TC Media Center from the Office of External Affairs

Section Navigation

Bottling the Magic

Images

DOING THE MATH

P.S. 112 pre-K student David Marcano repeats patterns as part of the Birthday Party Project. His progress is tracked on software on a handheld device.

LEARNING IS FUNDAMENTAL

Herbert Ginsburg, TC's Jacob H. Schiff Foundations professor of Psychology and Education, developed the Birthday Party Project and a program called VITAL, an online learning environment.

IN THE PALM OF HER HAND

Formative results after one of the curriculum-based measures in the mCLASS software.

SHARING ASSESSMENT

Fritz Mosher (left) and Tom Corcoran in TC's CPRE office.

MATH GOES HI-TECH

P.S. 112 student Angelo Borrero during a math assessment where his answers are input into a handheld device.

DOING THE MATH

Measurement of student's problem-solving strategy in the mCLASS software.

IN THE PALM OF HER HAND

Kiara Toribio, a first grader at P.S. 112 in New York City, counts as TC doctoral student Genevieve Hartman runs an mCLASS assessment.

SHARING ASSESSMENT

Lucy Calkins at a Reading and Writing Project training session.

Thirty years ago, Lucy Calkins was a teacher with a gift—a love of books and stories, a passion for words and a rare talent for fanning a spark of magic with any child.

Calkins, an intense woman who today is the Robinson Professor in Children’s Literature at Teachers College, also had a vision for sharing her approach with other teachers. She wrote two landmark books, The Art of Teaching Reading and The Art of Teaching Writing, and founded the Teachers College Reading and Writing Project—a team of coaches that now works with more than 700 schools in New York City and many more around the country.

“Lucy Calkins is a guru—the leader of a movement,” says Fritz Mosher, an education consultant with the Consortium for Policy Research in Education (CPRE). “It’s amazing to watch what she does.”

Can anyone bottle Lucy Calkins? In a sense, Mosher and his long-time colleague, CPRE Co-Director Thomas Corcoran, are trying to do that. For example, one of Calkins’ favorite injunctions to teachers is to “pull up a chair and listen” to kids. That’s not easy to do when you have 25 students in your class—or 150 to deal with every day. Yet it accurately describes how Reading and Writing Project staff members evaluate reading ability: by actually sitting next to a child, listening to her read and probing for everything from her overall comprehension to her ability to sound out vowels and recognize phonic patterns. The result is an assessment that, while it certainly doesn’t capture all that’s relevant about a child’s abilities, is more sensitive than the usual written, multiple choice tests—something that can actually help the teacher tailor instruction to the student’s needs rather than merely rank her on a bell curve.

One problem, though, oft-expressed by many principals and teachers: to date, the Reading and Writing Project has had no system with which to synthesize and track its assessments, to share these with parents, and to study patterns of literacy development within and across schools and districts.

Last spring, however, Mosher and Corcoran, helped set Calkins and the Project on a path that ultimately led them to collaborate with an internet services company.

The result is a Web-based program, now being used by the New York City public school system, that will enable teachers to enter and immediately view information generated by a TC Reading and Writing Project assessment. The reports, which will be posted on a Web site, will allow a teacher to view each student’s progress over time in reading fluency, accuracy, comprehension, sight words and letter sound identification. Teachers will even be able to track the kinds of spelling patterns that students use.

All of which will help even a rookie teacher get a quick handle not only on what students can do, but also on ways in which they are improving and ways they are struggling. For example, on a chart for Maria, a fourth grader, a brown line puts her overall reading capability at more or less grade level. However, the brown line has been flat since Maria was in the middle of third grade—a red flag that she’s dropping behind by staying static.

If the viewer rolls the mouse over the brown line, a message will pop up prompting the viewer to check other assessments offered by the program. A glance at the purple line on the chart shows that it flattened out even earlier than the brown line, which suggests that Maria first encountered problems with word recognition—which may have resulted from not doing enough reading.

“So often assessment is something that outsiders do, something that feels very far from teaching,” Lucy Calkins says. “The goal of our software is to help teachers know that assessment needn’t be outsourced. Expert teachers can watch a child read, and they can recognize signals that suggest the child is doing well or is struggling. This software distributes that expertise to all teachers, helping all of us recognize the signs of reading growth.”

