Doubts over 8th grade algebra for all
Some say keep it constant, other say variable
When it comes to flip-flopping, forget the Republican primary and take a look at California’s vacillation on when students should learn algebra. Yesterday, a year and a half after the State Board of Education adopted new math standards, researchers, educators, and policymakers once again sparred over the wisdom of requiring Algebra I for most eighth graders.
When Phil Daro helped write California’s Common Core math standards, he was instructed to base them on evidence, not politics, and to take a close look at math education in the world’s top-performing countries. “What we saw, and what we learned, contradicts a lot of the assumptions on which California mathematics policy is built,” Daro told several hundred people attending Thursday’s Middle Grades Math conference at Stanford University.
The most elemental difference, said Daro, who co-directs UC Berkeley’s Tools for Change, is that even though Algebra I is considered the single most important mathematics subject, California rushes students through it when they’re still in middle school, while high-achieving countries spread it out over three years. “We’re saying let’s spend less time on Algebra I, the most important math; it doesn’t make sense,” Daro said.
8th grade students scoring proficient or better on Algebra I, by race. (Source: SVEF) Click to enlarge
Seated at a table in the back of the meeting room, farthest away from the speakers, some of the heaviest hitters in California education glanced at each other and exchanged a quick whisper. Algebra I is a can of worms they’d like to see buried beneath a massive compost pile, preferably in a neighboring state.
It’s been dogging the state at least since the 1997 content standards, which included math standards only through seventh grade. Grades eight and up were organized around content tests, according to a 2011 report commissioned by the Silicon Valley Education Foundation.* Citing an Education Week article, the report’s authors wrote that “the goal was to increase the number of students enrolled in Algebra I, not to mandate enrollment.”
More than a decade later, under pressure to comply with No Child Left Behind, the State Board of Education made Algebra I mandatory for eighth grade students. That led to a lawsuit, an injunction against the mandate, and flexibility for eighth graders to take Algebra I or an Algebra prep class. Then came Common Core, and California, in a preemptive move, adopted two sets of eighth grade math standards, pre-Algebra for the national standards, and Algebra I for the state.
So it’s understandable if Daro’s recommendation to go more slowly to make sure that students fully comprehend the material – sound policy or not – didn’t elicit any huzzahs from policymakers at the meeting.
The core reason for mandating Algebra I in eighth grade is equity and access for all to college prep courses. Supporters hoped it would stop the practice of tracking low-income and other underserved students away from the A-to-G classes required for admission to the University of California and California State University. But researchers at the meeting warned that the policy, as it’s being implemented, could backfire and make it harder for those students to be successful.
There’s no doubt that it has achieved that goal. According to the SVEF report, the number of students taking Algebra I in eighth grade jumped by 80 percent between 2003 and 2010, with the most dramatic increase among low-income, African American, and Latino students. As that number rises, so too does the number of students reaching proficiency on the Algebra I California Standards Test. Nearly two times as many eighth graders met that bar, according to Algebra Policy in California, published by EdSource.
Then the laws of physics kick in an there’s almost an equal and opposite reaction, with 1.5 times as many of the students scoring below or far below basic. Even though more eighth grade students are taking Algebra I, that doesn’t mean they’ve been equally prepared for it, said Neal Finkelstein, a senior research scientist at WestEd. “There are many patterns of students who are not succeeding early, and are continuing to not succeed later,” said Finkelstein.
EdSource researcher Matt Rosin wanted to know what the chances were of a student who scored basic or below on the seventh grade California Standards test being put in Algebra I. When he analyzed algebra placements and test scores for nearly 70,000 eighth graders during the 2008-09 school year, he found that compared to middle class schools, more students at low-income schools were placed in Algebra I, and more of them scored basic or below on that state test.
“This is the achievement gap in action,” said Rosin. “Schools that have heard the call for greater access to Algebra I are answering the call, but they’re making decisions based on access, not on instruction and support.”
Others would disagree that standards alone are the issue. During a conversation with Daro after the conference, former State Board of Education president Ted Mitchell said teacher preparation is a problem, especially in elementary schools. He would bring in math specialists to help out.
Bruce Arnold seems to share that sentiment. He runs the Mathematics Diagnostic Testing Project at UC San Diego, where teachers learn to identify the specific reasons a student is having difficulty grasping a concept, and get ideas on how to teach that lesson differently.
