Category Archives: Research

Algebra II Revisited

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Algebra II Revisited

There’s a new (May, 2013) and, I think, very important report out from the National Center on Education and the Economy entitled “What does it really mean to be college and work ready?”  The organization and been around since 1988, and reports its work as “…researching the world’s best performing education systems to unlock their secrets.”  I strongly recommend you read it.  Here’s a video commentary on the report by their president, Marc Tucker, video commentary from http://www.ncee.org/college-and-work-ready/  Insert

I wrote about Algebra II and the Common Core in this previous blog, and NCEE’s research offers another commentary on the value of Algebra II as an indicator of being college and career ready.  I’ll offer some quotes from the report to expand my prior argument against Algebra II for all.

National Center for Education and the Economy Math Findings

NCEE opens their report, which actually covers both ELA and Mathematics college and work ready issues, by noting that 45% of students entering higher education for college degrees or for career preparation enroll in community colleges.  Hence, NCEE argues, looking deeply at the requirements for success in community colleagues is a practical and a real world indicator of what it means to be college and work ready.  About half of community college students go on to four year programs, further supporting their rationale for looking at community colleges.  The rest who graduate are taking a training program that leads to a career option.  The study examined “the most popular and diverse programs….” (p. 2) in randomly selected community colleges in seven states:  Accounting, Automotive Technology, Biotech/Electrical Technology, Business, Criminal Justice, Early Childhood Education, Information Technology/Computer Programming, and Nursing, plus the General Track.  For math, they looked at the math actually taught in the “initial credit bearing courses” in the programs (p. 2).  They looked at the textbooks, graded student assignments, tests and exams to “analyze the reading and writing skills that are required…” in both math and English Composition.

The findings were surprising.  Only one program required first year students to know Algebra II.  NCEE notes that Algebra II content is required for students who will take calculus or use calculus in their work, but citing a 2011 study from the Center on Education and the Workforce at Georgetown, NCEE notes that only about five percent of the working population needs to understand calculus.   “Indeed, community college first year programs of study typically assume that students have not mastered Algebra I.  The most advanced mathematics content used in the vast majority of the first-year college programs we analyzed can reasonably be characterized as the mathematics associated with Algebra 1.25, that is some, but not all, of the topics usually associated with Algebra I, plus a few other topics, mostly related to geometry or statistics (p. 3).”  They continue by noting that the math that ‘most enables” student success is middle school math, ‘especially arithmetic, ration, proportion, expressions and simple equations (p. 3).”

They observe that most high school grads don’t actually have good command of middle school fundamentals, and that competency in math that is rarely taught at any level — “schematics, geometric visualization and complex applications of measurement (p.3)” are also competencies that would lead to college success.

Algebra II is not a college and career prerequisite

Their conclusions on pages 4-6 make this clear statement about Algebra II:  “Mastery of Algebra II is widely thought to be a prerequisite for success in college and careers.  Our research shows that that is not so. The most demanding mathematics courses typically required of community college students are those required by the mathematics department,…but the content of the first year mathematics courses offered by the …. mathematics department is typically… Algebra I, some Algebra II and a few topics in geometry…. Based on our data one cannot make the case that high school graduates must be proficient in Algebra Ii to be ready for college and careers.”

They further conclude that rushing students into Algebra I early misses the opportunity to emphasize the very strong level of content mastery that should be obtained at the middle school level before moving on to higher math.  They suggest that understanding basic concepts at higher levels than now expected would permit students ‘to learn whatever mathematics they need for the path they subsequently want to pursue more quickly and easily than they can now( p. 4).”

More high school math options needed

Another noteworthy conclusion (p. 5) is “American high schools should consider abandoning the requirement that all high school students study a program of mathematics leading to calculus and instead offer that mathematics program as one among a number of options available for high school students … with other options available (e.g., statistics, data analysis and applied geometry) that include the mathematics needed by workers in other clusters of occupations.  By doing so high schools will almost certainly expand opportunity to many students who now find success in college closed off by a one-size-fit-all sequence of mathematics topics that actually fits the requirements only for a very narrow range of occupations.”

These are powerful words that fly in the face of Common Core standards.  But if the CCSS are expected to prepare students for college and careers, who determined the specifics of these standards?  When one considers the folks who wrote the math standards, one sees individuals highly vested in core math content who seem to have taken highly competitive college admissions criteria as their basic and their only competency target.  They ignored the career level requirements of most workers in the nation, despite clear research about what career mathematics competency standards should be.