 

 A GROWING REVOLUTION

 For the past 20 years, U.S. states have set increasingly detailed standards for what students are expected to study and know—part of a broader sea change in American education away from attempting to guarantee equal opportunity through access to good teachers, safe facilities and strong curriculum and toward trying to legislate universal achievement. The latter trend has achieved its fullest expression in the federal No Child Left Behind Act, which seeks to ensure that all kids will be proficient in reading and math by the year 2014.

CPRE, created in the mid-1980s as the nation’s first federally funded education policy center, was in the vanguard of analyzing the state standards movement. Yet today, the organization (which unites faculty from seven major schools of education, including TC), has shifted its focus from the statehouse to the classroom as the most important theatre for improving student achievement.

 “Policy mainly results in structural change and can take you only so far,” says TC President Susan Fuhrman, who founded CPRE when she was a faculty member at Rutgers. “Much of what happens in the classroom is beyond policy’s reach. Instruction is what makes it all happen, and policy can only support that.”

 And when it comes to instruction, the belief at CPRE is that what’s needed most is personalization—the ability to prevent individual kids from being left behind by teaching them based on real knowledge of what they understand, what they don’t and why.

 Recently, Mosher, Corcoran, Fuhrman and others have created a new unit within CPRE, called the Center on Continuous Instructional Improvement (CCII), through which they are trying to generate a national conversation about how to create that kind of teaching. Mosher and Corcoran are hardly the first to work this territory, but together the two men, who have known each other for years and tend to pepper each other with wonky questions even when others are part of the conversation, bring a lot of experience and contacts to the table. Mosher, the more soft-spoken of the two, is shaggy and wolfish, with long, silvering hair. He spent 36 years as a program officer with the Carnegie Corporation of New York, working on programs in international affairs, governmental reform and education at all levels, and now works with the Spencer Foundation and the RAND Corporation. Corcoran, a Co-Director of CPRE, is craggy, with the brusque manner of a newspaper managing editor. He was Policy Advisor for Education to New Jersey Governor Jim Florio and has consulted widely with urban school districts and national foundations on issues of quality and equity.

Operating out of a small office on the fourth floor of TC’s Gottesman Libraries, Mosher and Corcoran have been working with a range of partners that includes the Council of Chief State School Officers (CCSSO), the Vermont Mathematics Project and the state of Massachusetts, as well as the TC Reading and Writing Project and a software company called Wireless Generation. With funding from the Hewlett Foundation, Corcoran and Mosher also plan to convene a number of conferences and roundtables during the coming year to hammer out working models for successful personalized teaching on a mass scale.

“We want to build a field of work so that researchers come together and build better assessment tools, better curricula and better professional development for educators,” says Corcoran.

Successful personalized teaching, as CPRE sees it, must include four main components.

The first is what the National Science Foundation calls “learning progressions”—or, as Corcoran puts it, “what we know, from learning and developmental theory, combined with just plain empirical observation, about the order of strategies and tactics most kids go through to understand increasingly complex concepts.” While a number of learning progressions have been created to date, right now the classes mandated by most states and districts for students in each grade are, in the view of those who actively champion the idea of learning progressions, little more than laundry lists of information to be covered in a given time period.

Second, the approach advocated by CPRE calls for the bona fide use of formative assessment—frequent formal and informal assessments conducted in classrooms that are genuinely aimed at monitoring children’s understanding of what is being taught and diagnosing their learning needs. The best assessments would be the ones linked to learning progressions, because they could pinpoint, along a clearly defined spectrum, what a child knows, what he doesn’t and what he needs to learn next to improve.

Third, Mosher, Corcoran and others at CPRE are calling for the use of truly “adaptive instruction”—teaching that is frequently fine-tuned based on the results of formative assessments.

And the final piece is “knowledge management”—a fancy term for learning and sharing the kinds of adaptive instruction that teachers find to be effective, through better technology that, like the new assessment program for the TC Reading and Writing Project, will allow schools and districts to more efficiently share student assessment results and analyses. That’s especially important in big schools where kids are regularly handed off to teachers who have never worked with them before.

