Algebra II Revisited

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  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 I

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.

Why the Opposition to Testing and the Common Core?

I spent the last 20 years of my career dealing with data as a means to improve instruction, and I coached lots of people about how to make sense of data, standardized and local, as a useful component of daily instruction.  As teachers or administrators, we can’t know what our students have mastered without good tests, whether they are formative tests that are not graded, unit tests, interim benchmark tests, or standardized accountability tests.  In my own state of New York, there is a rising movement among some parents, some of whom are teachers, to opt-out of state NCLB tests.  Opposition to ‘national’ testing and the Common Core is growing in other states, supported by various groups who are concerned about increasing federal influence on local educational policies, costs, the misuse of tests for purposes other that what they were designed to do.

The two national testing consortia are talking about designing the tests to improve their utility as vehicles for instructional improvement, but whether these goals will be a part of the basic package of new tests or available at additional cost to local districts remains a bit fuzzy.  States are beginning to question the cost benefit analytics of the programs–both consortia are designing online testing while many school districts, including the low income districts that have always been the targets of the accountability movement, are going to struggle with paying for the Internet infrastructure and hardware required to support online testing.

So in broad terms, the growing opposition to the Common Core and the national testing programs represent multiple issues of concern to a growing variety of stakeholders, and they overlap significantly, making this a very complex situation.  Let’s review some of them here.

1.  Use of data for instructional improvement.  In New York, where at one time all state sponsored tests were released publicly after testing was complete, we could use the results for instructional improvement planning.  We had specific information about how the questions aligned to standards, we could see the question, and we had a p-value which told us how difficult the item was state-wide.  This was very useful for teachers, but that’s gone now that NCLB tests are secure.  Without seeing the questions, the rest of the information (how I did compared to anyone/everyone else) provides very poor instructional information.  I can still see whether I did well or poorly on a particular performance indicator, but I don’t have decent details about exactly what my kids have missed and I have to guess about why.  If I am in a district that has purchased commercial assessments that give me access to the questions, I have this capability during the school year, but many publishers tests are also secure and I have to rely on a generic description of academic trends that isn’t particularly useful.  I get far more information on what a student’s weaknesses are when I can review the test question and analyze the wrong answer responses as I want to plan interventions.

2.  Purpose of the tests.  Critics of NCLB testing write about this regularly.  The tests were not designed for either instructional improvement or teacher evaluation.  They have been co-opted by politicians and businessmen as a means to promote agendas other than school improvement.  Psychometricians who are not involved in developing or marketing these tests have written extensively about their concerns when they are used for high stakes teacher evaluation, or for determining student placement.  We don’t do the latter in NY, as far as I know, though there have been some examples of placement consequences for kids–it’s a local issue.  But in other states, testing occasionally has greater impact–promotion or retention, acceptance in accelerated programs or placement in remediation–based on results.  Often the uses of results doesn’t match the psychometric properties of the tests, which is problematic.  And in New York, where the state says it’s own tests count only for 20 of 100 points in a teacher evaluation, the rubric for the 100 points actually creates situations in which the 20 points on the state test can actually override the other 80 points.  This means everything about New York’s intricate evaluation systems can be blown away by a weak performance on the state 20% measure, meaning this 20% can, for some teachers, amount to the only measure of teacher quality that counts.

3.  Lack of transparency.  I hope this issue will go away with time.  It’s rather difficult to get information about the actual behavior of state tests–how did the results break out by student sub group?  By district demographics?  By years of teacher experience?  By class size?  By SES factors?  How did low income kids do in a district where they are 6% of the population compared to a big city, where they are a majority?

Moreover, everyone involved in rolling out new teacher assessments and new academic goals of the Common Core has been overworked and hard pressed to clarify what is coming.  As we heard repeatedly from the highest levels of New York State Education officials early on, these changes are like an airplane which is being constructed during flight.  Sadly, this is about the closest thing to  transparency I can think of early in the process–there wasn’t much more to be said.  They didn’t know how to get from where they started to the intended goal.

The proper answer to such comments from school boards and the public was often something like this:  “Where is the FAA?  Who approved the takeoff of this untested aircraft in the first place?  There’s too much being done here with no piloting, no research, no shakedown flights. But this concern was shoved under the rug.  New York adopted these changes to get $700 million of federal funds over 4 years, which was less than a half a percent of the per pupil spending on public education in the state.

And this is not just a New York issue, it’s national.  We don’t usually do this kind of take-off in other arenas, but it happens too often in education.  Let’s try the next new idea that some expert says is the solution to our problems, while we ignore the fact that it’s an untested and unproven program or methodology.  Did we know the Common Core was a singular organizational initiative from an educational think tank hired by the Council of Chief State School Officers which has, in effect unilaterally influenced the direction of public education?  Would truly empowered state education officials around the nation have adopted something this massive and unproven if they were not required to do so by other political forces, or if substantial federal funding during an economic downturn didn’t bribe them into agreement with Race to the Top conditions?  Would the public have found this a good use of funds if it were clear that there’s no evidence it would work?

