With so many studies indicating the United States is dangerously close to a failing grade in math, it’s not surprising that educators are seeking solutions that not only can help students improve their math skills, but also can give them a competitive edge to succeed in a knowledge-based economy.
U.S. students are lagging behind their peers in other countries in science and math, according to the most recent results from the Program for International Student Assessment (PISA), released in December. The test was last given to 15-year-olds in 30 industrialized countries in 2006 and is administered every three years.
The 30 countries, including the United States, make up the Organization for Economic Cooperation and Development, which runs the international test. The average scores for U.S. students were lower than the average scores for the group as a whole.
In math, U.S. students posted an average score that was lower than the average score in 23 of the other leading industrialized countries. Only four countries posted lower average scores that the United States, and two countries scored roughly even with U.S. students.
The test also was administered to students in about two dozen countries or jurisdictions that are not part of the industrialized group. When compared with the broader group, U.S. students fell in the middle of the pack in science and did somewhat worse in math.
There was no change in U.S. math scores since 2003, the last time the test was given.
The PISA results followed on the heels of a December report, funded by the National Science Foundation, that concluded middle school math teachers in the United States are not as well prepared to teach this challenging subject as are many of their counterparts in five other countries.
That study, titled “Mathematics Teaching in the 21st Century” and conducted by Michigan State University (MSU), examined how well a sample of universities and teacher-training institutions prepare middle school math teachers in the United States, South Korea, Taiwan, Germany, Bulgaria, and Mexico. Specifically, 2,627 future teachers were surveyed about their preparation, knowledge, and beliefs in this subject area.
“Our future teachers are getting weak training mathematically and are just not prepared to teach the demanding mathematics curriculum we need for middle schools if we hope to compete internationally in the future,” said William Schmidt, an MSU distinguished professor and director of the study.
In comparison with other countries in the study, future teachers in the United States ranked from the middle to the bottom on measures of mathematics knowledge.
“What’s most disturbing is that one of the areas in which U.S. future teachers tend to do the worst is algebra, and algebra is the heart of middle school math,” Schmidt said. “When future teachers in the study were asked about opportunities to learn about the practical aspects of teaching mathematics, again, we rank mediocre at best.”
The study found that the math knowledge of future middle school teachers in the United States was generally weaker than that of future teachers in South Korea, Taiwan, Germany, and—in some areas—Bulgaria. Taiwanese and South Korean teachers-in-training were the top performers in all five areas of math knowledge.
In late November, the National Mathematics Advisory Panel (NMAP), in a draft of its final report, found that successful performance in math courses—including algebra—depends on the lessons mastered in the early years.
The NMAP report deals with curriculum, teacher training, assessment, and research, among other topics, in math classes for students in pre-kindergarten through the eighth grade.
Coinciding with the recent national focus on algebra readiness, the panel’s draft tries to outline what, exactly, a strong algebra course should contain, and it also identifies often-ignored aspects of preK-8 math courses.
The report also highlights the need to improve teacher-preparation programs and boost professional development for math teachers.
Education Secretary Margaret Spellings said she expects to see the panel’s final report in late February or early March.
“I’m very excited about it,” she said late last year. “It’s going to be an important body of research and understanding around math … I think it will be well received, and I look forward to … talking about how we close the achievement gap in math as well.”
Education companies respond
Although the news might seem rather bleak, there could be some cause for optimism. Education companies are responding to the need for solid U.S. math performance with products that not only help strengthen students’ math skills, but also identify struggling learners and take steps to improve their skills before those students reach higher-level math classes.
Many of these products incorporate visual learning elements to help students—especially those who are visual learners—grasp complex mathematical concepts, and a growing number also build reasoning and problem-solving skills as the foundations for higher-level math.
One of these new products is Inspiration Software’s Kidspiration 3 software, which offers new tools to help students build a mathematical foundation for reasoning and problem solving by using visual representations to understand abstract math concepts. Students use the software across the curriculum to express and communicate their thinking with pictures, words, and numbers. The new visual math tools in Kidspiration address the National Council for Teachers of Mathematics (NCTM) Curriculum Focal Points for Grades K-5, including numbers and operations, measurement, algebra, and two-dimensional geometry.
