"The Math Myth and Other STEM Delusions"

[Andy Resnick]

I read Andrew Hacker's opinion piece in this Sunday's NYTimes and was intrigued:

http://www.nytimes.com/2016/02/28/opinion/sunday/the-wrong-way-to-teach-math.html?_r=0

The main thesis is that there's a disconnect between the K-12 content taught to students and the need for students to master numeracy. Has anyone here read his earlier book? I'll probably get the new one.

 

[gleem]

Hacker brings up the issue that has been or is being debated still. In our hurry to increase the number of scientists and engineer back in the sixties our educational system left behind the majority of citizens who only need the fundamentals of numeracy. Hacker has contriubted to the NY time in the past with this article "Is Algebra Necessary"

In an article by Don Byrd, he discusses one of the early articles on the problems of teaching math by Paul Lockhart "A Mathematician's Lament " musing in part on what if we taught music like we teach math. It would be unthinkable.

Bryd singles out two problems, over use of abstraction i.e., use of symbols, and poor environment for student engagement i.e. not creating an environment that stimulates students curiosity and interest.Keith Devlin further https://www.maa.org/external_archive/devlin/devlin_03_08.html using it as a springboard for his https://www.maa.org/external_archive/devlin/devlin_07_11.html , adapting Lockart's use of the proper teaching of music as a paradigm for math.

So when will educators get the message that we cannot all be mathematicians?

 

[Astronuc]

I had an interest in math and science, and I found algebra, geometry, trigonometry, analytical geometry and calculus fairly easy. However, the majority of students in high school weren't particularly interested in those subjects. In high school, I expected to go to university and do math and physics, which is pretty much what I did, but then migrated to nuclear engineering, which is more or less applied nuclear physics. So for me, STEM was absolutely necessary.

There were programs for kids who could only manage basic math, like consumer mathematics and some simple algebra.

If numeracy is a problem, perhaps there are problems with the way math is taught and/or a lack of support at home.

 

[brycenrg]

I had an interest in math and science, and I found algebra, geometry, trigonometry, analytical geometry and calculus fairly easy. However, the majority of students in high school weren't particularly interested in those subjects. In high school, I expected to go to university and do math and physics, which is pretty much what I did, but then migrated to nuclear engineering, which is more or less applied nuclear physics. So for me, STEM was absolutely necessary.

There were programs for kids who could only manage basic math, like consumer mathematics and some simple algebra.

If numeracy is a problem, perhaps there are problems with the way math is taught and/or a lack of support at home.

Did you have a support system in regards to math?

 

[Astronuc]

Did you have a support system in regards to math?

My parents gave me a lot of encouragement, but more in terms of getting me into summer programs (during summers between 7, 8, 9, 10 grades) at a local university, which did have math and science courses, an the summer program got me access to the university library. My parents bought an encyclopedia, which had a lot of natural history and historical information, which included articles on topics in chemistry, physics, and other subjects, including biographies of mathematicians, scientists and political figures. My parents bought my brother and me a chemistry set, and my folks bought me one of those 100-in-1 electronic kits.

Besides the university library, my dad took me to the city public library and another university library, but also to a technical book store where I was able to buy textbooks on analytical geometry and calculus, basically so I could teach myself some calculus. I did a lot of self study, and by grade 11, I was beyond my parents in mathematics.

The second high school I attended had a really good program in math. My 11th grade (algebra, trigonometry, analytical geometry) teacher worked closely with my 12th grade (calculus) teacher, and they worked closely with the chemistry teacher who had an MS in chemistry. The three of them prepared major works (MW)/honors and AP courses for 30 to 40 students, who were planning to go to the top universities in the country. We had numerous students going to Harvard, Yale, Princeton, MIT, Caltech, Stanford, Cornell, . . . , but some stayed in state and went to UT or TAMU.

 

[Andy Resnick]

<snip>There were programs for kids who could only manage basic math, like consumer mathematics and some simple algebra.

I think there's increased interest in reviving this type of program, in Ohio they are calling it 'financial literacy'. I envision the content in this type of program to be more than just arithmetic and algebra drills, but also include some statistics. In crude terms, the idea is to teach rational consumerism.

 

[JorisL]

Those programs have its merits but I feel there is some danger involved.
The big problem is students that are not interested in maths in the least.
Some classes will consist of students so uninterested it will be next to impossible to captivate and motivate students to do well.

A lot of those students will remain uninterested whatever efforts we do, helping them understand the maths necessary to allow people to spend rationally or do some quick calculations like finding the amount of carpet needed.