4.  New teacher and principal evaluation systems.  A few districts in my region of New York who closely monitor new evaluation regulations are concerned about how honors class teachers did–they have all the high performing kids, and they think their special ed teachers got higher evaluation growth scores in their state testing measures because a point or two of improvement at the lowest level of performance is easier to get than increases among students already at the top.  This is one of the general criticisms of accountability programs that use any version of growth or value-added scoring.  From state to state, have the data been made available to independent researchers for an objective review? Do we have multivariate analyses available to look deeply at the results?  If not, why not, or when will this happen?  And if we do, so what?  Most states are about to change their tests again, from what they have been using to the new PARCC or Smarter Balanced consortia tests under development.  So the nature of available data is changing from last year, before the Common Core curriculum implementation, to Common Core based testing, and then in two years, to tests from one of the two consortia.  This fundamentally means three versions of accountability tests in as few as 4 years in many states, making comparisons of student achievement a statistical challenge for accountability purposes, to say the least.

5.  Narrowing of the curriculum.  How many fewer art, music, drama, etc. classes are gone, and replaced by supports for ELA and math?  Why does the edu/politico establishment ignore the evidence about the utility of arts and music education and their connection to math and science success?   How many kids have no more recess because they are scheduled for support time?  How many schools have dropped career education options in high schools?  How have the fiscal pressures of the past few years forced districts to make narrowing curricular decisions because of the fear of poor test results?  Is the focus on ELA and math appropriate for all students?

6.  What is college and career ready, anyway?  In the Atlantic Monthly of October 2012, Dana Goldstein wrote an important feature called “The Schoolmaster” about David Coleman, credited by many as the leading creator of the Common Core State Standards.  A nonprofit Coleman founded, Student Achievement Partners, provided the intellectual basis to the Council of Chief State School Officers. If Goldstein’s work is as accurate as it feels, he is far more important than our Secretary of Eduction.  He clearly has had more influence on the direction of US education than any other single individual, likely in our history.  And he’s now the head of the College Board, where his concepts of college and career readiness could transform the nature of SAT tests in the near future.

I happen to agree with the concept of Common Core State Standards, and I think their emphasis on critical thinking skills are long overdue, but defining success with a narrowly defined concept of college and career reading misses some important options for a substantial population of students.  Many educators think this focus rather significantly neglects the notion of career ready–we have been eliminating career and tech education all over, or transforming it into expensive tech honors programs at regional BOCES or Intermediate School or Educational Service Agency  locations as career education begins to emphasize forensics and high tech.  So where will we get our plumbers and carpenters and cabinet makers and auto mechanics and house painters and landscape gardeners?

7.  Local control of education.  Here’s the philosophical issue of the day: Should states/local school districts have virtually given up their role in determining the direction of their children’s education?  Constitutionally, this is a state role (which all but one state, Hawaii, turn over largely to local school boards) and not a federal one.  Though the Common Core is an initiative of states working together, it was not an initiative that involved local professional educators from the beginning.  It was an initiative farmed out to Coleman’s nonprofit business, pushed by the business/political wing of K-12 reformers, gained support from those concerned about the generic failures in urban centers across the country, and then offered as fundamentally a take it or leave federal money on the table proposition to the educational establishment throughout the nation.  The claim that all the states were directly involved in these plans is technically correct, but practically speaking the results were top down impositions, not bottom up reforms.

8.  Lack of funds for professional development.  In New York, teacher and principal evaluation rules mandate districts to provide professional development for teachers in order to be able to terminate them.  Given that schools have to upgrade/update technology infrastructure and hardware to prepare for online testing, and given a new state property tax cap, and given that increasing numbers of districts around New York are facing real economic stress and even bankruptcy, there won’t be any money to provide PD for low performing teachers.  Even a mediocre lawyer can prevent the termination of a teacher because the district’s responsibility for support to a weak teacher will be missing.  So who thought this was a good idea?

Many states claim their test results will be used to guide professional development programs to improve the work of teachers.  However, it’s typical to observe the decline in funding for educational professional development nationwide.  Schools are spending the money on assessments, not on professional development, and the tests themselves, as noted earlier, are both secured and not designed for teacher use to promote instructional objectives.  So two forces disconnect assessments from teacher improvement–funding and inappropriate test design.

Nationally, the movement to tie teacher evaluations to test scores was fueled significantly by Federal Race to the Top eligibility requirements.  This is another ‘reform’ initiative fueled without a quality research base of support.  Proponents of testing, and those wanting to pry public money out of the hands of school boards so that it’s available to alternate commercial programs have jumped on the novel idea that one can appropriately predict a student’s future success based on the scores of a teacher’s students.  The model is appealing, as it suggests an easy metric on which to judge the performance of schools and individual teachers.  But having followed the arguments closely for 10 years, it isn’t working particularly well anywhere.