“I’m using Kidspiration with eighth-grade gifted students, and they love it,” said Patricia Ronkartz, a gifted and talented/enrichment teacher at Louisiana’s South Crowley Elementary School. “It doesn’t demean them, we can apply it to things they’re learning, and it helps them visualize fractions and percentages and things that [can be] vague to eighth-grade kids.”
Ronkartz sees her eighth-grade gifted students once a week, and they are in other math classes with different teachers for the rest of the week. She follows an open class structure—students are not given grades in their enrichment courses, but instead are able to take any topic that interests them and explore it further during class time.
Ronkartz said most of her students are visual learners and, when given the choice, prefer using Kidspiration to a pencil and paper, especially when studying lessons such as tessellations.
“That’s the nice thing about tessellations. For the kids who aren’t math-oriented, it was art—and vice-versa. They can produce it without being frustrated, and the bright colors stay in their minds.”
Also focusing on visual learning and instruction, Pearson Education launched enVisionMATH in January. Developed by the company’s Scott Foresman division, the product combines visual animation and graphic text, and it centers on conceptual understanding. It aims to help students improve their reasoning ability for problem solving, which is a critical foundation for higher-level math, said Randy Charles, professor emeritus in the mathematics department at San Jose State University and a former vice president of the National Council of Supervisors of Mathematics.
Designed in collaboration with a team of math teachers, the new curriculum blends digital and print content and includes daily, differentiated instruction. It is organized into 20 focused topics at each grade level. Assessment and prescriptions are embedded throughout enVisionMATH, so teachers can personalize instruction to ensure that students grasp each concept before moving on to the next lesson.
Visual and interactive learning components are included to help students who are learning basic English at the same time they are learning math. The program also includes a “Visual Learning Bridge” in each lesson, with step-by-step visuals that bridge the gap between the interactive learning activity and guided practice.
“With the digital Visual Learning animations, the concepts come alive for students,” said Charles.
“It’s visual, so it’s suited to kids who have grown up in this visual world,” said Stuart J. Murphy, author of the children’s MathStart book series. Murphy guided the development of the curriculum’s Visual Learning Bridge.
In looking at the performance of U.S. students in mathematics on international exams, Charles said, he knew enVisionMATH would have to challenge students and teachers.
“Taking that perspective forced us to try things no one has tried before,” he said. “This can help raise the bar for all kids.”
He added: “The major mission is to help kids move into middle school and algebra—that’s the gatekeeper to high school and higher math. We took seriously the need for expectations and success in algebra.”
“When you put verbal information together with visual presentations and add mathematical concepts, it leads to comprehension for all students,” said Murphy.
Math intervention programs
Schools also are experiencing success with math intervention programs, which identify struggling students and work with them to strengthen skills that are weak.
Students at Aliceville Middle School in Alabama reportedly demonstrated significant gains in math scores after using Voyager Expanded Learning’s Vmath, a math intervention program.
Vmath helps teachers identify students who are struggling with math and intervene with explicit, scaffolded instruction, while monitoring their progress until intervention is no longer needed. The product is intended to give struggling math students in grades three through eight 30 to 40 minutes of targeted, daily instruction to bring them to grade-level proficiency and improve their outcomes on standardized tests.
Using the software, it was reported, Aliceville sixth graders raised their scores on the Alabama Reading and Mathematics Test from a 57-percent passing rate during the 2005-2006 school year to an 82-percent passing rate in 2006-2007. Those same students reportedly moved from a 5.2 grade-level equivalent to a 7.4 during the course of the academic year, as measured by the STAR Math Assessment.
“Since the implementation of Vmath, we have seen an increase in student performance on various assessments that ultimately produced significant increases on state and national assessments. We will continue to use the Vmath program because it is making a difference in the lives of our students,” said Tammy Brown, Aliceville Middle School reading and math coach.
Apangea Learning’s flagship product, SmartHelp, is a supplemental program that uses a hybrid system of artificial intelligence and live tutors. The web-based, one-on-one application can be used for dropout prevention, intervention, or supplemental tutoring and follows a three-tiered coaching model.
