We believe that all students can learn mathematics at a high level and should be given the opportunity to do so. We strongly support challenging standards. Common Core Standards have the potential to drive substantial improvement in student achievement across the nation. This potential is most likely to be realized if the standards address those topics in mathematics which ought to be mastered by all students and do so in a way that educators can use them. We recommend the following:
1. The Common Core Standards document should focus openly and explicitly on the common mathematical needs of different populations of K-12 students. All students need a strong foundation in mathematics that allows them to be able to solve problems and understand how to apply mathematics to a variety of everyday settings, not just in the more formalistic settings described in the document. All students need to understand probability and statistics and other topics related to everyday life such as apportionment and how bar codes work. Students headed to college to major in science, mathematics, or engineering need a stronger emphasis on advanced algebraic techniques than those headed to college to major in humanities or the social sciences, or those who will enter the workforce directly. However, the skills and knowledge identified in the draft are not appropriate for the other two groups and, as noted in the document, are not sufficient for prospective STEM college students. We also recommend that the standards better reflect the broad array of mathematical topics referenced above, and have a greater focus on how mathematics is used in everyday life.
2. The Common Core Standards document should clearly be a next step which builds on and advances existing curricula and state standards. It can best do so by adhering to a relatively conventional organization and structure. The organization of the document neither matches existing state standards, nor textbooks, whether they are traditional textbooks (curricula) or reform textbooks (curricula), since these are typically organized by subject area within mathematics, even those that provided for integrated curricula. We agree that change in curricula and textbooks will be needed, but because of this divergence from all forms of current curricula and state standards, the standards that emerge from this draft will likely place an unnecessary burden on states, districts, and teachers that try to offer their students a curriculum that matches these standards.
3. While the Common Core Standards document should use international achievement comparisons and curriculum analyses to assure that our expectations are the equal of those of any country, it should not use these as a blueprint for our own curriculum. We believe that it is important for the United States to have mathematics standards that match in content and rigor the standards of high performing countries in international comparisons. However, it is well known that the populations taking international assessments vary dramatically from one country to another, that the assessments disadvantage countries that have broader curricula (since only topics common to all countries are assessed), and that these inconsistencies account to some extent for the differences in success rate on the assessments. Moreover, the district-based TIMSS-R results indicated that economics contributes more to higher scores than the curriculum used. Implications drawn from the analysis of these international assessment results must therefore be carefully reevaluated including the oft-stated criticism that the US curriculum is “a mile wide and an inch deep.” Even if current curricula contain too many topics, too often repeated across grade levels, this does not mean that only the most traditional, skill-oriented topics should be included in a newly designed curriculum. There is no research to indicate that leaving out mathematics topics in the curriculum will yield higher results. We also recommend that more research is needed to better understand cross-country comparisons, research that so far seems to indicate that the teacher, not the standards or the curriculum, is the most important part of the equation.
4. The Common Core Standards document should balance skills and understanding in every level of its rhetoric and detail, and, eventually, in the resultant assessments. Students need to develop both mathematical skills and mathematical understandings. However, the focus of the document is on rules and procedures, and not on students making sense of the mathematics, not on problem-solving and reasoning, not on exploring mathematical concepts. This is evident in the separation of “concepts” and “skills” in each area, the precise language used in speaking of the “skills,” and the vague language used in describing the “concepts.” As a result, this document would likely lead to a back-to-the-basics movement in the schools, whereas what is needed is for all students to go “beyond the basics.” We recommend greater emphasis on students’ reasoning and making sense of mathematics and greater integration of concepts and skills.
5. The Common Core Standards document should identify and enumerate curricular areas and concentrations that are comparable in terms of content coverage. We believe that the grain size is not uniform across the document. The term “principle,” for example, is used for small topics like expressions and proof, with geometry relegated to a small subprinciple. (This relegation is particularly problematic since our students’ performance in geometry and measurement on international assessments is most in need of improvement.) Some performance indicators are so specific that they can be directly used to write assessment items, while others are so general that they could cover a substantial part of the whole assessment. We recommend that the standards be more consistent in this regard, so that assessments can better evaluate a student’s knowledge and understanding of mathematics at various grade levels.
We look forward to seeing the next draft of the Common Core Standards, especially the grade level specific parts. You have an important task and we wish you well.