COMMENTS ON THE COMMON CORE STANDARDS FOR MATHEMATICS
March 2010 Draft K-12
Submitted by the U. S. Coalition for World Class Math
Download the complete document at the link above, Read the Executive Summary and Conclusions and Recommendations Sections here.
- The Common Core Standards for Mathematics fall short of the following goals:
- The math standards in grades K-8 should lead to mastery of key procedures, skills and problem solving abilities that will enable students to undertake a full course in authentic algebra; and
- The complete set of standards will fulfill the minimum mathematics requirements for 4-year universities in the United States and prepare students to take subsequent courses in mathematics without the need for remediation.
- If there are to be national standards, we would expect that such standards be world class—anything less than that is unacceptable. By virtue of the pedagogical ideas that are inherent in them, the standards may result in the adoption of severely deficient textbooks and programs that value process over content and that emphasize a student-centered and inquiry based approach.
- While some states may gain federal dollars in the short run by adopting these standards, the standards as written will potentially undermine our educational system for the next decade or more.
- We are extremely concerned over the fact that many of the standards are built around the word “Understand”. A standard should not call for a student to learn to do one thing and lend itself to assess them at a different level. Standards should describe what the understanding will enable students to do procedurally and the types of problems they should be able to solve. As written, the standards in the current draft fall far short of that.
- The K-8 Common Core standards are simultaneously over- and under- ambitious. Numerous computation skills are delayed or under emphasized, while, at the same time, children are expected to "understand" sophisticated ideas and principles that many teachers do not themselves understand.
- The standards mention mental math for adding and subtracting whole numbers within 20 and fluency is required for add/sub of whole numbers within 10. However, students need to have immediate recall of their facts within 20. Starting in grade 1 will enable students to accomplish this. The word "memorize" need not be something to avoid.
- Pacing and rigor are in need of improvement—for example, exponents/powers/roots are not explicitly covered until high school. STEM students should be covering much of the high school material in middle school to avoid boredom and enable acceleration through upper level math.
- The high school standards are inconsistent with current college entrance requirements. Students won't have the foundation for the study of College Algebra with these standards in place, nor will many students meet the requirements for most four-year universities in this country, which call for three years of mathematics inclusive of Algebra 1 and 2, and geometry. Many topics are missing that should be included in an Algebra 2 course.
- The geometry standards do not appear to require students to conduct deductive proofs beyond key theorems. As such, geometry courses will be watered down, focusing on problem solving by applying formulae and general principles, but without developing the skills to set up a series of statements (with reasons) that systematically lead from given conditions to a specific conclusion.
VI. Conclusions and Recommendations
The presentation of these standards is significantly different than standards have been presented and applied by states up to this point. As such, the practical approach may be to see how it will work before states are required to use them. (Diane Ravitch has said these new standards should be tried on a very small scale first before launching them nationwide.) And at the same time, using solid research methodology, compare results with results from the implementation of the Massachusetts, California, and Indiana standards. Let’s put something in place that has proven itself, rather than risk, not only untold resources, but the development of our students mathematical achievement. Far better to take the time now to field test these standards than to unleash them on our students.
On page 7, the standards document says:
“One promise of common state standards is that over time they will allow research on learning progressions to inform and improve the design of standards to a much greater extent than is possible today. Learning opportunities will continue to vary across schools and school systems, and educators should make every effort to meet the needs of individual students based on their current understanding.”
This would be a good reason for having several consortiums of states developing (preferably selecting a ready-made set and making modifications) sets of standards. In addition to giving states some choice (greater than 15%) then we can see which ones seem to work the best.
We recommend that the CCSSI do the following:
As the CCSSI goes about revising the standards, we recommend they give attention to and address all specific issues presented in this report. We feel it especially important that the CCSSI give priority to..
- Field test the common core state standards on a limited basis for a minimum of one year prior to state-wide use across the country;
- actively support, promote, and help states establish consortiums and develop sets of standards; and;
- declare the math standards from Massachusetts, California, and Indiana acceptable alternatives to the common core state standards so that states will have choices.
- Replace “understand” with more precise measurable verbs that will clarify the desired proficiency level;
- remove noted ambiguities regarding standard algorithms by removing strategy related standards and clearly requiring fluent use of standard algorithms to add, subtract, multiply, and divide whole numbers, integers, fractions, and decimals;
- specifically include standards that develop skills related to simplifying fractions, finding factor pairs, finding prime factors, finding common denominators, finding least common multiples or denominators, and finding greatest common factors to provide students with the necessary foundation for success in authentic algebra and beyond;
- ensure the geometry standards provide a fundamental foundation in synthetic geometry requiring students to construct deductive proofs; and
- ensure the standards fulfill the minimum mathematics requirement for 4-year universities and prepare students to take subsequent courses in mathematics without the need for remediation.
We find the March draft of the Common Core Standards for Mathematics K-12 to be a considerable improvement over the January draft. We also find the standards as currently written to be better than the standards of many states. These standards are not yet on an equal level or better than the current state standards for Massachusetts, California, and Indiana and as such are not world class. Anything less than world class standards for the students of this country is not acceptable. We hope the Common Core State Standards Initiative will bring these standards up to the level of excellence to qualify as world class.