Section 2: Standards and Assessments: Focusing for Essential Knowledge and Skills

The time has come for the nation to adopt more academically rigorous common standards defining what mathematics and science education ought to look like for all Americans. The Commission believes that math and science standards should be fewer, clearer, and higher and that they should articulate our best understanding of what all students need to know and be able to do in order to succeed in college, thrive in the workforce, and participate in civic life. We endorse the proposition, advanced by David Coleman and Jason Zimba in a 2007 memorandum to the Commission, that “standards must be made significantly fewer in number, significantly clearer in their meaning and relevance for college and work, and significantly higher in terms of the expectations for mastery of what is covered³⁵.” In testimony to the House of Representatives in April 2009, Commission member James Hunt, former governor of North Carolina, argued that new, common standards “must be based on evidence of what’s necessary and sufficient for students to succeed in college and in work.… It should be a tight common core that teachers can teach and students can understand and master³⁶.”

Further, we believe that, if common standards are to serve their intended purpose—to guide stronger math and science instruction for all American students and improve the performance of teachers, schools, and classrooms—they must be linked closely with new, high-quality assessments and more effective systems of accountability. The Commission also urges the adoption of guidelines for the periodic review and revision of standards and assessments to reflect new evidence about how students learn and what they need to know.

Common standards would be a strong platform upon which to build a more effective instructional infrastructure for American math and science education: educators, along with the schools, districts, and states in which they work, would be able to concentrate on how math and science are taught and on how much students are learning rather than on what to teach. Common standards would provide the framework for a widespread, national conversation about how educators can best help students in all groups—from struggling to advanced—to master academically rigorous content and acquire essential skills. They would provide a similar framework for the preparation of future teachers.

Developed collaboratively by states for the nation but not federally promulgated or required, common standards would be national in scope and would provide a common frame of reference as states and school systems upgrade math and science education, rethink curriculum and course sequences, demand better textbooks and curriculum materials from vendors, and build math and science into students’ learning across the curriculum. They would provide needed focus to teacher preparation and ongoing professional learning. For states that choose to adopt them, common standards would make tangible a set of thoughtfully considered, research-validated objectives for students, educators, and schools—objectives that could be refined over time as we learn from ongoing research on their implementation in different states.

High-quality common assessments, based on the proposed common standards and supporting their implementation, would encourage and reward effective instruction. Meaningful assessments that reward good teaching and learning would enable states and school systems to establish priorities, design instructional programs and approaches linked to the standards, and set long-range and interim targets for student and school performance. Assessments linked with common standards could be used in many states, thus opening the possibility of reducing costs and achieving more efficient processes for analyzing and improving the quality of the instruments. Common assessments would also enable states to assess the pace at which their schools are improving more effectively and to measure performance against international benchmarks.

Objectives

• Establish common mathematics and science standards that are fewer, clearer, and higher and that stimulate and guide instructional improvement in math and science and lead the way toward preparing all American students for a global economy

• Develop sophisticated assessments and accountability mechanisms that, along with common standards, stimulate and guide instructional improvement and innovation in mathematics and science

Discussion

When the Commission began its work in 2007, the prospect of establishing core academic standards for the nation’s school systems seemed like a distant prospect. The picture has changed dramatically over the past year, largely through the leadership of a few key organizations. In July 2008, Achieve, Inc., issued Out of Many, One: Toward Rigorous Common Core Standards from the Ground Up, which identified a “common core” of English and mathematics standards that 16 states had already adopted voluntarily as college- and career-ready expectations for their high school graduates.³⁷. All 16 states, scattered across the country, are members of Achieve’s American Diploma Project. This demonstration of a good level of agreement on key learning objectives among a diverse group of states suggests that finding common ground among most if not all states may well be achievable.

In September 2008, Achieve and two other groups—the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO)—joined forces to establish the International Benchmarking Advisory Group, an effort with the announced goal of ensuring that “American students in every state are receiving a world-class education.” The advisory group issued a report, Benchmarking for Success: Ensuring U.S. Students Receive a World-Class Education, in December 2008, which “provides states a roadmap for benchmarking their K-12 education systems against those of top-performing nations³⁸. Like Out of Many, One, the international benchmarking group report confined its recommendations to language arts and mathematics, but its call for higher expectations for all American students has clear implications for science.

Developed collaboratively by states for the nation but not federally promulgated or required, common standards would be national in scope and would provide a common frame of reference.

