We have a special treat today by a local Maine teacher/poet, Anne Tommaso. She teaches Junior English at Yarmouth High School in Yarmouth, Maine and she recently finished a MA degree at the Bread Loaf School of English at Middlebury College.”Poetry demands you return when you are different.” Take that thought with you on this Poetry Friday.
On Returning to Attend Poetry Class Ten Years Later
This coming back softens me like the worn curbs, filled in with sand,
below the torn clapboards and listing porches of this town.
I’ve had to follow signs to get here. The new building feels like an airport;
our room is carpeted and busy. There is cider in the corner for later.
The students make room before delicately scratching their notebooks,
following their professor’s quick and quiet cadence,
which only I know is unchanged in pitch and pattern.
“Poetry demands you return when you are different,”
he has said.
Which is why, the next day, I feel farther from my own
students as I maneuver between desks, looking
more at their hunched backs than their vacant pages.
Sometimes they peck and shrill like crows, leave dirt behind them in clods,
plug themselves into machines that fill their head with clamor
and then leave the room empty in detached silence.
How to get them to come back to this human pleasure of words?
To be alert and pungent, like onions?
We have two great interviews to share with you today!
The first audio interview is with Bruce Lesh, the author of “Why Won’t You Just Tell Us the Answer?” Bruce and a fellow history teacher discuss the recent NAEP test results and what they mean for history education in America. The program was recorded by the Historical Society of Rockland County.
The second interview we want to share with you was recorded with Kelly Gallagher at California State University Dominquez Hills. Kelly talks about his career as an English teacher and about his new book, Write Like This.
Our math quick tips continue on this sunny Tuesday with another number sense routine by Jessica Shumway, exclusive to the Stenhouse blog. Her new book, Number Sense Routines, is still available for full preview on the Stenhouse website!
Using Algebra and Arithmetic Routines to Improve Number Sense
What goes in the blank?
Pose this problem to your students. Many of them will write 14 in the blank. Some will add 7+7+8 and put 22 in the blank. Others say that the equation is impossible. Some might answer 6.
During a Cognitively Guided Instruction training, my math coach Debbie Gates challenged me to present this problem to some fifth grade students. I was surprised that many of them wrote 14 or 22 in the blank. Some of them wrote 7+7= 14+8=22. Through their elementary school years many of these fifth grade students had developed misconceptions about the equal sign and what equality means.
A couple of years later I was part of a study group that read Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School by Carpenter, Franke, and Levi. It really got me thinking deeply about students’ misconceptions about the equal sign as well as the critical importance of encouraging students to think relationally. I saw these factors as critical to my students’ number sense development, so of course, we made it a Number Sense Routine in our classroom.
At the beginning of the school year, I simply started with a series of True/False Statements that Carpenter el al. suggested in their book (see page 16 of Thinking Mathematically):
I wrote these equations on the board (one at a time), and the students discussed whether each statement is true or false and, of course, explained how they know. This was the beginning of our conversation about equality and what the equal sign means. Many students believed that the second and third equations were false! I recorded students’ ideas about equality during the course of our discussion:
We did similar series of equations like these over the next two weeks. Other examples include:
True or False?
True or False?
True or False?
As we worked through these daily routines, we continued our discussions about equality and the meaning of the equal sign, but students also began to dive into important ideas like the commutative property of addition and multiplication, how to compose and decompose amounts, and relationships among each side of the equal sign (relational thinking). This was exciting!
At this point, I began using equations like these:
My students agreed that the first equation is false. Some solved for both sides and said that 20 does not equal 19. One student said, “I knew right away that it was false because there is a three on both sides, but 16 is one less than 17.” This student was thinking relationally—this is a critical component to algebraic reasoning! Additionally, the student was using her number sense and looking at relationships among the numbers. She actually did not need to solve for both sides, rather understanding the relationships on each side of the equation helped her figure out that the statement is false. Her explanation of her reasoning helped other students look at the other two problems in the same manner.