If students misunderstand any of the prerequisite materials, that will stay with them and trip them up as they move to more advanced classes, explained Arnold. He falls somewhere in the middle when it comes to how much time to spend on the big concepts. Definitely not the three years that schools take in Singapore, however. “I would argue that students should take Algebra I as soon as they are ready,” said Arnold, “and that our goal should be to move students along as fast as they can be moved with success.”
* TOP-Ed is an editorially independent project of the Silicon Valley Education Foundation.
A forthcoming paper from three Duke University professors — “The Aftermath of Accelerating Algebra: Evidence from a District Policy Initiative” — analyzes the results of Charlotte-Mecklenburg Schools’ mandating algebra for all 8th graders for the 2002/2003 school year. The results were not pretty: “students affected by the acceleration initiative scored significantly lower on end-of-course tests in Algebra I, and were either no more likely or significantly less likely to pass standard follow-up courses, Geometry and Algebra II, on a college prepatory timetable.”
As the attorney for the state of California who represented the State Board on this issue, I advocated to the utmost of my abilities to implement its decision. But as a citizen who cares passionately about the education of California’s kids, particularly those from low-income communities, the more I delve into the research on 8th-grade algebra, the more I struggled with what I believed was the right policy decision. Unquestionably, California has made great strides in increasing 8th-grade algebra enrollment, and I believe there is a very real benefit to continuing to push (and push hard) for expanding its instruction. Yet, the consequences of placing a student in algebra who is not prepared can be disastrous, as our intuition suggests and the Duke study confirms. What is the right trade off? I don’t know, despite having spent many hours pondering the question.
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Yet another good reason to get the state and federal governments out of the business of micro-managing schools and out of mandating standards and standardized instructional practices. Sacramento doesn’t know best.
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I greatly respect this site’s willingness to follow the facts wherever they may lead, and to keep the readers informed of expert findings and important developments, despite occasionally challenging some of the SVE Foundation goals or recommendations (I know, Johh, the SVEF recognizes that not all kids are ready for Alg I by 8th grade, so the answer is to help prepare them in advance, but today’s reporting does challenge the underyling premise of force-feeding theoritical math on kids prematurely or when their not adequately prepared). The two writers of this Blog do credit to its employers by their honest reporting.
It should be obviously apparent to anyone following education policy that simply demanding MORE of the same is not a prescription for success. The 8th grade mandate from the SBE was a purely political stunt, albeit one led by genuine sentiments to help all kids — particularly disadvantaged ones — to preserve all postsecondary options entering high school.
But it was based on bootstrapping logic and a fixation on college-prep for all. And need I remind the readers of this post that the path to hell is laiden with good intentions?
I am proud to affiliate with the only Schwarzenegger SBE apppointee who resisted the political pressure and voted against this silly, politically motivated mandate. The Get REAL coalition of labor groups, employers and educators have come together in a single-minded quest to bring more relevance and meaning back into the K-12 education experience for every student. In our short 3-year history we have been met by detractors who level all sorts of charges against us, both policy-related and personal in nature, in their quest to protect the status quo.
Despite those attacks, we have remained true to our mission to pursue policies aimed solely at serving the true interests of kids … and by extension, the interest of California’s economy.
We opposed the 8th grade Algebra mandate because we knew far too many kids would be hurt by it. We witnessed what happened to far to0 many LAUSD freshmen when they were buffetted by the same mandate back in 2006 (which became the single most cited reason for students dropping out, since those who struggled with this course their freshmen year were compelled to take additional, remediation courses in the same subject each subsequent year).
Can we all take a step back from the feel-good, politically sensitive policy proposals for just a second and consider what is in the best interest of young students? And can we use hard data and experience, as well as some common sense, to gauge the wisdom of any curricular mandate, accountability metrix, or funding scheme? Is this possible any more, given so many adults and their well-heeled interest groups are making so much money off the K-12 sytem?
For the sake of our kids and state, I hope we can get real about educating the next generation of Californians.
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Unfortunately, based on what’s written in this article, I have to report that Mr. Daro does not understand the mathematics curriculum of Singapore and similar leading countries in mathematics. He’s right, they do take three years to complete the algebraic content of the courses we call “Algebra”, while concurrently teaching our geometry content; but that includes Algebra II as well as Algebra I. For example, quadratic functions are taught to the stronger mathematics students in leading educational systems in the ninth grade, before the end of middle school.
