Concerned about what they see as a dearth of instructional materials aligned with the Common Core State Standards in math, several educators in Utah, with support from the state office of education, are taking matters into their own hands. They’re in the early stages of developing a set of e-textbooks for high school math that will be freely available.
In fact, two-thirds of the first e-book, for 9th graders, is already online for schools to use, with the rest expected later this fall.
“There was not a textbook out there that we felt reflected the common core,” said Janet M. Sutorius, a math teacher at Juab High School in Nephi, Utah, who is a co-author. “We felt like the textbook companies were just reorganizing the chapters of their old books.”
She added: “We wanted to teach our students in a different way, to make sense of the mathematics and make connections.”
Finding strong materials has been especially challenging, those developing the e-textbooks say, because Utah has adopted a statewide policy of using an “integrated” model of high school math under the common core, dispensing with the traditional Algebra 1-Geometry-Algebra 2 pathway in favor of blending math subjects in each course.
So, Utah public schools are grappling not only with new standards, but also a reconfigured set of courses the state calls Secondary Mathematics I, II, and III. (In some Utah districts, 9th grade is taught in junior high school.)
A Task-Based Approach
Ms. Sutorius is joined on the writing team by another classroom teacher, two academic officials in the Salt Lake City district, and a professor of math education at Brigham Young University.
The authors describe the enterprise, dubbed the Mathematics Vision Project, as embracing a “task-based” approach to fostering math proficiency that is closely aligned with the common-core standards.
A set of mathematics e-textbooks being developed to align with the Common Core State Standards for high school bring a task-based approach, as seen in this example from a unit on arithmetic and geometric sequences.
SOURCE: Mathematics Vision Project
Diana Suddreth, the STEM director for Utah’s state education agency, said she sees great promise in the project, which the authors began before the state stepped in to offer financial and other assistance.
The need is urgent, she said, given that Utah is now implementing the math standards.
“To leave teachers without any resources is something we can’t do,” Ms. Suddreth said. "[They’re] writing what we hope to be a coherent and rigorous and focused set of textbooks.”
It’s up to districts to decide whether or not they want to use the materials. Ms. Suddreth notes that about one-quarter of Utah’s 41 school systems have reported using the first e-textbook so far.
The math project is part of a broader push in Utah to promote greater use of online, “open source” materials that meet the needs of Utah educators and help districts save money. In January, the state education agency announced plans to help produce and support open textbooks in several areas, including high school math, English/language arts, and science, expanding on an earlier pilot project. The state office will encourage districts and schools statewide to consider using the textbooks.
A separate, state-supported effort with the University of Utah, meanwhile, is crafting e-textbooks for middle school math.
With Utah now pursuing an integrated approach to high school math under the common core, Ms. Suddreth said it’s been difficult to find appropriate materials.
“The publishers were giving us what I call these crazy-quilt textbooks,” she said.
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Jay Diskey, the executive director of the Association of American Publishers’ schools division, said the industry is working hard to deliver aligned materials.
“Publishers large and small are doing everything they can to meet the market need that the common core presents,” he said. “In some cases, that means creating whole new things, in others it may mean looking at what they have and making significant adjustments.”
He added: “If a group of Utah educators says, ‘We didn’t see the sort of things that we need,’ I certainly take them at their word, but perhaps they didn’t look as far and wide as they should have.”
Although the common-core math standards are organized by grade level in grades K-8, at high school, they are organized by conceptual categories, such as algebra and geometry. An appendix added later to the standards documents outlines four model pathways for states to consider, including a “traditional” approach consisting of two algebra courses and geometry (with some data, probability, and statistics included in each). Another approach suggested, and common in other countries, is an “integrated” sequence of math courses, each of which blends material across math-content areas.
Integrated Math
Utah and West Virginia appear to be the only states that have adopted as statewide policy the integrated approach, state officials and experts say, though in many places there is no state policy so districts may use an integrated model.
A statewide task force in Utah decided on the integrated approach after examining the issue carefully, Ms. Suddreth said.