Corcoran uses the analogy of medicine to explain this idea: “In countries such as Great Britain and Spain, and even in a few places in the U.S., there are databases that a general practitioner can call into or access by computer to say, ‘I’m seeing this array of symptoms, the patient is a 71-year-old male’—and then get back an answer that says, ‘OK, do this or that test,’ or ‘Here are several possible treatment regimens.’ But teachers have no equivalent of that—no organized body of knowledge that would provide that kind of guidance.”

It’s not easy to find current teaching models that combine learning progression, formative assessment, adaptive instruction and knowledge management, but some of the best examples are happening at Teachers College.

“What’s always made TC special is its breadth,” Susan Fuhrman says. “We have neuroscience and cognitive people, we have curriculum people and we have people working with technology and computers, all under one roof. When they come together, it’s incredible what can be accomplished.”

HAPPY RETURNS

One effort where they are coming together is something called the Birthday Party Project, an assessment system, still in development, designed to determine what very young children understand about math. There’s no pencil or paper, no multiple choice questions. In fact, the kids involved (preschoolers ages three to five) don’t know they’re being evaluated; instead, they’ve been told they’re going to a make-believe birthday party. They play games, including activities such as counting presents and adding candies, and identifying shapes and patterns. Then the grown-ups running things ask them questions about how they arrived at their answers. Tapping with a stylus on small, hand-held computers, the evaluators record each child’s answers and note the problem-solving strategies he or she uses to try to figure out how many objects are on a plate or whether one grouping has more objects than another.

“Kids love to be tested if you can do it well and make it enjoyable,” says Teachers College faculty member Herbert Ginsburg, a mild, bespectacled man who is the Birthday Party Project’s progenitor. “That means making assessment fun but still something that yields valuable information.”

To an expert like Ginsburg, whose oeuvre ranges from a preschool math curriculum grounded in the work of Jean Piaget to Two Two the Tooth Fairy, (a story book about spatial relations in which his grandson Matthew is a key character), the kids’ birthday party choices reveal where they stand cognitively, and more specifically, “how their mathematical minds operate.

“We’re not doing intelligence testing,” he says. “That’s essentially irrelevant for teaching math. The goal is to help teachers understand each kid’s thinking so that they can teach better, and in a more personalized and effective way.”

Ginsburg’s efforts to do that are predicated on an idea many find radical: that very young children can, in fact, do real math—and enjoy it, too.

“Research has clearly shown that nearly from birth children develop an ‘everyday mathematics’—informal ideas of more and less, taking away, shape, size, location, pattern and position—that is broad, complex and often sophisticated,” he wrote in an essay in TC Today in spring 2008.

Ginsburg has co-authored a preschool curriculum, “Big Math for Little Kids,” with Carole Greenes of Arizona State University and Robert Balfanz of Johns Hopkins. And at TC, he teaches a course called the Development of Mathematical Thinking, in which students are taught partly by analyzing video clips of young children in various situations, from free play to focused interviews to instruction, in order to identify behaviors that shed light on children’s mathematical thinking, learning and understanding. For example, one demonstration sequence that Ginsburg uses in class shows two little boys, Armando and Keithly, laying long blocks across a square foundation they’ve created, like roofers finishing a house.

“Two more to go, we need two more,” Armando shouts as they get close to filling in all the space—a possible sign that, among other things, he has the ability not only to count, but also to follow a pattern, eyeball space and estimate what’s needed to fill it.

These video clips are currently stored in an online learning environment called VITAL (Video Interactions for Teaching and Learning) that Ginsburg conceived and developed in collaboration with the Columbia Center for New Media Teaching and Learning (CCNMTL), which is directed by TC faculty member Frank Moretti. Using VITAL, students in Ginsburg’s course can select their own segments of video, analyze them and insert them into their electronic papers as clickable multimedia citations—pieces of viewable evidence that buttress their analyses and interpretations.

“I don’t like my students to talk in vague ideological terms, like ‘it’s great to let kids construct knowledge,’” Ginsburg says. “I want them to integrate what they learn about kids from observation with what they read and with their own skills of teaching. Unfortunately, many teachers don’t learn to think very well about what kids know and how they can use that information to teach more effectively.”