Most recently, the NGA Center for Best Practices and CCSSO, in partnership with Achieve and other groups, have moved the country a major step closer to common standards with its Common Core Standards Initiative³⁹. The development process has not yet been fully elaborated, but states have been offered a memorandum of understanding that spells out the principles of the work and guidelines for engagement. The goal is to release core high school standards in English-language arts and mathematics in late summer 2009 and develop grade-by-grade standards in those areas during the fall. Gene Wilhoit, a member of the Commission and executive director of CCSSO, signaled the group’s intention to ensure the high quality of the work by assuring prospective state participants that “no state will see a decrease in the level of student expectations that exist in their current state standards.”

Meanwhile, in both the mathematics and science education communities, there has been forward movement to find common ground and address the shortcomings of earlier efforts to create national standards.

Mathematics education has long been divided by contentious debates about curriculum and instruction. A breakthrough occurred with the 2005 Common Ground project, sponsored by the Mathematical Association of America, which brought together scholars and educators representing different orientations. They produced a set of understandings that all could agree to, demonstrating that there was less division than had previously been assumed⁴⁰. The following year, the National Council of Teachers of Mathematics (NCTM) issued the Focal Points report, which spelled out a set of core ideas for mathematics in grades K-8. Prior NCTM standards had been criticized for not offering grade-by-grade guidance to teachers, a failing that allowed students to be taught the same subjects year after year. Focal Points provided that guidance and was well received by a wide range of mathematicians and mathematics educators. In 2008, the National Mathematics Advisory Panel, appointed by President Bush, embraced and embellished the central themes of the Focal Points work in its Foundations for Success report⁴¹, thus creating a foundation on which a full set of standards for grades K-12 might be constructed.

Developed collaboratively by states for the nation but not federally promulgated or required, common standards would be national in scope and would provide a common frame of reference.

In science education, progress has been similar, although debates about curriculum and instruction have been less contentious—save for the special case of evolution. In 2007, the National Research Council issued Taking Science to School, which decried the “mile wide/inch deep” dilemma that plagues most states’ science standards and curriculum. The report also acknowledged that the Academies had themselves contributed to the problem through their 1996 National Science Education Standards. The new study, looking exclusively at K-8 education, called for the development of new standards to focus instruction on core foundational ideas of science that all students need to learn. It also offered a new definition of science education that places greater emphasis on the practice of science and the importance of inquiry, not just memorization of key facts.

The Commission is heartened by these forward steps and urges widespread participation by states, educators, and the mathematics and science communities. The Obama administration has shown particular interest in promoting fewer, clearer, and higher standards for all students. As President Obama has asserted, “the solution to low test scores is not lowering standards—it’s tougher, clearer standards⁴².”If successful, the effort to establish common standards will provide an unprecedented basis for creating aligned systems of high-quality assessment that would guide effective instruction and strengthen the nation’s ability to improve its schools.

1. On establishing common math and science standards that are fewer, clearer, and higher

Common standards would enable states, and the country as a whole, to prioritize math and science learning and incorporate math- and science-related content, concepts, and processes into learning expectations for all grades and in all areas of the curriculum. Our lack of common standards and expectations makes it difficult to focus teacher education around essential knowledge and ideas that every student ought to gain command of and every teacher needs to know inside and out. It compromises the quality of textbooks and other resources by forcing publishers to aim for materials that cover too much at too superficial a level. But the ill-effects of a plethora of learning objectives cascade on, compromising teacher practice and state assessments as the push to cover required content makes it impossible for teachers to delve deeply into the most important content. The end result is American students deprived of the chance to develop scientific and quantitative reasoning skills, understand core concepts, see the relevance of math and science learning, or experience its excitement.

Common standards, such as those being developed by the Common Core Standards Initiative, would address these shortcomings and enable educators and the educational system—nationally and in states and districts—to concentrate their efforts on creating and testing curricular materials, instructional strategies, and other resources that would serve the learning needs of the wide diversity of American students, from struggling to advanced learners, and enable deep learning. When complete, the standards will be available to all states on a voluntary basis.

There is also substantial agreement that mathematics and science standards must be fewer, clearer, and higher than those currently in use by states and recommended by national organizations. Standards that are fewer in number would reflect well-supported judgments within the field of what is essential for students to learn for future success in college and the workforce, the sequence in which they should learn it, at what depth, and over what period of time. Standards that are clearer would be well understood by educators and capable of being implemented coherently. Standards that are higher would guide the development and implementation of curriculum that is more academically rigorous and would result in many more students being prepared for higher levels of postsecondary education.