Later, after changing the routine from True/False Statements to Open Number Sentences, I had students come up with their own Open Number Sentences that I could use for future Number Sense Routines:
Luis’s Open Number Sentence encourages his peers to use relational thinking rather than solve for both sides. Students who use relational thinking will likely use a compensation strategy, which is a strong mental math strategy.
These routines helped my students negotiate meaning around the equal sign, dispel misconceptions about the equal sign, learn to think relationally, and use important arithmetic and mental math strategies. Through our various conversations each day for several weeks, I watched my students’ number sense flourish. I found these algebra routines to be extremely effective! The students immediately get sucked into the discussions and lose themselves (and find algebraic thinking!) in debate and negotiations about the mathematics. Additionally, a focus on the symbolic (the equations) was a nice addition to our visually focused dot cards and ten-frames routines. At many points in our discussions, I found it helpful to students to link the dot cards with our True/False Statements. This routine is extremely rich and can be adapted and enriched in a number of ways!
At each stop Kassia will answer questions and each blog will raffle off a copy of her book (or if you already have her book, your choice of any other Stenhouse book) among those who leave a comment or ask a question. If you order Math Exchanges between now and October 3, you will also receive free shipping on the Stenhouse website. Just use code MATHX.
This week we have a math poem by Mary Cornish that appears in Kassia Omohundro Wedekind’s new book, Math Exchanges. Enjoy this poem and then head over to the Stenhouse site to preview the book online. Kassia will be embarking on a four-stop blog tour starting October 3.
I like the generosity of numbers.
The way, for example,
they are willing to count
anything or anyone:
two pickles, one door to the room,
eight dancers dressed as swans.
I like the domesticity of addition—
add two cups of milk and stir—
the sense of plenty: six plums
on the ground, three more
falling from the tree.
And multiplication’s school
of fish times fish,
whose silver bodies breed
beneath the shadow of a boat.
Even subtraction is never loss,
just addition somewhere else:
five sparrows take away two,
the two in someone else’s
There’s an amplitude to long division,
as it opens Chinese take-out
box by paper box,
inside every folded cookie
a new fortune.
And I never fail to be surprised
by the gift of an odd remainder,
footloose at the end:
forty-seven divided by eleven equals four,
with three remaining.
Three boys beyond their mothers’ call,
two Italians off to the sea,
one sock that isn’t anywhere you look.
We continue our math quick tip series with another idea from Jessica Shumway’s recent book Number Sense Routines. Counting the days in school is a routine that Jessica uses at the end of the day to help separate it from the calendar routine, after she and fellow teachers realized that students were confused about counting the days of the month and the days spent in school at the same time. Read more about this routine here and then head over to the Stenhouse site where you can still preview Jessica’s book in its entirety!
Counting and keeping track of the days in school is an especially beneficial routine for kindergarten and first-grade students. This routine lends itself to talking about numbers, thinking about patterns, and seeing amounts. It provides an opportunity for these young students to count every day, see and experience an increasing amount, and think about numbers beyond 100. For second and third graders, there are a variety of reasons and ways to keep track of the days in school, from organizing a growing amount to developing sophisticated strategies for comparing two sets of numbers (days in school versus days on the calendar).
As a mathematics coach at Bailey’s Elementary, I worked with a team of kindergarten teachers who described a problem they came across with keeping track of the days in school. They realized that students were getting very confused between how many days are in a month and how many dayswe had been in school during that month. “What are we counting?” became a common question. Teachers were not asking students to compare the days in a month versus the number of days students had been in school. The problem was that there were too many different numbers (day of the month and the number of days in school) for them to keep track of, especially early on in the year.
One of the kindergarten teachers and I decided to use this routine of Counting the Days in School at the end of the school day as a way to remedy the confusion. That way, the calendar routines, which students worked on during morning meeting or at the beginning of the math lesson, were separate from the Counting the Days in School routine. We used Counting the Days in School as a check-off system: “We are finishing the ninth day of school. Let’s add 9 to our counting tape and move our circle on the number grid from 8 to 9. Wow, you’ve just finished up another day of kindergarten. You are nine days smarter!”
