In a traditional, teacher-centered algebra class, students sit passively while a teacher demonstrates strategies for solving various problems. Recently, Anne Collins—co-author with Linda Dacey of The Xs and Whys of Algebra—visited two classes where students were actively engaged in solving multi-step problems while teachers were using formative assessment techniques to understand their thinking and monitor their progress. Here’s Anne’s account of her visits:
On a recent visit to a middle school I had the opportunity to attend two different math classes. I walked into one eighth-grade algebra class and was overwhelmed by the buzz of excitement. Some students were working at the board, others were working on individual white boards, while still other heads were bent over the same problem with the students discussing the next steps.
It took me a moment to find the teacher in this busy classroom. I found her standing between two students at the board. She was asking clarifying questions of one student as she tried to understand what he was thinking at a particular point in the solution process. I came to discover that this teacher was using a round-robin exercise with part of her class as a means of determining how proficient her students were with solving multi-step equations. She had organized her class into groups of three and had given each student the numbers one, two, or three. She began by sending student two to the board to record the equation she announced. Student two recorded the equation and solved only the first step. Student three replaced student two at the board to complete the second step, followed by student one. This continued until the problem was solved. The teacher explained to me that by using this round- robin activity she is able to determine at a glance how well each student is able to enter into the solution process and whether or not any students display misconceptions about solving problems.
I asked some students what they thought about going to the board and was pleased to hear Luis say, “I really like going to the board and the fact that I can get help right away if I need it. I can even help my teammates. And B.J. shared his relief that they go to the board because, “I need the extra time practicing and when I work alone I don’t know if I am doing the math correctly but when I go to the board, I get all the help I need from my team mates or my teacher.”
Next I visited another eighth-grade class and found that in this class students were grouped into triads and were trying to solve the problem Is It a Function? Each student had two clues that they had to share orally within their group to answer one question. I listened to one student asking, “What do I need to know about perpendicular lines?” A teammate responded, “I think there is something about the slopes of perpendicular lines but I don’t remember what it is. Why don’t we draw two lines that make a right angle and see what we get.” I was thrilled to hear the questions and see the strategy that this group used to make sense of the problem. Still another group was working on finding the slope of the line they had identified. They had graphed the ordered pairs given in the clues and were working on the equation. I also observed the teacher walking around listening to the groups, stopping to ask questions as she deemed necessary.
These interactive algebra classes are the polar opposites of how traditional algebra classes are run where the teacher shows and explains to students how to manipulate symbols. The students in the classes I visited actually knew what questions they need to ask to deepen their understanding. In both of these classes I was delighted to see students trying to make sense of the algebra on which they were working. These two teachers engage their students in solving rich problems. The collaborative nature of these classes illustrates just how much students can achieve when they are given the opportunities to solve interesting problems which require them to apply the procedural skills they have learned. And the teachers I observed model the positive impact effective formative assessment has on student learning.
A collage of second-grade poetry. This collage became the cover for our class poetry anthology.
As a final poetry project a few years back, my students and I put together a class poetry anthology. Included in this poetry anthology were typed copies of each child’s poem. This project provided an authentic way to showcase
the final pieces of an entire class of young poets, and this book was a great gift for parents, administrators, and students at the end of the study. Long after the poetry study was over, students, teachers, and family members returned to this anthology on the shelves of classrooms, offi ces, and home libraries. The anthologies I’ve since created with other classes have also been a great model for new classes and new students as we begin the next year’s poetry study. Children learn lots from the writing of their peers, and this book houses class sets of writing by former students of equal age to my new class of students.
White copy paper (8 ½” X 11″)
Glossy photo paper
Computer, digital camera, printer
Fine-tip permanent markers
Colored card stock (enough for the entire class to have a front and back cover oneach individual book)
Plastic ring binding/binding machine
Clear plastic presentation covers (to protect the front and back covers of the anthology)
Color copier (or class donation money to make color copies at local copy center)
Tips and Techniques
*Depending on the age of your students, their profi ciency with word processing, or the time you’ve allotted to this project, you make the decision whether students type their poems or someone else—a parent volunteer, teaching assistant, or teacher—does the typing.
*It’s visually interesting and more appealing to the eye of the reader when every poem is typed in a different font—or a font that matches the mood, tone, or feeling of the piece. It also gives each child more ownership and adds a touch of original quality to each piece.
*Before putting the poems together in book form, each child is given the final typed piece of his or her poem. Since color copying is so expensive, I ask the children to illustrate their pieces like the pictures in a coloring book. We first draw in whisper writing, and then the children outline their pencil drawing in black fi ne-tip permanent markers (so that the illustrations will show clearly on each poem when copied).
*Not only do the children have a typed poem for the anthology, they have also previously published this same exact poem on a poetry poster to hang in the school. This poster was illustrated with watercolor and oil pastels.