Backed by a five-year National Science Foundation grant, Ginsburg and CCNMTL have been refining VITAL, and Ginsburg has been developing a curriculum modeled on his TC course for export to other universities and colleges that train teachers. This is the final year of the grant, and six institutions—Arizona State University-Polytechnic, Georgia State University, Howard University, Hunter College, Rutgers University-Newark and San Diego State University—are or soon will be piloting the program.

And meanwhile, though the Birthday Party Project is still in development, Ginsburg and Wireless Generation have completed development of mCLASS:Math, which uses a similar approach to help teachers understand the mathematical thinking of students in grades K–3. The mCLASS software enables teachers to use handheld devices to give formative assessments in early reading and math more easily and efficiently, receiving data about each child’s learning strengths and needs immediately, along with guidance for applying the information to instructional decisions.

mCLASS:Math is already in use by some 1,500 teachers in 15 states. Teachers receive prompts for questions to ask that probe students’ mathematical understanding. They can record students’ answers under pre-determined category headings for different problem-solving strategies. And they can also use the mCLASS handheld device to upload such information onto a Web site maintained by Wireless Generation where they can view assessment results and analyses. The reports graph students’ progress and milestones over the course of a year and recommend new instructional activities targeted to what each individual student can do and how he or she thinks mathematically.

For example, in one mCLASS: Math assessment, a child is asked to solve an addition problem—say, 6 plus 3—and is given a choice of how to go about it. He can count piles of chips, or make figures on a piece of paper, or count on his fingers—whatever he likes. Some kids who count chips will make a pile of six and a pile of three, and then count all of them from the very beginning: “One, two, three,” and so on, straight through to nine. Others will make a pile of six and then “count on” the next three: “Six… seven, eight, nine.” The latter strategy obviously is more economical and sophisticated than re-counting all the chips from the beginning.

Teachers can also record assessments of children’s “metacognition”—that is, kids’ own explanations of how they know what they know. That’s important, because research by Ginsburg and others has shown that a child who can describe a good problem-solving strategy, even if it has resulted in a wrong answer, may be on firmer ground than one who has simply memorized a procedure and can’t explain a correct answer.

“We’ve built our product based on Herb’s methodology of really talking and listening to kids as a way to get at their thinking,” says Doug Moore, mCLASS: Math Product Manager. “There’s so much richness of detail to be revealed just by asking and observing, and the beauty of this technology is that it can capture that richness.”

 

REAL-WORLD CONCERNS

Work like Ginsburg’s and Calkins’ is impressive—but can it really be implemented on a mass scale?

One question mark relates to learning progressions—the sequenced approach to organizing course content that CPRE is championing. In a recent funding proposal to the Hewlett Foundation Education Program, Fritz Mosher and Tom Corcoran concede that while some people see learning progressions as “the primary solution to our teaching and learning problems, others see them as prescriptive and threatening—another attempt to teacher-proof the curriculum. Some believe that they are simply a dressed-up version of a ‘scope and sequence,’ while others want them to be scientifically validated before they are used.”

Mosher and Corcoran “hold to a more pragmatic view” that effective learning progressions will most likely emerge from trial and error.

Lucy Calkins’ work shows the wisdom of this approach. Calkins and her colleagues have created a series of “curriculum calendars”—recommended stepwise units of study that “support students’ progress along a spiral of work,” Calkins says. These are, in essence, de facto learning progressions for students in grades one through eight. In the Project’s first grade curriculum calendar for November 2008, teachers are encouraged to help children realize that when they read, they come to know the characters they meet in books. Jump ahead a grade level and teachers help seven-year-olds realize that in fictional stories, characters go on journeys that are both external and internal. (“They go somewhere physically, they change emotionally,” Calkins says.) And by fifth grade, children think about not only the major characters as they read, but also the minor characters.

Calkins and her team meanwhile work weekly with principals, literacy coaches and teachers to bring curriculum to life. The Project staff may think about how to provide different levels and kinds of support to learners moving at different paces, or how to ensure that each year, children’s work stands on the shoulders of what they accomplished the year before. It’s an astonishing effort to raise the game of entire school systems, and it has created communities of professional study—and yes, even helped boost reading scores—in places as far flung as New York City, Seattle and Chicago.

But are the curriculum calendars rooted in scientific knowledge?