I have seen many different ways to keep track of the days of school. Many teachers use a place-value pocket chart, with each pocket labeled from left to right as Hundreds, Tens, and Ones. They add a straw to the Ones pocket for each day they are in school. Every tenth day of school, students bundle the straws into a ten and place the bundle in the Tens pocket on the chart.
Although this routine is effective in third-grade classrooms, it does not seem to be very effective for kindergarten and first grade. Students at this age are in the process of constructing early ideas of number sense and are not yet near understanding why you bundle straws every tenth day of school. This routine requires students to have an understanding of unitizing—counting ten straws as one bundle of straws or one ten. Students in kindergarten and first grade are grappling with early ideas of how we count objects and represent the count with symbols. Counting ten objects as “one” is difficult when you are still constructing the early ideas of counting, one-to-one correspondence, cardinality, and hierarchical inclusion. Understanding unitizing is a huge leap.
Many teachers believe that the straws routine for keeping track of the days in school is planting the seed for strong place-value understanding as students move into second and third grade. I used to believe that, too; however, I have seen time and again that these young kindergarten and firstgrade students are more focused on what that quantity means and what it looks like. Using cubes instead of bundling straws seems to be an easier way for students to construct early ideas of unitizing and of the importance and efficiency of ten. Opportunities to see ten ones being connected to one ten (without the exchange that takes place with bundles of straws or base ten blocks) will help these younger students construct the ideas of “ten-ness.”
The idea of ten as a group is at the core of unitizing. Early on, though, many children are learning that 1 means one item. It is too confusing to bring in the idea that 1 can also mean one group of ten. That will come later. It is more important for very young children (kindergarten and first grade) to build visual images of the amounts rather than focus on unitizing. Collecting items (like rocks or cubes) for each day of school and counting by ones seems to be a more authentic and age-appropriate task for students who are still figuring out what twenty looks like, how to count twenty efficiently, and how to represent that number. The place-value chart does not yet make sense. Let’s shift the focus for these young learners and instead create routines that will help them see amounts, learn the counting sequence, construct a sense of quantities, and recognize patterns.
“Books are meant to be read in different ways,” they write, “and this one isn’t necessarily a book you’ll sit down and read cover to cover (like a mystery novel) prior to using it. Begin Everyday Editing by reading the Introduction plus the first three chapters. This much, Part I, sets the stage for setting up lessons, and will help you understand the premise of the book–which is to invite students into the world of editing through literature and fascinating examples.”
The review then offers 10 steps for making the most of Jeff’s book.
“Why would we spend time tediously correcting errors that just happen to pop up in students’ writing when we could engage our writers in dynamic discussions about real writing, sparked by brilliant examples from today’s best writers,” the reviewers ask in the conclusion. “Thanks to Jeff Anderson for inviting us on an incredible journey that virtually electrifies editing instruction. Don’t miss this book.”
This week we have the last poem in our series from California English teacher Gayle Hobbs. If you have a poem you would like to share about your teaching life, send it to email@example.com!
By Gayle K. Hobbs
There they sat waiting.
impressive thoughts flung through the air
so they could be grasped and absorbed.
Thoughts came and floated
endlessly among the laughter
anxious and ignored.
Some seized at passing
concepts, while they floated
slightly hackneyed and worn.
Precious few partook of
the knowledge and experienced
a new abundance being born.
This event was a daily endeavor
practiced in the halls and caverns
of our princely schools,
While those at home
saw not the visions and
impatiently aborted these tools.
Yet, thoughts survived,
and spontaneously thrived,
Waiting for extraordinary minds
as they bloomed fresh, anxious,
In her new book Number Sense Routines, author Jessica Shumway shares a series of routines designed to help young students internalize and deepen their facility with numbers. For the next four weeks, we are going to share four routines that will help build students’ number sense. Today’s routine — an exclusive not included in the book — is about using quick images with dot cards to build a community of learners in your classroom at the beginning of the year. Check back next Tuesday for more ideas!
