work is proudly displayed.

What about you? What did you read from this chapter that’s going to bring about a change in your classroom this year? Please share! 🙂

Hello to all of you taking part in this online book study — I am thrilled both by your participation and your comments. Donna has done a fabulous job responding to your thoughts, questions, and suggestions — I find myself nodding in agreement with you, the readers, and Donna as well.

A few general comments I will add:

~ I love that the “pomegranate” quote resonated with some of you. If any of you ever had the privilege of listening to and learning from Father Stanley Bezuszka from Boston College, you can agree that his passion for both the teaching and learning of mathematics was a central focus of his life’s work — and incredibly contagious!

~ Many of you shared that a goal for the upcoming year will revolve around supporting the development and understanding of math vocabulary via Word Walls – you will not be sorry and will be excited about the benefits your students will reap from this. As someone put, building a “numeracy-rich environment” is a great idea – kudos to all taking this on for the new year.

~ Yes – student-made anchor charts – nice idea!!

~ You are so right to think about taking the time before school starts to organize / re-organize your math manipulatives / materials. While this certainly can be done all throughout the year, it is easier to do it before the day-to-dad demands absorb so much of your time. By the way, I laughed out loud when someone mentioned how it was time to “quit trying to audition for Hoarders’ episodes and weed through resources!!!!”

~ LOVE the idea about having a Thursday night homework assignment be a discussion about how math has been used that day / that week!!

~ Donna did a great job explaining the rationale behind having a number line that extends to 180. To the person who shared how a pocket chart is used to represent the days in school – that, of course, is a good thing to do. I would just add that an additional power of the number line is to use to show where you are in the school year – Day 1, we are here, and the year will end after 180 days. As you move through the year, you can start to talk about fractions in an applied way — the kids love noting they are less than half but not too much less, etc.

Thank you all for your participation – I am hopeful that the rest of the book will give you some support as you start and then move into the year. To those of you starting this week – best of luck and remember to take some time to step back and enjoy the excitement of starting this new journey with those wonderful hearts and minds coming to your classrooms!!

Welcome, Christine! How wonderful to have you involved in our conversation. Thanks for taking the time to join in!

I just ordered my book so will be behind you all! I was wondering if you had suggestions on how I should display student work & anchor charts if I am teaching 3 different Kindergarten classes in my room. My collegues and I are teaching core subjects so that we can be strong in one area instead of spreading ourselves over all the subject areas (I will be teaching math). I want my classroom to be a strong math room that like the author suggested should be meaningful and valued.

I recommend creating the anchor charts with the kids, Laura, so I’d say you’d make each chart three times and leave the last one displayed. As far as student work goes, if you’re only teaching one subject you should have wall space. I think I’d probably combine work from the different classes, instead of making separate sections for each class. Does anybody else have any ideas or thoughts?

Donna, you spoke of your “environmental checklist”…? Can you share? I have really been thinking of how I teach math & beginning to reevaluate my classroom math environment. I would LOVE to see your checklist..You have become my MATH “Go to” Teacher….Thank YOU! wendy [email protected] 1stgradefireworks

PS…Bought Van De Walle’s new book! Can’t wait!

Hmmm, let me try again. Try this

link.Hello, came back to read today’s post and check in on the checklist here. Unfortunately, the link isn’t working. Thanks for taking the time to share.

Sure thing! It’s totally a work in progress–I’m sure we’ll tweak it this year. Literacy and math are combined on one checklist. Click

hereto grab it!I would love to see a copy of the environmental checklist as well. So much can be found on literacy rich environments; math not so much.

Sure! I’ll get an electronic copy at work tomorrow and post it.

Most of the teachers in my school have most of the important “landmarks” in their math landscapes. The one that struck me as missing most of the time is a Designated Mathematics Center/Area. They may have their math manipulatives all in one place, but the area is not as inviting an area as the reading area. It is more of a storage area, not a place to come and explore math. The part where the author talks about the library having a place that makes you want to “stop and nestle in for as long as I can” is not usually how the math area is perceived. I think that this takes math out of the realm of enjoyment and discovery and puts it in the realm of things that you have to endure to get through the day. Maybe if we concentrate on making it a more inviting place to be, more students will choose to “stop and nestle in” for as long as they can, and mathematics will become something with which they can become more comfortable.

That is a great observation! We definitely need to make math feel more inviting!