The writers of the new Common Core mathematics standards have failed in their mission to provide internationally competitive benchmarks for American students. We can only hope it wasn’t because of simple incomprehension of curriculum documents publicly accessible on the Internet.
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Actually, what Phil Daro said was that pre-algebra content ( such as the ability to think proportionately and master percentage, rate, and a deep understading of fractions) is the most important content students should learn (as reported by high school and college teachers of non STEM students). Thus, schools should spend more time on these areas to make sure almost every student is proficient. Many students who pass Algebra I still don’t have a deep enough understanding of these topics.
The policy dilemma should be easy to solve. All students by 8th grade should have mastered the common core content focused on these topics and districts should maximize the number of students who PASS 8th grade algebra. As Kathryn has reported, the equity issue cuts both ways. Nothing stops non stem bound students who are adequately prepared in pre-algebra topics from taking Algebra in the 9th grade and meeting A-G requirements.
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I wonder how much the bludgeon of Program Improvement has impacted kids’ attitude toward math, and as a consequence, their progress. My kids are coming to the end of high school now. While they were in middle school, math support classes were created for students “on the bubble”, taking kids off the regular track and doubling them up on math (at the expense of electives and in some cases, science). By the time they tested out of these classes, many of these kids came to loathe math (and school). Their reward for popping above the CST bubble was to jump right onto the Algebra treadmill.
There are bright kids, now Juniors in high school, still taking Algebra 1. I know much of this has to do with the district’s implementation, but c’mon people! I know these kids. Their parents are college-educated professionals, they are not disadvantaged…they are, however, disillusioned. Their classmates with bigger personal hurdles bailed long ago. We have seen an enormous spike in alternative schools and dropouts due directly to the force-feeding of algebra. School has become a Dickensian place of gloom and drear. I want to slap the “Rigor” right off the school website.
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It is unsurprising that Phil Daro doesn’t like to promote taking Algebra in grade 8. After all, the Common Core standards which he participated in writing did not offer Algebra 1 in grade 8 (or Algebra 1 plus Geometry by grade 9) as most high achieving nations do. So he needs to cover up the fact that Common Core lies when it claims it is internationally benchmarked to international high achievers. (More details about Common Core being below international benchmarks can be found here, including a clear admission to this fact by Bill McCallum, one of the other two Common Core math authors, as recorded by John Fensterwald himself.)
I agree with Eric Premack that the federal government should get out of the business of micromanaging curriculum. It was, indeed, the federal government stubborn stupidity that forced California into trying to force every kid into Algebra 1. I was associated with it at the time, and I will be the first to admit that in this matter the Spellings’ dept. of Ed exhibited the worst attribute of central planners – pigheadedness. Unfortunately, with Common Core, will will just get even more of that.
I agree even more with Bruce William Smith that Phil Daro does not understand what countries like Singapore do. Luckily, Kathy is incorrect when she mentions that Daro “helped write California’s Common Core math standards.” He did not. He helped writing the Common Core standards, but had nothing to do with the California version of them. Last time Daro had anything to do with California math at the state level was in 1994 when he co-chaired Delaine Eastin’s Math Task Force, and a wonderful mess he did with that.
Finally, I feel for Benjamin Riley. He, and our State Board, were indeed placed in a no-win situation because of the federal meddling in 2008. Yet the solution is simply what California has shown that works reasonably well: Promote preparation for Algebra 1 in grade 8, but do not force it on anyone who is unprepared to take it. Ed Source and SVEF work shows the risks of this approach but also suggests ways around them. Wholesale dumping of Algebra 1 in grade 8 will doom the prospects of tens of thousands of students from disadvantaged backgrounds — places like Palo Alto and elite private schools will not give up on it, but places like San Jose will. And we know who will suffer from that.
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Kathryn Baron wrote “According to the SVEF report, the number of students taking Algebra I in eighth grade jumped by 80 percent between 2003 and 2010, with the most dramatic increase among low-income.”
There is a simple explanation as to why the increase in 8th grade students taking algebra 1, API Score. When an 8th grade student does not take algebra 1 the school gets dinged on it’s API.
