Blogstitute 2017: Which Comes First in the Fall–Norms or Tasks?

In this last post of our Summer Blogstitute series, Tracy Zager, author of Becoming the Math the Teacher You Wish You’d Had, shares her ideas for kicking off the school year in your math classroom ready to notice, imagine, ask, connect, argue, prove, and play.

Which Comes First in the Fall–Norms or Tasks?
Tracy Johnston Zager

I periodically hear discussion about whether it’s better to start the new school year by establishing norms for math class or to dive right into a rich mathematical task. I’m opinionated, and I’m not shy about my opinions, but in this case, I’m not joining one team or another. They’re both right.

The first few weeks of math class are crucial. You have a chance to unearth and influence students’ entrenched beliefs—beliefs about mathematics, learning, and themselves. You get to set the tone for the year and show what you’ll value. Speed? Curiosity? Mastery? Risk-taking? Sense-making? Growth? Ranking? Collaboration? You get to teach students how mathematics will feel, look, and sound this year. How will we talk with one another? Listen to our peers? Revise our thinking? React when we don’t know?

In Becoming the Math Teacher You Wish You’d Had, I wrote about a mini-unit Deborah Nichols and I created together. We called it, “What Do Mathematicians Do?” and we launched her primary class with it in the fall. We read select picture-book biographies of mathematicians, watched videos of mathematicians at work, and talked about what mathematics is, as an academic discipline. We kept an evolving anchor chart, and you can see how students’ later answers (red) showed considerably more nuance and understanding than students’ early answers (dark green). [Figure 2.1]

Figure 2.1

Throughout, we focused on the verbs that came up. What are the actions that mathematicians take? How do they think? What do they actually do?

In the book, I argued that this mini-unit is a great way to start the year if and only if students’ experiences doing mathematics involve the same verbs. It makes no sense to develop a rich definition of mathematics if students aren’t going to experience that richness for themselves. If professional mathematicians notice, imagine, ask, connect, argue, prove, and play, then our young mathematicians should also notice, imagine, ask, connect, argue, prove, and play—all year long.

In June, I saw this fantastic tweet in my timeline.

It caught my eye because Sarah’s anchor charts reminded me of Debbie’s anchor chart, but Sarah had pulled these actions out of a task, rather than a study of the discipline. I love this approach and am eager to try it in concert with the mini-unit. The order doesn’t matter to me.

We could (1) start with a study of the discipline, (2) gather verbs, (3) dig into a great task, and (4) examine our list of mathematicians’ verbs to see what we did. Or, we could (1) start the year with a super task, (2) record what we did, (3) study the discipline of mathematics, and (4) compare the two, adding new verbs to our list as needed. In either case, I’d be eager for the discussion to follow, the discussion in which we could ask students, “When we did our first math investigation, how were we being mathematicians?”

Whether we choose to start the year by jumping into a rich task on the first day, or by engaging in a reflective study about what it means to do mathematics, or by undertaking group challenges and conversations to develop norms for discourse and debate, we must be thoughtful about our students’ annual re-introduction to the discipline of mathematics.

How do you want this year to go? How can you invite your students into a safe, challenging, authentic mathematical year? How will you start?

1 comment August 1st, 2017

Now Online: Becoming the Math Teacher You Wish You’d Had

becoming-the-math-teacher-you-wish-youd-hadTracy invites you on a journey through this most magnificent book of stories and portraits…This book turns on its head the common misconception of mathematics as a black-and-white discipline and of being good at math as entailing ease, speed, and correctness. You will find it full of color, possibility, puzzles, and delight…let yourself be drawn in.

— Elham Kazemi from the foreword

While mathematicians describe mathematics as playful, beautiful, creative, and captivating, many students describe math class as boring, stressful, useless, and humiliating. In Becoming the Math Teacher You Wish You’d Had, Tracy Zager helps teachers close this gap by making math class more like mathematics.

Tracy spent years observing a diverse set of classrooms in which all students had access to meaningful mathematics. She partnered with teachers who helped students internalize the habits of mind of mathematicians as they grappled with age-appropriate content. From these scores of observations, Tracy selected and analyzed the most revealing, fruitful, thought-provoking examples of teaching and learning to share with you in this book.

Through these vivid stories, you’ll gain insight into effective instructional decision making. You’ll engage with big concepts and pick up plenty of practical details about how to implement new teaching strategies.