“When you think about mathematics and how people use it, we use it in an integrated way,” she said. “We don’t think, ‘Now I’m going to do some algebra, or now I’m going to do some geometry.’ ”
Ms. Suddreth concedes that the e-textbooks being designed by the Mathematics Vision Project may be seen as unorthodox.
“Everybody kind of has a picture in their mind of what a textbook is: some explanatory text, some problems, and homework,” Ms. Suddreth said. “We’ve replaced the explanatory text with math tasks. ... The book is really a guide to help teachers take students through learning experiences.”
The teacher’s edition does include explanatory text for each task, helping teachers understand the task’s goal and the particular standards addressed, and suggesting whole-class and small-group activities. The student edition has homework assignments for each task.
The authors say there’s plenty of places students may go online for explanations of particular concepts.
In an introduction, the authors explain their approach, saying it is “neither purely constructivist nor purely traditional.” The materials aim to get students engaged in problem-solving, guided by teachers, to promote math proficiency. Each unit, they write, has been designed and sequenced with “rich” tasks that develop concepts in the standards, with careful attention to the way math knowledge emerges.
Also, there will be regular and “honors” versions of each book.
“We wanted materials that were task-based so that students were ... engaged in the practices and making sense of the mathematics for themselves,” said Barbara B. Kuehl, a co-author and the director of academic services for the 24,000-student Salt Lake City district.
Ms. Sutorius from Juab High School said one challenge has been to generate the materials rapidly.
“We’re just running barely faster than [districts] are,” she said. “We work full time, so we’re working evenings and weekends, but there was just such a desperate need for the textbook.”
An Impressive List
William G. McCallum, a math professor at the University of Arizona who was a lead author of the common math standards, said he was not prepared to comment on the content of the e-textbooks being developed, but that he’s encouraged to hear of such projects.
“Anything that is trying a different way of writing textbooks is a good idea,” he said, so long as the materials are well-designed and adhere to the standards. He said he was especially encouraged that the effort appears aimed at tailoring materials to the state’s needs.
“There is a temptation to recycle old material and arrange it in different ways,” he said.
Mr. Diskey from the publishers’ group said he has no objection to educators creating their own e-textbooks, but he cautioned that it’s not easy work.
“Developing a core instructional program, particularly one that meets the needs of all types of learners, is a very difficult task,” he said. “There is scope and sequence, standards alignment, research, editorial development. All of these things come into play.”
Ms. Sutorius acknowledged that the e-textbooks may not have universal appeal: “Not everyone is going to like it.”
She added: “There are lessons I’ve struggled through, and they need to be improved.” But as an e-book, she notes, it’s easy to revise.
Brigham Young University plans to conduct research on the project, tackling such questions as whether the tasks are accessible to students and spark the intended student discourse. Later research will try to gauge the effect of the curriculum on student achievement.
Travis L. Lemon, another co-author and a math teacher at American Fork Junior High School, in North American Fork, Utah, said he’s pleased with his classroom experience using the material so far.
“The students have a lot of opportunity to problem-solve, make sense of problems, listen to other students’ reasoning, and refine their own thinking,” he said, “and we solidify those understandings.”
But student reaction varies.
“Some students respond much better than others,” he said. “If they’ve been encouraged in the past to persist and dig in and make sense of things, they’re more willing and apt to do that now. The ones that aren’t, it’s a little more challenging.”
The first e-textbook is being used by 9th graders in the 7,300-student Uintah district in Vernal, Utah, said Keith D. McMullin, a math instructional coach for the system.
“It’s been very positive,” he said of the district’s experience so far with the material, especially after teachers attended a workshop with two of the authors. “I was excited, and all the teachers that were there were excited.”
He commended the teacher’s edition for its thoroughness in guiding instruction, and said that, overall, the emphasis on tasks in the e-textbook brings the math to life for students and covers a lot of concepts.
“If you look at the tasks that are in there and really list all the things you can teach, ... it’s a very impressive list,” he said. “You’re always building on what students learn the day before.”
