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
“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.
Poet and author Shirley McPhillips is back today with a post on how to harvest students’ interest around a specific topic so that it opens up writing possibilities. For more tips on poetry in the classroom, head over to the Stenhouse website to preview Shirley’s book Poem Central.
All I Want to Write About is ——: Poems Around a Theme
By Shirley McPhillips
What to do about Jerome. “All he wants to do is write about dogs.” Mandy’s a head-scratcher. “She draws stars and spaceships all over everything.” Lawrence is exasperating sometimes. “He’s been scribbling for two months with one topic to show for it. Basketball.”
I read somewhere that writers have only one or two seminal themes in their lives. That everything they write comes out of those. I have no data but I think that’s probably true for many writers. The ideas, situations, experiences, beliefs that infuse and fuel what we think, what we do.
So why not share this notion with Jerome and Mandy and Lawrence? That it’s okay, even grand, to pull different types of writing out of the same writing well. Get them making a collection around a theme. Many poets do.
I’ve given Mary Oliver’s Dog Songs to so many friends for one dog reason or another over the past couple of years. For these folks, one dog poem is not enough. It’s about that special human-canine relationship. It’s also sharing what that relationship reveals about the meaning of our own lives. If I could locate Jerome, I’d put a copy of Dog Songs in the mail.
A few years ago, Tess Gallagher wrote a serious, playful, sassy book called Portable Kisses. “There are as many nuances and inflections for kisses as there are lips to kiss,” she said.
Swirl by Swirl, Joyce Sidman’s nonfiction poems celebrate the elegance and usefulness of spiral shapes in the natural world and across galaxies. Mandy could have used this for inspiration.
Lawrence’s passion for basketball might have been greatly validated as a force for writing if he could have read the 2015 Newbery Medal Winner: The Crossover, by Kwame Alexander. In this coming-of-age novel in verse, we come to know something of the lives of two brothers, both on and off the court. Also, imagine Lawrence being inspired by another sports enthusiast, poet and anthologist Paul B. Janeczko. That Sweet Diamond, a collection of his own baseball poems, shows all the magic, grace and grit of the game from “Prayer for the Umpires” to “How to Spit.”
As we’ve said, collecting around a theme of one’s own poems is an instructive and rewarding project. So is making an anthology around a theme of other poets’ work.* Imagine Jerome getting to read lots of dog poems by other poets. And him, as editor, deciding what poems he would include in this collection. Why this poem? Why would I put these poems together in a collection? Do they fit together in some way? Do I want a variety of style? Length? Tone? In what order will I arrange them? What’s a good poem to begin? To end? What title will reflect this collection as a whole?
Recently, I was asked to submit a poem to a future anthology called Amore: Love Poems being edited by Johnny M. Tucker, Jr. Such an engaging project for me to peruse some of my poems asking: Is this a love poem? What makes this a love poem? Can love lost, or love denied, be considered a love poem? Can it be a love poem without reference to a person? Looking through the lens of “love,” poems took on new meaning. A couple were obviously love poems from the title on—“Love, Off Guard.” Others, like “Selfies of Autumn,” may not be as obvious to a reader until the epigram is considered and the story beneath the text blooms.
This poem appears in a new book, Acrylic Angel of Fate (2016, Finishing Line Press, KY).
Selfies of Autumn
(for Barbara Caldwell)
The day drips with the elixir
of autumn—a dark honey
of orange, a sadness of red,
the steadfastness of green.
A rainpool of birds slap
the summer’s heat from their wings;
beaks strip their feathers as if
to neaten up for a brave new day.
In the garden, I pose with the ghosts
of spring peonies. I can still breathe
their ambrosia heavy as wine, still feel
their heads lean.
Along the woodpath, squirrels
tear and leap, leap and tear, delirious
with an onset of primal intuition.
Above them the bittersweet vine,
blood-burned, still wants to reach,
A windburst stirs the leaves
to the gripping point. One golden
soul, all lightness and fluttering heart,
twists and soars.
But time just won’t, I think,
allow for drift. I’ll snap a picture
for eternity, I say. You and me
against the starry cold.
A large part of our everyday communication involves argumentation and reasoning—for example, when we want to persuade others, make good purchasing decisions, or analyze the messages we receive from advertisers and politicians. But how well do we prepare students for these tasks?
In Good Thinking, Palmer shows teachers of all subjects how to transform the activities they already use into openings for improving student thinking. Building on his previous work in Well Spoken and Digitally Speaking, he reveals how all students—not just those in advanced classes—can begin developing sophisticated reasoning skills that will improve their oral and written communications.
Blending theory with practice, Palmer shares a wide range of classroom-tested lessons and explains complex concepts in simple, practical language that gives teachers a deft understanding of the principles of good arguments, proper use of evidence, persuasive techniques, and rhetorical tricks.
