• by Cathy Seeley, Ed.D. • IDRA Newsletter • March 1998 •
It is easy to worry about recent newspaper reports on the Third International Mathematics and Science Study (TIMSS) results. The performance of U.S. 12th graders is abysmal compared to the rest of the world, even for our top students. The TIMSS data are not particularly surprising given the pattern of the TIMSS data released in prior months showing U.S. eighth grade students performing at a fairly mediocre level and U.S. fourth grade students doing somewhat better (TIMSS, 1998). But that is not the whole story. During the last few years, there has been good news about test scores as well.
Performance of U.S. students on our own National Assessment of Educational Progress (NAEP) continues to show growth at every level, with Texas making major gains, especially at the fourth grade level (NAEP, 1997; Fuller, 1998).
In terms of the Texas Assessment of Academic Skills (TAAS), all groups of students improved ever since the TAAS replaced the TEAMS test in 1990, with even greater gains since copies of each test were released beginning in 1995. This improvement includes students at every grade level. Disaggregated data show that gains are noteworthy even within groups broken down by gender, ethnicity, and free-and reduced-price lunch program status (TEA, 1997).
Nevertheless, we continue to see significant disparities in performance among these groups on other assessments at the state and national levels.
So, what is working and what is not?
What is Working
In many classrooms, teachers have made positive changes in the mathematics they teach and how they teach it. Based on the best thinking of the mathematics education community, these teachers have: tightened the mathematical focus at every grade level, provided the depth of understanding students desperately need, found appropriate ways to use powerful tools such as computers and calculators to elevate the level of mathematics students address, and incorporated all of this within a healthy balance of basic skills and more complex thinking and problem solving.
Students in these classrooms are actively engaged in learning mathematics, by writing about, discussing and demonstrating important mathematical ideas and problems. They know how to work alone and in small groups to extend their learning.
Even teachers who have always done a good job teaching mathematics have recognized that they must continually improve and shift what they do to prepare their students for a rich and varied future.
Most of these teachers did not start out teaching this way. In their teacher preparation programs, they – like most other teachers – learned that a well-prepared teacher of elementary or secondary mathematics was one who could clearly explain mathematical procedures and manage large group instruction. They learned about the traditional redundant mathematics curriculum that does little to extend what students know and focuses instead on fragmenting mathematics instruction digit by digit to increasingly larger numbers with essentially the same computational rules as the year before. Even though this traditional curriculum has included some non-arithmetic strands of mathematics, most teachers have had too much to teach and, many of these other topics were never addressed in depth – or at all.
Several factors contribute to teachers’ ability to improve their teaching and their students’ learning. Certainly, effective professional development is critical to improving what happens in mathematics classrooms. In Texas, a statewide network of professional development in mathematics and science makes such quality professional development available and cost-effective for educators throughout the state (Texas SSI, 1997a). This program provides a series of modules and institutes focused on the Texas Essential Knowledge and Skills (TEKS).
The TEKS themselves can provide a powerful positive influence on what happens in classrooms. They represent a strong consensus-based mathematics curriculum that has somewhat sharpened the focus of mathematics instruction at every grade level. They are comprehensive yet forward-thinking. The TAAS will reflect these TEKS as of spring 1999, thus providing a positive driving influence on classroom instruction.
What is Not Working
In some schools, concern about student performance on measures such as the TAAS have led to less than constructive approaches, to say the least. It is useful for teachers to know what will be assessed, but it is not useful to overemphasize exercises that look like sample test items. It is both dangerous and inadequate to so strongly stress the TAAS that teachers are told to have their students practice TAAS-like items to the exclusion of all other instruction. Even if short-term gains may appear (which is not always the case), these gains cannot possibly serve students as they progress through the mathematics curriculum.
Trying to build a brick house on a foundation of shaky twig supports can only lead to trouble. As students attempt to learn the mathematics that come in the next grade or the one after that, they are forced each time to memorize fragmented rules and procedures since they do not have the deep understanding that would enable them to anchor their learning and make their memorization more efficient. Not only will they learn only a shallow level of mathematics, but their future test scores may also be in jeopardy as their misconceptions and forgotten facts multiply.