A final remark is the fact that all students seem to benefit from at least a few stronger students in the group (stronger as in faster, more inquisitive and more enthousiast). Unfortunately I only found a reference in a dutch book.

tl;dr
Introducing such a program needs a lot of consideration in advance.

 

[Astronuc]

I think there's increased interest in reviving this type of program, in Ohio they are calling it 'financial literacy'. I envision the content in this type of program to be more than just arithmetic and algebra drills, but also include some statistics. In crude terms, the idea is to teach rational consumerism.

There was/is a similar program in the high school my son attended. I think it was termed 'consumer math' or something like that.

 

[gleem]

A final remark is the fact that all students seem to benefit from at least a few stronger students in the group (stronger as in faster, more inquisitive and more enthousiast). Unfortunately I only found a reference in a dutch book.

My primary and secondary education ( '47 - '59) of course was exactly this scenario. I think it did spur especially the average student (me at the time) to exert more effort. In my schools and at this time I suppose most where graded on a straight scale. You know what you had to do to get an A. You knew who the good students were. So yes I think there is a benefit for a heterogeneous group. Did it affect all students in the same way I cannot say. Did it to paraphrase Goethe -make a man better because you took him as he should be not as he is?

A common critique of the type of class is that the less able students hold up the class and bore the more able students. But this criticism begs the question "Is the course overly sensitive to the needs of the less able students"? Could the course especially an elementary one be structured so as to remain significantly challenging to the able students without demoralizing the less able. Certainly at some point one must create separate pathway according to ability and/or interests. That brings up the question of when should this occur.

 

[alw34]

in Ohio they are calling it 'financial literacy'. ... the idea is to teach rational consumerism.

I am unsure what is taught currently here in New Jersey, for instance, but 'financial education' would be an extremely valuable lesson for most...issues such as compound interest when saving, economic growth and GDP, stocks, bonds, borrowing costs of credit cards, incorporating businesses to limit liability, wills, unemployment insurance, Roth versus traditional IRA's, defined contribution versus defined benefit plans, leasing versus buying, financial security, retirement saving, health savings plans, life,disability and liability insurance, effects of government debt and deficits and borrowing, strong versus weak currency, diversification of investments, risk/reward, etc.

 

[gleem]

I am unsure what is taught currently here in New Jersey, for instance, but 'financial education' would be an extremely valuable lesson for most...

Yes, consumer math or financial math is useful to the more mathematically inclined too. Certainly not from the mechanics of the math but certainly from the context that are relevant to applications. Sometimes one has to pull facts out the the provided statistics or numbers i.e., do some math, to get a handle on their significance.

 

[Astronuc]

My primary and secondary education ( '47 - '59)

Mine was in the 60's.

Reflecting on the earliest years, my first and second grade classrooms had cuisenaire rods.
https://en.wikipedia.org/wiki/Cuisenaire_rods

They were very practical with respect to learning the relationship of numbers, e.g., 5 x 2 (or 2+2+2+2+2) = 2 x 5 (or 5+5) = 10. One could understand addition and subtraction. I don't know if is sank into my classmates as readily.

In second and third grade, I had a classmate with whom I competed. On rainy days, when we had indoor recess, he and I used to write numbers (1, 2, 3, . . . .) on a personal chalk board to see who could achieve the highest number during the recess period. He always got to higher numbers. It was also good way to start to see relationships between numbers, e.g., multiples of 2, 3, 4, 5, . . . I think we just naturally discovered patterns. I don't think our other classmates were invested in such activities. By the time I got to number lines, counting and natural numbers, reals numbers and so on, I had a pretty easy time with understanding numbers, i.e., arithmetic was pretty easy, whereas many classmates struggled at various levels.

 

[gleem]

Reflecting on the earliest years, my first and second grade classrooms had cuisenaire rods.
https://en.wikipedia.org/wiki/Cuisenaire_rods

They were very practical with respect to learning the relationship of numbers, e.g., 5 x 2 (or 2+2+2+2+2) = 2 x 5 (or 5+5) = 10. One could understand addition and subtraction. I don't know if is sank into my classmates as readily.

There seems to be some connection between having some visual representation of numbers and learning their relationships.. What about the Abacus as a teaching aid?

 

[Andy Resnick]

<snip>A common critique of the type of class is that the less able students hold up the class and bore the more able students. But this criticism begs the question "Is the course overly sensitive to the needs of the less able students"? Could the course especially an elementary one be structured so as to remain significantly challenging to the able students without demoralizing the less able. Certainly at some point one must create separate pathway according to ability and/or interests. That brings up the question of when should this occur.