All teachers can move toward increasingly authentic, delightful, robust mathematics teaching and learning for themselves and their students. This important book helps us develop instructional techniques that will make the math classes we teach so much better than the math classes we took.

Add comment December 15th, 2016

Now Online: Which One Doesn’t Belong?

Danielson’s book reveals the wonder and freedom of expression that many children don’t often experience in mathematics. A single, simple question puts children in a position to speak mathematically even at early ages. Ask students of all ages “Which one doesn’t belong?” and revel in the reasoning and conversation that results.
—Dan Meyer

How can I recommend this highly enough? Christopher Danielson emphasizes the stimulation of curiosity and that math is about making precise things that we—and children—can informally observe, without having to learn any mathematical language first. Which One Doesn’t Belong? is a glorious book for adults and children to explore together, and the Teacher’s Guide makes it into a profound mathematical resource.
—Eugenia Cheng, pure mathematician, University of Sheffield and School of the Art Institute of Chicago, and author of How to Bake Pi

Which One Doesn't Belong student bookWhich One Doesn’t Belong? is a children’s book about shapes. More generally, it’s a book about mathematics. When children look for sameness and difference; when they work hard to put their ideas into words; when they evaluate whether somebody’s else’s justification makes sense—in all of these cases, children engage in real mathematical thinking. They build mathematical knowledge they can be proud of. They develop new questions. They argue. They wonder.

In the accompanying teacher’s guide, author Christopher Danielson equips teachers to get maximum benefit from Which One Doesn’t Belong? Through classroom stories, he models listening to and finding delight in students’ thinking about shapes. In clear, approachable language, Danielson explores the mathematical concepts likely to emerge and helps teachers facilitate meaningful discussions about them.

You can preview portions of the teacher’s guide online now!

2 comments August 4th, 2016

Taking apart the “key word” strategy

Today we have a guest blog post from Christine Moynihan, author of the recent math books Common Core Sense and Math Sense. Christine takes a close look at the often-used “key word strategy” and explains why it might not be the best way to help your students get to the right answer.

Taking apart the “key word” strategy
By Christine Moynihan

Christine Moynihan

Christine Moynihan

“Does your answer make sense?” Can you estimate how many times you have asked your students this question in regard to word problems? Even if you are a beginning teacher, I am willing to bet that it has been, on a daily basis, several times a day, five days a week, 180 days a year! Do the math and you will find that you have asked that question of your students a staggering number of times.

Even if your students answer in the affirmative — “Yup, my answer makes sense”!what may pass for their answers making sense is that they’ve  checked to see if their computation is correct; if it is, they assume they are good to go. Tucking their answers back into the context of the problem after they have completed the computation still may not come naturally to them, even though you and their previous teachers have tried to build it into your practice, their practice, and the practice of mathematics in general.

In my pre-service math methods classes, I was told that when I was helping students learn to solve word problems, I had to support them first in making sense of the problem so that they could then determine which operation they had to perform. One way to do this, considered good teaching practice, was to tell them to search for key words.  The next step was to get them to underline those key words, underline the numbers in the problem, and then to use the key words to write a number sentence to solve the problem.  My guess is that many of you may have had the same experience in pre-service as well as having been taught that way when you were in elementary school yourselves.  A few of the key words/phrases you most likely learned are: for addition – in all, altogether, total, increase, combined; for subtraction – difference, left, fewer, decrease, gave away, take away; for multiplication – of, times groups, twice, double; for division – per, groups, share, out of.

So what’s wrong with the key word strategy?  I have had to answer that question countless times in my previous roles of mathematics curriculum specialist and building principal, as well as in my current role of educational consultant. The short answer is that using the key word strategy has limited scope and value.  Further, it can be incredibly misleading and steer students to wrong answers that make no sense at all within the context of the problem.  Additionally, it sends students the wrong message in terms of them thinking that solving problems can be done routinely, formulaically, and without much deep thought.

Let me share a recent experience I had with one of the fourth grade students with whom I have worked for two years.  We were going over a sheet of problems he had done in class, as he had to make corrections to the ones he had gotten wrong.  Now Jared is a very bright fourth grader who excels in reading, is highly engaging, and knows a great deal of information about a wide variety of subjects.  He likes to work fast, think fast, move fast, and complete his work fast.  Mathematics is not always his favorite subject and he often shuts down his thinking if he cannot see a solution path quickly.  Here is one of the problems he had done:

Mr. Smith bought 14 new globes that his students could

use in class as they studied Earth.  Each globe cost $76.

