A Perfect Storm of Data: We Must Take Action!
By Matt Larson, NCTM PresidentJanuary 17, 2017
Despite all the concerns about testing, it would be unwise not to look for lessons and take actions based on the recently released results of large-scale national and international assessments. Some educators will be unhappy with this sentiment. Some will argue that large-scale assessments are too blunt an instrument to capture student learning in an enterprise as complex as education, particularly in light of differing societal expectations among countries and severe economic and racial inequalities. Others will correctly argue that focusing on dominant measures of mathematics learning narrows the focus to college and career readiness while ignoring other important aims of mathematics education, such as citizen readiness, self-actualization, and social justice. Still others will argue that the assessments are simply unfair and therefore any international comparison is misguided at best. I am empathetic to these perspectives: the assessments are imperfect and do not capture all that is important with respect to mathematics teaching and learning. Despite these limitations, there is still much we can learn from a combined analysis of the results of the 2015 fourth- and eighth-grade and the 12th-grade National Assessment of Educational Progress (NAEP) scores, the Trends in Mathematics and Science Study (TIMSS), and the 2015 Programme for International Student Assessment (PISA).These results paint a mixed picture of U.S. students’ mathematics achievement. At the elementary and middle levels, the evidence suggests the U.S. is making progress in mathematics teaching and learning. The long-term trend in both fourth- and eighth-grade achievement in the United States is positive. Slight stagnation on the fourth-grade TIMSS and very small declines on the fourth- and eighth-grade NAEP may have more to do with the alignment of these assessments with dominant national standards in the United States and less to do with any actual decrease in student achievement. For example, in 2015 fourth-grade mathematics achievement as measured by the NAEP declined one point from an all-time high score in 2013. But subscale scores reveal an increase in “Number Properties and Operations,” while the most significant decreases were in “Geometry” and “Data Analysis, Statistics, and Probability.” The Common Core State Standards for Mathematics (CCSSM) significantly reduce the last two topics from the elementary standards while increasing the emphasis on the first. Because the vast majority of students in the United States are educated in states that have adopted the CCSSM or have state standards closely aligned with the CCSSM, the subscale scores are significant. Similarly, the largest declines at the fourth-grade level on TIMSS between 2011 and 2015 occurred in “Geometric Shapes and Measures” and “Data Display.” Because opportunity to learn is a strong predictor of what students actually learn, the most recent fourth- and eighth-grade TIMSS and NAEP results are to be expected—scores declined in areas that received less instructional emphasis. Mathematics achievement at the elementary and middle levels in the United States has been trending positive over the long term—even in an international context. Not enough, not fast enough, and certainly not for each and every student, but positive nonetheless. In a country as large, decentralized, and complex as the United States, incremental but steady improvement should be viewed positively.High school is another story. High school mathematics scores as measured by NAEP have remained flat for more than a decade, and have been sliding relative to our international peers as measured by TIMSS Advanced and PISA. High-performing countries share some features in common, including the fact they have implemented common, rigorous, and focused standards across all classrooms. Andreas Schleicher, Director for Education and Skills, and Special Advisor on Education Policy to the Secretary-General at the Organization for Economic Co-operation and Development (OECD), has observed that Americans should have more patience with their recently adopted common standards and that “the Common Core concept is quite well aligned with what we see in many high performing education systems.” At the K–grade 8 level it makes sense to stay the course, support the professional learning of teachers with respect to new standards, and focus on the fundamental elements of effective education: common and high expectations for each and every student, high-quality, research-informed instruction provided in supportive environments that build on the strengths of students, and a culture of continual and relentless collaborative improvement. However, high school mathematics is a far different matter. The data indicate that too many students do not have access to effective educational opportunities. Access to high-quality curriculum and instruction—with balanced attention to conceptual understanding, reasoning, and problem solving, in addition to procedural fluency—is not universal and is reflected in the PISA results, where the premium is on students’ ability to understand and use mathematics. To be clear, these issues are not the fault of teachers. The vast majority of high school mathematics teachers are committed to their students and their success, and do their best within a historically and increasingly