# Solving America’s Math Problem

*Tailor instruction to the varying needs of the students*

In the 21st-century workplace, mathematical capability is a key determinant of productivity. College graduates who majored in subjects such as math, engineering, and the physical sciences earn an average of 19 percent more than those who specialized in other fields, according to the American Community Survey of 2009 and 2010. Precollegiate mathematical aptitude matters as well: math SAT scores predict higher earnings among adults, while verbal SAT scores do not.

These facts help explain our national focus on improving math performance. International comparisons made possible by standardized testing reveal just how American students lag behind their global peers (see “Are U.S. Students Ready to Compete?” *features*, Fall 2011). Judging the nation purely by its own historical performance yields the same conclusion. Between 1972 and 2011, real GDP per capita doubled in the U.S., but the average math SAT score of college-bound high-school seniors and the proportion of college graduates majoring in a mathematically intensive subject barely budged.

Concern about our students’ math achievement is nothing new, and debates about the mathematical training of our nation’s youth date back a century or more. In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the “new math” movement sought, unsuccessfully, to bring rigor to the masses, and subsequent egalitarian impulses led to new reforms that promised to improve the skills of lower-performing students. While reformers assumed that higher-performing students would not be harmed in the process, evidence suggests that the dramatic watering down of curricular standards since that time has made our top performers worse-off. Even promised improvements in the lower part of the distribution have at times proved elusive, a point illustrated below by the disappointing results of a recent initiative to accelerate algebra instruction in the Charlotte-Mecklenburg school district.

America’s lagging mathematics performance reflects a basic failure to understand the benefits of adapting the curriculum to meet the varying instructional needs of students. Recently published results from policies such as Chicago’s “double dose” of algebra, which groups students homogeneously and increases instructional time for lower-skilled math students (see “A Double Dose of Algebra,” *research*, Winter 2013), support differentiation as the best way to promote higher achievement among all students.

**Decades of Hand Wringing**

Figure 1 uses data from the American Community Survey of 2009 and 2010 to track a basic indicator of math proficiency over a 75-year span: the proportion of college graduates who majored in a math-intensive subject (math, statistics, engineering, or physical sciences) in each cohort. The sample is limited to male college graduates in order to address possible concerns about changing gender composition of the college-graduate population, although the figure looks similar if females are included.

Fluctuations in this indicator over time support a basic argument: American attempts to homogenize the math curriculum in secondary schools, although sometimes successful at improving the performance of the average student, have come at the cost of preparing the nation’s most promising students for mathematically intensive study.

At one point in time, 3 college graduates in 10 majored in a math-intensive subject. These cohorts grew up in an era when advanced math topics—algebra, geometry, and trigonometry—were considered “intellectual luxuries,” worthy of instruction to a select few, but of little to no relevance for the vast majority of the workforce. From the 1930s through the mid-1950s, educational practice codified these beliefs. Less than one-third of all high-school students enrolled in algebra, substantially fewer in geometry, and only 1 in 50 proceeded to trigonometry.

Among cohorts educated in the post–World War II era, there have been three distinct periods of decline in this measure of math performance. The first decline is modest and occurred very soon after World War II. Students graduating in the 1950s and early 1960s majored in math-intensive subjects less often than those graduating in the late 1940s. Trends in college completion, also shown in Figure 1, suggest that this early decline in math intensity corresponds with a run-up in college attendance and completion associated with the GI Bill. Given the restriction of advanced mathematical training to a select group of high school students in the first half of the century, it’s reasonable to think that the expansion of college access, presumably to less-prepared students, explains this first decline.

Expansion of access might explain a portion of the much larger decline occurring between 1962 and 1974. But the access and math-intensity trends don’t line up perfectly, and changes in enrollment and completion rates are not sufficiently large to explain the full decline in math intensity in these years.

If the admission of mathematically marginal students can’t explain this decline in math-intensive study, what can? One might hypothesize that math-intensive subjects are subject to “fads,” implying that college enrollment fluctuations have little to do with the underlying ability of students. The midcentury decline in math intensity, however, occurs at a time when math-intensive study should have enjoyed great popularity. The graduating class of 1974 commenced its formal education immediately following the Soviet launch of *Sputnik* in 1957, and graduated from high school shortly after the United States put a man on the moon. Nevertheless, this cohort chose math-intensive majors at roughly half the rate of classes from the 1940s.