The fewer, clearer, higher criteria for developing standards for K-12 education could also serve as a framework for research and periodic review of the standards and their further refinement. In other words, the review process would look across states to determine whether or not the standards are promoting significant school improvement and meeting the instructional and implementation objectives of the fewer, clearer, higher framework. The experiences and resources of the country as a whole could be used to identify and address the strengths and weaknesses of existing standards, based on state, district, school, and student outcomes. With the right systems of review and research capacity, the United States would for the first time have a strong evidentiary basis for making major decisions about mathematics and science instruction and for periodically upgrading its K-12 academic standards.

Our emphasis should be on enabling students to develop the competencies that characterize scientific thinking and a more thorough understanding of foundational concepts and theories.

In math, the Commission believes that instruction should emphasize inquiry, relevance, and a multilayered vision of proficiency such as the National Research Council spelled out in its important study of mathematics education, Adding It Up and carried forward by the National Mathematics Advisory Panel in its report Foundations for Success⁴³. As articulated in Adding It Up those proficiencies are⁴⁴:

• Conceptual understanding (comprehension of mathematical concepts, operations, and relations)

• Procedural fluency (skills in carrying out procedures flexibly, fluently, and appropriately)

• Strategic competence (ability to formulate, represent, and solve mathematical problems)

• Adaptive reasoning (capacity for logical thought, reflection, explanation, and justification)

• Productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy)

We also recommend careful consideration of the creation of a rigorous high school mathematics course sequence giving more attention to statistics, data analysis, and other discrete mathematics applications through secondary school and college. The standard high school math sequence of Algebra I, Geometry, and Algebra II as a precursor to Calculus has been urged upon states as a requirement for all students in recent years. There is little question that the traditional sequence provides a strong foundation for more advanced study for students interested in pursuing careers in science, math, or engineering, even while there is legitimate debate about the precise content of courses along the pathway. The Commission also believes, however, that an equally rigorous pathway, branching from the same core foundation as the calculus pathway, to include a thoughtfully reconfigured Algebra II course and subsequent courses through secondary school and college, might provide greater benefit to many American students.

As mathematics expert Philip Daro noted in his recommendations to the Commission, Singapore’s highly regarded educational system “illustrates how it is possible to design multiple pathways to college entrance while still serving more specialized interests in the student population⁴⁵” A statistics-oriented pathway through high school to college could be of real utility to students headed for careers in business, information technology, law and social science, and many other fields. Furthermore, additional study of statistics, probability, and data analysis would enhance the quantitative literacy students need for full participation in civic life. The widespread development of instruction in this area would also help introduce new content and pedagogy focused on problems that students might well find relevant and highly engaging.

The Commission recommends this change with the intention of strengthening the engagement of high school students in academically rigorous mathematics and encouraging them to pursue more mathematics at the college level. We are cognizant of concerns about educational equity: we emphasize that, in urging the development of this new approach, we are not recommending a return to dual-level, stratified math courses but the creation of two equally rigorous pathways to mathematics mastery. To ensure equity, the new courses would need to be developed in concert with a broadening of four-year college admissions requirements to recognize the new high school mathematics sequence.

Mathematician and educator Sol Garfunkel, in a paper prepared for the Commission offers this reasoning: “As a mathematician, I recognize the beauty and centrality of calculus, but it should be more than clear by now that in terms of applications of mathematics in the work force, in daily life, for good citizenship and even for success in further academic studies other branches of mathematics along with the processes of mathematical modeling are increasingly more relevant. Again this must be about the needs of students. We know that their future will involve many different jobs and the 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 mathematical understanding and awareness of the tools mathematics provide in order to achieve their career goals.” Drawing on experience in identifying skills needed in the workplace, Garfunkel proposes that students be offered rigorous “curricular alternatives—high school and college courses emphasizing discrete ideas taken from statistics, geometry, and operations research with case studies and applications to a variety of disciplines, work place settings as well as the kind of social decision making all of us will face⁴⁶.”

Our emphasis should be on enabling students to develop the competencies that characterize scientific thinking and a more thorough understanding of foundational concepts and theories.

In science, the Commission recommends that standards be reshaped to counteract the tendency in American education to cover too much material in too little depth. The challenge is substantial in science: unlike in mathematics, science knowledge has proliferated enormously in the past 50 years and is likely to continue to do so. Our emphasis should therefore be on enabling students to develop the competencies that characterize scientific thinking and a more thorough understanding of the foundational concepts and theories that provide a baseline of scientific literacy and serve as building blocks for further studies.