Let’s have a look at job requirements.  I’ve read elsewhere (See Andrew Hacker’s New York Times 2012 opinion piece or this commentary from Get Schooled, by Maureen Downey.  This comment excerpt from penguin mom on the Get Schooled piece reproduces my argument rather well:

I was a math/computer science major in college. I did use what I learned in my Algebra 2, Trig, and Calculus high school classes… in college. Once I got out of college, I did Not use that information again even when working in the computer field. You do not need to know logs or rational equations or trig to write a cash register program or pretty much any program besides an engineering one. I didn’t pick Algebra 2 back up until I entered the teaching arena and started teaching the concepts again. Besides the general logic skills learned from solving the problems, I really don’t know of a lot in Algebra 2 that will translate into real world usage for the vast majority of the students. Graphed a line or parabola recently anyone? Used the quadratic formula? Solved a Trig equation? I think it would be Much better to require strong Economic, Personal Finance, Business Accounting and (usable) Statistics courses for every student. That information would be used in just about any field. Figuring interest or profit. Understanding (at least somewhat) what poll numbers actually mean. Keeping a budget and balancing a checkbook. Those are all useful skills.

Get this NCEE report, read the math section, and if you are a generalist, read the English Literature findings as well.  These are a topic for another time.

Poverty and Educational Attainment, Part II

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Poverty and Educational Attainment, Part II

In Part II, I’ll continue my commentary on poverty as the elephant in the educational reform movement.  Read my first post, Part I, here.  Once again, I am reading from the May issue of Educational Leadership.  Susan B Neuman, an education professor from the University of Michigan, reports on a 10-year study she and colleagues conducted which compared two neighborhoods in Philadelphia.  One, Kensington, is 90 percent poor, multiethnic, with a 29 percent unemployment rate.  Chestnut Hill, on the other hand, is gentrified, 80 percent white and 20 percent black, with parents who tend to be educated professionals, surrounded by parks “and … somewhat geographically isolated from the rest of the city.”

Over the 10 years of the study, the researchers examined how these disparities contributed to reading and ‘the development of information capital.  They noted three important differences they suggest are related to the economic disparities of the neighborhoods, the families, the community resources, and the schools.  These differences are print resources, adult supports, and independent reading.

In Chestnut Hill, there are multiple sources available to parents selecting a book for their children, with thousands of books, magazines and comic book titles.  Kensington, in contrast, had a small fraction of that number.  Neuman reports 13 titles per child on one hand, and just 1 per child on the other.  Tellingly, schools in Chestnut Hill had a wide assortment for children while Kensington has a limited and “merely adequate” selection.  The libraries in the former had twice the titles as the libraries in the latter.

The adult supports were also noticeable different.  Observing differences among the public libraries of the two communities, the researchers noted that in Chestnut Hill, children were read to by adults for 4 minutes of every hour observed, with adults recommending and guiding book selection.  In Kensington, “not one adult entered the preschool area…”  The observers estimated hat Chestnut Hill children “heard 14 times the number of words read in print per library visit as” their counterparts across town.  As background to this analysis, Neuman cites the research of Annett Lareau (2003), in Unequal Childhoods, (Berkeley: University of California Press).  This work describes differences in parenting styles between working class and middle class families.

In describing the differences in independent reading, the researchers focused on children ages 10-13.  Once again, they recorded what students were reading at the library, the grade level of the text, and whether it as informational or entertainment.  They also examined similar elements of student computer use at the libraries.  They found that only 58 percent of Kensington students were reading at grade level, and frequently the texts were designed for younger children.  In Chestnut Hill, 93 percent of students read at grade level and 7 percent were reading at higher levels.  Differences in time spent were also notable, and Kensington children also spent the majority of time reading for entertainment.  The same patterns were observed on the computers.  “In fact, {Chestnut Hill] students spent about 12 times the amount of time on informational reading materials in print and about 5 times more on informational websites than they spent on entertainment content…”

What are the consequences of these differences?  One significant difference is the well-known vocabulary differences that are found when comparing low-income children with middle and upper class children at virtually any grade level.  These late affect the accumulation of academic content–when children do not have the vocabulary to delve into grade level or increasingly complex text, they will remain at a significant advantage their entire school careers.  No amount of good teaching, by itself, can overcome these kinds of class-based disadvantages on a consistent, scalable basis.