“No,” Calkins says with a cheerful shrug. “It’s not as if someone said to me, ‘Kids think about journeys when they reach age seven’ or anything like that.”

Still, the curriculum calendars are a product of Calkins’ three-plus decades of observing and working with children, and of the hard work done by literally thousands of other contributors. They have a carefully structured internal logic, and they have met with widespread approval and validation from teachers and other educators around the country. And of course, the curriculum calendars provide a very clear framework for assessing children’s progress.

“In literacy and in writing, I’m pretty convinced that learning cumulates,” Calkins says. “First a young writer learns to chronicle an event, then to imbue that event with special significance—to bring out the meaning she decides to highlight. So, first, it’s ‘I went to Grandma’s house,’ and later it’s, ‘My visit with Grandma made me realize I’m getting older.’ And as the teacher, it’s helpful to see where someone is and to figure out where to take them next.”

The work of Calkins and the Reading and Writing Project is a rare instance of mass-scale change being successfully implemented in education today. Thus, despite these accomplishments, another and perhaps more immediate concern about the formative assessment/adaptive instruction model being advanced by CPRE is: With all the extra work it seems to entail, will classroom teachers ever be willing—or able—to adopt it?

Another hopeful sign comes from studies of fifth and sixth graders conducted last year by TC faculty member Madhabi Chatterji of a methodology called Proximal Assessment for Learner Diagnosis (PALD).

The method requires teachers to break down math problem-solving—or any academic task they want students to learn—into a set of connected skills and concepts. The teachers organize the tasks by difficulty and then assess student performance at each step to understand precisely where students make errors or show lack of understanding.

So, for example, with a long division problem that asks students to divide 175 by 5, students are first asked to choose between possible restatements of the problem (i.e., “The problem is telling me to multiply five by 175” (wrong) versus “Find out how many groups of five are in 175” (right)) to demonstrate that they understand the concepts involved. A little further on, they would be given a choice of an appropriate first question to ask to start actually solving the problem (i.e., “How many times does 5 fit into 1? And if not, how many times does 5 fit into 17?” (right) versus “What is 5 divided by 17?” (wrong).)

Chatterji, with funding by the National Science Foundation, followed 44 teachers and nearly 1,000 students in four East Ramapo, New York, elementary schools for two years. She found that sixth graders taught using PALD scored significantly higher on standardized math tests than their peers who weren’t exposed to the method, and that they were also stronger in long division. Fifth graders in PALD classrooms outperformed their peers in geometry, and sixth graders taught with PALD were stronger in long division than peers not taught with PALD.

But perhaps even more importantly, she also found that the East Ramapo teachers, who were initially resistant to using PALD, became converts over time.

“The fundamental questions we are asking through this work are, ‘Can we teach teachers to look at children and their learning processes more diagnostically? And if teachers gain the skills to conduct close-up examinations of where children’s learning stalls, would they take actions to turn things around?’” Chatterji says. “We were also interested in determining if their attitudes towards tests and testing would change. Would they come to believe more in diagnostic tests as an aid to teaching and learning? And the answer to both questions was ‘Yes.’”

Andrea LaMantia, a sixth grade teacher at Hillcrest Intermediate School in East Ramapo, was one of the converts to PALD.

“When they first came to us and proposed the study, it all seemed very overwhelming,” she says. “But my principal is always telling us to work smarter, not harder, and that’s really the concept here.

“In the past I’d give a whole test—10 questions—to see if kids understood a concept. That’s very time consuming, because I have to make up the quiz, give it and then grade it—and if I have 20 kids, that’s 200 problems I have to correct. But with this system, I could give two questions or maybe even just use homework they’ve already been assigned, and by breaking down the concepts involved, I can get just as much information about what the kids really know. Then I can teach a smaller group of kids who don’t understand something, which is much easier to do. The faster kids won’t be bored, and that decreases the potential for disruptive behavior.

“You know, I’ve always said that all it takes is a few days out sick or one bad teacher to ruin a kid’s whole math career, because after that, he might never catch up. But I can tell you this. At the beginning of the year, during math period, some kids would cry or put their heads down on their desks. By the end of the year, no more. I didn’t have one student who was math phobic.”

For more information on these programs, please visit www.cpre.org, or rwproject.tc.columbia.edu.

previous page