How much did the new globes cost in all?

Jared’s answer?  I bet many of you can predict what his answer was.  If you thought that he had written $90, you would be correct.  I had him read the problem aloud and asked why he thought his answer made sense.  His response was, “I did the right thing because 14 plus 76 equals 90.  I did it in my head, but I know it’s right and I even put a dollar sign in front!”

I asked him to draw a picture that represented the problem.  He drew 14 circles to show the globes. When I asked what the cost was for the globes, he wrote 76 under the first one and then did the same under the others.  He then said, “This won’t work.  Look at the problem – it says ‘in all’ and that means you have to add, so the real answer has to be $90.”

My next question was, “How much did two globes cost?”   He immediately replied, “Well, it could be $152 but that can’t be right!  They told me to add!”  I had him continue to work and after he had successfully solved the problem, he looked at me and said with utter conviction and even a bit of indignation, “It’s not my fault!  They put in ‘in all’ so how I am supposed to know I shouldn’t add?”

I know for certain that there isn’t anyone who teaches key words as the only and/or best problem-solving strategy. But the rigidity with which Jared applied the strategy reinforced for me just how limiting and misleading it can be. I continue to work with him with one of my goals being that he understands that the responsibility for making sense of a problem rests with him and that he needs to add to his repertoire of problem-solving strategies to ensure his answers make sense.

1 comment April 27th, 2016

Now Online: Well Played, K-2

Well PlayedK2Well Played, K-2 is the second in a series of three books by Linda Dacey, Karen Gartland, and Jayne Bamford Lynch that helps teachers make puzzles and games an integral part of math instruction.

Following the same accessible format as the first book in the series (for grades 3-5), 25 field-tested games and puzzles are each introduced with math areas of focus, materials needed, and step-by-step directions. Readers will see how they play out in the classroom and get tips on maximizing student learning, exit cards for student reflection, variations, and extensions. The rich appendix has reproducible directions, game boards, game cards, and puzzle materials, and each chapter includes assessment ideas and suggestions for online games and apps.

Get your K-2 students talking and learning more as they play games and build their thinking as mathematicians. Well Played, K-2 is available now, and you can preview the entire book online!

1 comment December 15th, 2015

Blogstitute: Got Common Core?

Today’s Blogstitute post comes from Christine Moynihan, whose latest book is Common Core Sense: Tapping the Power of Mathematical Practices. In this post Christine introduces the GOLD framework that helps make the Standards for Mathematical Practice more accessible to elementary teachers. Be sure to leave a comment or ask a question for a chance to win 12 Stenhouse books! On Twitter you can follow along using #blogstitute15.

Got Common Core?
By Christine Moynihan

FC FINAL CommonCoreSense.inddSomething I hear from many teachers is that it is challenging to be up-to-date on everything that teachers should and must know in order to be effective practitioners. This is especially true for elementary teachers, who are asked to be content experts in reading, writing, grammar, spelling, science, social studies, and, of course, mathematics. Not only do they need to have expertise in these curriculum areas in terms of content, but they must also be experts in the best instructional practices that will support their students in learning in each of these areas. (I’m not even going to go into how they also have responsibility for social and emotional growth, health and wellness, behavior management, and the list goes on. . . . )

So, as a former classroom teacher, I get it. As a former curriculum specialist, I also get it. As a former principal, I most certainly get it. As a current educational consultant, not only do I get it, I hear it all the time—there is just so much to know, so much to learn, so much to do. As a result, when I ask a variation of the “Got Common Core?” question, many teachers respond that although they “get” the basics of the Common Core in terms of the standards for mathematical content for their specific grade levels, they believe that they have a somewhat light understanding of the standards for mathematical practice. Most teachers report that what they know about the MPs has been by way of an introductory look at them at a professional development session and/or staff meeting, with little or no follow-up.

My major purpose in writing Common Core Sense: Tapping the Power of the Mathematical Practices emanates from my desire to help teachers gain a foothold in understanding the MPs and how they can affect their practice. The book is meant to be a vehicle for making the eight Standards for Mathematical Practice more accessible to elementary teachers, for I see them as the core of mathematical proficiency. As I wrestled with how to do that, I defaulted to something that has always worked for me as a learner—to devise some kind of a framework, a mnemonic of sorts, to aid in understanding and then activating that understanding. Because I had been saying over and over again that “the gold of the Common Core really lies within the mathematical practices,” I constructed the GOLD framework to help teachers see some of the major components of each MP and then think about what they may look and sound like in classrooms, and what might need to be done to support the incorporation and implementation of the MPs into daily practice.

