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For the past 20 years, studies such as TIMSS (the Trends in International Mathematics and Science Study) and PISA (the Program of International Student Assessment) have played a transformative role in how educational researchers think about K-12 teaching and learning. Being able to examine students’ academic performance comparatively across countries, as well as studying differences in teaching practices, has been an eye-opener in many countries across the world and has led us to examine our own educational system with a fresh perspective.
At times the results from these international comparative studies have not been especially surprising, such as the continued high performance of East Asian countries such as China - although even these unsurprising results have prompted us to understand why these countries consistently excel.
On the other hand, results from these studies sometimes contain a few surprises, prompting us to study the educational systems of countries whose performance was higher than we might have anticipated - Finland being a prime example. In the US, we tend to scrutinize each cycle of results of TIMSS and PISA to look for clues as to whether recently implemented educational reforms are having their desired effects.
Some scholars have raised concerns about what can be reasonably inferred from the results of international comparative studies. There are lively scholarly debates about the appropriateness of data sampling procedures, the kinds of questions that appear on the tests, and the extent that analyses of test results can adequately control for the often substantial differences in countries’ economies and educational systems. Concern is also raised about whether instructional practices are so culturally situated as to make it difficult, if not impossible, to successfully export them from one country to another.
But despite these concerns, TIMSS and PISA have played a central role in shaping research and policy about K-12 teaching and learning in the US - impacting every facet of our education system, including curricula, instructional practices, standards, and teacher professional development. Through these types of studies, we can not only compare the performance of US students to peers across the globe, but we can also track changes over time (as these studies are repeated every few years) and break down results by grade and performance levels.
The PISA 2015 results recently came out, and the news was not good. The performance of US students dropped significantly - both in comparison to other countries as well as from our score during the 2012 administration of the same test. Various explanations for this decline have been proposed over the past few days. While it is impossible to definitely know why our PISA 2015 math scores dipped, nevertheless these results need to be taken as a wake-up call about the urgent need to improve high school mathematics instruction.
Recall that unlike TIMSS, which tends to focus on the performance of 4th and 8th grade students, PISA examined the performance of 15-year-olds - typically 9th or 10th graders in the US. These results suggest that the ambitious educational reforms of the past 10 years or so - including No Child Left Behind and Common Core - have largely not penetrated US high schools.
Despite our best efforts, math teaching in US high schools has remained relatively unchanged over the past decade - and perhaps much longer. Apart from the presence of different technology such as computers and smart boards, the high school math classroom of today would be quite familiar (both in terms of instruction as well as curriculum) to what we experienced, and even what our parents or grandparents experienced.
Why has high school math instruction been so resistant to change? Certainly it is not for lack of effort from US mathematics educators, including high school teachers themselves. In the last few years we have seen the development of coherent and rigorous standards, innovative textbooks, and newer models of teacher training and professional development - all intended to improve mathematics instruction at all grade levels.
These efforts sometimes produce results - there are fantastic and inspirational math teachers at many high schools. But these pockets of excellence have not been enough to right the unsteady ship that is high school mathematics instruction in the US. Whatever advances our students appear to have made at the elementary and middle grades (recently released TIMSS 2015 results point to some areas of growth and improvement in 4th and 8th grade), these gains seem to evaporate when these same students arrive in high school.
I would argue that our instructional improvement efforts have not been especially successful because they tend to be overly broad and all-encompassing, especially from the perspective of a typical high school math teacher. Certain instructional practices are deeply ingrained and difficult to change among high school math teachers - teacher-led instruction, for example. How can we create sustainable results and more permanent gains?
Rather than invest heavily in ambitious reform agendas that call for broad and substantial changes to high school teachers’ practice, a more pragmatic and effective strategy would be to consider improving instruction incrementally by identifying small powerful changes that teachers can implement relatively easily in their classrooms. Teachers will view these changes as tweaks or small adjustments to their existing teaching practices, increasing the likelihood that the changes will be implemented and perhaps beginning a progression toward broader reforms in the future.
It is somewhat unusual to advocate for incremental changes, given that there are strong incentives to find the newest, biggest, and most innovative ways to solve educational problems. Yet incremental change may actually be the best approach and a way to hedge bets in case that efforts at transformational change are generally unsuccessful - as has frequently occurred in the past. Incremental changes are relatively easy to implement and have the potential to significantly improve classroom instruction.
In essence, incremental change seeks 10 percent improvement for 90 percent of teachers, rather than 90 percent improvement for 10 percent of teachers. This approach begins with the elements of instruction that teachers recognize, support, and/or perceive themselves to be already using and then leverages these instructional practices for future change. By taking small steps forward and meeting teachers where they are, our hopes for larger, more substantial, and long-lasting changes in instructional practice may be achievable.
Profesor Jon R. Star is an educational psychologist at the Harvard Graduate School of Education who is an expert in children’s learning of mathematics in middle and high school
