Ze’ev Wurman is a former senior policy official in the US Dept. of Education under George W. Bush, and served on the California Academic Content Standards Commission which reviewed the Common Core standards for California. He was recently sent a couple pages from Utah’s No Child Left Behind waiver application which talked about how Utah was going to accelerate math under their new integrated approach to Common Core. Those of you that missed reading the article on how the integrated approach is going to hurt math in Utah, please read Reigniting the Math Wars over the Death of Calculus.
Ze’ev generously responded with the following analysis.
Comments on Utah Waiver Application, Pages 24-25.
Ze’ev Wurman, Palo Alto, Calif.
(Blue italics are direct quotes from the Waiver Application)
Myth: The structure of the new math standards are in line with that of countries with high mathematics achievement.
Fact: CCSS are not any closer to high achieving countries than Utah’s 2007 standards. CCSS stopped claiming that they reflect what high achieving countries are doing and now they only claim that the standards are “informed by top-performing countries,” whatever it may mean. In particular, the high school programs of the high achieving countries closely resemble the 2007 Utah traditional sequence (Algebra I, Geometry, Algebra II) and are completely different from the CCSS integrated Math-I, Math-II, Math-III sequence that Utah recently adopted.
Myth: The rigor and complexity of the new standards begins in Kindergarten and continues to accelerate through high school using an integrated approach. For example, students in ninth grade will be studying topics formerly common in Algebra, Geometry and Algebra 2.
Fact: It is true the CCSS are quite demanding in the early primary grades, but they significantly slow down by the third grade, and by grade eight they are one to two years behind what top-achieving countries expect of their students. The only mathematician on the CCSS Validation Committee refused to certify the Standards writing: “…large number of the arithmetic and operations, as well as the place value standards are one, two or even more years behind the corresponding standards for many if not all the high achieving countries.” (Appendix B, http://www.pioneerinstitute.org/pdf/common_core_standards.pdf )
Myth: The new core’s structure allows more flexibility to accelerate learning for students as they progress through their secondary education.
Fact: The new high school core is, if at all, less flexible and less demanding than the previous one. It is composed of loosely defined “integrated” courses in contrast to previous traditional coherent curricular courses of Algebra I and II, and Geometry. Further, these integrated courses exclude chunks of content that was traditionally taught in Geometry and Algebra II such as logarithmic and trigonometric functions and identities, complex number arithmetic, conic sections, infinite geometric sequences, mathematical induction, and more. As the result, it is expected that with this curriculum students will have more difficulty to take Concurrent Enrollment courses, or Advance Placement Calculus, in their senior year.
Myth: The new core includes Honors courses beginning in seventh grade and provides higher level math courses such as Calculus or AP Statistics for students who are ready to accelerate.
Fact: The accelerated (“Honors”) program in the seventh and eighth grade that is newly offered by Utah is a poor replacement for the honest pre-Algebra and Algebra courses that Utah offers today. The proposed seventh and eighth honor program adds content about history and uses of mathematics, and about set theory and different counting bases, that are poor preparation for acceleration of algebra, geometry, and pre-calculus that are key to STEM education.
Myth: In seventh and eighth grade, Honors courses contain extra topics not included in the former core. These topics include elements from discrete mathematics, non-traditional geometries, different counting systems, and other mathematics that would be interesting to advanced middle school students. … These courses have increased rigor and advanced content that will challenge the minds of high-ability students.
Fact: The seventh and eighth grade Utah’s Honors curriculum touches on discrete mathematics and different counting system and in that reminds us of the original 1960s failed “new math.” It also includes elements of graph theory that students are unequipped to handle at that point yet which it grandly calls “non-traditional geometries.” This assemblage of quirky bits and pieces of applied mathematics does not support accelerated and/or deeper acquisition of algebra, pre-calculus, and calculus. Consequently the promise to productively challenge high ability students rings hollow.
Myth: Courses for all students are much more advanced than in previous class work. Students on the regular pathway will be prepared for Pre-Calculus, AP Statistics, or CE in their senior year. In the accelerated pathway to high school (AP), calculus is a compacted version of Secondary I, II, III and Pre-Calculus and will begin in ninth grade. This pathway allows students successfully completing the three high school Honors courses to be ready for AP Calculus as seniors.
Fact: As already mentioned before, the new CCSS high school core has eliminated significant content in comparison to the 2007 core and, contrary to the claim above, are not “much more advanced”. In fact, just the opposite is true – the regular three CCSS integrated courses are at significantly lower level than the current core. Consequently, students taking the regular program will not be able to access AP calculus at they are now, using the 2007 core.
The suggested Honors program does, in fact, in theory prepare students for AP Calculus in their senior year. But it should be compared with the current sequence that potentially prepared all students, rather than only Honors students, for AP Calculus as Seniors. In fact, the current core also prepared accelerated students for AP Calculus already as Juniors.
But the new proposed Honors program is highly ambitions and untested, and faces significant challenges. Rather than use grades seven and eight for deeper preparation of Honor students in algebra and geometry, it spent those grades on inessential activities of counting in different bases and games-related bits and pieces. Consequently, it now needs to push a lot of content, including content that CCSS forgot like parametric equations, infinite series, polar coordinates, etc., into three heavily packed years. Time will tell how many students will be able to scale this steep three-year HS challenge, all to end up where the current core already gets them in much more relaxed rate starting with pre-Algebra in grade 7: to be ready to for AP Calculus as Seniors.
Given the abundance of lofty claims unsupported by the actual new Utah core, one should treat the picture on p.24 that pretends to summarize the differences in rigor between the old (2007) Utah Core and the newly adopted CCSS Core as a work of fiction. The implication that old core’s 12th grade is equivalent to the new core’s 10th is beyond ridiculous. Anyone with more than a bit of understanding of actual mathematics rather than of educational mumbo-jumbo can easily satisfy himself that just the opposite is true for the regular CCSS Core, and that they are effectively equivalent in case of the Honors Core.