The midcentury decline in math intensity coincides with the rise of the “new-math” movement. This movement to improve the math skills of average students was sparked in part by national security concerns. During World War II, many rank-and-file soldiers were unable to calculate the trajectory of artillery shells, among other things, in an era when hand computation in the field was still a necessity. The Cold War–era “arms race” and “space race” amplified calls to steer more American students toward math, science, and engineering. The new-math movement reflected a shift in curriculum design from professional educators to professional mathematicians. Where “old math” was pragmatic, focusing students’ efforts on tasks they were likely to perform in the course of their future careers, “new math” valued mastery of fundamental concepts, some of them quite abstract. It is during the new-math era, for example, that calculus was introduced as a high school subject, albeit only for a select group of students. Ironically, a curricular reform designed to introduce new rigor and bring higher-order subjects to more students in secondary school appears to have resulted in a strong movement away from math at the collegiate level.

Given that the substitution of rigor for practicality appears to have turned students off to math, it stands to reason that substitution in the reverse direction would undo the effect. And indeed, the wane of the new-math movement in the late 1960s and early 1970s might explain the resurgence of interest in math-intensive majors, the only such episode observed over a period of 75 years, among those graduating from college in the late 1970s and early 1980s.

The resurgence was short-lived. From the 1984 class onward, the proportion of college graduates completing math-intensive majors dropped steadily. This second major decline in math intensity reflects a second nationwide effort to improve the math performance of average students. The alarm bells sounded by the influential *A Nation At Risk* report in 1983 pointed not to the performance of the elite but rather to the prevalence of remedial education in colleges and universities. It lamented the fact that a small fraction of high school students managed to complete calculus, in spite of the fact that most attended a school that offered the course.

Six years after *A Nation At Risk*, the National Council of Teachers of Mathematics introduced new standards that favored calculators over pencil-and-paper computations, cooperative work over direct instruction, and intuition over solution algorithms. Educational rhetoric of the “No Child Left Behind” era has continued to prioritize the performance of average or even below-average students. The proficiency standards mandated by the No Child Left Behind Act impose sanctions on schools that fail to serve their worst-performing students, but enact no penalty on schools that accomplish this goal by shifting resources away from their top performers. Studies have verified the predictable consequence: gains to students just below the proficiency level have in some settings been offset by losses among more-advanced students.

**No Improvement in High School**

Evidence from the National Assessment of Educational Progress (NAEP) provides further indication that curricular reforms have improved performance in basic subjects without providing a stronger foundation for more advanced study. Successive waves of testing show that students born in 1981, for example, outperformed the 1977 birth cohort at ages 9 and 13, but had lost their advantage by the time they reached 17. The performance of American 15-year-olds on the Programme for International Student Assessment (PISA) exam in 2000 and 2009 confirms the lack of progress among secondary school students. The United States is among those countries whose math performance worsened over this time period. American students also fell behind those from several other countries: Luxembourg, Hungary, Poland, and Germany. International comparisons focused on younger students, such as the Trends in International Mathematics and Science Study (TIMSS), however, show more signs of progress in the United States relative to other nations.

This evidence of stagnation among secondary school students seems at odds with statistics on the math course–taking patterns of American students. In the mid-1980s, about one student in six took Algebra I in middle school. In more recent years, the national average has been closer to one-third, a doubling over the course of a generation. In some areas, including California and the District of Columbia, the majority of students take Algebra I as 8th graders.

How can students simultaneously proceed to advanced coursework earlier and perform no better on national and international assessments? Figure 2 yields some insight by listing the tables of contents for two introductory algebra textbooks: George Chrystal’s fifth edition, published in 1904, and *Algebra 1*, published by Prentice Hall exactly one century later. While there are similarities in the curricula outlined by these books—both, for example, cover quadratic equations late in the manuscript—the early book covered many more topics in greater detail. There is no mention of series in the later book, nor logarithms, interest and annuities, complex numbers, or exponential functions beyond the quadratic. Ironically, the only topic covered in greater detail in the 2004 textbook is inequality—of the mathematical variety.

A distaste for inequality has clearly motivated mathematics curricular reforms over the past quarter century. While the intent of equality-minded reforms is to boost low-performing students, in the case of American mathematics achievement, decline among higher-performing students has been part of the bargain. Furthermore, results from Charlotte’s algebra acceleration initiative indicate that an unthinking pursuit of equality can in fact harm all students, not just those at the top.