One of the 'new' ideas is called 'competency-based instruction'. In this model, students progress at their own pace, determined by passing exams. This is fairly easy to implement on computer-based instruction (math, spelling, etc). My dystopian view is that it helps train students to be mindless cubicle-dwellers, interacting only with computer programs.

 

[bcrowell]

[A moderator deleted almost all of this post, so that what remained was not an accurate indication of my thoughts. Therefore I've deleted the small amount of remaining content.]

 

[billy_joule]

One of the 'new' ideas is called 'competency-based instruction'. In this model, students progress at their own pace, determined by passing exams. This is fairly easy to implement on computer-based instruction (math, spelling, etc). My dystopian view is that it helps train students to be mindless cubicle-dwellers, interacting only with computer programs.

Well hopefully there's some middle ground as the traditional one size fits all approach has been clearly failing. I find the modern classroom to be much less cube-farm-like, there's a lot more active participation, collaboration and group work while still being assessed individually, back in my day it was sit down shut up and do your sums! And everyone took the same tests. My 'day' was the 90's - 00's so pretty recent, I'm comparing changes in the school I attended that my daughter now attends.

Let kids drop out after 5th grade if they really hate fractions. The only trouble is that lack of a college education seems to produce the kind of voters who would vote for Trump.

I don't think anything I learned though high school and university math made me a more well informed voter (bar a small amount of statistics).
What did hurt my political viewpoint was not taking a single humanities or social science class since I was 14 (as is fairly normal for engineers in my country). Taking only math & science classes gave very little insight into how the 'real' world works.

 

[gleem]

K-12 education in the US is free and compulsory. The problem is that so many students don't actually want to be educated -- especially in math. I would propose keeping it free, but no longer making it compulsory. Let kids drop out after 5th grade if they really hate fractions. The only trouble is that lack of a college education seems to produce the kind of voters who would vote for Trump.

Do you have kids? Kid make bad choices and not wanting an education is one of them. You can't dump them on the street where they will make many more bad choices. There is a reason that education is compulsory and its not to just to babysit them. You want as many functional and educated adults as possible. All cultures have rites of passage to prepare kids for adulthood and in civilized society schooling is one of them.

What is a rite of passage? Why is it Important?A rite of passage is a ceremony and marks the transition from one phase of life to another. Although it is often used to describe the tumultuous transition from adolescence to adulthood, it does refer to any of life’s transitions (Births and Beginnings, Initiations, Partnerings, and Endings or Death). There are many passages in our lives if we choose to mark and celebrate them.

Journeys is most concerned with initiatory rites of passage. Initiation is defined in the dictionary as, “the rites, ceremonies, ordeals or instructions with which a youth is formally invested with adult status in a community, society or sect.” We extend that definition to include rituals and ceremonies that help adults transition to new life roles along the path of adulthood – all the way into meaningful elderhood.

When we design rite of passage experiences, we work to assure that initiates come out of the experience with a new and empowering story that helps them take responsibility for the decisions that set the course of their future. We help initiates create the story of who they are and the kind of life they want to build based within the exploration of their own personal values. We also help them find the story that connects them to their community. Through this self-exploration initiates emerge with a stronger sense of personal responsibility to all aspects of their lives – stretching all the way out to the larger world of which they are a part.

In this way both the community and the initiate benefit from a rite of passage. An intentional rite of passage experience provides the space for the community to transmit its core values and confer the role responsibilities appropriate to the initiate’s stage of life, thus insuring cultural continuity, a sort of knitting together of the generations.

 

[Astronuc]

K-12 education in the US is free and compulsory. The problem is that so many students don't actually want to be educated -- especially in math. I would propose keeping it free, but no longer making it compulsory. Let kids drop out after 5th grade if they really hate fractions.

That would be taking it to the extreme.

Do you have kids? Kid make bad choices and not wanting an education is one of them. You can't dump them on the street where they will make many more bad choices. There is a reason that education is compulsory and its not to just to babysit them. You want as many functional and educated adults as possible. All cultures have rites of passage to prepare kids for adulthood and in civilized society schooling is one of them.

Yes, children, young adults, and even some adults, make bad choices. However, the sooner someone reaches an individual, the sooner hopefully the individual will learn to make better choices.

I think it is necessary to make arithmetic/mathematics, science, humanities relevant, and it seems for many, it is not.

Perhaps I was fortunate, because I knew, probably from first grade, that my education was relevant, and that I could some day be one of those adults who practiced math and science. I have encountered so many in the past, and I encounter so many as a professional, who struggle in this world.

 

[Fervent Freyja]

I imagine that the No Child Left Behind Act of 2001 has had much to do with many issues of this sort. I was around 12 when this was implemented into the school system, standards were lowered in order to meet progress reporting but there was no longer much support for children that loved to learn. They become an additional "problem" for the teachers and were suddenly pulled from accelerated/gifted programs.

