When I attended the public schools in Davis, college-track students took Algebra I in 9th grade. Today, as was the case back then, the A-G requirements for UC and CSU require at least 3 years of high school level mathematics. Very few students took Algebra I in 8th grade; as I recall there were three classes of Algebra I for the 9th graders and one small class of Algebra I for 8th grade.
Today, of course, a very different reality faces our students. Because the State Board of Education created an accountability motivation for schools to enroll their students in Algebra I in 8th grade, remarkable growth occurred. Today, well over half of 8th graders in California enroll in Algebra I. At the same time, some of the most sobering statistics in public education paint a reality about the state's experience with Algebra I across the grades that most of us would not wish on anyone. Consider:
- The "typical" entering freshman at the University of California has completed 4.6 years of high school math; this means that for these students 8th grade Algebra 1 would be their default course
- Those students who enter the University of California having completed the bare minimum of three years of high school math (through Algebra II) constitutes between 3-4 percent
- The California Department of Education and State Board of Education administer about 60 California Standards Tests each year. Of these, the Algebra I CST has the lowest percentage of proficient students of all the CSTs.
- According to a 2008 EdSource report, California's Algebra I student performance looks like this:
Of students who took Algebra I in 2006–07, 38% of 8th graders scored advanced or proficient on the CST, compared with 17% of 9th graders and 8% of 10th graders.
Proficiency on Algebra I CST by grade level, 2006-07
Data: California Department of Education (CDE)
EdSource 2/08
- According to a Riverside County Office of Education presentation in September 2008 on the State Board of Education's decision to require all 8th graders to enroll in Algebra 1 beginning in 2011-12, California's incoming 7th graders would, as a class, need to make 4.5 years of progress between their 6th and 7th grade years to be on grade level entering Algebra I.
Enough already. This is not fun stuff. As I see it, we have a reality of extreme contrasts:
1. Students intending to enroll in a 4-year university should target 8th grade Algebra I
2. Students who do not intend to enroll in a 4-year university may experience a reality-bender by enrolling in Algebra I in 8th grade and waiting until their senior year in high school to take a general mathematics course. This absurdity satisfies the state's mathematics courses graduation requirements (though districts can set higher requirements).
3. California has succeeded wildly in expanding enrollment in 8th grade Algebra I, but overall Algebra I proficiency rates remain very low.
So where does this put the Common Core Math standards? There's plenty for the commissioners to consider when they meet next week. To me, it's clear that the commission (and the State Board of Education) should ensure that those students who are prepared for Algebra I by 8th grade have the opportunity to take that course. Beyond that, there are a ton of really crucial policy decisions that will need to be decided.
I hope these policy decisions are informed by the presentation that Professor Hung-Hsi Wu of UC Berkeley made to a gathering of policymakers last month. Wu, who worked on both California's 1997 math standards and the Common Core, provided a memorable lesson on mathematics and content standards. His presentation slides can be viewed here:
http://www.stanford.edu/group/pace/PODCASTS/slideshows/2010_6_10_WU.pdf
Among his thoughts:
1. The Common Core Math Standards do not require all students to complete a full Algebra I course in Grade 8. Wu asserts that the Common Core, like Japan, introduces about half of the full course in Grade 8.
2. The two most compelling mathematics issues for student preparation to succeed in Algebra 1 are complete (and deep) preparation in fractions and similar triangles (We provides in-depth analysis of this).
3. The current California Math Standards have a fatal flaw--a developmental gap--in these areas, as identified in the 2006 California Math Framework (p. 181):
An additional comment about Standard 7.0 is that, although it singles out the
point-slope formula, it is understood that students also have to know how to
write the equation of a line when two of its points are given. However, the fact
that the slope of a line is the same regardless of which pair of points on the line
are used for its definition depends on the considerations of similar triangles.
(This fact is first mentioned in Algebra and Functions Standard 3.3 for grade
seven.) This small gap in the logical development should be made clear to
students, with the added assurance that they will learn the concept in geometry.
The same comment applies also to the fact that two nonvertical lines are
perpendicular if and only if the product of their slopes is −1 (Standard 8.0).
Wu goes on to explain that the key grades for mathematics development are 5-7.
At the first Academic Standards Commission meeting, Professor Jason Zimbra represented the Common Core Math Standards and he made many similar points. But he also encouraged commissioners to address squarely how the state's authority to add an additional 15 percent of standards was meant to ensure that California could maintain fidelity to its policies and practice.
It is my sense that these are extraordinarily challenging issues and items with high stakes (for students) attached. I don't see how the Academic Standards Commission or State Board of Education can ignore the data that tells us Algebra I for a significant number of California's students is necessary for their ability to compete for 4-year university slots. At the same time, these two institutions have more and better data in front of them cautioning them to fully reflect what students must master before exposing them to Algebra I.
