The following were exerpted from Rick Hess' Interview with Hung-Hsi Wu. The full interview can be viewed by clicking on the title of this post.
Background: Hung-Hsi Wu is professor emeritus in mathematics from UC-Berkeley, who has just penned the cover story on this topic for AFT's magazine American Educator. Dr. Wu, who started teaching at Berkeley in 1973, has been actively involved in math education for the past two decades, helping write California's 1999 Mathematics Framework and California's Standards Tests. He was also a member of NAEP's Mathematics Steering Committee, 2000-2001, that contributed to the revision of the NAEP Framework.
CCSS math: What are they? Why do we need them?
The Common Core math standards place great emphasis on mathematical integrity, [in other words] the statements of the standards are mathematically correct and the progression from topic to topic is logical. In this regard, it is at least comparable to the best state standards, such as those of California and Massachusetts.
The Common Core math standards, however, ask that students "understand solving equations as a process of reasoning" and say explicitly what needs to be taught about this process (see Standard A-REI 1 in High School Algebra).
When state standards ask that the concept of congruence be taught in middle school, they do not realize that what students will end up getting is that congruence means same size and same shape. As a mathematical definition, the latter is completely unacceptable. By contrast, the Common Core standards explain that congruence means what one gets by a sequence of rotations, reflections, and translations (grade 8, Standard 8.G 2). Such sensitivity to the existing defects is absolutely essential to any meaningful improvement in our math education; in this regard, the Common Core standards leave all rivals far behind.
Integrated vs. Traditional Math
The 9-12 standards of the Common Core are what they are because the Common Core made a conscientious decision to stay neutral in this debate by describing only the mathematical content of the various strands in high school and allow[ing] each state to make its own decision. This flexibility makes it possible to formulate a high school program that conforms to neither the traditional nor the integrated format.
Algebra I in 8th Grade
"There is no intrinsic merit in finishing Algebra I by grade 8. When it comes to school algebra, it is not how early you teach it but, rather, how well you teach it. The standards of those states in the U.S. that mandate the completion of Algebra I in grade 8 manage to do so only by stinting on the necessary background material that students need in order to learn linear equations and their graphs. Furthermore, the math standards of both China and Japan postpone the teaching of quadratic equations and functions to grade 9, and these are two of the highest-achieving nations in the world in math education.
Spread Concepts Across Grade Levels
Common Core math standards' design to optimize mathematics learning by giving students enough time, whenever feasible, to absorb the material as well as time for teachers to teach the material. For children, the addition of fractions is so conceptually complicated that they need the time to internalize the whole process. This particular treatment of fraction addition (teaching of fraction addition over three grades: grades 3 to 5) is one of the outstanding features of the Common Core standards.
Strengths of Common Core math standards:
1. provide guidance to the teaching [of] fractions in a way that is pedagogically sensible and mathematically correct. Since the fear of fractions has almost become a national pastime, these standards---if properly implemented--- will bring relief to many parents and students.
2. The same can be said about these standards on negative numbers.
3. the teaching of geometry in middle and high schools is so defective at present that it cries out for a new approach; essentially nothing can make things worse in most cases - provide a seamless transition from middle school geometry to algebra and high school geometry.
Teacher Capacity and Preparation
We need better teacher preparation and improved professional development in order to stay educationally afloat no matter what the standards may be. If we cannot get better teacher preparation or improved professional development, then we would be better off with a set of standards that is at least mathematically sound.
Help for Teachers: Resources
1. A set of Progressions documents that highlight the main ideas of each major strand in the standards.
2. The Illustrative Mathematics Project that will provide problems to illustrate the standards
Concern - Status Quo Not Good Enough
What I find most worrisome is the fact that many educators and administrators believe that the status quo (of doing nothing) is plenty good enough. It is not. We need effective professional development, period.
I want to make sure that students will not be in any way over-assessed, and that the mathematical quality of the test items be above reproach.
CCSS: Good or Bad
Nobody can pass judgment on the success or failure within a year of the kind of profound change promulgated by the Common Core math Standards unless the standards are an immediate disaster (which I hope they are not).
I think a more reasonable date to make such a judgment is 2017. If things go well, teacher preparation will begin to concentrate on the most urgent need of the moment: better content knowledge. Math instruction in classrooms will be long on reasoning and short on giving out orders, and textbooks will at least be free of ghastly errors.