Summer… a time to recharge and a wonderful time for reflection on the past school year as well as planning for the fresh start in the fall. During the summer I plan out the core classroom routines that will build a strong community of learners with my new group of students at the beginning of the school year. I hope these suggestions in the Math Quick Tips will help you do the same!
Teaching students to share ideas, listen to each other, support one another, and learn to value a variety of ideas are critical components to successful discussions in my classroom. One way to begin negotiating our norms for classroom discussions is using the Quick Images with dot cards. I love the Quick Images with dot cards because children naturally see the amounts in different ways. Using these will help you establish the norm that “we value various ideas and strategies.” For example, showing this dot card:
and then asking “how many dots did you see? How did you see the total?” will elicit responses such as “5 and 3 is 8” or “I saw 3 on top and 3 on the bottom, which is 6 then two more—in the middle—is 8 total.” Some students might count by twos to 8.
A student might say “I saw 4 and 4 which makes 8.” To encourage listening to one another, discussion, and flexibility with amounts, ask “Can someone explain what Julia saw? Show us on the dot card.” After someone restates her thinking, then ask Julia, “Is that how you saw the 4 and 4?” Emphasize all the different ways of thinking about the amount by recording equations that students describe:
3+3=6 and 2 more is 8 or 3+3+2=8
2+2+2+2=8 or 2×4=8
Then say, “look at all those different ways we made 8. Your brains think differently and we saw the amount in so many ways. How cool is that?!”
Another possible format to teach students to have math discussions is to show, then hide a dot card followed by “turn and talk” with a partner. Show and hide the following combination of dot cards…
then, ask students to turn and talk to their partner (knee-to-knee, eye-to-eye). Challenge your students and say, “see if you can figure out how your partner figured out how many dots on the card!” The colors on this dot card combination may encourage certain strategies, such as counting by threes and/or combining groups of threes. However, other students will focus on the arrangement (rather than the colors) of the groups of fours. After students discuss their process for figuring out 12 dots on the cards, ask a few students to explain what their partner did to figure it out. This teacher move encourages students to listen to one another as well as learn new ways of seeing an amount.
Students turning and talking knee-to-knee and eye-to-eye
The beauty of Quick Images with dot cards is that it is a useful routine for setting up classroom norms and building a strong community of learners while doing important mathematics at the same time. You can use this routine to teach students to listen to each other, guide students with how to hold a respectful discussion, and value multiple ideas in one classroom. Simultaneously, students are building their number sense as they utilize their abilities to subitize, build visual sense of quantities, compare quantities, combine and separate amounts, and discuss part-part-whole relationships. During the discussions, you will likely write equations based on the children’s descriptions, so they are also seeing pictorial representations of amounts (the dot cards) connected with the symbolic representations (the equations). Students become more flexible in thinking about amounts like 8 and 12 which will help them become more efficient with composing and decomposing numbers (as well as computations and mental math!).
This routine is extremely rich and students love it! It is amazing that such a mathematically rich Number Sense Routine only takes 5 or 10 minutes at the beginning of each math lesson!!!
Do you feel a bit giddy when you go through your stack of books, trying to decide what to read next? If you do, Terry Thompson shares that feeling. In this installment of Questions & Authors, the author of Adventures in Graphica shares his ritual for “Choosing Day,” and wonders how he could instill the same excitement about choosing a book in his students.
Today is Choosing Day.
I’ve been looking forward to this all day. I’ve cleared my evening and carefully organized a comfortable spot on the sofa.
I rushed straight home from work (no tutoring or after school meetings!), picked up a light dinner on the way (Chicken la Madeleine!), walked the dog, and silenced my phone.
I’ve taken care of everything.
My pile of books waits patiently. It always does.
Last night, I finally finished Edward Rutherfurd’s New York, and I’m ready to pick my next book. I relax into my spot and turn my attention to the stack that’s been gathering on my night stand for some time. Today is Choosing Day. Today I pick a new friend.