We are happy to celebrate National Poetry Month with Stenhouse’s resident poet and author, Shirley McPhillips. In this guest post, Shirl talks about finding connections between paintings and poems, about creating “art from art.” At the end of her post, be sure to look at her paintings and try your hand at writing a few lines inspired by the images. Share it in the comments section for a chance to win a copy of Shirley’s book, Poem Central.
A picture and a poem: An intimate connection
By Shirley McPhillips
I’m growing more and more to believe thatour fundamental task as human beings is to seek out connections—to exercise our imaginations.
—Katherine Paterson, The Spying Heart
It’s all about making connections, both in learning and in life. When objects and activities of the outside world meet an inner world of consciousness and imagination, there is a chance for new perspective, new possibility. In this exchange we develop a sense of self, an anticipation of finding new ideas.
Recently my friend Molly and I had the opportunity to set up an exhibit of our art work for a month in a local library: watercolor, acrylic, found-wood sculptures. Being poets as well, we wanted viewers to find connections between the visual and the word.
We mounted some of our original poems along with one or two established and student poems and placed them among the paintings. The content of poem and art may have suggested a direct alliance—e.g., “Birdhouse on the Old Outhouse” next to a watercolor of that scene. Or a loose connection like a sound poem next to the abstract “Rooster Ruckus.” Or a random juxtaposition with no obvious connection. Better, we thought, for reaching. Or head scratching.
Poems and art together on display
As an added opportunity to interact with the art work, we set up a “Poet’s Corner.” A place for viewers to invite the muse. To sit in a quiet place, contemplate what they were observing and reading and to compose a short poem of their own. They could write off things around them in their lives, or think off a mounted poem or work of art in the exhibit. If the muse was busy right then, folks could compose at home and put the poem in the book later.
It was important for us to make the “corner” writer-friendly:
-A framed invitation to write, with a quote from Seamus Heaney:
“Between my finger and my thumb / The squat pen rests. / I’ll dig with it;
–a small bistro table;
-a Tibetan bench:
-a blue, glass pen holder for pencils (If any disappeared, we imagined they were greatly needed elsewhere, and just replaced them.);
-various types of Post-It notes and paper;
And most importantly, an elegant, flat-lying, “guest book” for poems and art with a photo of a George Bellows painting we mounted on front.
As the book opens, Jack’s hand-printed poem graces page one. He writes of a painting by Eli Rosenthal. His poem encourages those who come after, eliminating “first page shock.”
On Poetry Night, visitors browsed the exhibit, chatted with one another about the art, the poems (and the “nuance” of the Pinot Noir), then settled down for an evening of presentation. Presenters responded in various ways: Expressive readings, movement inspired by a painting or poem, a reading with shamanic drum interpretation, telling a memory connected with a painting, and so on.
At the end of the evening, a few folks who had contributed to the “Guest Book” read their poems and told about connections they had made which resulted in this work.
People who participated in “A Picture and a Poem: An Intimate Connection” said it best:
Ted: The painting of the birdhouse on the old outhouse cast me right back to my grandmother. Visiting her in the summer.. The weathered boards. Wasps’ nests inside! Her standing outside humming a tune so I wouldn’t be scared. A big hug afterwards. I haven’t felt that safe since.
Marley: “Ah sunflower weary of time.” Blake’s poem. We had to memorize it in high school. I went up to that painting first. Sunflowers are my favorite flowers. I wanted to think about why. Their faces. The connection to the sun. The casting off of so many seeds.
We invite you to look at Shirley’s paintings below. (Or choose an artwork you like.) What do you notice? What does that make you say? Ask? Remember? Pretend you are sitting or standing somewhere inside this painting. Look around. Write a short poem and leave it in the comments section or e-mail it to firstname.lastname@example.org. Have fun with it!
We will be in San Francisco next week for NCSM and NCTM. Stop by our booth (204 and 932, respectively), to meet some of our authors and receive 25% off our books and videos and to pick up one of our fancy tote bags!
Lucy West will be signing at the NCSM bookstore at 1 p.m. Monday, April 11, then later that afternoon at 4 p.m. at the Stenhouse booth. You can preview her latest video Adding Talk to the Equation here.
At NCTM you can catch up with Jessica Shumway at 11 a.m. and with Lucy West at 1 p.m. on Thursday, April 14.
Friday is also ShadowCon time, starting at 5 p.m. For details, follow #shadowcon16 on Twitter. Our own Tracy Zager will be there, so be sure to say hello to her!
For more than twenty years, Lucy West has been studying mathematical classroom discourse. She believes that teachers need to understand what their students are thinking as they grapple with rich mathematical tasks and that the best way to do so is through talking and listening. Adding Talk to the Equation helps teachers learn how to skillfully lead math conversations so all students stay in the game, stay motivated about learning, and ultimately deepen their understanding.