**The Charlotte-Mecklenburg Algebra Initiative**

This section summarizes research I undertook with Duke University colleagues Charles Clotfelter and Helen Ladd. The complete report, available as a working paper from the National Bureau of Economic Research, studies the impact of an algebra acceleration initiative in one of North Carolina’s largest school districts.

North Carolina’s Charlotte-Mecklenburg School (CMS) district is generally regarded as a model education agency. It serves more than 100,000 students, ranking among the 30 largest in the United States. Among the 18 large school districts identified in 2009 NAEP assessment results, CMS ranked first in 4th-grade math performance, the only large district to post scores exceeding the national average. The district covers an entire county, incorporating both urban and suburban communities. While it is more affluent than most large districts in its NAEP peer group, it has a higher student poverty rate than North Carolina as a whole. A majority of students in the district are either black or Hispanic.

A decade ago, CMS superintendent Eric Smith instructed middle school principals to enroll a larger proportion of students in Algebra I, the first course in the state’s college-preparatory high-school sequence. He told PBS that middle school math is “the definition of what the rest of the child’s life is going to look like academically.” His goal was to “make sure that kids were given that kind of access to upper-level math in middle school.”

Figure 3 documents the impact of the policy initiative, using administrative data on CMS students from the North Carolina Education Research Data Center. It divides students into five groups of roughly equal size (quintiles), based on their performance on the state’s end-of-grade math assessment as 6th graders. Students are further divided into five age cohorts.

Students whose 6th-grade test scores place them in the top quintile of the distribution are consistently likely to take Algebra I by 8th grade. For students closer to the middle of the 6th-grade distribution, however, Algebra I enrollment rates varied considerably across cohorts. In the cohort entering 7th grade in 2000–01, about half of moderately performing students (those between the 40th and 60th percentile) took Algebra I as 8th graders; low-performing students in the same cohort had virtually no chance of taking algebra in middle school.

Over the next two years, the effect of Smith’s algebra policy can be readily observed. Moderately performing students in the 2002–03 7th-grade cohort had an 85 percent chance of taking Algebra I as 8th graders; even the lowest-performing students had a one-in-six chance.

Just as quickly as the policy was introduced, a return to the status quo appears in the data. The cohort of students entering 7th grade in 2004–05 took Algebra I in 8th grade at rates similar to or even lower than their counterparts in the first cohort. One might conclude from the rapid reversal that the policy did not lead to the anticipated effects. We’ll present the evidence on that score momentarily.

Smith’s initiative was inspired by basic observational evidence. In the United States, as elsewhere, students observed taking advanced courses at an early age tend to accomplish more later in life. In a later interview, Smith cited evidence documenting higher rates of AP course completion and better SAT scores among students who had taken Algebra I by 8th grade. But to infer from this that early entry benefits students, one must assume that the students in the advanced courses were no different from their counterparts, on average, before taking the course. This assumption is clearly misguided. As Figure 3 shows, those who in 2000 had the highest math scores in 6th grade (the top two quintiles) were much more likely than those with lower scores to take Algebra I by 8th grade. While it is theoretically possible that early progression to advanced coursework compounds this advantage, empirically it is very difficult to disentangle this benefit from the profound baseline differences between early and late algebra takers.

The CMS policy initiative provides a rare opportunity to perform this disentangling. Moderately performing students born just two years apart were subjected to radically different algebra placement policies. Were students in the accelerated cohort more likely to perform well in Algebra I? In the standard follow-up courses of Geometry and Algebra II? Figure 4 summarizes the evidence, which is based on student performance on North Carolina’s standardized end-of-course tests in the three subjects. The analysis on which the figure is based isolates the impact of Algebra I acceleration by comparing the performance of otherwise identical students who were subject to different placement policies by virtue of belonging to different age cohorts.

Students perform significantly worse on the state’s Algebra I end-of-course test when they take the course earlier in their career. The decline in performance is approximately one-third of a standard deviation, or 13 percentile points for an average student. The course material forgone in the acceleration process, plus the additional maturity that comes with a year of age, contribute positively to Algebra I performance.