My professional book club is reading one of Richard Allington’s books next, but I figure that can wait. A book I want to study for church calls to me, but I’m going to hold off on that one a bit longer.
I decide that I’m in the mood for something historical (no surprise there, it’s my favorite!), so with that, I move on to several, more specific options. A recent trip to Illinois landed Devil and the White City: Murder, Magic, and Madness at the Fair that Changed America in my stack, and that same trip prompted an interest in an Abraham Lincoln book, Bloody Crimes: The Chase for Jefferson Davis and the Death Pageant for Lincoln’s Corpse. My editor recommended Year of Wonders and Dissolution, but both seem a bit heavy for my mood right now. And – even though I’m dying to – I’m hesitant to start Ken Follett’s new book, Fall of Giants, because his work is such a rare treat and I don’t want to use it up too quickly.
I revisit each title, remembering what originally drew me to them, and reread the jacket flap summaries. I shuffle through the stack several times. Deliberating. I take my time here. This is an important decision for me, and I don’t want to rush it. I finally settle on Devil in the White City. It’s a lightweight paperback making it a perfect choice for all the poolside reading I’ll be doing on my upcoming three day weekend.
I put the leftover books back in the stack on my night stand (until next time) and get ready to spend the rest of the evening immersed in a true crime historical murder mystery. I’m pleased and content. It doesn’t get any better than this.
I’m not sure when Choosing Day became such a big deal to me, where it began, or even how it got its name. But, it’s been a constant ritual in my life for years. Although not as childlike and giddy as it may seem, I really do get a boost of excitement from the thrill of deciding which book I’ll read next.
I often wonder, though: how many of our students feel this way? Certainly, it might seem unreasonable to expect every student we work with to gush with excitement for their next book, but what are their practices when they go to choose their next independent reading selection? Are their choices purposeful? Haphazard? Nonexistent?
Come to that, what are our practices that help promote an eager anticipation around book selection? I want my young readers to know this feeling. Granted, some of our learners will cultivate a similar type of choosing day for themselves, but just as many won’t. What conditions can we put in place that can promote an excitement for book selection in our students?
When teachers share their own excitement and process about book selection (and encourage students to do the same) they promote a classroom culture of enthusiasm for choosing texts. In a classroom that supports book selection, you’re likely to see students who are encouraged to share out about their selections and teachers that share favorite titles with the entire class or individual students who would take to them. Hearing trusted adults and peers share their reasoning for choosing particular texts lets students in on this valuable part of what it means to be a reader.
I get my best reading choices through recommendations from friends who know me well and know what I like to read. I bet you do, too. Offering a variety of recommendation options is a great way to get students interested in their next book. Whether you schedule time for readers to share their favorites out loud, have them use a classroom chart with sticky notes, or let them use a private note passing system for sharing books, making recommendations to friends – just like real readers do – can go a long way to foster enthusiasm for choosing that next read.
Keeping a Stack
Most readers don’t wait to finish their current book before considering their next one, preferring instead to keep a physical or mental stack of titles ready to pick from. For some, it’s a stack on their nightstand. Others keep a running list on their cell phone. In classrooms where there are enough books and space, readers could collect titles in their book boxes for later. If this seems difficult logistically (think: space and number of books available), students could easily keep a list of books they’d like to read next in their journals.
Real readers know what they like. They know themselves as readers. They have favorite titles, series, subjects, and genres. They can talk about them and justify what makes them personally important. When they go to choose their next read, they do so in tune with their interests and their mood. They consider which titles they’re willing to commit to and pass on the others. Teachers who model, push for, and encourage this type of self-reflection help foster excitement about book choice.
Book choice in many of our classrooms is a hurried afterthought. We tell students they have five minutes to get to the library and back or we relegate independent reading book choice time to that space between attendance and announcements. But, when we set aside unrushed time for it, young readers come to learn that book selection is premeditated, thoughtful, and intentional. Classrooms that honor and celebrate book selection, allow students the contemplative time they need to get excited and give them permission to celebrate that excitement with others.