This video features five case studies filmed in grades 1–6 and shows teachers at various stages in their practice of generating and managing rich mathematics conversations. Lucy emphasizes the progression that occurs as teachers get more comfortable with new talk moves and as they learn to tune in and respond to the math conversations taking place among their students. Although these discussions occur during math instruction, the strategies used to create an environment for respectful, productive discourse can be applied to any subject area.
The video segments examine the importance of creating a safe learning environment; the value of thinking, reasoning, and questioning; the role of active, accountable listening; and the necessity of giving all students a “You can do this” message. Lucy also emphasizes that slowing down, even in the face of time constraints, is crucial for creating a classroom where all students feel they have something to contribute.
The 84-page companion guide includes transcripts of all of the case studies, with detailed commentary from Lucy that gives you a window into her thinking and the complexities of the work she is doing with teachers, as well as her reflections on missed opportunities.
Teachers everywhere are concerned about students whose reading development inexplicably plateaus, as well as those who face challenging texts without applying the strategies they’ve been taught.
In their follow-up to Reading Wellness, Jan Burkins and Kim Yaris explore how some traditional scaffolding practices like read-aloud, shared reading, guided reading, and independent reading, may actually rob students of important learning opportunities and independence. They argue that if we want students to use these reading strategies indepdendently, we must question the ways our scaffolding is getting in the way.
Who’s Doing the Work? suggests ways to make small but powerful adjustments to instruction that hold students accountable for their own learning. It offers a vision for adjusting reading instruction to better align with the goal of creating independent, proficient, and joyful readers.
Students love math games and puzzles, but how much are they really learning from the experience? In the third book of the popular Well Played series authors Linda Dacey, Karen Gartland, and Jayne Bamford Lynch help you engage students in deep mathematical discussions, enhance students’ conceptual understanding, develop students’ fluency with number systems, ratio and proportional relationships, expressions and equations, statistics and probability, and patterns, graphs, and functions.
Each book in the series shows you how to make games and puzzles an integral learning component that provides teachers with unique access to student thinking.
The twenty-five games and puzzles in each of the Well Played books, which have all been field-tested in diverse classrooms, contain:
explanations of the mathematical importance of each game or puzzle and how it supports student learning;
variations for each game or puzzle to address a range of learning levels and styles;
clear step-by-step directions; and
classroom vignettes that model how best to introduce the featured game or puzzle.
We continue to reflect on the role of stories today with an examination of the stories that surround us every day. At the end of her post, follow Katie’s tips on bringing stories to the forefront of your teaching. And then tell us on Twitter: What is your story today?
Investing in Stories
Katie Egan Cunningham
These days it seems like every industry is talking about the power of stories. Want your advertisement’s message to stick? Tell a story. Want your shareholders to keep investing? Tell a story. Want to bring in more customers? Tell a story.
In fact, if we want students to be college, career, and life ready, an investment in stories looks to be one of the most important investments we can make. Here are a few examples across industries that caught my attention.
In the December 2015 issue of Inc. magazine Thomas Goetz, CEO of Iodine, a digital health startup, says, “The story, it turns out, is the most important thing. It can’t just review what we’ve done; it must also excite the imagination about what the world will look like once we do more. It won’t be enough to present a plausible, worthy case for our future—our story must convince people that it’s worth millions of their dollars to see that future happen.”
At the online health hub HospitalityNet, consultants in the hospitality industry advise business leaders to use the structure of fiction to improve their forecasting and strategic thinking: “A good fictional storyline may seem like a whirlwind of characters and events, but for exactly that reason it can captivate and motivate an audience to grasp real issues and see different possibilities, all within a framework that everyone understands could plausibly evolve from the world as it actually exists today.”
The streets of New York City’s Chelsea neighborhood have a new retail store that changes the shopping experience—including the store’s layout and merchandise—every few months. The name of the store? Story. The driving idea is that the store is a place for discovery and maybe even reinvention. What is your story? What do you want it to be? Come in, look around, and find a new story for yourself.
Audible, the audiobook giant, advertises finding “stories that surround you.” Folding laundry? Surround yourself with a romance novel. Eating cereal? Surround yourself with the French Revolution. Sitting on the beach? Surround yourself with a noirish thriller.
Finally, the world’s biggest media brands now trust the “social media evangelists” at Storyful to “discover, verify, and acquire social media for their storytelling.” Businesses want to know which stories are worth telling.
All of this points to what, I believe, we as educators have always known—that humans are addicted to stories. That when we listen to someone else’s story we encourage a sense of belonging and make change possible. That stories are a pathway to connection.
As teachers, this gives us even more justification that time spent on powerful stories is time well spent. Here are some simple and joyful ways to keep stories at the forefront of your teaching:
Make read-aloud a daily ritual, without exception. Create space for discussion before, during, and after reading.