The decline in end-of-course test performance implies that students’ risk of failing the course increase when they are accelerated. One could adopt a relatively sanguine view, arguing that accelerated students who have to retake the course ultimately aren’t any worse-off than those who weren’t accelerated in the first place. And the second effect shown in Figure 4 supports this view, showing that in spite of their worse performance, accelerated students actually become a bit more likely to pass the course on a college-preparatory schedule, that is, no later than their 10th-grade year. For most of these students, the acceleration provided three chances to pass the course rather than two.

It’s a different story when we consider the next outcome: whether students manage to pass the state’s end-of-course test in geometry by the end of their 11th-grade year. Accelerated students were 10 percentage points less likely to meet this threshold, in spite of the fact that acceleration gave them two chances, rather than one, to retake a course in the event they did not receive a passing grade.

By forgoing a year of prealgebraic math, students miss an opportunity to receive some instruction in fundamental topics underlying geometry. Although certain topics in geometry flow naturally from algebra—translating an equation with two unknowns into a line in a two-dimensional plane, for example—there are others that do not. In North Carolina’s standard curriculum, geometry incorporates emphasis on area and volume calculations, trigonometric functions, and proof writing, topic areas with zero coverage in the standard Algebra I curriculum.

To complete the college-preparatory curriculum in North Carolina, students must at a minimum pass the set of courses culminating in Algebra II. Accelerated students were neither more nor less likely to clear this hurdle by the time they would ordinarily complete 12th grade. The data show that many accelerated students who passed Algebra II did so without ever passing Geometry, implying that they had not completed the full college-preparatory math sequence. The struggles of accelerated students undoubtedly explain why CMS so rapidly reversed course, returning to its initial placement policy after only two years of acceleration.

**Policy Implications**

American public schools have made a clear trade-off over the past few decades. With the twin goals of improving the math performance of the average student and promoting equality, it has made the curriculum more accessible. The drawback to exclusive use of this more accessible curriculum can be observed among the nation’s top-performing students, who are either less willing or less able than their predecessors or their high-achieving global peers to follow the career paths in math, science, and engineering that are the key to innovation and job creation. In the name of preparing more of the workforce to take those jobs, we have harmed the skills of those who might have created them. Although there is some evidence of a payoff from this sacrifice, in the form of marginally better performance among average students, some of the strategies used to help these students have in fact backfired.

To some extent, the nation has reduced the costs of this movement through immigration. Foreign students account for more than half of all doctorate recipients in science and engineering, two-thirds of those in engineering. Many of these degree recipients leave the country when they finish, however, limiting their potential benefit to native-born Americans. Immigration policy reform that emphasizes skills over traditional family reunification criteria, much like the policies in place in Australia, Canada, and other developed nations, could change this pattern.

A second possible policy option would be to implement a curricular reform more radical than tinkering with the timing of already existing courses. Many schools have adopted the so-called “Singapore math” model, which emphasizes in-depth coverage of a limited set of topics. There are concerns, however, regarding whether a curriculum developed in a different cultural and educational context could produce similar results here. Singapore’s public schools, for example, use a year-round calendar, obviating the need to review basic subjects after a summer spent out of the classroom. Evidence also indicates that Singapore’s teachers have a firmer grasp of math than their American counterparts.

The United States need not import its science and engineering innovators, however. It need not borrow a faddish curriculum from a foreign context. And it need not sacrifice the math achievement of the average student in order to cater to superstars. It need only recognize that equalizing the curriculum for all students cannot be accomplished without imposing significant lifelong costs on some and perhaps all students.

Curricular differentiation might, for its part, exacerbate test-score gaps between moderate and high performers, if high performers move ahead more quickly. A narrow-minded focus on the magnitude of the gap, however, can lead to scenarios where the gap is closed primarily by worsening the performance of high-achieving students—bringing the top down—without raising the performance of low-achieving students. Society’s goal should be to improve the status of low-performing students in absolute terms, not just relative to that of their higher-performing peers. A growing body of evidence suggests that this type of improvement is best achieved by sorting students, even at a young age, into relatively homogenous groups, to better enable curricular specialization. Recent results from Chicago, cited above, provide evidence that differentiating the high school mathematics curriculum can have long-run benefits, even for students assigned to remedial coursework.

Not all children are equally prepared to embark on a rigorous math curriculum on the first day of kindergarten, and there are no realistic policy alternatives to change this simple fact. Rather than wish differences among students away, a rational policy for the 21st century will respond to those variations, tailoring lessons to children’s needs. This strategy promises to provide the next generation of prospective scientists and engineers with the training they need to create jobs, and the next generation of workers with the skills they need to qualify for them.