The Framework:
Go for the goals—What are the major purposes of the practice?
Open your eyes & observe—what should you see students doing as they utilize the practice? What should you see yourself doing?
Listen—What should you hear students saying as they utilize the practice? What should you hear yourself saying?
Decide—What do you need to do as a teacher to mine the gold?

I identified three major goals for each mathematical practice, fully aware that there are many more goals to be found within each. In the link you will find what I have identified as the second goal of Mathematical Practice #3: Construct viable arguments and critique the reasoning of others. What’s not to love about MP3? When you can analyze your thinking enough that you can clarify it, defend it, justify it, and represent it, you have learned something that will be valuable in all areas of life. In terms of mathematics, that ability leads you straight to the path of being mathematically proficient—a goal we all have for our students. I hope that the chart for the second goal I identified for MP3 can help in your work to make this MP come alive for the students in your classrooms.

Accept that viable explanations of mathematical thinking must be organized, reasonable, and justifiable/laden with proof.

8 comments July 6th, 2015

Now Online: Well Played

well-played-grades-3-5In addition to fun, math games can be an important part of your curriculum and give teachers unique insights into student thinking. In their new book, Well Played, Linda Dacey, Karen Gartland, and Jayne Bamford Lynch offer 25 field-tested games and puzzles that go beyond computational fluency to engage students in grades 3-5 with key mathematical concepts.

Each game or puzzle is introduced with math areas of focus, materials needed, and step-by-step directions. Readers will see how it plays out in the classroom and get tips on maximizing student learning, exit cards for student reflection, variations, and extensions. The extensive appendix has reproducible directions, game boards, game cards, and puzzle materials, and each chapter includes assessment ideas and suggestions for online games and apps.

Well Played will help you get students talking and learning more as they play games and build their thinking as mathematicians. You can now preview the entire book online, order the e-book version, and preorder the print version which ships early next month.

1 comment June 19th, 2015

Six calls to action at Shadowcon

We are excited to have a guest blogger today: David Wees is a math teacher in NYC and he recounts Shadowcon — the alternative NCTM conference  — for us.

Six calls to action at Shadowcon

Imagine six engaging speakers, each with ten minutes to convince you to make a specific change in your teaching. At the end of the night, you select which change you want to work toward, and ideally you take action. So describes the experiment in professional learning called Shadowcon, hatched by Dan Meyer, Zak Champagne, and Michael Flynn and shared for the first time at the NCTM Annual Meeting in Boston.

Kicking off the night was Tracy Zager, a mathematics educator who lives in Maine. Tracy shared with us her heartbreaking story of working with elementary school preservice teachers, a majority of whom have negative feelings about mathematics. She described how these feelings were very likely caused by the early experiences in mathematics and how too often these teachers use the same teaching practices that caused their own math anxiety, creating a generational cycle of fear of mathematics. Tracy called on all of us to break the cycle by opening conversations about our experiences with mathematics in school and to start closing the gap between school math and the way mathematicians experience math.


Next up was Elham Kazemi, a teacher-educator at the University of Washington. As part of her work, Elham collaborates with teams of elementary school teachers. Elham asked this thought-provoking question: “What would it look like if we designed schools to be places where teachers learn together alongside their students?” Teaching is complex work! Elham suggested that trying to learn how to do it alongside a colleague is best. Her call to action: Plan together, rehearse together, enact together, reflect together, and everyone improves together.


Laila Nur, a high school math teacher in Los Angeles, California, spoke about how she realized that her students talked much differently outside her class than within it, and decided to experiment with humor in her class as an antidote. Her takeaway from this experiment is that when kids laugh together and with their teacher, it helps break down some of the negative feelings associated with math. Her students enjoy class much more and consequently have fewer emotional barriers to learning mathematics. Her call to action is to incorporate humor in our classrooms, at least four times, and to see how that affects our students.