Neuman offers four suggestions.  First, un-level the playing field by providing educations resources in low income schools that match those available in middle-class communities.  This is a major task–it really means extra funding for resources and for additional adult services in poor schools, going well beyond Title I.  Second, she notes that strengthening parent involvement by providing programs to help parents by teaching them about “skills and strategies children will need to be successful in school.”  Such programs are often suggested but simply are too rare so far to make a real difference.  Third, she suggests “people underestimate the capabilities of students who live in poor neighborhoods.”  This isn’t at all controversial, and is the basis for the notion that simply by staffing schools with brilliant and highly successful teachers, the problems of urban poverty and educational low performance will disappear.  Fourth, and likely far to idealistic, she suggests economically integrating schools, and cites research suggesting that such efforts can help to equalize the resources, improve school stability, decrease discipline problems and increase volunteer support in schools.

If these notions pique your interest, read the next article by Eric Jensen, entitled “How Poverty Affects Classroom Engagement.”  Eric is the author of two ASCD books:  Engagement with Poverty in Mind, 2013, and Teaching with Poverty in Mind, 2009.  He offers seven ways in which children of poverty struggle with engagement:  Health and nutrition; vocabulary; effort; hope and the growth mind-set; cognition; relationships; and distress.  He has multiple citations to the research suggesting these seven concerns, with suggestions on what a teacher can do.

When we hear President Obama supporting universal preschool, it’s an encouraging to think that at least a few politicians are thinking about how to address obvious gaps between the haves and the rest of American society.  The American Dream and upward mobility are hitting a wall of unequal opportunity that has grown higher and higher for the last 40 years.  Without breaking down this wall, or building steps by which the poor can climb the wall, the Dream will fade to dark.  And the major movers of education reform are simply paying no attention to such realities

Do get a copy of the May 2013 Educational Leadership.  It’s the best issue I’ve read in several years, and poverty is the most important and most neglected issue in American education today.

Poverty and Educational Attainment, Part I

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In recent week, several excellent publications have crossed my desk or shown up on the Internet resources I read regularly. In this first of several postings on poverty and it’s effect on educational attainment, I’ll continue to build on one of my regular themes in this blog–that the effects of poverty on children are the elephant in the education reform movement. Everyone knows poverty impedes learning, but the well-know reform leaders, ostrich-like, refuse to confront the realities that researchers have elucidated again and again.

The Income-Achievement Gap

The theme of the May issue of Educational Leadership is “Faces of Poverty.” I think this issue is among the best I’ve ever read, and is particularly important to those of us who are concerned that this fundamental impediment to educational progress is being overlooked or intentionally ignored.  If you don’t subscribe already, you can purchase this issue for $7.00 on the ASCD website.  The first article is entitled “The Widening Income-Achievement Gap,” from Sean Reardon. Sean has looked at 50 years of data on the relationship between achievement and family income, using data from 12 national studies in which the achievement measures were standardized reading or math tests.

The Income Achievement Gap is Growing

Reardon points out that in the 60’s the income achievement gap between the 90th and 10th income percentiles was 0.9 standard deviations on standardized test scores. Today it’s 1.25 standard deviations. Over the same period, the black-white achievement gap has gone in the opposite direction–from nearly 1.25 SDs to about 0.6 SDs. This, he suggests, represents considerable success within schools in addressing racial equality, but highlights the problems that increasing economic stratification has created. The income achievement gap is growing across all racial populations is now at an all-time high in American life.

Furthermore, these income gaps are showing up in other measures of educational attainment such as college completion rates, enrollment at selective colleges, and participation in ‘soft skills’ like sports, clubs, and participation in extracurricular activities and community life.

The Gap Starts Early and Continues Through School

Gaps are observable in early childhood and kindergarten programs, and as students progress into higher grades, the gap continues. It grows slowly, but not significantly, and Reardon suggests this demonstrates that the cause of the gap is not unequal school quality (emphasis Reardon). Further analysis of the data suggests the gap actually closes during the school year and widens in the summer.

Increased Economic Stratification

Several changes in American society are suggested as causes of the gap. In the 50’s, families at the 90th percentile of income earned 5 time that of families at the 10th percentile. Today that gap is 11 times. Upward social mobility has also decreased as middle class jobs have disappeared. Today, upward mobility in the US is lower than in almost every other developed country of the world.

High income families usually have two parent caregivers supporting their children and providing resources for their success. Low income families are far more likely to be headed by single women with low educational attainment.

At the extremes of family income, between 1977 and 2007, the income of families at the 90th percentile increased 90 percent, while families in the bottom 20th percentile saw increases of only 7 percent, falling farther and farther behind every year. (Duncan and Murnane, (Eds.), 2011, Whither Opportunity?, New York, Russell Sage Foundation.)