Hello Donna and all

I am really enjoying your blog and resources Donna. It is lovely being inspired by your ideas and finding the resources to support them too, and also finding the ones by surprise that I’ve been intending to make! I got very excited by this book but it doesn’t seem quite as relevant to me here in England due to how we structure maths lessons after our National Numeracy Strategy in 1999, which is very much about whole class lessons leading into group work with roughly the same LIs, and was very prescriptive over resources or manipulatives/ples/ates/apparatus. We are also all expected to have visual timetables (http://displays.tpet.co.uk/?resource=253#/ViewResource/id253 http://www.sparklebox.co.uk/toolbar/no/thumbs22/sb5912.html#.UhUujxusiSo )

However, I really like the idea from this book of the 4 corners working wall with the word, picture, definition AND personal link/reminder. It is really clear from all my googling this holiday that you are all much better educated in precise language there, though I can’t find ‘addends’ or ‘subitize’ in any of my heroes’ books, including my guru Derek Haylock, nor Fosnot and Dolk whose ‘mathetize’ I love!

I also really like the idea of maths stations which are a bit ad-hoc here from classroom to classroom, besides the labelled drawers of apparatus which we all are expected to have. We are expected to have interactive displays but because most of our maths time is directed there is always a feeling of, great, but when will they be used? I read online an idea from an American teacher of a time for free choice after lunch, which I really like and hope to feel brave enough to try with my 5 year olds come September.

I am so sorry to be going off the point of the book even more now, but what I will take with me into my school from the snuffling around and following suggested link to pop-up, will be sticking to a few key images to help my Year 1s (5 year olds going into the second year after their first year at school)develop their number sense. I love that ‘number sense’ is all over your websites. Here, I’ve only read it in Julia Anghileri books. I will be focusing on Rekenreks, tens frames and dot patterns, along with numeral cards, number lines and 100 squares, but only after turning our daily count number line into one. I am loving the morning routines too, especially the weather tally, which I have never thought of doing. I have so many now, though, that we may need to have afternoon routines too. Sorry. I know this wasn’t the best place for all of this. It was my birthday on Saturday and it’s taken me a while to let all I’ve read mull around and then regain focus and time to write. Thank you for all you do. Your resources are fantastic. I have in my head a great one for an investigative approach to fractions. If/when I get it made I’ll get it put on somewhere to share.

Thanks again Donna. Sorry to highjack your book club. It wasn’t my intention at all to go off track.

This comment has been removed by the author.

Not off track at all! It was really interesting to me to read more about “maths” in England. I love that you are finding ways to inject more flexibility into what sounds like a fairly rigid system. And, Dawn, I LOVE that book!

Have you read Teaching Number in the Classroom (http://www.amazon.com/Teaching-Number-Classroom-year-Recovery/dp/1412907586)? One of the authors, Jim Martland, is British and you might find some good connections there. You will also make lots of connections to the resources Donna shares.

As I read through chapter 2 I was very happy/relieved to see that I already have most of the items listed in my classroom. The one thing we don’t have in our Kindergarten class is number lines. I have ordered a standard horizontal line to post on the walls but I think we are going to make our vertical one together as a class. I am wondering how important it is to have negative numbers on it in my JK/SK classroom – will this confuse them? Also why is 180 the magic number? I understand going above 100 but why 180?

Last year we built our 100’s chart together as a class as we counted the days we were at school. This was incredibly effective. We are going to do this again this year but will we continue past 100, I totally understand when they say kids sometimes think everything stops at 100.

We don’t start until after labour day but I went into my classroom this morning for the first time. The first thing I did was start organizing our ‘Math Corner’. All of the components: manipulates, literature, math word wall, etc, we had in the class last year but they were spread out. This year they are all in the same area – near a few tables the students can take materials to for exploration. We always have student work samples on display but I am going to work on more carefully displaying work that they can refer to for future learning.

Oh, absolutely, Sandi!

We keep track of the number of days in school using a pocket chart- would that work as well? The kids put a number card in every day. I have a number line posted up to 110, but not to 180.

I was curious about the reference to 180, so I asked the author! She and I have been communicating about the book study, and she’s thrilled with the dialogue that’s taking place. She hopes to jump in Monday night!! Her explanation makes perfect sense. The school year is around 180 days in most districts, so students have a great reference point for the number line. Pretty neat, right?