 

[Derek H]

On the one hand, I agree that not every student needs or wants to be a mathematician. On the other hand, students often don't know what they want or need at this age and a lot will opt for "consumer math" as an easier path through school just because they get indoctrinated into thinking math is "hard" or "geeky". The proposal to reduce the math taught strikes me as elitist. I'd rather see math instruction that makes the problems relevant -- why do you need algebraic skills? Because there are practical applications in adapting recipes when you're cooking (or brewing), hunting, fixing your car, hiking in the woods, etc.
The big problem I see isn't that schools teach math, it's the way some of them teach it. Most of the problems I've seen circulating as "Common Core" are just asinine (of course, the problems sets people object to are the ones most likely to be circulated) and I have to wonder about the practical experience of the people who generated them. I know I am more "math-friendly" than most as a working engineer but I have also worked with teenage boys for nearly 30 years and have always endeavored to make any skills I teach both relevant and interesting. I haven't seen how my nephews are taught but some of the homework problems I've looked at are just abominable.

 

[houlahound]

We had the perfect system when I was at school. General math for every day life, advanced math...for obvious and ordinary math for students that didn't care or had trouble.

Seniors earned credit points for tutoring juniors.

Every kid could achieve at one or more of these classes. Students could freely go up or down across the three subjects.

Teachers were happy students were happy and parents were happy.

Education academics destroyed this proven system for their ideologies by assuming all children can be scientists and engineers.

 

[bcrowell]

Since my #15 was phrased in a way that seems to have bothered a moderator, I'll try again in less colorful language.

There is a broad consensus in the US that education is a public good. I'm using "public good" in the nontechnical sense: that education is widely believed to help society in general. There are several completely different ways in which education can be a public good:

(1) Education increases wealth, and this effect is not just limited to the individual who gets the education. Wealth produces more wealth, and that wealth ripples outward through society so that we all become richer.

(2) Education may enhance social mobility (although I think it's actually very poor at doing that in practice in the US today). Social mobility is arguably a public good because our society is constructed in such a way that it gets its stability by giving lots of people economic hope (so they don't become revolutionaries), rather than getting its stability by having a rigid class system.

(3) Democracy without education is destined to fail. In #15 I gave an example that I'm sure any American right now can guess, but there are plenty of other examples in other times and places. For example, Egypt is a failed democracy, and Egypt also ranks very low in the quality of its educational system.

Andrew Hacker's opinion piece cites poor numeracy in the US, and says that "We should be doing better," but he doesn't explicitly say why he thinks it's important that we do better. Should we do better because of compassion for individuals? Because numeracy is a public good? The only hint is that the study he cites was done by the Organization for Economic Cooperation and Development. This suggests that he thinks numeracy is a public good, and that the reason is #1 above.

The trouble here is that if we don't think about his unexamined assumptions, we may be led to the wrong conclusions. He advocates teaching "an undergraduate class I call Numeracy 101, for which the only prerequisite is middle school arithmetic." He claims positive results. Are these positive results a public good? I suspect not. If we consider the three reasons above why education is a public good, I suspect that in each case, his plan would be the opposite of a public good -- a "public ill."

Education increases wealth. Math education certainly increases your wealth if you're an engineering major. But what evidence is there that the much narrower goal of numeracy would increase people's wealth? It seems unlikely to me. A huge chunk of the US population is innumerate, and they're not all unemployed.

Education may enhance social mobility. I haven't seen any evidence that numeracy enhances social mobility. Hacker is educating non-STEM majors. Is there really a difference in social mobility between numerate people who have a degree in history from Queens College and innumerate people who have the same degree from the same school? That would be very surprising.

Democracy without education is destined to fail. A country like Egypt might not have become a failed democracy if there had been better education. Italy might not have brought Mussolini to power if more Italians had been educated. (I would take up the case of my own country at the present time, but discussion of that seems to be prohibited.) But what evidence is there that more numerate Egyptians or Italians would have preserved their democracies? It seems much more likely to me that there is something about the experience of college that immunizes people against authoritarianism. US college students meet people who are Muslims. They meet people who are immigrants. They discuss a wide range of topics, and their professors require them to carry out that discussion using facts and logic. There are multicultural education requirements, history requirements, and so on. It seems far more likely to me that these general features of the college experience are what provide the social good -- not anything as specific as numeracy.

People might say, but what's wrong with promoting numeracy? It's clearly desirable.