College and Career Ready as the Measure of Achievement

Today, we are laboring under increasing pressure to get children ‘college and career’ ready, with educational programs that claim to be designed to prepare kids to continue in higher education after high school completion. One can question whether new standards appropriately reflect career readiness, unless the career required academic training–we do an abysmal job of meeting the needs of young adults who want to learn a trade. Much of society has gone along with the notion that success in life requires an advanced college program of some kind, of 2 years or more.

With the decline of formerly middle class jobs, overall generic data suggests that many of the employment sectors that are expanding, and that pay middle class wages, require higher educational levels, thus justifying the push toward college standards. This ignores the kinds of jobs that keep the backbone of the nation running. The national infrastructure continues to erode, and the vast majority of construction jobs don’t require college level training. So too, many manufacturing jobs–assembly lines in the auto industry have a few highly skilled tasks, but most are not. In general, the construction trades are not technical jobs either. And we rely on low-skill jobs for our day to day operations–retail sales, care of the elderly, clerical work, … the list goes on and on.

As a nation, we are very close to defining college ready as the only measure that counts. This is short-sighted, and indirectly suggests that certain employment opportunities will increasing be filled only by the children of the bottom 20%, who simply, overall, do not have the resources to thrive in a society with an ever-increasing income opportunity gap.

Neuroscience Nonsense

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Yes, that’s an in-your-face title, but having written previously about how education isn’t particularly good at using research, but is good at jumping at fads, here are two links that illustrate the misuse of research in education.

Sarah Sparks writes a blog for Ed Week which I don’t regularly read, but after running into this entry I think I’m going to subscribe.  On August 11, she wrote “Making a Mountain of an Educational Neuroscience Molehill,” in which she links to a Nature journal article that takes a critical look at the hype surrounding several educational applications of neuroscience clamining to improve student performance.  The article, “Power failure: why small sample size undermines the the reliability of neuroscience,” offers a somewhat statistically dense explanation of why many of the reported positive effects of various neuroscience educational applications are of questionable value: They come from studies with too few students/cases to be reliable.  This means they can’t be replicated with any regularity, and the likelihood that the results are actually true is not very high.  

Over the years, education has been peppered with a wide range of proposals to improve student performance based on weak research followed by someone’s feel-good suggestions about how our brains work.  Sparks notes the left-brain/right-brain research in her article.  This is among the most popular fallacious notions about learning approaches, very popular among educators, the subject of many books, and unsupported by well-designed neurological research.  Another notion that feels good and sounds good to teachers is learning style research, which suggests that we have to identify a preferred learning style for children in order to design instruction that will be effective for them.  This too, is unsupported by carefully designed research, and might have even more books written about how to implement learning styles than the right-brain/left-brain theories.

That learning styles is unsupported is a shocker to me: It just feels like it makes sense to me.  My doctoral dissertation research was heavily invested in Myers-Briggs type, and my early research looked into several variations of learning styles and communication styles and how they might influence administrative behaviors.  It seems to me that I can identify students from my 20+ years in the classroom that responded differently to changes in my teaching style.  That children can learn in many ways is clear.  That they respond differently to different teachers is also clear.  That this has to do with learning styles is not, in hard-core research terms, demonstrable.

Another ‘movement’ that was going to help our low achievers blossom was the effort to reinforce positive self-esteem among all students, including the low achievers.  Praise, praise, praise.  Always find something to praise even when results were dreadful.  Praise effort over results.  Most good teachers, fortunately, had a hard time doing that, because they knew that low-performing kids understood clearly that they didn’t get it and the praise was artificial.  Fortunately, enough good research evolved over time that I think this sugar-coating of low performance is no longer in vogue.  Kids benefit from successful learning experiences for which they deserve praise, not praise for performance they know is mediocre.

What does this mean in practice?  Many things, I think.  First, while we would like to see education as a science that can be nailed down with research-based explanations for everything so we can teach everyone how to do it, unfortunately it’s not all that easy.  I believe in research to attempt to understand want works, but I also believe that we have to pay attention to research that debunks the ‘innovations’ we emotionally adore.

Many educators want to say that teaching is an art, not a science.  I’m not one of them–there is a lot of science to teaching well.  We know a lot about what works.  Most teachers should be able to use that science to improve their teaching.  That some teachers can take the science of what works and do considerably better than average is where the artistry comes in.  I think it’s an interpersonal talent–an ability for a teacher to connect to students more completely or more consistently than other teachers.  Every teacher can connect with a few students every year: Some teachers connect with more than others.  A few teachers are magicians with kids.  We haven’t figured out the magic yet.  If we ever do, it will transform education.