*Jacob Vigdor is professor of public policy and economics at Duke University.*

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I’m not sure if I am understanding the first graph correctly. By the graph it looks like a big drop in Math majors in the late 60s and early 70s compared to say 1944. However, it appears that the dotted red line is a subset of the number reflected in the blue line. If you consider the much larger percentage of the population that got a four year degree in the late 60s, it seems that the total percentage of the population that graduated in Math in 1944 vs 1969 might be a steady 7 to 8 %. Not sure that matters because hopefully Math majors are growing, but the graph makes it look like a large drop in Math majors when actually it seems there was just a large increase in graduates in other areas.

Makes sense. Thanks for the thought-filled article.

There’s no disagreement that some kids are smarter than others. Most people know that you can’t just set a standard (like algebra in 8th grade) and do nothing else. But Vigdor overlooks overlooks that issue and then claims that the failed initiative defines some IQ/algebra correlation. There are many other variables to consider–which he doesn’t.

The “Math Wars” are about curriculum and teaching methods, but this article skips over that analysis. Most schools separate kids starting in 7th grade. In affluent areas, since “enough” students get onto the top math track in high school, (often due to tutors, learning centers, or help from parents), educators will not look for any fundamental issues in K-6. They only assume that it’s a relative problem.

Why not interview parents to see what is done (or not) at home and try to find out how the best students got there? There may see an IQ connection, but it’s not that simple. There are things one can do to separate the variables. But too many authors of the recent spate of articles about math, algebra and its need, either can’t or won’t.

In his report, he pooh poohs the idea of introducing Singapore Math into classrooms, citing the usual cultural differences argument which is specious. (Teachers in Singapore have better math background; students go to school all year round, so there’s no forgetting concepts during the summer; the culture promotes education and hard work, etc). He neglects the fact that Singapore’s texts present the material clearly and succinctly and that there have been successes in schools in the US that have used it).

At the elementary level, the second to last paragraph is absolutely what I have seen and almost been explicitly told to carry out: Forget the advanced kids and focus on almost proficient kids and basic scoring kids. It’s all about closing the achievement gap in Anne Arundel County, MD (Eric J. Smith went there after CMS). Homogeneous grouping is not an option – you must have a class with completely mixed abilities and teach math in mini-lessons dividing your class into 3-5 small groups. That, of course, is homogeneous grouping but in a more PC fashion and also at the expense of good practice as teachers and disregarding the amount of time it takes to do such planning.

But it isn’t as if the focus on “almost proficient” and “basic scoring” kids is actually effective. Using sub-par programs like Everyday Math, and Investigations in Number, Data and Space does neither group any good. The thinking is that advanced students will do well no matter what, and therefore don’t need to be challenged. At the same time, the non-gifted group is held to very low expectations. This has a number of bad effects. One is that the resulting instruction is ineffective and poorer performing students who might have had a chance to be prepared for algebra are not. Another is that with proper instruction and a good program, some students may qualify as “advanced”.

Chrystal’s Algebra is divided into two volumes. Inequalities are covered in the second book, as you can see http://goo.gl/WRsv4. The article only mentions the first book, which is actually much less interesting. The second book is rather extraordinary — not only does it contain material appropriate for an honors precalculus course (complex numbers, series, sequences, probability, permutations and combinations, limits), but it contains rarely covered subjects such as continued fractions, hyperbolic functions, and number theory. The second book is still used as a textbook for students studying for the International Mathematical Olympiad.

Very good essay and the comments are also instructive. One thing however-seperating ‘homogenious groups’ based on ability and aptitude is a tough row to hoe. First, the schools of equal outcomes-know as education departments-will have to dump Dewey and the ‘progressives’ who have lead to the decline in K-12 education-and who, unfortunatly, seem to be in the drivers seat. And then there are the diversity mavens-in California you have the CTA and they run the state. Equal outcomes, diversity and tolerance without judgement are their mantra and their bread and butter.

