Tag: Algebra

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.

I, II punch of algebra proficiency

If only Aristotle were around to argue the case for Early Algebra I, the debate might not be so….litigious. Here’s the gist of a quasi-syllogism based on results of the 2009 NAEP High School Transcript Study by the U.S. Department of Education’s National Center for Education Statistics: High school graduates who took a rigorous curriculum earned the highest scores on the 12th grade National Assessment of Educational Progress (NAEP); nearly two-thirds of students who completed a rigorous curriculum in high school took Algebra I in 8th grade; therefore, students who take Algebra I in 8th grade are more likely to earn the highest scores on NAEP.

Hey, I said quasi. It’s not that simple, and it’s not universal. Not all students do well, or even pass, Algebra I in 8th grade. And some who do squeak by so narrowly that they opt out of geometry and Algebra II, two of the a-g courses required for admission to the University of California or California State University. And many aren’t even given the chance to take it in middle school. “A student should be prepared by 8th grade to master algebra standards; unfortunately not all students have access to algebra,” said Linda Murray, a superintendent in residence at The Education Trust-West, where she’s working with districts to identify where students are “hitting the wall” in Algebra I and to develop interventions to keep them from spiraling down.

NCES findings

Increases in numbers of students taking rigorous STEM courses. Chart from the NCES 2009 NAEP high school transcript study
Increases in numbers of students taking rigorous STEM courses. Chart from the NCES 2009 NAEP high school transcript study. (Click to enlarge)

First, a little more about the NCES study. Researchers examined a nationally representative sample of the 2009 transcripts of 37,700 high school graduates. They compared them to 1990 transcript studies for number of courses, rigor of those courses, and differences in race, ethnicity, gender, and parents’ level of education. NCES defines “rigorous” for math as Algebra I and II, geometry, and pre-calculus or higher.

Since 1990, more graduates from every subgroup have taken this level of courses. Six percent of African American students completed the most rigorous classes in 2009, compared to 2% in 1990; percentages of Hispanic students jumped from 2% to 8%; and grew from 13% to 29% for Asians and Pacific Islanders.

The NCES study doesn’t just look at high school math, it covers all core academic subjects, and the findings are similar to those for math. Average NAEP mathematics scores closely correlated with the level of math courses taken in high school. Students enrolled in classes below Algebra I scored below basic; those in Algebra I reached basic on the test; add geometry and Algebra II and the students move into the proficient range.

NAEP is such an “unwavering standard on which to measure the progress of American students,” said Neal Finkelstein, a senior scientist at WestEd, the nonprofit regional education lab, that “when we all see patterns that are interesting in NAEP, those are notable.”  The patterns show a “dilemma” as much as they show progress, said Finkelstein. What to do about the huge numbers of kids who don’t do well in math?

Unintended consequences

The push to get more 8th grade students into algebra is clearly working. Their numbers jumped from 32% in 2003 to 57% in 2010, according EdSource. During that same time span, the percentage of 8th graders who scored proficient or better on the California Standards Test (CST) rose from 39% to 46%. Even students in so-called “at-risk” groups improved. Here’s what the EdSource report had to say:

“Nearly four-and-a-half times as many economically disadvantaged 8th graders scored proficient or higher on the test in 2010 as in 2003. In addition, three times as many African American 8th graders and more than four-and-a-half times as many Hispanic/Latino 8th graders scored proficient or higher on the Algebra I CST in 2010 as in 2003.”

But there’s a flip side. As more students take algebra I in middle school, cracks in the support system are beginning to widen.  Of the 80,000 8th graders who took the Algebra I California Standards Test in 2010, 29% scored below basic or far below basic and, of these, nearly 51,000 were Hispanic and 8,000 African American. Arun Ramanathan, executive director of Education Trust-West, says there are gaps based on income and on race.  “One of the sources is clearly opportunity; they don’t get the support,” said Ramanathan.

Many of these students wind up taking it again, and not just those who do poorly. Forty-five percent of 8th grade algebra students who met or exceeded standards on the state’s Mathematics Assessment Resource Services (MARS) were placed back in Algebra I in 9th grade, according to a 2010 study commissioned by the Noyce Foundation. More than half the 10th and 11th graders were also repeat performers.

A blueprint for improvement

Sending students back to the same class they failed isn’t the best way to help them, says Murray. “The student fails the course, there’s nothing in place to catch them along the way, so when they fail they’re re-enrolled in the same course with no changes in the teaching method, sometimes with the same teacher, and these student fail again.” Murray is working with nine school districts to develop what she calls “Just in Time” interventions. They may include having an intervention class built into the student’s schedule so “the very day he or she is struggling with a concept, they have a class that day to help them get back on track.”

Teachers and counselors are in need of more targeted professional development. If they have low expectations, they’ll pass those on to the students who may then see themselves as incapable of doing math. Chris Roe, the CEO of the California STEM Learning Network, says if these studies have taught us anything, it’s that we can’t wait until a student has failed to start providing help. “The system needs to be flexible enough and innovative enough that we can identify where those students are, and catch them early enough to provide them with additional resources,” said Roe, “So it’s not all of a sudden, ‘Oh my God, we need to make up three years of basic math skills over the next few months.'”

Roe and the others are hopeful that California’s participation in the Common Core standards will force the state to be more proactive. “The Common Core has made it pretty clear what those standards are, what students should be able to know and do,” said Roe. “It’s the first time we’ve had national agreement on that.”