I know exactly what you mean!! We developed an Environmental Checklist last year listing items we thought we should see as evidence of quality math instruction, and our list matched up really well with the list in this chapter! Whew! I like having the negative numbers displayed, and I don’t think it would confuse them. I think a good example of negative numbers is temperature. I’m not sure why 180 is the magic number either. Let me see if I can find out more! I’ll bet your Math Corner is gonna rock! 🙂

The sentence that struck me was the very first: “mathematics is much more than memorizing and spilling out ‘learned’ definitions and procedures”. Last year our PLC was focused on improving mathematics instruction at our school. Our focus was on communication in math. As we went through the venture of working with our students to help them communicate their learning I quickly learned that many of my students knew much less than I thought they did. They had become very good at memorizing and giving me the answers they thought I wanted to hear. When I listened closely I realized that some of them really struggled to really understand the math. We worked very hard on changing the culture in our classroom from answer based to process and thinking based. When possible I tried not to highlight the answers they came up with but instead the communication of their ideas.

What a GREAT focus your school chose. Did you also find that your kiddos were more engaged in math and enjoyed it more the more they communicated? I know it was probably hard for them at first, but I’ll bet it really livened up your classes!

My goal this summer was to improve my math instruction. I was excited to see that many of the things I had already added to my room were listed in Chapter 2. My number line, however, only went to 100 so I am working on finding a way to keep my cute number line that goes with the theme of my room but adding to it to make it go to at least 180.

Hmmmm, what if you let the kids extend the number line? 🙂

Thank you for allowing me to join this book study. As a math consultant in a regional education agency I am anxious and excited to be learning and discussing this book with classroom teachers. I’m looking forward to your insights.

The more the merrier, Denise!! I’m thrilled with the thoughtful dialogue we’ve got going so far! 🙂

The phrase that I hung on for that extra split second was “there are essential elements of mathematics teaching that can and should be seen, heard, and felt.”

The second chapter fits in with a goal I had set for myself as the last school year was winding down — having a dedicated math area. My classroom is on the small side and since it’s not been renovated since technology has made it’s way into our daily lives, I lose quite a bit of space because of my teacher station and all the wires! So, I have decided to quit trying to audition for Hoarders’ episodes and have been weeding through resources, materials, etc. that I no longer use. I don’t start school until after Labor Day so I am just going back and starting the unpacking this week and have also gotten rid of some furniture that was just cluttering my room. My only other issue to contend with is that, since I teach all subjects, I also have to have word walls and such for my other subjects, too. I don’t have all that much wall space, so I’m going to have to get creative.

What an awesome way to approach the new school year, Beth. I got a chuckle out of your hoarders comment! I’m sure you’ll figure out a great solution for your word walls. 🙂

Chapter 1-

Two phrases that stood out to me- “. . mathematics is much more than memorizing and spilling out “learned” definitions and procedures. .” and “computational speed is not the defining mark of a good mathematical thinker.” I’ve observed that math, particularly in the younger grades, is viewed as a body of knowledge that can be mastered through the memorization of facts and procedures. The “thinking” part of math is often not fleshed out in our teaching. Few teachers would approach reading or writing in this way, knowing that the process is much more complex than learning how to decode words, etc. One of my year-long goals for my classroom this year is to build a numeracy rich environment as the text mentions. We are literacy “heavy” in our school and I hope to provide more balance through Math Workshop, Math Warm-ups, etc., and mostly by being more conscious of connecting math to students’ real lives.

Chapter 2-

The Math Word Wall and the Student Work Samples were two items I will be adding to my room. As Terri mentions in her post, I like the four corner approach and bringing in the real world connection. This year in my class a standing Thursday night “homework” activity will be for families to talk about how they’ve used math that day or that week. Students will have a chance to talk about it during a special Math share time each Friday.

I never really thought about how work samples could be beneficial in math. As you mentioned, I like how the text explains why each item is important and doesn’t just leave us with a list and a few vague thoughts. I’m appreciating the thoroughness, but yet the simplicity of the explanations.

“The “thinking” part of math is often not fleshed out in our teaching.” Love this thought, Sandi! We need to spend more time teaching our kiddos the habits of mathematicians, otherwise known as the Standards for Mathematical Practice.