Commission member, cell biologist and former president of the National Academy of Sciences Bruce Alberts emphasized in a recent editorial in Science magazine that “rather than learning how to think scientifically, students are generally being told about science and asked to remember facts⁴⁷.” Alberts assigns a portion of the blame to scientists themselves. After all, he contends, “college courses set the model for teaching science in the earlier years,” and “any objective analysis of a typical introductory science course taught today in colleges and universities around the world… would probably conclude that its purpose is to prepare students to ‘know, use, and interpret scientific explanations of the natural world’ (strongly emphasizing the ‘know’). This is but one of four goals recommended for science education” by the National Academies. From the earliest grades through college, all students need rich, educational experiences that enable them to develop the four strands of scientific proficiency identified in Taking Science to School

• Know, use, and interpret scientific explanations of the natural world

• Generate and evaluate scientific evidence and explanations

• Understand the nature and development of scientific knowledge; and

• Participate productively in scientific practices and discourses⁴⁸.

Rethinking science standards will depend, as well, on our ability to develop a more integrative way of organizing scientific knowledge than is currently available to most American teachers and students. Scientific research and advanced university education are moving decisively toward more interdisciplinary approaches. The Commission believes that the nation should embark on a broad-based conversation, led by and drawing on the expertise of our national scientific institutions, about the concepts, information, and areas of inquiry in which all students should develop foundational knowledge—and from which many students will proceed to much higher levels of learning.

As a starting point for that conversation, the Commission offers as an example a taxonomy of “core science knowledge” proposed by physicist and educator Jason Zimba⁴⁹. Zimba offers five major categories, each vividly relevant to the daily lives of students of all ages, able to accommodate a wealth of topics, and cutting across the standard scientific disciplines:

• Where we are in the universe
• How we came to be
• The organizing principles of contemporary science
• Human health and well-being
• What science and technology can do today

The National Research Council, through its Board on Science Education, will convene a meeting during the summer of 2009 as a critical first step toward a process to revise the National Science Education Standards. This planning meeting, sponsored by the National Science Foundation, will focus on core disciplinary ideas in K-12 science education. As preparation for the meeting, the Board on Science Education will commission papers that will synthesize key issues around what constitutes a core disciplinary idea from the vantage points of the science disciplines and the learning sciences⁵⁰. Further discussion by the Board on Science Education on the process for undertaking identification of core disciplinary ideas, and the relationship of this work to the possible revision of the National Science Education Standards, will follow this initial planning meeting.

The Commission applauds this step and encourages the National Research Council and other parties to take advantage of the momentum gained through the recent work of the Common Core Standards Initiative toward developing common standards in mathematics and English language arts.

2. On developing sophisticated assessments and accountability mechanisms

The development of new, high-quality classroom assessments and accountability mechanisms, linked to common standards, is an important priority—indeed, a necessity if common standards are to achieve their maximum effect for improving math and science education for all American students. Assessments aligned with common standards will also be essential to the creation of useful, accurate measurements of teacher, school, district, and state performance.

As Stanford University professor and assessment expert Edward Haertel wrote in a paper presented to the Commission, “assessment is woven into the fabric of educational practice in the United States. Individual assessments help determine the classifications of students as gifted, learning disabled, English Learners, or ADHD. The quizzes, unit tests, and final exams that teachers create or choose help determine the pacing of classroom instruction, instructional grouping, and marks and grades, as well as informing students about expectations for learning and about their success in meeting those expectations. Advanced Placement and International Baccalaureate tests define ambitious curricula for respected high school courses. The SAT and the ACT are central to the sorting and selecting process at the point of college admissions. High school exit examinations are viewed as a form of quality assurance, but also stand as significant barriers to graduation for substantial numbers of students. State testing systems mandated under the No Child Left Behind Act of 2001 (NCLB) define school-level success or failure, and a range of sanctions are imposed if scores repeatedly fall short of targeted levels⁵¹.”

The development of new, high-quality classroom assessments and accountability mechanisms, linked to common standards, is a necessity if standards are to achieve their maximum effect.

Of these, the most important for raising mathematics and science achievement for all American students are classroom assessments and assessments for accountability. If well crafted and administered appropriately, classroom assessments can provide information about student learning and help teachers improve instruction. If well aligned with standards or other clear statements of expectation, assessments for accountability can provide information about how students, teachers, schools, or even states and nations are performing and whether or not students are learning prescribed curriculum; that information, in turn, can help shape improvements to instruction and to educational practice and policy. Experience has shown that it is not easy to get assessments right: assessments are frequently used for purposes they were not designed for, and rote preparation for “high-stakes” tests displaces or distorts other learning goals. In science, for example, the need to obtain reliable results from tests that are easy and inexpensive to administer has driven assessments—and instruction—toward the first strand described in Taking Science to School (“know, use, and interpret scientific explanations of the natural world”) and away from the other three more complex and difficult-to-assess competencies.