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Agreed, Ze’ev (and Eric): placement decisions of this sort ought, at least in our current conditions, to be made more locally, not in a state or federal capitol. Perhaps later, if we ever solve major issues with more equitable funding and conditions and the mathematical preparation of primary school teachers, we’ll be able to move on to higher standards throughout the state; in the meantime, we’ll all have to do what we can now with the children we have now, who cannot wait while our educational leaders work themselves up in endless debates. Escaping an increasingly oppressive state orthodoxy looks ever more likely to be the only way to make sure our own children don’t get left behind.
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@MWM: Your are essentially correct that when 8th-graders don’t take Algebra 1 schools are dinged on API (they are dinged if student take it beyond 8th grade). But this explanation is anything but “simple.” It does not, in itself, explain that while the algebra takers by grade 8 doubled since 2003 (Kathryn is incorrect about the 80% — it rose from 32% to 67% of cohort) the fraction of successful taking also rose from 39% to over 50%. Nothing “simple” about that — it is the other way around when students are simply packed into Algebra. Can we do better? Sure. Can we be more judicious in placing students? Sure. But abandoning Algebra 1 as an aspiration in 8th grade is not a way to higher achievement.
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I’d like to correct Ze’ev Wurman’s characterization of my remarks at the Joint Math Meetings in January 2010. Fensterwald described my remarks as follows:
“While acknowledging the concerns about front-loading demands in early grades, he said that the overall standards would not be too high, certainly not in comparison other nations, including East Asia, where math education excels.”
Wurman appears to be interpreting the phrase “not too high” as “not very high.” But there is another possible meaning for “not too high,” the one I intended, which is “not excessively high.” My comment came in response to a question from someone in the audience, expressing concern that the standards, when completed, would be too (as in excessively) high. I replied that they would not be, especially compared to high-achieving East Asian countries.
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Ze’ev Wurman’s “details about Common Core being below international benchmarks” include a reference to a study by the education researcher Andrew Porter and his colleagues.
Porter et al.’s analysis seems to omit the CCSS Standards for Mathematical Practice and some conclusions apparently rely on a mistake in a table. Porter et al.’s measures of focus and cognitive demand miss important characteristics of intended curricula in the US and other countries. The authors acknowledge this possibility, saying, “Judging the quality of the Common Core standards is of great importance, but it is only partially and tentatively addressed here” (emphasis added).
In particular, Porter et al. compare the CCSS with the mathematics standards from 14 US states and with grade 8 mathematics requirements in Finland, Japan, and Singapore. Aside from the question of whether any region’s curriculum should be characterized by a single grade, there are other technical details that suggest a less sweeping conclusion than “below international benchmarks.”
For example, solving an equation is classified under “perform procedure” in Porter et al.’s analysis (see Table 5, p. 109). However, in countries outside the US, a problem coded as “solving an equation” is not necessarily only a matter of using a procedure. When discussed in the classroom, for example, in Hong Kong, it can look like a task with “higher order cognitive demand.”
More details are here.
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“places like San Jose will. ”
Places like San Jose *should* drop mandatory Algebra I for all. What happens is that close to 50% of the students lose an entire year of pre-algebra instruction–instruction that they desperately need–to take algebra, which they are entirely unprepared for. Then they are forced to take it again in their freshman year, if they don’t score above proficient on the CST. And then, if they fail it in their freshman year, they have to take it again.
THey have qualified teachers who are dedicated and passionate. What they don’t have is ability and pre-requisite knowledge. And if you don’t think that schools are putting kids into Algebra to avoid taking a hit on the API, then think again.
“And we know who will suffer from that.”
*We* know nothing of the sort. *You* think you know….what? Kids who aren’t prepared to take algebra in the first place will “suffer” for taking a year of pre-algebra?
Or are you suggesting that San Jose is a racist district that would actively work against putting qualified low income students into algebra?
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Bill McCallum doth protests too much. It is clear that he would love to take back what he had said in front of an audience of mathematicians, captured when he couldn’t equivocate or use mealy-mouthed language, as is typical when he speaks in front of wide-eyed audience of politicians and educators.
He shouldn’t try so hard. Jim Milgram of Stanford, the only real mathematician on the Common Core validation panel, said it clearly:
“While the difference between these [Common Core] standards and those of the top states at the end of eighth grade is perhaps somewhat more than one year, the difference is more like two years when compared to the expectations of the high-achieving countries — particularly most of the nations of East Asia.”