*In the years I’ve made the poetry anthology with students, I’ve simplified the project a bit, and rather than writing completely new poems, the students used previously published poetry to be included in the anthology. It’s up to you and your class of students to decide whether you’ll use the same poems published as poetry posters or create entirely new poems for an anthology.
*Through class fund money or parent donations (or me saying it’ll be a tax write-off and paying for the copies myself), we are able to make a color copy of the cover for each child’s anthology.
*After enough copies of the book are made so that each individual student will have his or her own copy, they are bound using the school binding machine with plastic ring binding (found at most offi ce supply stores).
*Each child then has an opportunity to add color inside to each poem or to just a few selected poems. Their color choices for the inside poems make each child’s book unique and personal.
Author Rick Wormeli (Metaphors & Analogies, Differentiation) has become concerned with growing criticism of differentiated instruction, particularly from recently published books and articles by Mike Schmoker (Focus: Elevating the Essentials to Radically Improve Student Learning) and Daniel Willingham (Why Don’t Students Like School?).
He explains: “Some administrators are telling me that their teachers refuse to implement differentiated instruction or don’t give credence to seminars and books on the topic because of the arguments put forth by Schmoker, Willingham, and others who’ve jumped on their bandwagon.”
In the October issue of Middle Ground magazine, Rick responds to what he views as a mischaracterization of differentiated instruction, especially the generalization of “learning styles” criticisms to the breadth of DI. You can read Rick’s article here.
You can read Mike Schmoker’s September 2010 EdWeek commentary, “When Pedagogic Fads Trump Priorities,” here.
Sage Carnahan’s first grade classroom at Askew Elementary in Houston, Texas, was abuzz with activity last week — and not just because of his lively students. Debbie Diller was shooting her new math work stations video, due out mid-2012. The kids were especially fascinated by all of the recording equipment, especially the huge boom mike and camera stands. On the last day of shooting, the students spent some time drawing what was going on in their classroom.
One of the students, first grader Lesly, seemed intrigued by the camera stand and spent quite some time taking in all of its details:
Here is the final result:
Another student was taken with the red and black striped sweater worn by James, the sound engineer:
A few weeks ago we shared a poem from Kelly Gallagher’s new book, Write Like This. This week we have another poem from his book, this time from one of his students. Kelly uses the video and poem The Lost Generation as a mentor text for writing reverse poems. Watch the video here and then read what Kelly’s student Rebecca wrote:
Framing My Future
By Rebecca Bausan
My future is in ruins
Therefore I will discard the impression that
I will be able to achieve what others could not
This may be surprising to some but
Education is overrated
I will not accept the concept that
I can make a difference through my education
So I will let others know that
It is not worth it.
Hard work pays off but
I see things differently.
It is apparent that
Beauty and luxury are vastly more important than brains and wisdom
I am completely against the assumption that
Personal achievement will be able to thrive in a world so corrupted
I am certain that
In the future
There will be an increase in college dropouts
It cannot be said that
My peers and I will benefit from a higher education for
Our betterment comes from pleasures of selfishness
It is a false belief that
Success is an option.
All of this will stay a reality unless I choose to reverse it.
We just a posted a clip from Patrick Allen’s new video, What Are You Thinking? The author of Conferring: The Keystone of Reader’s Workshop takes you inside his classroom as he confers with nine different students over two days. Patrick demonstrates how to connect with readers, how to monitor their progress through individual records, and, perhaps most important, how to encourage children to love books and reading while honoring their individuality.
Let’s face it: conferring in reader’s workshop is hard work. Throughout What Are You Thinking? Patrick provides a strong model for navigating the open-ended possibilities that each reader brings to a reading conference.
Algebra is a challenge for teachers and students alike. Teachers have their hands full trying to focus on key concepts while imparting procedural knowledge, relating algebra to arithmetic, and connecting it to real-world experiences.
The Xs and Whys of Algebra is an 84-page flipchart that cuts through the confusion to help you prevent common misconceptions. Following the same practical format as their popular Zeroing in on Number and Operations series, Anne Collins and Linda Dacey provide 30 modules that focus on key ideas with instructional strategies, activities, and reproducibles for:
• using variables meaningfully;
• using multiple representations for expression;
• connecting algebra with number;
• connecting algebra with geometry; and
• manipulating symbols with understanding.
All teachers of algebra should have this handy flipchart at their fingertips during planning and instruction. You can preview two of the modules—Systems of Linear Inequalities and Posing Problems for Inequalities—online now.
We have a special treat on this Poetry Friday. Kate Messner’s poem Revolution for the Tested is inspirational and true and funny in all the right places. Read it. Share it with your students. And, most important of all: live it.
Revolution for the Tested By Kate Messner
But don’t write what they tell you to.
Don’t write formulaic paragraphs
Counting sentences as you go
Put your pencil down.
Don’t write to fill in lines.
For a weary scorer earning minimum wage
Handing out points for main ideas
Supported by examples
From the carefully selected text.