Kristin Gray, a fifth-grade teacher and math specialist, described how she pays attention to student thinking as evidenced by what they say and what they write and then journals what she notices. This stems from her genuine curiosity about her students’ mathematical thinking. She asked three questions, “What are you GENUINELY CURIOUS about in the content you teach and how you teach it?” “What are you GENUINELY CURIOUS about in your students’ math conversations?” and “What are you GENUINELY CURIOUS about in the math work your students do each day?” Her call to action was for us to start a math journal and record our reflections about our students’ work and to share how this affects our teaching.


Christopher Danielson, a mathematics educator in St Paul, Minnesota, started by sharing a pair of stories with essentially the same moral: listen to your students. In the first story Christopher realized he had not heard something a student said and that the difference between what he heard and what was said was small but incredibly important. He also noticed that sometimes when we aren’t listening to students very well we can hear things and make assumptions about how they understand the world that just aren’t true. He implored the audience to ask follow-up questions when they think they understand what a student means, and then to share our reflections on any differences we notice between what we thought we heard and what the students actually meant.


The final speaker of the night was Michael Pershan, a mathematics teacher living in New York City. Michael has spent much of his career thinking about the mistakes students make and what they mean. He has also spent much of this past year thinking about the feedback teachers give students and how we can make this feedback more useful. He described four potential pitfalls of the hints we give, and offered us the final challenge of the night: to plan our hints in advance and then share the ones that worked so that we can collectively build a pool of effective hints to give to students when they are stuck in specific areas of mathematics.


The six speakers, with their six calls to action, were inspiring. It made me reflect on how I can incorporate their ideas into my own practice. Of the six calls to action, I will start with Elham’s proposal and find someone with whom to plan, rehearse, enact, and reflect on my lessons so that I work in less isolation.

Which call to action are you going to choose? You can see what others are doing on the Shadowcon website.

1 comment April 28th, 2015

Blogstitute Post 5: On Being a Mathematician

Welcome back on this lovely Monday to our Summer Blogstitute! We have a lovely post from Kassia Omohundro Wedekind this morning, author of Math Exchanges and How Did You Solve That? Kassia talks about how her students’ attitudes change throughout the year when it comes to thinking about themselves as mathematicians. And while Kassia talks about math here, the question could be asked in all classrooms: “What is the legacy of our (math) classrooms?” Be sure to leave a comment or ask a question for a chance to win a package of eight Stenhouse books! Last week’s winner is Terri R. Keep commenting!

On Being a Mathematician

2014-02-19 11.48.08In the last days of the school year I always think about how far we are from the first days of school. So much change and growth happens in a classroom between September and June, and as a math coach I get to watch these changes happen in many classrooms and throughout many grades. I had been thinking specifically about how students’ mindset about mathematics can change throughout a single school year when fifth-grade teacher Mary Beth Dillane and I sat down for a coaching session to reflect on our work together this year.

The fifth graders in Mary Beth’s class began the year with a variety of different feelings about math. Some hated it. Some loved it. Some loved it as long as it came easily and quickly. One cried at Mary Beth’s table in the back of classroom, “I’m bad at math. I’m always going to be bad at math.” And most had just not thought much about themselves as mathematicians: people who construct meaning and contribute mathematical ideas.

And yet the first day I visited Mary Beth’s classroom, about midway through the school year, I could immediately tell how much she valued community. The students huddled together in groups working collaboratively on chart paper, lingering over a single problem. A class-constructed number line labeled with fractions, decimals, and whole numbers from zero to two hung in a prominent spot on the wall. Above it were the words and ideas of Mary Beth’s students. (“Connor and Khalil’s rule: Decimals and fractions are the same shown in different ways.”) At the front of a class was a hand-written quote from Mary Anne Radmacher, “Courage doesn’t always roar. Sometimes it is the voice at the end of the day that says I’ll try again tomorrow.” Already Mary Beth’s students’ ideas about learning and what it meant to do math were expanding and changing. We continued to work on this throughout the year, explicitly teaching behaviors and practices of mathematicians.

So it didn’t surprise me when our last coaching sessions turned to the topic of how the students have changed as mathematicians and how they view the learning of math in general. We discussed our own ideas about how each student had changed (“Did you see how they persevered on that problem? They spent the whole class working on it and didn’t want to stop!”), but we wanted to hear from the students themselves too. So, a couple of weeks before the end of the school year, I decided to interview some of Mary Beth’s students about how they viewed themselves as mathematicians and their general mindset about math. I asked them several questions (Who is a mathematician? How do you feel about math? What is math? Are there some people who are just good or bad at math?). I want to share just a few of their ideas and words with you.