The Commission believes that better assessments will be crucial to guide and reinforce improvements to mathematics and science instruction in American schools and colleges, and that those assessments should be closely linked to the new fewer, clearer, and higher standards. In addition, as Haertel has argued, it will be essential to improve and clarify “the rules by which [assessments] are used or interpreted,” which may require “decoupling the multiple purposes for which some tests are used” and making appropriate changes in federally mandated accountability systems. Following Haertel’s recommendations, the Commission therefore urges development and implementation of five interconnected types of classroom-level and accountability assessment:

• Portfolio-based school accountability, which should incorporate student- or classroom-level math and science portfolios

• Performance assessment component for school accountability, which should include matrix-sampled school-level performance assessments

• Classroom assessment for learning, using improved curriculum-embedded formative assessments

• Better high-stakes tests that are closely linked to new mathematics and science standards

• Better decision rules for evaluating school-level assessment results

Developing these systems and putting them into place would need to be phased with care, with supports provided to districts, schools, teachers, and parents and communities about what each component is intended to measure and how it operates.

The Commission also believes that new assessments should be informed by and calibrated against the most reliable international measurement systems in mathematics and science—the Programme for International Student Assessment (PISA), which periodically assesses the skills and knowledge of 15 year olds in mathematics, science, reading, and problem solving and measures changes in student performance, and Trends in International Mathematics and Science Study (TIMSS), which periodically measures the performance of fourth and eighth graders—and the skills and knowledge those systems assess. Wider use of internationally benchmarked assessments would give states and the federal government a more meaningful picture of student and school performance and would inform district and state efforts to improve American schools. The science framework for the 2009 National Assessment of Educational Progress also lays out a well-regarded, comprehensive approach to assessing content knowledge, its application, and students’ command of the process and practice of science for students in grades 4, 8, and 12. The new NAEP framework should inform the development of new common state and classroom assessments.

A number of groups are deeply engaged in developing college-ready assessments, which are designed to help increase students’ academic readiness for college by articulating college expectations clearly and enabling schools to develop student competencies accordingly. For example, as part of making college readiness a nationwide goal, the American College Testing organization (also known as ACT), developed its College Readiness Standards for the middle school and high school grades, drawing on extensive knowledge of what students are likely to need to know and be able to do gained through administering its widely used, integrated series of assessments and career planning programs (including the EXPLORE assessment for grades 8 and 9, PLAN for grade 10, and the ACT assessment for grades 11 and 12). More recently, ACT also launched its Quality Core end-of-course assessments in English, math, and science, which are designed to support college-ready high school curricula and are accompanied by course syllabi, suggested sequencing guidelines, model instructional units, and professional development; together, they create an aligned instructional approach that research suggests has real potential to lift student performance⁵². The College Board is currently in the midst of redesigning its Advanced Placement courses and exams in biology, chemistry, and physics, based largely on recommendations by the National Academies in 2002⁵³. The new exams should accelerate improvements in classroom practice in both high schools and colleges.

While assessing students’ college readiness skills, it is critical that stronger links be made between assessments, professional development, and classroom practice. The Educational Policy Improvement Center (EPIC) in Eugene, Oregon, for example, is working with more than 40 Urban Assembly public schools and California Early College High Schools to develop the College-Readiness Performance Assessment System (C-PAS), designed to gauge student progress in grades 6–12. C-PAS is a series of classroom assignments (or performance tasks) that teachers incorporate into class work and score with a common scoring guide. Teachers can use the results to consider how well their curriculum is helping students to reason, solve problems, interpret information, conduct research, and generate work with precision and accuracy. Assignments, or tasks, encourage students’ development in these key cognitive strategies over time. The goal of the project is to create formative assessment systems that teachers, schools, and school districts can employ to help ensure students are ready for college.

The Commission also encourages the development of more sophisticated formative assessments for classroom use, along with systems by which teachers can access proven assessments, share techniques and instruments, and collaborate in refining them. At its best, a formative assessment delineates and measures a student’s progress not only against a rigorous standard in totality but against component skills as they fit together. A good assessment, by illuminating the broad spectrum of skills required for mathematics or science success, can inform instruction by revealing strengths and gaps in a student’s understanding and enabling a skilled teacher to calibrate the needed instructional response. Sophisticated, multilayered, and rigorous assessments are the essential counterpart to fewer, clearer, higher common standards, as the former drives accountability and practice in alignment with the latter.