Standards and Assessments

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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.