Kassia Omohundro Wedekind

Kassia Omohundro Wedekind

Who is a mathematician? What kind of person is a mathematician?

“A person who looks at different perspectives to find their answer.”

“A mathematician is a thinker, a strategy person, shares ideas.”

“A mathematician is a person who, like, thinks, thinks about the problems . . . risk-takes about the problem. If they think it’s hard, they still do it.”

“A mathematician is a person who checks and checks if it makes sense.”

What is math?

“Mostly calculating.”

“Numbers—decimals, fractions, everything.”

“Like, stuff. Like diameters, circumference.”

As we talked about the student interviews, Mary Beth and I realized that while the students had broadened their understanding of what kind of people they are as mathematicians, they still have very narrow definitions of math. We know that so much of math isn’t about calculating and numbers. It’s more than the “stuff”—it’s the thinking. We know we need to explore different ways of communicating that to our students.

I think asking these kinds of questions of our students is important. (Next year, Mary Beth and I plan to do a similar interview with students during the first week of school as well as at a couple of other points in the year so we can reflect on how we are helping them grow as mathematicians.) But perhaps it is even more important to ask these questions of ourselves as teachers. What is the lasting legacy of our math classrooms? We hope that it is deep understanding of mathematical content. But just as much, we hope that it is the sense that all people are mathematicians who are capable of the problem solving and persistence required of mathematics.

As Mary Beth’s class of fifth graders prepares to head off to middle school we both ask ourselves, “Are they ready? Are they independent enough? Do they know enough about fractions?” We think about our students who have struggled this year, who have made so much progress, but who still would be thought of by many as “behind.” Like overprotective parents we’ll have to fight the urge to drive over to the middle school in the first days of the next school year and peer through the windows of their classroom, shouting, “Brian, use the number line in your head!” “Giselle, think about what makes sense!” But we won’t. We’ll watch them go, those mathematicians, and take on the world. And we’ll keep working on helping kids be “thinkers,” “strategy people,” and sense makers.


22 comments June 30th, 2014

Profiles in Effective PD Initiatives: Fitchburg Public Schools

We continue our series about effective PD initiatives around the country with a visit to the Fitchburg Public Schools in Massachusetts and looking at how school leaders and teachers worked together to elevate the quality and the quantity of professional development in their schools.

A decade ago, when leaders of the Fitchburg Public Schools in Massachusetts realized that few teachers were regularly reading professional resources, they decided to organize a series of online book studies. They hoped the sessions would enable teachers to read and reflect on their own time and encourage them to use the materials strategically to address students’ learning gaps. The district offered to pay for the books and a small honorarium, provided that teachers responded to prompts from facilitators, participated in online discussions, and completed written reflections about how they were using recommended strategies in their classrooms.

The result? Most of the district’s 450 faculty members have completed at least one of the 160 collaborative studies, and collegiality and classroom improvements have soared.

“The level of professional discourse has really been elevated with the book studies,” says Donna Sorila, director of mathematics for the Fitchburg school district. “It’s anecdotal, but it’s palpable. You can actually hear the change in the discourse.”

Technology director Eileen Spinney says teachers now request studies of books they’ve read or heard about, in addition to using the resources identified by facilitators. With about eighty professional books already shared by faculty members, she says, “We’re starting to get that professional culture.”

Hybrid Learning

Over the years, Fitchburg leaders have refined the professional development sessions to include both online learning and face-to-face meetings that typically involve classroom observations. Often the facilitator will also ask participants to try out a lesson or project adapted from the book, videotape the instructional sequences, and then share them with colleagues so they can reflect on the experiences together., a free online service, enables participants to use web-based conferencing and share resources through an interactive platform. Facilitators post prompts and ask group members to respond to the question and to one another’s comments. Each person also turns in a journal or notebook of collected reflections at the end of the session.

“That is their more personal piece,” shared only with the facilitator, Sorila says. “We ask them to think about, ‘What are your strengths? What area do you want to focus on for your practice?’ Not only are they doing things collaboratively with the group, but then we’re trying to push them a little deeper with reflections in the journals.”

In addition to refining the hybrid book study model, Fitchburg’s leaders now limit each group to fifteen members to ensure greater participation and camaraderie. They’ve also begun including administrators in the sessions, which has reinforced the value of incorporating trade books into professional development. Summer book study sessions usually last about a month, whereas sessions during the school year can stretch to six or eight weeks.

