Whether you are a parent or a politician, whether you work in business, industry, government or academia, the state of U.S. mathematics education is of fundamental importance to you and those you care about. As the importance of mathematical and quantitative thinking increases, we must become more focused as a nation on providing our children a better mathematical education. This is not simply about economic competitiveness or getting higher scores on international comparisons. Rather it is about equipping our children with the necessary tools to be effective citizens and skilled members of the workforce in the twenty-first century. Mathematics as a discipline and the applications of mathematics to the world around us have grown and changed significantly in the past 50 years. Our system of mathematics education must reflect that growth and change. Quite simply, math is more.
Plank 1: Students need to see mathematics and the people who use mathematics in the broadest possible light.
What do we mean by mathematical literacy? First, math is more than dividing decimals or solving equations. It is more than algebra or geometry as defined by a particular syllabus or set of textbooks. Math is the use of a graph to model a street network to solve traffic snarls; it is finding the ‘distance’ between two strands of DNA to improve our understanding of the human species. It is about deduction, visualization, statistical and probabilistic reasoning, representation, and modeling. It is what enables our cell phones to work, and our MRIs to function. It gives us insight into medicine, biology, economics, business, engineering, and the ways we reason and make decisions. Mathematics education at all levels and in all courses must engage students with the practicality, the applicability, the power and the beauty of mathematics. This can be accomplished when students see mathematics as including skills, conceptual understandings and a way of reasoning.
Plank 2: Mathematics education must be viewed as a complex system requiring coherent coordination and a long-term investment in the quality of curriculum, instruction, and assessment.
We do not believe that there are quick fixes or magic bullets that will lead to significant improvements in mathematics education. Rather, we believe that improvements in this complex system will be the result of a series of substantive changes that are informed by research and guided by experimentation with the proper and rigorous evaluation of the results. But change of this magnitude takes time. Among other things, both established and new teachers need to learn and experience mathematics as the rich discipline we know it to be. Professional working conditions for teachers must allow time and opportunity for developing new understandings about mathematics, its applications and the teaching of mathematics.
Plank 3: Mathematics education at all levels, including advanced college programs, is a form of vocational and professional preparation.
We must recognize that there is a compelling national (and local) interest in the state of mathematics education. While we do not see this as a zero-sum game, with our country (or state) vying to do better than another, our overall mathematical literacy and competence is important to our economic health. Industry, in addition to government, needs to be heavily involved. Employers are after all parents and vice versa. Surely, having good high school math grades or SAT scores must be about more than getting into a good college. Being able to analyze and solve problems using quantitative reasoning is an increasingly necessary job skill. We believe that not enough emphasis has been placed on the needs of students. Their future will involve many different jobs. They will need to master current and emerging technologies. We know that they will need creativity, independence, imagination and problem-solving abilities in addition to skills proficiency. In other words, students will increasingly need advanced mathematical understanding and awareness of the tools mathematics provides to achieve their career goals.
Plank 4: A coherent set of broad national curricular goals allowing for new results from educational research should be created.
While we believe in accountability and we recognize the need for curricular coherence, we worry about the Babel of ‘Standards’ being designed by individual states, districts, and more nationally-based organizations and think tanks. National standards in the spirit of curricular goals can serve a unifying purpose. Standards must, however, be generic enough to allow for the evolution of content and pedagogy. Although there must be room for trying new ideas, standards should increasingly be grounded in robust research demonstrating student learning of important mathematical ideas. Standards at the grain size of individual skills must be avoided. We also believe that the present multiplicity and specificity of standards is a barrier to innovation by both the authors and publishers of mathematics materials.
Plank 5: The quality of instruction continues to be of critical importance to the improvement of student achievement.
The mathematics classroom is more than where students encounter formal mathematics. It is where students decide if mathematics is “for them” and where the ideas must inspire and engage. Active learning produces life-long learning. There is no substitute for curiosity, engagement, pursuit of ideas, use of prior knowledge followed by exploration, experimentation, practice and mastery. The use of applications, the design of rich interactions among students, and the creative use of technologies have produced promising results when accompanied by careful attention to students’ progress through well-understood learning progressions. Accountability is hollow if it is not accompanied by robust efforts to improve instruction, by using exciting materials, by including opportunities for teachers to be learners and to experience broader views of mathematics. Our task is to introduce students to the wonders of mathematics, while providing the discipline to regulate their own learning and to ensure proficiency and mastery. Students should not be viewed simply as consumers of mathematics education, but as active participants with the most to gain or lose. Their voices should be solicited and taken into serious consideration.