Dear Mathematics,

American children are just not that into you. No, it’s nothing you did; it’s just that Americans have no problem admitting and even relishing their mathematical incompetence. Why? It’s complicated but Hofstadter nailed it decades ago http://www.amazon.com/Anti-Intellectualism-American-Life-Richard-Hofstadter/dp/0394703170

Ignoring college deferments during the Vietnam War make the analysis of the big spike in enrollments for those graduating around 1974 completely bogus. College attendance for males in that era was largely driven by avoiding the draft, and many students chose easy subjects in order to ensure staying in college. The numbers here probably had nothing at all to do with math education at the time.

thank you, gasstationwithoutpumps. That’s a big blind spot we have. But then, Americans aren’t renowned for learning from their own history, scant as it is.

Well, I wonder if the cognoscenti who run this blog will care to comment…

I’m wondering what the criteria was for admitting students in each quintile into 8th grade algebra? Does the article discuss this? As a K-5 educator, I prefer envision math. It is conceptually challenging and helps students to explain their thinking. My personal belief is that american students do not study as much as their overseas counterparts.

Another situation is where they have the students skip the Pre-Algebra class because the students are above average (but not in the gifted group). My son is now taking Algebra I in 7th grade at his charter school because it had two classes to fill. He is only successful because I have to really push him and help him a lot. He may spend up to 2 hours on his math homework per day which cuts into the time he can spend on the other 5 subjects. He is somewhat disillusioned with math already and has asked if it gets easier. The schools need to take emotional maturity into the equation so the student understands why math is so important in the long run. Most of his friends are doing fairly poorly versus the 6th grade scores.

My experience is that the reason that children who have to wait to take Integrated Algebra One in 9th do better as a group than those who take the course in 8th is simply because they have a better background in arithmetic and mathematical thinking than those whose influential parents got them the seat in the ‘honors’ course and a tutor to go with it. The school of course aided the effort by giving a lot of extra credit to the ‘honors’ students as well as having the teachers grade the eighth graders on a curve….no such grade-boosters are made available to nonhonors students. The same results are seen in SAT math scores.

As a nation, we need more honors seats available for the talented. Right now, home schooling and talent search providers are the options of choice, since school districts refuse to open sufficient seats.

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i have three children, all engineers. Why? because my husband and i made math and science,and their education in general, a priority in the home. card games, board games, discussions about savings and investing and their direct experience with these concepts, cost, tax percentages in retail purchases. And, while their teachers both public and private schools wanted to “dumb down” their math–i made sure that they checked their math– subtraction and division, plugged back in the answers to the original equation to ascertain correct answers and any math work whether class work or test that came home without a “check” or without showing their work in logical sequence was done in our home and returned to the teacher–not for a change in grade but to let the teacher know that higher math standards were normal operating procedures in our home. My husband and I also signed waivers for honor math classes and helped with tutors occassionally if needed. Math is a game and our elementary and middle school kids are so busy “feeling” their math with manipulatives, they are not learning the fundamentals and thus have difficulty with simple and advanced computation. Because of this, they dont “perform well” and the parents and teachers can not help with these lost holes. nothing worse than seeing a 10th grader using fingers to subtract 8 from 13!

Lastly, engineering is just problem solving–if children are told that if they can solve math problems they can solve real world problems and make excellent money doing what comes natural to them–there will be more engineers and others in math required fields like aviation and medicine.

Well said, mom-4-three! Unfortunately, many math educators are not chosen from the science and engineering curricula, where the “correct answer” means more than a good grade. The consequences of a collapsing bridge or a crashing plane makes for the need to develop not only mathematical rigor, but a deeper understanding of numeric (as well as in algebra and beyond, more abstract) processes. As more people in this country complain about their higher school and property taxes, perhaps they should also ask why they are getting less in terms of “output” from their school systems. After all, doesn’t that “output” equal the “input” of the nation’s workforce?

I agree.

Go back to tracking. You can “test out” those who are math whizzes as well as the average and the poor performers. You send the whizzes to the pre-college math sequence and the average and poor performers to somewhat easier and more varied sequences–like statistics, quantitative methods, etc.

They tracked 30 years ago–and for good reason. It works. Nobody likes to be “average,” but they are!

I loved math when I was growing up, but the public school system literally killed it for me.

I did mental math as a child, and one teacher would do drills with me. I would work on speed, accuracy, and new ways to calculate and break down problems. I won a contest between five schools in third grade, and planned to improve at my next school.

Only, my next school did not believe mental math ‘appropriate’. They introduced the ‘show your work’ concept, and made me write down *everything* down to the most basic 2+2. They did not care if the answer was correct or fast, just that I ‘knew the process’. My speed went down, my errors went up. Ironically, they still entered me in the competition for mental math, but I only took third that year.