The hybrid learning model has continued to give teachers flexibility in when they read and respond but has also led to more accountability and implementation of recommended practices. For example, when reading Math Work Stations: Independent Learning You Can Count On, K–2 (Stenhouse, 2011), math coaches wanted to see how teachers in the district’s four elementary schools were organizing math learning centers and developing students’ conceptual understanding and skills.

“Teachers are a little reluctant when we bring in a video camera, but when they think about having that second set of eyes or being that second set of eyes they become much more reflective,” Sorila says.

Julie Basler, math coach at South Street Elementary School, led a study of Math Work Stations last year for about twenty teachers, including those from special education and Title I departments. The school’s K–2 teachers were already incorporating strategies from Debbie Diller’s book, and Basler and principal Monica Poitras wanted to spread the practices to all classrooms. A key goal was ensuring that teachers were intentionally using math manipulatives as tools for learning, not just toys to make math seem more fun.

“I think one of the better results was greater camaraderie among the people who took this class together,” Basler says. “There was a lot more insight into how other teachers teach. Sometimes when you see what someone else is doing in the classroom it might not be exactly what you need in your own classroom, but you are able to take that idea and adapt it and grow from it.”

Teachers still talk about what they learned during their collaborative study of Math Work Stations, Basler says. “All of the comments were positive, but I remember some from the end of the session where people said, ‘Oh, I wish we had done this from the get-go because I would have set up my classroom completely different.’ They really saw the value of just about every part of the book.”

Greater Respect for Reading About Math

Paula Carr, a third-grade math teacher at Crocker Elementary School, has led about twenty book study sessions for educators throughout the Fitchburg district. She usually asks teachers to create a lesson plan based on some aspect of the book in addition to responding to online prompts and reflecting in journals. She said guiding studies of math books has been so rewarding because traditionally professional reading was thought to be the responsibility of literacy teachers. One of the most valuable book studies she conducted featured Number Sense Routines: Building Numerical Literacy Every Day in Grades K–3 (Stenhouse, 2011). Author Jessica Shumway shares how teachers can help students develop strong number sense by practicing routines, just as athletes and musicians do. For example, they can learn to make reasonable estimates, see relationships among numbers, and design number systems.

Carr says the book resonated with teachers. “Every single journal entry I have read, every dialogue I have heard, there are lots of aha moments: ‘I never thought of doing it that way. I never thought that younger kids could do that.’ Quite honestly, coming into teaching years ago, I myself didn’t realize how building strong number sense was so unbelievably important in laying a foundation for when students get older. Sometimes we move through so many topics so quickly, thinking kids have it, but this has really helped me focus on how deeply they know it and also focus on techniques that will help them really grasp the concepts.”

Carr says she now incorporates number sense practice into every class, no matter what else students are working on. For example, when considering a subtraction problem of 154 minus 27, Carr will ask students to talk about the “reasonableness” of the answer, which is one of the ways they learn to perform mental math and develop flexibility and fluidity with numbers.

In their online conversations, teachers noted many great strategies from the book, including Count Around the Circle, which asks each student to contribute a number that builds on an identified routine, such as counting by tens. Teachers also mentioned the Organic Number Line routine, which helps second- and third-grade students develop a mental linear model for fractions and decimals. The line is “organic” because students add to it throughout the school year, and it changes based on the experiences in the class.

Crocker teachers said Number Sense Routines helped them appreciate the importance of sharing visualization strategies, particularly with special education students and second language learners who may need to see number representations as well as hear them.

“My teachers taught me the standard algorithm, and I memorized it,” one teacher wrote on Nicenet. “Now I find that my number sense is growing deeper as I teach.”
Another teacher quickly replied, “I too was a standard algorithm kid! Then when my own children needed help with their math homework I was told I was not doing it right, but I only knew one way. As a teacher I find that ten frames really help the students with number sense, and I am amazed when the students can tell me the different ways they solved a math problem.”

For Paula Carr, the collegial book studies show how much teachers need and want to learn from one another. Reading and reflecting with teachers in other schools has been especially valuable, she says, offering glimpses into classrooms they might not otherwise see.

“It opens it up to everyone valuing each other’s opinions and learning from each other instead of re-creating the wheel,” she says. “You can discover people who are already doing fantastic things and get ideas from them.”

Add comment May 22nd, 2014

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