Chapter 2 thoughts (and comments on your post)

There is so much to talk about! I am going to focus on the Word Wall. So many times I walk into a room and see a list of vocabulary words on the bulletin board with nothing to go with them. When I ask the same answer is given “they definitions are in their notebooks/index cards” I love the four corner approach, I have had my kiddos draw pictures, write the word and definitions, but the part that says “personal connection” WOW! how much meaning with that give to kids, and therefore make it easier for them to remember it. I am sure there are some words that will be difficult for them to do that with, I know I would struggle with some myself, but what a powerful tool that is. Then to display that work on the word wall – it shows ownership, as well as giving the kids the pride that they were the ones to create the board that others are using when they need help.

I am a math specialist, I go into rooms for 1/2 hour to and hour 1 – 2 times a week and work with the teachers with what they need for that time – small group, interventions, extensions, as a second person to help with or to lead the lesson, or as a co teacher – changes all the time! there are many things here that I would love to do with the teachers I work with – some would be interested in hearing it – others just want me to come in and do what they want – I am hoping that these are some things I can implement with the teachers that want to, and perhaps I can with some that don’t 🙂

You make an excellent point, Terri. You can lead a horse to water and all that. I think the key is just what you said. Work with the teachers who are open to new ideas. The enthusiasm and engagement that happens in their classroom just might be contagious!

That same quote is one that I highlighted as I read the first chapter. Another one that had me bobbing my head was the “we continuously work to improve our teaching so that our students’ learning improves”. Which is one of the reasons I decided to join in on this book study. One of the gals that I am teaching kindergarten with this year and I just had a long chat about math and the fact that our score on the MAPS test showed that the Kindergarten didn’t fair well. I want to figure out how I can be a better math teacher, which bring in some of what I took away from the 2nd chapter. Since we still don’t have the students, I have decided that I am going to try and incorporate a math wall where I will display student made anchor charts, I can statements for each unit, calendar, 100’s chart, number line, all in all just create a classroom where math is fun.

Megan

What an accomplishment, Megan!

Well it only took me an hour but I got it done. I organized them into types and then I have a white bin for each table that will house any manipulatives that they might need for the lesso. Even though the manipulatives aren’t located in my math corner, they are still easily accessible for all the students. I feel so much better to have those organized and ready to go.

Megan

Great timing, and I admire your commitment to want to get it done right away. 🙂

The teachers officially go back to work on Monday and we really only have one day with meetings, after reading this first chapter and realizing what a disaster my math manipulative are, I am going to tackle that first! Thanks to summer school my room is set up and ready to go so I can work on other areas of my room!

Megan

Megan, my hat is off to you!! How can we hope to teach our students to be life-long learners without modeling it? Love your action plan. 🙂

Chapter 1 thoughts (and comments on your post)

I love the idea of the pomegranate analogy! It makes sense, so many little ideas and methods, put together to give you this one larger entity that is so delicious!!! 🙂

I agree, that math has gotten a bad rap, and the ability to say, “I’m bad at math” and not be ashamed, like you would be if you said that about reading, is amazing to me. I remember teaching a workshop on the math standards through 5th grade to teachers in K-2, and they said to me “I teach first grade, why do I need to know how to do 4th grade math?” I was astonished, the progression that is needed in math is not something many teachers in younger grades thought about. Many teacher would teach their kiddos it was ok to change the order of the numbers when they were doing addition, but never really talked about why, and they were so frustrated when they would switch the numbers in subtraction. I told them, adding a few words when they talked about it would help. “You can do this because it is addition,” always lead to the question “Can you do it with subtraction?” and then it was talked about and the problem was eliminated.

In third grade when multiplication is taught and the “repeated addition” and your answer will always be larger is great, but when they get to 5th grade and start multiplying fraction and they can’t use the repeated addition or the answer is smaller, then they are confused. Adding the words “with whole numbers” in third grade will help alleviate some of that confusion.

Didn’t mean to be so wordy! I will do a separate comment on chapter 2 as I haven’t quite finished it yet. 🙂

Don’t apologize for being wordy, Terri! Sharing great thoughts is the point of the book study. I think Common Core has really put the spotlight on the ‘why’ behind the ‘how’, and that’s a GREAT thing!

The phrase from the first paragraph that resonated with me is “…that it can, should, and must be accessible to all students.”

In the second chapter, the component that I would like to see more of (especially in intermediate grades) is manipulatives. Too many teachers think that students only need manipulatives in primary grades. They don’t recognize that visual should be used whenever students are introduced to a new concept.

Amen, Dawn!! The CRA sequence of instruction (concrete, representational, abstract), is for ALL ages! Just look at fractions as a great example. Not really taught until 3rd grade and definitely a skill that requires lots of concrete experience!