In the first tier, SmartHelp’s system monitors students’ progress while an animated tutor helps them work through problems. The tutor gives students support and guidance where appropriate. The program’s second tier is intended for students who need more support, and they are assisted in real time by live, certified teachers—“problem tutors.” When a problem tutor determines that a student needs to work on his or her understanding of the mathematical concept in question, the student enters the system’s third tier of help and is transferred to a “concept zone,” in which the student receives an interactive, one-on-one lesson conducted by a live teacher in real time through a virtual whiteboard.
Curriculum Advantage’s Classworks program offers computer-based instruction in multiple subject areas, including math. The company customizes specific editions for each state, fine-tuning the instruction to meet specific curriculum and learning standard requirements and aligning it with high-stakes testing.
The Box Elder School District in Brigham City, Utah, about an hour north of Salt Lake City, decided to use much of the $1 million it received for district-level educational software to bring Classworks into all 16 of its elementary schools, as well as a middle school and high school.
In particular, Box Elder administrators were interested in using Classworks to raise math achievement within the fourth through sixth grades, as studies within the district have shown a direct correlation between students failing to achieve at those grade levels and the continued underachievement of these same students in high school.
“We had to sit down and figure out what we were going to do with this money. There were so many products out there,” said Mary Kay Kirkland, Box Elder’s assistant superintendent for curriculum. “We started looking at … what would fit our needs district-wide. Classworks has been great.”
Administrators with the Gaston County School District in suburban Charlotte, N.C., have implemented Classworks in the district’s middle schools. All 11 Gaston County middle schools—each of which failed to meet Adequate Yearly Progress goals under No Child Left Behind last year—have begun using Classworks. Additionally, one high school and one alternative school in the district is implementing Classworks.
Beverly Kellar, the district’s deputy superintendent for instruction, said administrators are looking for Classworks to make a quick impact.
“We’re anticipating some positive results this year,” Kellar said. “Several of our schools are rotating students through Classworks labs daily, and others are using flexible schedules. Our students who are most at risk of not meeting the proficiency levels are getting priority, and there is a lot of excitement about having those students work with the program.”
While most often associated with textbooks, Saxon Math has launched a new K-5 technology suite that lets teachers build lesson plans and monitor student progress, while at the same time giving students math-related activities to do outside the classroom to reinforce the concept of math as a life skill.
Teachers can use the Teacher’s Manual eBook to plan and print out lesson plans, planning guides, or section overviews. The program also contains a presentations CD with whiteboard-ready slide presentations that are aligned with Saxon Math lessons.
Assessment tools, such as benchmark tests and practice exercises, help teachers keep track of student progress, and teachers are able to create customized tests or draw from a bank of questions provided with the software. These assessment tools give teachers the option to print or publish to the web.
A “Manipulatives in Motion” CD illustrates abstract math concepts through interactive exercises that correlate with Saxon Math lessons.
Better teacher training
Universities, with the help of supporting organizations, are doing more to increase the number of graduates with enhanced math and science teaching skills.
For example, the nonprofit National Math and Science Initiative (supported primarily by a $125 million grant from Exxon Mobil Corp.) has donated more than $25 million to 12 U.S. universities, including Florida State University and the University of Florida.
The grants of up to $2.4 million each will help the universities start programs modeled by UTeach, a teacher-preparation program at the University of Texas at Austin.
“UTeach has proven a very successful model for preparing our next-generation science and math teachers,” said Mary Ann Rankin, dean of the College of Natural Sciences at UT-Austin.
The strength of UTeach, which began a decade ago, lies in its unique collaboration between the Colleges of Natural Sciences and Education. The program encourages math and science majors to enter the teaching profession by offering a math or science degree combined with teacher certification, financial assistance, and early teaching experiences for undergraduates.
“The UTeach program invests in the teachers of those who will become future leaders in key technology industries critical to the development and competitiveness of the United States,” said Tom Luce, chief executive of the National Math and Science Initiative. “As society demands more and more technological advancements, investments in those who teach in math, science, and technology become critical for continuous success and long-term growth.”
At the core of many math improvement programs is the realization that today’s students need not just passing grades, but real skills, to succeed in future schooling and in the professional world.
“Kids have to realize that math isn’t just a school skill—it’s a life skill,” said Pearson’s Murphy.