Vary the kinds of stories you share to highlight different perspectives and life experiences.
Explore the structural elements of narratives as both readers and writers.
Zoom in on craft techniques storywriters use to hook readers.
Listen to songs and have students rewrite the lyrics as a narrative.
View print and media advertisements, noticing how they tell stories to persuade their market.
Listen to audiobooks as a class to “surround” yourselves in stories.
Make it a year-long goal to build a classroom culture of story every day.
Where do you notice other industries spotlighting stories? How do you build a world of story in your classroom?
We are excited to kick off this week with Katie Egan Cunningham, author of Story: Still the Heart of Literacy Learning. We invite you to read her post below and then think about the role of stories in your classroom. What is your story today? Share with us here on the blog or on Twitter using this template and #Story.
Each Day Should Be a Story-Worthy Day
Katie Egan Cunningham
We are, as a species, addicted to story. Even when the body goes to sleep, the mind stays up all night, telling itself stories.
― Jonathan Gottschall, The Storytelling Animal: How Stories Make Us Human
Each morning I wake up to the human alarm clock that is the sound of my children’s feet climbing out of bed, letting me know it’s time to get up. Once my eyes are open, I grab my five-minute journal and jot down three thoughts about what would make today great, three things I am grateful for, and an affirmation of who I am. Before I close my eyes at night, I grab my journal once more to process the day—to remember three amazing things that happened that day and how I could have made the day better. This journaling ritual in my life began as a Valentine’s Day gift from my husband. Better than flowers or chocolate, he somehow knew that envisioning the story of my day before it happened and remembering storied moments at its end would be a simple way to bring me happiness every day. He was right. For a year now, I have been hooked.
When my children hop on the bus or walk through the doors of their schools, I envision their day, knowing that there will be story-worthy moments. I wonder what amazing things will happen to them. What stories will they hear that inspire them to be kind or to take new risks? What will friends say that make them laugh or make them cry? Will they bravely share an idea out loud? How will it be received? I know there will be Morning Meeting stories. Talking in the hallway stories. Monkey bars stories. Roaming in the library stacks stories. P.E. team-picking stories. Bus riding stories.
In my work with teachers and students, I’ve started to adopt the five-minute journal philosophy—that is, that envisioning and remembering the stories of our days in a few simple words and phrases is a way of building a story-worthy attitude about every day.
I also believe that, as teachers, we have the power to be story changers for our students. Every Monday, I work in an afterschool program supervising soon-to-be literacy specialists working with fourth and fifth graders. I tell my graduate students that their primary role is to learn as much as they can about the students’ stories—what matters most to them—and to use that information to drive their decisions as teachers.
One day, during the afterschool program, I read aloud The Best Story by Eileen Spinelli. With each turn of the page, children nodded their heads in agreement—oh yeah, lots of action makes the best stories. Plenty of humor makes the best stories. Stories that make people cry are actually the best. Rather than go along with the chorus of agreement, a boy named Andrew talked back to every page, letting us know he was resisting this particular story and maybe even the story of our time together. We needed to show Andrew that he had choice and challenge in our time together, and that what mattered to him was valuable to us. As the weeks went on, Andrew became the first student to arrive and the last one to leave. He stayed to work on his new comic book, to write about Yo-Kai Watch characters in their fantasy world, to talk to me about his soccer match and what he wanted to read next. His identity in the afterschool program changed from resistor to most passionate contributor. Andrew unknowingly convinced me each week that what we were doing together as readers, writers, and thinkers mattered, and that as teachers we have the power to change the narratives we tell ourselves about our students.
I am convinced that human connection is the pathway to knowing each other’s stories, so I decided to use heart mapping in my work with teachers last fall. Through the process of jotting and sharing, I learned that one teacher was battling throat cancer as she tearfully explained the cancer ribbon drawing she made on her map. I learned that I grew up in the same small New Jersey town as someone sitting across from me. I learned that other teachers also had two sons. Our relationships to one another changed. We came to know more of one another’s stories.
To help your students (and yourself) take note of the story that happens each day, try starting with these simple methods:
1. Take time at the start of the school day to jot down what would make today great.
2. Take time at the end of the school day to jot down three amazing things that happened and one thing you could have done to make the day better.
3. Build in time for students to share their interests through heart mapping, community mapping, and hopes and dreams mapping.
4. Provide time for partner talk, emphasizing the importance of listening as much as speaking.
5. Tap into students’ interests to support their book shopping—what connections do they have to characters, real-life figures, and settings?
6. Step back and observe your students, both in and out of the classroom. Notice and jot down the storied moments you see, and share them with students as fuel for their writing.
7. Share your own jottings about the story of your day.
8. Remind students that every day is a story-worthy day.
What are the stories you are grateful for each day in your classroom? When have you been a story changer in a student’s life? When have students changed your story?