I was fortunate to be homeschooled in fifth grade and go to private school in sixth. At private school, they had a PACE system which would correct any former gaps in learning (I had to do a lot of second grade handwriting and english work, for example), and then move one along at his own pace. In this way, I was able to move ahead to a seventh and eigth grade level in most courses by the end of the year, including math.

However, back at public school in seventh grade, they refused to let me take either 8th grade math or Algebra 1. (Which for me, would have been a review!) This made very little sense, as there were four other girls in the class allowed to take Algebra 1, and my grades were equal with theirs. As such, I was relegated to seventh grade math, and spent a year reviewing concepts I had already learned.

“Open Ended Math” was also very popular at the time, it was a state thing, where we had to spend *two pages* writing out how we ‘arrived’ at an answer in two different ways, complete with charts and diagrams, and every 1+1 and minor thought process and formula had to be described. Needless to say, again my speed slowed and my errors increased.

I had a fabulous teacher in highschool. He was tough, but good. I actually started to like math again, even if I had to spend two hours a night on homework ‘showing my work’. (I eventually learned the trick of just solving the problem in my head and putting my ‘check’ answer in the notes ;)) I only took three years of highschool though (skipped tenth), so I only made it to pre-calc. I also had a bit of fun annoying my science teacher by using math formulas to solve labs when I got stuck ;)

Unfortunately, while math and science started out my favorite subjects as a child and were my hobbies well into highschool, I did not pursue them into college.

What makes mathematics special is that .. it is!

No other subject is capable of giving a precise description of the laws that govern the universe we live in.

Michael Jordan isn’t appreciated and idolized because he was an ordinary, run of the mill player. He was idolized because he was special and no one would even begin to think of trying to create an interest in who he was or is by starting out by ignoring what made him special. At that point he becomes boring.

People and especially college students that are bored with mathematics are boring people and basically have no sense of its power and strength and no watered down package approach to teaching it will ever change that perception.

It is like my wanting to motivate basketball by taking my students an intramural tournament or game.

The failures of the US educational system is far more complex than analyzing high school test scores. The primary question needs to be—How did we get here and what is causing scores to be stagnant or falling? Personally, I attribute the downward trend in Math and Reading skills to three changes in education over the past 25 years. First, we have gotten away from basics. Second, we have required teachers to “teach to the test”. Third, this means that teachers have no latitude or time to address a lagging students missing skills as they must attempt to keep as many as 30 students on the same page, all moving a the same pace.

Multiplication table memorization is a third grade skill– that many middle school students today lack. Phonics is rarely taught today, so the majority of students now lack the ability to sound out words or comprehend new words based on the origins of the word (that is no longer taught either). This lack of basic skills has created students (from first grade on) who are ill prepared to successfully move on to higher math and reading levels. I have seen the majority of students in elementary and middle schools inappropriately promoted to the next grade due to social promotion. The design of our educational system is based on age appropriate building blocks, with each concept or skill built to support the next. We have entered an era (in the last 20 yrs or so) where the educational system believes that the retention of a child is more damaging than the lack of competency. The popular belief is that retention will damage a child’s self-esteem. How much greater is the damage to a child’s self esteem if we simply push them through the grade levels without achieving increasing levels of success ? Then everyone frets about the overwhelming high school drop out rate…. the success or failure of childhood education is a self-fulfilling prophecy— if students don’t have the requisite skills to build onto the next, they eventually see themselves as failures and quit trying.

Is it necessarily what schools and curricula are doing that have the biggest influence on math test scores? What about large societal changes? How has the time spent watching TV influenced math scores? How has texting influenced them? What about the introduction of preservatives, pesticides, artificial sweeteners and flavors, into our food system? Americans have a shorter attention span than ever before and that is certainly not because of the teachers, or the instructional methods they use. As an elementary school teacher I put passion, energy, and sleepless nights into figuring out new ways to engage students in the complex thinking that grows math minds because I see so many of them check out whenever I introduce a problem they can’t solve in 2 minutes or less. I have to cheer-lead them on, “Yes, it’s complex! Yes, it will take you a long time! That’s a great thing because you’ll get to practice perseverance! You can do it! Where will you start?” Was it always this challenging to get children to stay with a problem?