Prof. Milgram refused to sign off on the Common Core because he didn’t believe they met the claim they are “comparable to the expectations of other leading nations.” Another two foreign members of the Common Core validation committee refused to sign, one of them clearly stating in his refusal that he cannot endorse Common Core because he also disagrees the standards are comparable to the expectations of other leading nations. Prof. Sandra Stotsky, another validation committee member that declined to sign off, wrote the same of Common Core in the area of reading and literacy. Prof. Jonathan Goodman of the Courant Institute at NYU found the Common Core math standards have “significantly lower expectations with respect to algebra and geometry than the published standards of other countries.”
So Prof. McCallum doesn’t need to work so hard on back-pedaling from what he had said. Similar and even stronger sentiments has been said by much more prominent mathematicians.
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Honestly, I question the necessity of every student taking Algebra I. Every student will pursue a different career path. Some will need it for their career, but some will not. Only those who will need it ought to take it.
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Posted on behalf of Doug McRae. (Other readers who have trouble posting comments should contact me at john@svefoundation.org):
California’s ambitious goal of Algebra I for all 8th graders, initiated by the 1997 math standards, needs to be viewed from two perspectives:
(1) Any initiative as big as moving a cornerstone discipline such as Algebra to an earlier grade level statewide, while simultaneously calling for census enrollment for all students, will take a substantial amount of time to implement;
(2) Any such initiative is bound to be controversial. For a substantial amount of time, I’d suggest it will take 25-30 years before we really know the big picture results of the initiative. But, after almost 15 years, we have moved from about 1/6 of 8th grade enrollment statewide taking Algebra I in 1997 to 1/3 of 8th grade enrollment taking Algebra I in 2003 to 2/3 of 8th grade enrollment taking Algebra I in 2011, while simultaneously improving our proficient and above statewide scores on the STAR Algebra I CST from about 40 percent in 2003 to almost 50 percent in 2011. Those data reflect tremendous progress to date, and it is not hard to forecast that by 2025 California is likely to have 80-90 percent of students taking Algebra I by grade 8 statewide with proficient and above achievement levels reached by 70-80 percent of 8th grade enrollment. Such an increase in grade 8 math achievement over a long run would be a tremendous accomplishment, and would undoubtedly stand California very well in terms of status against performance of other states as well as international comparisons. As the post describes, the pros and cons of the initiative are still with us after 15 years, essentially a continuation of the “math wars” of the late ’90’s (per Peter Schrag). While one can focus on problems in manpower to adequately teach Algebra I to all 8th graders, on achievement gaps both absolute and relative over time, and on faulty or questionable implementation strategies from district-to-district, it is hard to argue with the overall progress to date. Such progress certainly justifies current policy strategies to maintain and further California’s 1997 grade 8 Algebra I initiative.
Doug McRae
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The goal of the policy wasn’t so much that kids would take Algebra in 8th grade, but that they’d finish out with precalculus in 11th grade or calculus in 12th grade. I’d be interested to see numbers that show whether the 8th grade Algebra initiative increased the level of terminal math classes for California’s high school students.
It seems to me that any policy that results in students failing a class and having to retake it two or three times in large numbers needs significant rethought. I don’t know what the right answer is, policywise, but I don’t think that what we’re doing now is good enough nor is it serving all students well.
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Algebra 1…for ALL, by 8th grade, is an intriguing debate. Ms. Baron’s article and the comments that followed certainly highlight the complexity of the issue. However, I feel one important reality has not been touched upon. What defines “algebra 1?” Individuals and organizations are bragging about increased enrollment in 8th grade algebra 1 classes but I have to wonder how far math teachers (the ones in the trenches) have had to water down the course to accomodate large numbers of unprepared and underprepared students. Unfortunately, what looks good on paper isn’t always what’s good for kids.
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@el:
STAR data provides a glimpse of what I think you are after. HS juniors and sophomores take the “summative” math CST if they have completed Algebra 2 in prior years. In other words, at that point they take a math course beyond Algebra 2, typically pre-calc. Between 2003 and 2011 the number of summative takers rose from 75K to 140K (87%), while the sophomore-junior cohort size grew only about 13%. At the same time the fraction scoring Proficient & Advanced rose from 43% to 55%, while the fraction of scoring Basic and above rose from 65% to 78%. Somewhat impressive.
I am unaware of federal collections that break out similar data by state. High School Transcript Study (HSTS, most recent in 2009) provides some trends, but only at the national level.