Plank 6: Programs must be developed to help all students, recognizing their diverse needs, interests, talents, and levels of motivation.
“Mathematics for All” is an important rallying cry. But to be meaningful, it requires that we recognize and act on the fact that different student populations need to be provided for differently. For a multitude of reasons, some students may be more motivated to learn than others. Some students have stronger background knowledge than others and some learn more quickly. One size does not fit all. There is research that can be brought to bear on these issues—and we need to know and do more. We cannot afford a mathematics education system that works for the few and not the many.
Plank 7: We must test what we value, both locally and nationally.
Mathematical literacy is becoming a survival skill. We strongly believe in accountability to a rich set of mathematical goals. We want students to master core facts and procedures, but this is not enough. We want conceptual understanding, problem-solving, and flexible use of the mathematics to solve both pure and applied problems. Like standards, assessments must reflect our goals—most importantly, the ability to apply mathematical reasoning to analyze and attack real-world problems. If mathematical literacy includes the ability to make use of mathematics, and we believe in the importance of mathematical literacy, then we must align our testing accordingly. Testing must not be about punishment for failure, but about giving students and teachers a clearer understanding of what they do and do not know. Testing should inform instruction, not determine it.
Plank 8: We must continue to develop and research new materials and pedagogies and translate that research into improved classroom practice.
Education, as a scientific discipline, is a young field with an active community focused on R&D—research on learning coupled with the development of new and better curriculum materials. In truth, however, much of the work is better described as D&R—informed and thoughtful development followed by careful analysis of results. It is in the nature of the enterprise that we cannot discover what works before we create the what. Curriculum development, in particular, is best related to an engineering paradigm. In order to test the efficacy of an approach, we must analyze needs, examine existing programs, build an improved model program, and test it—in the same way we build scale models to design a better bridge or building. This kind of iterative D&R leads to new and more effective materials and new pedagogical approaches that better incorporate the growing body of knowledge of cognitive science. We understand that educational research has not yet provided all of the answers to how to best help children learn mathematics. However, there is a great deal that we do know about the motivational power of applications, the effectiveness of appropriate learning technologies, the use of collaborative learning with children, and the use of lesson- and case-study programs with teachers.
Plank 9: Our country must make a major investment over the coming decade to sustain and rejuvenate the ranks of mathematics teachers in our nation’s
Many mathematics classrooms are staffed with unqualified teachers. This is because school administrators can neither find enough qualified teachers nor provide adequate resources to upgrade staff qualifications. Mandates that every teacher be qualified won’t improve the situation until there is a sufficient supply of mathematics teachers to meet the demand. To stave off this foreseeable crisis in our math classrooms, our nation needs to act to increase the numbers of young people entering mathematics and mathematics education disciplines in our universities and to significantly improve the continuing education of existing teachers. We must ensure that their education prepares them for current educational realities and that their working conditions as teachers permit them continuous mathematical and pedagogical improvements. We need to find more ways to support new teachers through the difficult induction years, especially young people who commit to teach in our least successful schools.
Plank 10: We must build a sustainable system for monitoring and improving mathematics education.
Perhaps the most important point is that our work must be sustainable. Just as with our students, we need to be there throughout the learning process—watching out for necessary course corrections and building with a long-range view. Too often in the past we have reacted to crises, whether it be Sputnik and fear of losing the space race, being overtaken economically by Japan, or out-sourcing our manufacturing jobs to China and India. Reports are written decrying the current state of affairs and funding is made available. But the need for excellent mathematics education will always be with us. We must build an infrastructure that recognizes this fact, and devotes consistent attention and resources to addressing the challenge of high quality mathematics for all, rather than a cycle of investment, neglect, investment…
The authors of this document share many beliefs—that mathematics is important as a discipline, as a field full of wonder and beauty, as a tool for modeling our world, as a prerequisite for knowledgeable citizenship in a participatory democracy, and as a means to better jobs and a better quality of life. We hold strong views on the importance of education in general and mathematics education in particular. We do not agree on all things, but we are, and intend to remain, inclusive. Clearly there is much substance and detail that can be added to these planks. We need many voices and many hands and we call on you to join with us to ensure that every child receives the best mathematics education possible and recognizes that in their future, math is more.
If you support these ideas and would like to work with us to make these planks a reality and/or receive regular updates on Math is More activities please click here.
||- North Carolina State University, Raleigh
||- Knowles Science Teaching Foundation
||- American Mathematical Society
||- Vanderbilt University (Emeritus)
||- American Institutes for Research
||- York College, CUNY
||- Teachers College, Columbia
||- Key Curriculum Press
||- Ithaca College
||- University of California, Berkeley
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