In some schools, teachers work primarily in isolation from each other, each trying his or her own strategies and approaches, sometimes with different programs and materials. This piecemeal approach to teaching may provide a high degree of teacher autonomy, but it accomplishes little for students who progress from one philosophy to the next, from one program to the next, or from one set of standards to the next. There is little opportunity to build on what students have previously learned. Teachers are likely to become frustrated and give up their efforts when they operate without the interactions with and support from each other.
Furthermore, some teachers, administrators, parents and students continue to operate with a belief system about who is able to do what in mathematics. We have believed the myth that only certain students can think at a high level and only certain students can think mathematically. We have bought into the idea that every student needs to be proficient in arithmetic before he or she can do anything else more challenging and interesting in mathematics, in spite of mounting evidence to the contrary.
For example, a middle-aged man I met recently – who I will call “Robert” – confessed to me that he did not yet know his multiplication facts. He thought he might have a learning disability since he never could figure out how he was supposed to memorize them. In spite of this lack of computational facility, Robert had earned a bachelor’s degree in physics, a master’s degree in economics, and a doctorate in electrical engineering. He travels around the world designing computer chip manufacturing plants, without knowing his multiplication facts.
We simply know better than to withhold the best part of mathematics from students just because they cannot yet recite their facts or do long division with three-digit divisors. And we surely know better than to assume that only certain students can do well in mathematics.
With varied instructional approaches (especially emphasizing mathematical communication, connections, reasoning and problem solving), there is no reason any student cannot learn far more mathematics than we have ever thought possible. We cannot let our inadequacies handcuff students. For every student we might judge as unable to learn mathematics, some teacher somewhere can disprove that judgment. Thank goodness.
What is Next
How can educators do what is best for every student? Educators must deeply examine beliefs about students and mathematics. When teachers and administrators say “All students can learn,” how is this statement implemented for the least successful students without holding back the most successful?
Teachers must be armed to make professional decisions by participating in ongoing high quality professional development.
Teachers should be supported in selecting quality instructional materials that support their philosophy and the standards they are implementing, such as the TEKS (Texas SSI, 1997b).
Teachers should learn the most effective teaching approaches possible to make mathematics meaningful and approachable to a wider range of students than ever before.
Finally, schools can multiply their efforts to improve their mathematics programs by working schoolwide toward common goals, building on a common foundation of beliefs, and utilizing common materials and professional development.
Changing what and how we teach is hard to do. Sound standards, like the TEKS, provide a good starting point, and knowledgeable, confident mathematics students are the end product. Along this road, there is much work to do in every school to understand the mathematics curriculum and learn new strategies for teaching and assessing it. The cost is high, but the investment is essential. Our students deserve nothing less.
Fuller, E.J. (compiler). Texas Highlights from the National Assessment of Educational Progress in Mathematics (Austin, Texas: Texas Statewide Systemic Initiative, 1998).
NAEP (National Assessment of Educational Progress). 1996 Mathematics: Report Card for the Nation and the States (Washington, D.C.: Office of Educational Research and Improvement, U.S. Government Printing Office, February 1997).
TEA (Texas Education Agency). 1997 Interim Report on Texas Public Schools: A Report to the 75th Texas Legislature (Austin, Texas: Texas Education Agency, 1997).
Texas SSI (Statewide Systemic Initiative). Texas Teachers Empowered for Achievement in Mathematics: 1997 Guidebook (Austin, Texas: Texas Statewide Systemic Initiative, 1997).
Texas SSI (Statewide Systemic Initiative). Issue Brief #1: What It Means to Implement the TEKS (Austin, Texas: Texas Statewide Systemic Initiative, 1997).
TIMSS (Third International Mathematics and Science Study). Internet posting (February 1998).
Cathy L. Seeley, Ed.D., is the director of policy and professional development for the Texas Statewide Systemic Initiative at the Charles A. Dana Center at the University of Texas at Austin. Comments and questions may be directed to her via e-mail at firstname.lastname@example.org.
[©1998, IDRA. This article originally appeared in the March 1998 IDRA Newsletter by the Intercultural Development Research Association. Permission to reproduce this article is granted provided the article is reprinted in its entirety and proper credit is given to IDRA and the author.]