Incidentally, I am not sure from where you picked up the idea that California (or the Standards) expects most (all?) students to reach calculus, or even pre-calc. in HS. The Framework is quite clear that only content up to and including Algebra 2 (with some stats) is envisioned for all students (p. 78).
@bMac: California is one of the few states that has Algebra 1 well-defined in its current Standards, and its associated CST. Consequently, one can expect that most Algebra 1 classes cover at least that base content.
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@Ze’ev, what I meant by expecting pre-calc was that I always understood that the reason it was felt Algebra needed to be taken in 8th grade was to give those kids the option to finish with calculus as seniors. If they only have to get to Algebra 2, then it wouldn’t matter if they took Algebra 1 in 9th or even 10th grade.
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@el: I see the source of your confusion. The reasoning behind the push for Algebra in grade 8 is much more complex and multifaceted. Hard to give it a full treatment in a series of comments. Anyway, the data suggests that success on pre-calc has, indeed, both broadened and deepened.
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As someone who has taught Algebra I in middle and high schools, I would like to point out two problems with the implementation of the algebra mandate:
1. Class size. The Morgan-Hart academic class size reduction law applies to 9th-grade classes but not to 8th-grade classes. Districts are exiting Morgan-Hart or flexing the funds, so high school algebra classes now tend to be as large as middle school ones, but several years ago, a student who was studying algebra in 8th grade might well have been enrolled in a larger class than his counterpart who was studying algebra in high school — quite a paradox!
Pundits will say that there is no evidence that class size matters. I do know two things, though. First, I accomplished a lot more for classes of 20 high school algebra students under Morgan-Hart than I did for classes of 28 middle school algebra students (school-based funds used to “reduce” algebra classes from 32 to 28 in that school), or 35 high schoolers (in a non-Morgan-Hart district). Note the difference in daily contacts: 100/120 in the first case, versus 150/180 in the second, or 175/210 in the third case, depending on the school’s choice of a 6- or 7-period day. Second, as Diane Ravitch put it, rich folks want small classes for their own children.
2. Social promotion. It is the rare middle school that still retains students in individual courses, let alone in 8th-grade as a whole. In my experience, students who fail 6th-grade math are rewarded with a placement in 7th-grade math, there being no other 7th-grade math class. Similarly, those who fail 7th-grade math are placed in 8th-grade algebra. And those who fail 8th-grade algebra are cheerfully promoted to the local high school. A colleague of mine chuckles at a remark from a student: “Mrs. X, I know what I’m doing. I’ve taken this class three times.”
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(Sorry, the middle daily contacts figure should be 140/168, not 150/180.)
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“The reasoning behind the push for Algebra in grade 8 is much more complex and multifaceted. ”
No, it wasn’t. the reasoning behind the push for Algebra in grade 8 was that without the push, unqualified and/or uninterested students (who were disproportionately black or Hispanic) would not get to college level math in high school–or exactly what el suggests.
Were that not the goal, then the only “complex and multifaceted” reasoning that fits the behavior is “Hey, let’s have a third of our students take algebra two or more times!”
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For all the high-minded reader comments above, no one has discussed the most important action-oriented quote in Baron’s column: “‘This is the achievement gap in action,’ said Rosin. ‘Schools that have heard the call for greater access to Algebra I are answering the call, but they’re making decisions based on access, not on instruction and support.’”
Advanced math studies take work. College-prep studies demand diligence.
Rather than debate how many Algebra 1 students fit on the head of a pin, we should be discussing the need for extra time at the study table. If a student comes from a household where both parents are not strong in Algebra, that student is at a learning disadvantage. Who then should step in to help?
1) The school system must figure out ways to increase weekend study and tutor opportunities;
2) Community groups, including churches, absolutely have to step up to assist local pre-teens and teens with math study support;
3) Parents must be prepared – starting as early as Kindergarten – to anticipate the amount of math homework that will be required as their child grows.
Whether a student earns Algebra 1 proficiency in 8th or 9th grade is of little major consequence – provided that student truly achieves proficiency. To begin earning college credit – whether at a Community College or a 4-year University – a student has to have Algebra 1, Geometry and Algebra 2 well-learned. A University English major may not need Calculus, but all engineering students, information technology students and hard science students surely do.
