Prepare more students for algebra but be fair to those who aren’t ready
One of the most intractable problems facing California schools is the shockingly low performance of students in our middle grades. In 2009, on the respected NAEP (National Assessment of Educational Progress) test, only Mississippi, Alabama, and Washington, D.C., scored lower than our state. It’s true that many of our students take Algebra, which is not tested in NAEP, but NAEP does assess important mathematical knowledge that 8th graders should know, so it is relevant to all students. What to do?
First, it is crucial that we get the policy framework right. In 2008, the State Board of Education, with the governor’s support, adopted the educationally unsound standard of requiring all students to take Algebra in the 8th grade. They did this in response to a terrible decision by the Feds to force California to only have one standard pathway for 8th grade math. This policy was subsequently tied up in the courts and, currently, although policy guidance is in limbo, many districts are acting as if it were the state standard.
One can sympathize with the motives for adopting this 8th grade “algebra for all” standard — to propel more students into four-year colleges and as a tool for putting pressure on the 4th through 7th grades to improve instruction. Indeed, many districts have substantially increased the number of 8th graders taking, passing, or becoming proficient in an Algebra I course. These increases have been especially pronounced among minority children.
However, as a major series of reports by EdSource and others have demonstrated, these improvements have come with a substantial cost. Many ill-prepared students, especially in low-income areas, are cruelly dumped into 8th grade algebra, where they become completely frustrated, force the class to be watered down, fail, do worse when they try to repeat the course than they would have if they hadn’t taken and failed it the first time, and increase their likelihood of dropping out. It’s telling that higher-income districts determine who takes 8th grade algebra much more carefully and minimize the number of students erroneously place in Algebra I.
More importantly, relying on a policy alone to put pressure on instructional improvement has not worked in this country and is not what other successful school jurisdictions do in the United States or worldwide. Successful solutions concentrate instead on articulating a clear definition of what needs to be taught and then building the capacity to improve instruction.
Importance of understanding numbers
So how do we solve the dilemma of encouraging more kids to pass 8th grade algebra while being fair to those students who are not ready, without returning to wholesale tracking? There is a common-sense solution. It hinges on the reality that if a student does not have a deep understanding of numbers – decimals, fractions, percentage, ratio, and proportion – and the ability to use that understanding in solving increasingly complex problems, that student will most certainly fail algebra. The national Common Core standards adopted this approach, aiming to get everyone prepared to pass algebra in the 9th grade (while allowing many to take it in the 8th). Additionally, if you ask high school math teachers, college professors, or business people who hire, they will tell you that the ability to use percentages, decimals, fractions, etc. in sophisticated situations is much more important than knowing quadratic equations. High school math teachers also complain that even many students who pass Algebra I have a shaky understanding of numbers.
So the first step is to adopt a three-part policy for the state:
- All students meet a demanding numbers standard by the end of 8th grade (as promulgated by the national Common Core standards and adopted in this state); this becomes the basic standard for California;
- All students pass algebra by 9th grade;
- Districts are encouraged and have incentives to increase the number of students passing or proficient in algebra in the 8th grade (as a component of any accountability program).
California was essentially following this multiple strategy before badly reacting to the Feds.
There is a misconception among many that somehow passing algebra in 8th grade determines who gets into a 4-year college. Passing algebra in 9th grade for those students not intending to be math or science majors in college is more than sufficient to be on track to meet the A-G requirements for the University of California and California State University campuses. Another misconception is that other countries require students to take algebra in the 8th grade. Actually, they spread algebra over several years and do not require quadratic equations in 8th grade, as California – a major outlier in this regard – does.
Secondly, there should be a requirement that districts adequately assess which students are prepared for 8th grade algebra and which students will be harmed, with some leeway so students (with family participation) who may have weaker preparation but high desire can still take the course. See here.
Thirdly, the alternative course now derided as general math, often consisting of a weak review of past materials, should be redesigned. This course would then be the culmination of a 4th - 8th grade sequence that demanded a sophisticated understanding and application of number topics to complex situations. The State Board and Department of Education made a good start at this in 2004 when they evaluated what students who did not take algebra or who did not do well in algebra needed to know and adopted materials aimed at these students. Another positive step occurred last year, when they adopted such a sequence for 4th – 8th grade (actually accelerated a bit).
Finally, there is a misguided assumption that passing an “8th grade for all” algebra standard, as the State Board of Education did in 2008, and holding schools accountable for how many take the course will by itself improve performance. On the margins, maybe. But for real improvement there needs to be a widespread statewide effort aimed at improving the proficiency of students in critical middle-grade numbers topics. Unfortunately, this part of the program never got off the ground.
Such an initiative would include:
- Adopting strong standards for 4th - 8th grade (done, except 8th grade needs some clarification, as the State Board last year under time constraints packed in both the numbers standard and a complete set of algebra standards for 8th grade);
- Developing curricular guidance (for an example go here);
- Adopting materials based on these standards and curricula;
- Undertaking widespread professional development for teachers and principals, which includes site-based assistance and school team building;
- Implementing an accountability system that is discrete enough to measure the performance of students on each of the major domains of middle-grade math — fractions, decimals, percentage, ratio, proportion, etc. – and feeds that information back to the school (potentially available from California’s joining the SMARTER Balanced national assessment collaborative); and
- Providing organized interventions to assure that students who are falling behind receive appropriate help.
More importantly, a statewide collaboration of districts, math-oriented organizations, and teachers interested in tackling this problem needs to be initiated and supported. There are pockets of high performance in middle-grade math in this state which can inform others, and many districts will be more than willing to participate in such joint efforts.
Also critical is an effort to improve the quality of prospective middle-grade math teachers. Currently, unlike high school teachers, middle-grade math teachers aren’t required to pass a math test that includes math understanding, how best to teach difficult topics, and what to do when students have trouble learning those topics. Additionally, there needs to be a recruitment effort aimed at high-quality candidates, a revamping of their preparation, and induction support when they start to teach.
In my opinion, only this multifaceted approach will turn around the dangerously low math performance of our middle-grade students.
Bill Honig began his career in education as an elementary school teacher before becoming a California State Board member and district superintendent. He was elected in 1982 to serve the first of three terms as California Superintendent of Public Instruction. He subsequently published “Teaching Our Children to Read” (Corwin Press) and founded the Consortium on Reading Excellence (www.corelearn.com). CORE works throughout the nation helping schools, districts, and states implement best practices in reading and math. He is a Bay Area native, father of four, and grandfather of five.