By Dr. John Woodward
We understand the issue more and more every day. For years, we’ve been told that our students don’t stack up in math when compared with their peers in other countries. Our performance isn’t that bad at the fourth grade, but TIMSS and PISA data clearly show significant comparative declines as our students end eighth and tenth grade. One of many interpretations of these data is that math at the intermediate and middle grades is an exceedingly weak link in our educational system.
Were that not enough, the link between mathematical competence and success in the workplace is becoming ever clearer as the economy slowly emerges from a deep recession. A recent and fascinating issue of the Atlantic Monthly (Davidson, 2012) provides a lucid account of the extraordinary gaps in knowledge between highly successful manufacturing workers and their less-skilled counterparts who are employed, at least for now, on the same factory floor. The former possess increasing amounts of quantitative knowledge, while the latter live in fear of automation or outsourcing. Success in math at the middle grades, which is obviously fundamental to success in high school and beyond, is a cornerstone for securing the future for American students.
Standards such as the Common Core are one way to renew our commitment to raising mathematical performance. Yet the challenges are significant, as evidenced in a recent survey of school districts from around the country (Center on Education Policy, 2011). Most districts agreed that the Common Core State Standards are more rigorous than most state standards and that, if implemented well, they will improve student math skills. Yet respondents also felt that new curricular materials, as well as fundamental changes in instruction, would be needed.
The Need for Professional Development
Every business organization, including school districts, wants to hire “turnkey” employees. These are teachers who can hit the ground running and deliver instruction at a high level. Yet with changing standards and what we know about how long it takes any professional to develop a high level of skills, this desire is unrealistic. The hope for turnkeys also puts aside the millions of teachers who already work in our schools. Again, the international message is clear and consistent: high-achieving countries hire the best candidates they can, but they continue their professional development through many years of employment (Akiba & LeTendre, 2009; McKenzie & Company, 2007). We need to adopt this thinking if we have any hope of raising the math performance of our students in today’s schools.
There are distinct features to high-quality professional development in mathematics for today’s teachers. First, it is crucial that teachers understand the concepts they are teaching. Some would argue that this means extensive refresher courses in college-level mathematics, most of which are taught in a traditional, symbolic fashion.
Learning more formal mathematics can possibly help some teachers, but it is an unlikely solution for most. Also, there is little guarantee that any of this kind of professional development transfers to the classroom. Instead, teachers need vivid demonstrations of key concepts (or “big ideas”) as well as opportunities to engage in learning activities that promote the kinds of instruction advocated in the Mathematical Practices component of the Common Core. Teachers – and their students – need opportunities to analyze, discuss, and reason about concepts. They also need to solve the kinds of problems that promote strategic thinking and persistence. Naturally, how to integrate thoughtful skills practice is also part of the picture.
Teachers also need to see the “big picture” within the different strands of mathematics. For example, they need to see how rational numbers develop in complexity over grades 3 through 7. This kind of connected understanding of a strand helps teachers see how the big ideas link together, how what was taught at a previous grade level needs to be reviewed, and how what students do at one grade level is important for the next grade level.
Vivid examples of classroom practice are also critical. How do I use fraction bars effectively? How do I orchestrate a classroom discussion with an eye toward students who do not normally participate? How do I assist students when they get stuck grappling with rich mathematical problems? Well-designed video examples can go a long way to improve practice, and they are something teachers can return to again and again.
Finally, teachers need a tremendous amount of assistance when it comes to instructional planning. Linking the contents of a district’s math adoption to Common Core State Standards is challenging in itself. Even more, creating opportunities within a unit of instruction for students to engage in mathematics at a high level is new to many teachers. It is easy to skip this kind of instruction, particularly if it is a new kind of classroom practice. Teachers need guided assistance doing this as well as developing a variety of assessments that tap into the kind of thinking we want today’s students to do in math.
There is good news. We can provide the kind of professional development our teachers need. Our challenge is to accept the fact that this kind of work is an unavoidable feature of today’s successful school systems.
Dr. Woodward is a professor and dean of the School of Education at the University of Puget Sound. In a project funded by the U.S. Department of Education, he worked with the REACH Institute on a collaborative five-year program that examined teaching methods for helping students in grades 4-8 with disabilities succeed in standard-based instruction. Dr. Woodward is coauthor of the TransMath mastery-based intervention solution for middle and high school students and a lead trainer for NUMBERS math professional development.
Akiba, M., & LeTendre, G. (2009). Improving teacher quality: The U.S. teacher workforce in a global context. New York: Teachers College Press.
Center on Education Policy. (2011, September). Common core state standards: Progress and challenges in school districts’ implementation. Washington, DC: Center on Education Policy.
Davidson, A. (2012, January/February). Making it in America. The Atlantic Monthly. Retrieved January 26, 2012 from http://www.theatlantic.com/magazine/archive/2012/01/making-it-in-america/8844/
McKenzie & Company. (2007). How the world’s best-performing countries come out on top. Retrieved January 26, 2012 from http://mckinseyonsociety.com/downloads/reports/Education/Worlds_School_Systems_Final.pdf