Math does not come easy to all students. But neither do languages, music, arts or sports. Most of today’s elementary school students must expect to earn math proficiency.
And, our community’s adults should acknowledge that learning is hard work that requires way more than “access.” Students need time, focus and significant expectations of achievement – both in class and, especially, off campus.
- Chris Stampolis
Trustee, West Valley-Mission Community College District
State Board Member, California Community College Trustees (CCCT)
stampolis@aol.com * 408-390-4748
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@ Chris, your suggestions assume an earnestness that is not present in most young people. The Algebra I achievement gap, if there is one, is small. The effort gap is vast.
We can invest all we want in tutoring, community support, and so on, but we cannot force students to invest in their own education. Most of the middle and high school students that I have taught are lazy. You should hear the whining! “Oh, we have to do homework?” “Oh, we have to graph that?” “Oh, we have to use a ruler?” “Oh, we have to be on time?” “I lost my pencil.” (Repeated 3x daily.) “Oh, we have to bring our books to class?” “Oh, we have to read the textbook?” “Tell me if it’s right.” (Heaven forbid that students should, as the NCTM suggests, take responsibility for assessing their own work.) “Can I go to my locker?” “Can I go to the bathroom?” (As if learning takes place in the hallway or in the bathroom.) “Can I listen to my iPod?”
Most students who fail Algebra I do so because they are lazy.
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“Math does not come easy to all students. But neither do languages, music, arts or sports. Most of today’s elementary school students must expect to earn math proficiency.”
But unlike math, not only do schools not require any particular level of proficiency in languages, music, arts or sports (though they should), most are cutting these programs back or eliminating them altogether.
Silicon Valley educational advocates seem to be in a bubble, exhibiting liberal sympathy but not understanding of problems faced as close as San Jose.
Discussing standards in high-achieving countries is easy; it is even easier to ignore the difference in instructional time. These same countries both have longer school years and longer school days, but instead of focusing on restoring cuts to instructional time, let alone matching the high-achievers, the no-tax-in-hell policy of the Republican Party is condemning many California schools to cut instructional time further. It’s up to business leaders to decide whether the GOP will receive the campaign funding to maintain an absolute 1/3 block.
As business people, you understand that there are trade-offs between choices:
1. Increase instructional time to match the peer countries whose standards we wish to emulate.
2. Adopt tougher standards while slashing instructional time, ensuring that a high portion of students will fail, leading them to dropping out, with dropping out being one of the best indicators of future performance in “masters” of crime in “higher educational” prisons that cost more than a Stanford education every year at taxpayer expense (hey, great results from that Algebra I mandate!)
3. Relax standards and accept lower numbers of students taking all the classes Silicon Valley would ideally like to have in its labor pool, but without the damage of exacerbating school dropouts.
So, which choice does SVEF recommend?
How much do Intel and AMD invest in R&D every year? If Silicon Valley leaders want world-class STEM results from students who thus far have been inflicted with third-world levels of instructional time, you need to take the California Chamber of Commerce and the California Manufacturers and “Technology” Association head-on to prevent opposition to ballot measures that would actually increase funding for education, like those of Molly Munger or the California Federation of Teachers. The Governor’s initiative, while necessary, is not sufficient: it is just a band-aid that prevents even more severe cuts.
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Paul, who is lazy? It is the teacher who fails to inspire his students, who fails to achieve results. Exhibit A in why we not only need to get more training support for new teachers, but also get rid of the dead wood. Your candid admission is a perfect example.
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Hmm … InstructionalTime … haven’t we had funding to match instructional time with the “peer countries” until now (or very recently)? Our typical year is 180 days of 6 hours, or 1080 hours/year. Finland? 700-800. Korea? 700-800. Japan? 800. Australia? 950 . (Source: EAG 2011). So how were we doing a couple of years back? Just askin’
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@ Ze’ev, thank you for correcting the misconception that more instructional time must be better!
@ Who Is Lazy, my “candid admission” is an example what occurs in spite of access to a dedicated teacher. I maintain an NCTM membership at my own expense, study theirs and other organizations’ publications on my own time, participate in math professional development on my own time and at my own expense, bring ideas from innovative math curricula such as CPM into non-CPM schools, and supply my own math teaching equipment and consumables whenever I can afford to supplement what a school district provides.
The choice of whether to invest enough effort to benefit from these approaches and resources rests with students.