dysfunctional system riddled with longstanding structural obstacles. These structural obstacles, such as a narrow curricular emphasis on procedures that lack relevance and meaning to students, lack of student engagement, and the continued tracking of students into low-level mathematics courses, must be discarded. These ineffective practices have been embedded in high school mathematics instruction for decades. We simply aren’t serving each and every student well enough. The National Council of Teachers of Mathematics (NCTM) calls for the elimination of these structural obstacles while acknowledging that we must be more responsive to the backgrounds and experiences students bring to the classroom. In addition, NCTM has called for and is working on a substantial reconceptualization of the high school mathematics experience so that it is more relevant and better serves not only the needs of each and every student but the needs of society at large as well. Assessment is only as valuable as the informed actions taken based on the results. If we fail to act on what multiple sources of data so clearly show, the next round of assessments will only reveal that the problems have grown worse. It is our collective responsibility to act. Clear themes can be found in the data, and the actions necessary to improve mathematics teaching and learning in the United States are similarly clear: support the current common and rigorous standards in K–grade 8; support the professional learning of teachers; create structures to enhance teachers’ professional collaboration and continual improvement; eliminate structural obstacles that stand in the way of the learning of each and every student; and substantially reform high school mathematics curriculum and instruction. It is our professional responsibility as educators not to ignore these lessons and take action. Our future depends on our response. Matt Larson is president of the National Council of Teachers of Mathematics (NCTM), a 70,000-member international mathematics education organization. Previously, Larson was the K–12 curriculum specialist for mathematics in Lincoln (Nebraska) Public Schools for more than 20 years.
Thank you for your clear and thoughtful analysis of these results. There's a lot to celebrate around the US for sure. We need continued training and reshaping of people's beliefs and understanding of maths and maths ed. in the US and it's really cool to see organizations like NCTM, NCSM, Achieve the Core, and YouCubed casting a greater vision of maths for all our students.
Thank you so much for making a clear statement about the "real" state of mathematics in the U.S. We always have work to do and it is wonderful having you to help us point our compasses in the correct direction. Thank you for your insight!
I feel I must agree with Corey Andreasen’s statement, ‘you may be cutting teachers a little too much slack. While the structural obstacles are there, in many places teachers choose the curriculum materials, and they choose what's familiar over what's good and then teach accordingly.’ As reason for my agreement and concern, I would like to use as one specific example a fraction of the Common Core.
I have examined the mathematics standards labeled Numbers and Operations—Fractions from the initial statement for grade 3, ‘Develop understanding of fractions as numbers’, to the final Standard of grade 5, ‘Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions’. These standards for fractions set a goal for our schools: Understand fractions as numbers. This seems so evident you might ask, ‘What else might a fraction possibly be?’ Yet this remains a concept some resist.
Most frequently I hear the term ‘part-part-whole’, a confusing but widespread method of introducing young children to fractions. The concept is ingrained and may seem even reasonable to many who have endured it, but part/part/whole muddles future understanding because it uses portions of sets as models for fractions. For example: “I have four pencils. If I give you half of them, how many will I have left?”
There are several problems with introducing fractions using sets and this part/part/whole explanation: first and most importantly, 2 out of 4 is actually a ratio expressed in fractional terms (The standards introduce ratios in grade 6.); also, young children might easily confuse the number 2 with the number ½; but more, as they progress, children can’t translate part/part/whole into an equation.
This is just one example of ingrained teaching tools which remain difficult to overcome.
I so agree with your sentiments! I have been a math coach in elementary/middle schools for a decade and have seen how hard it is to change instructional practices. I also see it harder to get middle school teachers to change than elementary teachers. The better teachers were also the ones more open to trying something different! I believe a focus on coaches in high school classrooms would help reform instruction at that level. High school teachers do not know what they don't know! I also believe a change in textbooks would help the transition to a more reasoning based approach as well.
I think you may be cutting teachers a little too much slack. While the structural obstacles are there, in many places teachers choose the curriculum materials, and the choose what's familiar over what's good, and they teach accordingly. That needs to change in addition to the other issues you've raised.