Today, many groups are finally responding to some or all of these concerns by pushing back.  Some of the parent arguments arise out of fear for the well-being of their children, some out of frustration at loss of local control, some out of growing awareness of rising assessment costs and little demonstrable efficacy in using tests for instructional improvement.  Some opponents are teachers who are fearful of adverse consequences to themselves.  Academics, politicians and the occasional state education official are more openly questioning the speed of implementation, the lack of piloting, the unintended consequences, the public relations disasters in states where Common Core based testing produces a drop in test scores (teachers are not yet trained in the new curriculum objectives), and the mismatch between test design and the use of test scores.

Does the push-back accomplish much?  To date, not really.  Does it make a statement that might force politicians to take a second look at the unintended consequences of parental opposition?  The consequences of testing?  A real cost-benefit analysis of CCSS and national testing?  I personally hope it does, but I don’t think it will amount to much unless it continues to grow.  Get up to speed, and get involved!

The Algebra Proxy

In the last few years, Americans have been told repeatedly that we’re not internationally competitive because of our public schools.  We’re told that students are not college and career ready.  We’re told that Algebra is a key to being college and career ready, and the Common Core standards have pushed algebra into elementary grades, with substantially more material at the middle school level than most state curriculum models have included in the past.  Does this make sense?

Indicators of College Success

I spend several hours reviewing Google searches about the indicators of college success.  Indeed, from an educational research perspective, algebra is usually found to be the most significant high school course that is associated with college success.  If one adds other indicators, often the next most significant indicators are additional advanced math courses–Geometry, Algebra II, Trig and Calculus–the more a student completes, the more likely the student will be successful in college.

As an English and Social Studies educator who values the increased emphasis on critical thinking in the Common Core,  (see my Critical Thinking post here) this is inherently problematic to consider.  What’s going on?  Are math teachers so much better at getting kids ready for college than other teachers?  And how many of you are using Algebra in your everyday lives?  I suspect–excuse me, I know–that most adults could no longer pass a typical high school Algebra or graduation level math exam.  This assertion is regularly validated throughout the country every few years whenever reporters jump on a story about issues with high school examinations.  They get a sample test, give it to a few hundred folks, and report on how awful adult math skills are, even for college grads.

I took a strong high school program, went to a quality college, studied physics for a year before changing to English and the Humanities, and had a much better math academic training program than most adults.  I could not pass the current New York Algebra I Regents Exam within the allocated time.   Today, despite an earned Ph.D. and years of successful teaching and administration, I would have a significant chance of being labeled not ready for college and career based on scores I would earn on New York Regents exams in math and science.  There’s something amiss here.  I’ll do fine on the English and Social Studies exams: These represent the content I have used throughout my career.  I haven’t used much math, chemistry, biology, or physics, and while I still read the science section of the New York Times and understand the content, I’m glad it’s written for a general audience and not for science majors.

I think we need to consider the concept of proxies to understand the research results about algebra.  The nation is looking for a ‘quick and dirty’ way to make judgements about kids, and algebra is that way.  By a quick and dirty proxy, I mean we want a low-cost and easy to calculate measure that represents the concept of college and career readiness.  There’s something about success in high school math classes that suggests a student is ready to take on the increased challenges of life beyond grade 12.  Students who do well with advanced math classes (and for other researchers, Advanced Placement courses in general–the harder courses in high schools) do better in college.  (See p. 10 of “Moving Beyond AYP” and a good set of references here)  What underlying skills do successful math students have that correlate to the skills needed for successful college course-taking?  It’s not the math itself that is the key to college success–most students don’t go on to study math in college, so they didn’t need the math skills themselves–they needed the underlying skills for which math is a quick and dirty proxy.

There are many possible answers.  Here are a few I’ve interpreted from my scan of the research–you can add more from your own readings.  Math requires persistence from students: they often need to struggle to ‘get it.’  Math doesn’t come easily–there are problems to solve, and for many that’s hard work.  It requires a level of academic self-discipline to master.  There are right answers to the problems even when there are multiple pathways to arrive at the solutions, so results are clearly measurable and students can see where they stand.  It’s more concrete than literary analysis or historical interpretation, but there are still creative and abstract challenges in arriving at solutions, even though many folks think that because math has right answers, it’s a linear subject.

We need to look more carefully at this proxy for success.  What, exactly, are the skills kids need, and why can’t we build these skills into other high school, middle school and elementary school courses so that we open up college and career readiness to more students, and improve teaching the complex thinking college requires in all our subjects.

As I’ve said in another way in my blog on Critical Thinking, I believe that the emphasis on deep reading and analysis across nonfiction text that we find in the Common Core is the start of a pathway toward making all of our K-12 curriculum a preparation for success in college and careers.  It’s overdue. Those who teach other subjects (not math, and not the science courses that depend so much on math concepts) should be considering our roles in deepening the intellectual expectations we have for students.