As an aside, it’s funny to me that test-based accountability systems (NCLB, value-added, etc.) punish districts, schools and teachers for what is essentially a lack of effort on the part of students. I know of only one California public school — a unique, high-performing charter in the East Bay — that truly holds students accountable for CST results. At this school, a student who does not score proficient on the Algebra I CST must repeat the class, regardless of the teacher-assigned grade.
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Reading, writing and arithmetic are the three most essential skills students needs to master. Schools spend a lot of time on literacy, making sure children can read so they are able to communicate effectively with you and others. From the very first day of school, reading and writing are constantly reinforced, from the ABCs to identifying colors and words. But what about the arithmetic?
Many students are good readers and advanced writers, but have a really hard time with mathematics. Why is this so? Is math and English created equally? How much time is spent ensuring your child is numerate? If schools spent as much time on mathematics as they did on reading and writing, students would not perform so poorly and have such a fear of numbers.
It is expected that every student can count backwards and forwards like they recite the alphabet. Is your child able to add, subtract, multiply and divide without a calculator? Do students cringe at the thought of fractions? These are skills that are imperative a student’s success in school. When these skills are not reinforced and mastered on a consistent basis, then students usually struggle with mathematics throughout their entire educational careers. How can schools and parents help boost their student’s numeracy?
Here are some things you can do as a parent to strengthen, to reinforce and to enhance your students’ math skills that can be a “super star” in mathematics. Buy literature that tells a story involving math, involve math in your day to day activities, buy multiplication flash cards, play board games like Uno or Monopoly. Incorporating these fun-filled mathematics activities not only makes your child a math whiz in school, but gives you quality time with your family.
One of the biggest problems in mathematics is students are not exposed to enough “math stories.” Students hear a plethora of fictitious stories to help them with grammar. How about using literature to teach basic math concepts? Find stories that talk about counting, problem solving and basic arithmetic. The more they read about it, the more comfortable they will be around numbers.
Students should be numerate as well as literate. Committing basic mathematics facts to memory is the single important skill a child can master. Students struggle in algebra and higher mathematics courses because of their deficiencies in basic computational skills. A solid foundation in number sense does a world of good for students’ success in algebra and beyond.
Numeracy is more than just mastering computational skills. Critical thinking is a skill that is virtually nonexistent. Helping children to think critically about a mathematics situation helps them perform well on standardized tests. In addition, it also helps students become better decision makers and become more responsible, productive adults.
The foundation of high school mathematics is algebra. This is the basic building block of high school math. Why is it that most students do not master algebra? We know it is coming and it is a requirement. Are students fully equipped with the tools needed to be successful in algebra? What tools do students need in order to be a superstar in algebra?
The biggest problem is that algebra is abstract; a misconception is that is useless, “just a bunch of letters and numbers that have no meaning.” Algebra must have meaning and relevance to the students. Also, algebra must be concrete, something that can see, draw, relate to, manipulate in order for students to internalize, conceptualize, and understand algebra.
Since we are talking about making algebra concrete, let’s look at the concept of a linear function. The linear function is the foundation of algebra. It is the idea that relationships display a constant pattern that is consistent. Most of the relationships we experience in life are “linear” anyway. We can use our real world experience to teach the foundation of linear functions!
Here’s an example I like to use: You call a plumber to come look at your toilet. He tells you it costs $50 an hour to fix your toilet. He also charges you $50 just to look at it! From this point, it is relatively easy to write a linear function. There are two things to consider: how much it’s going to cost and how much time it is going to take.
This is how we write the function: we need to use two variables, c for cost and h for hours. Our function looks like this: c = $50 + $50h. Now, from this point, there are several directions we can take, such as graphing cost vs. hours or creating a table. The point is that algebra does not have to be hard and tedious. However, you must start with the basic building blocks of algebra in order for students to have a solid foundation.
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Seriously algebra 1 is unbelievably basic. The fact that there is a debate over teaching this as late as 8TH GRADE is just ridiculous. Students in America seem to be woefully incompetent at math and even debating whether algebra 1 should be taken in 8th grade is pretty crazy. Algebra 1 in fact should be started in 5th grade or so…because it is extremely basic math, and requires no more prior knowledge than a 5th grader would have anyway. The fact that this debate exists at all simply is a testament to how behind America is compared to other countries and shows how poorly the students in America perform in mathematics.
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