I think the opposite may be true. Numeracy education may be a public ill. Hacker doesn't propose supplementing math education with additional courses to promote numeracy. He proposes replacing challenging coursework in high school and college with a second, easier track in which the sole goal is numeracy. The problem with this is that it's likely to work against the public-good goals of wealth and social mobility. For example, if you go to an inner-city school, the only math AP course may be AP Numeracy. They won't offer AP Statistics (which Hacker depicts as if it's some kind of cruel and unusual punishment).

We had the perfect system when I was at school. General math for every day life, advanced math...for obvious and ordinary math for students that didn't care or had trouble.

This appears to be exactly what Hacker is proposing: a return to what was known in the 60s as "tracking." The trouble is that tracking can very easily contribute to educational inequality. The brown kids get put in Math for Daily Life, while the white kids take calculus. This is why tracking lost favor in the 70s. There's probably an argument to be made for more tracking, but you can't just ignore its potential to cause inequality.

 

[houlahound]

May I challenge your assertions, paraphrased, that education increases wealth and democracy.

As brutal as it sounds an uneducated slave work force has historically supported more wealth; refer any historical regime eg British empire.

I would argue the Asian tigers have increased wealth initially by having a work force with no rights or education to be exploited by western democracies.

Just saying.

 

[bcrowell]

May I challenge your assertions, paraphrased, that education increases wealth and democracy.

As brutal as it sounds an uneducated slave work force has historically supported more wealth; refer any historical regime eg British empire.

I would argue the Asian tigers have increased wealth initially by having a work force with no rights or education to be exploited by western democracies.

About education and wealth, you could conceivably be right, although I don't think it's that easy to extract lessons from history. There are too many uncontrolled variables. For example, there have been various debates about US history and whether the slave-labor system in the antebellum South was actually economically better than free labor would have been. These debates are always going to be inconclusive, because we can't do a controlled experiment and compare with a system that was identical except for the labor system. (The North had a completely different type of economy.) The debate is also going to be inconclusive because the result depends on what you use as a measure of wealth. If you use GDP, you could get a certain answer, but that answer would ignore the fact that a big segment of the population (the slaves) had nothing. BTW, slavery is not the opposite of education. There were many educated slaves in the ancient world. In the antebellum US, during the early period of slavery, it was not uncommon for slaves to be educated, sometimes very well educated. That didn't changed until the end of the slavery period, when it became illegal to educate slaves.

About education and democracy, I would be interested to know if you could come up with a counterexample. That is, has there ever been a country with (a) a healthy, sustainable democracy; (b) widespread lack of education, and (c) universal suffrage? In the examples I know where a and b both apply, they were a long time ago, and c didn't apply. E.g., in the early US, suffrage was reserved for white male property owners.

Note that my argument about Hacker's proposal doesn't actually depend on the truth or falsehood of the belief that education is a social good in general. I'm simply arguing that even if it is, there is no reason to believe that numeracy is a social good.

 

[houlahound]

I have no basis for my claims in terms of studies.

I do note anecdotally that from a teacher that taught in China for years streaming kids heavily has made great gains.

The low ability kids are identified and redirected rather brutally for productive but menial futures to contribute to the economy while the flashy whiz kids get redirected and stupid levels if resources thrown at them.

In the west streaming is generally considered the greatest evil in education due to alleged impacts on self esteem.

I think the assumptions on streaming kids needs to be put on an objective basis and less ideological.

 

[DelcrossA]

May I challenge your assertions, paraphrased, that education increases wealth and democracy.

As brutal as it sounds an uneducated slave work force has historically supported more wealth; refer any historical regime eg British empire.

I would argue the Asian tigers have increased wealth initially by having a work force with no rights or education to be exploited by western democracies.

Just saying.

You can't use systems that are strictly non-democratic as a counterexample for whether or not education benefits a democracy.

I would say the biggest reason why replacing course like Algebra for a Citizen Math course is a bad idea is because of how negatively it impacts "mobility". As it currently stands, many high school students are basically set-up to fail in college because of how deficient they are in basic math, so what happens when you decide to offer a track that doesn't even teach basic algebraic thinking? Well the argument for it seems to be that not everyone needs algebra. This is a very poor rationale, in my opinion, as it anticipates a person knowing their desired career path as a 9th grader at 14 years old. Let's say that a high-school student opted for this "citizen math" course and then as a junior or senior develops a passion for anything STEM/computer science related. This student is then royally screwed over as the chances of getting a decent score on the ACT are poor, and then if a school happens to accept the low score (as they unethically do) he or she will waste thousands of dollars only to, likely, drop out of college or at least graduate with a very poor record. It seems ridiculous to be able to expect students to have planned their life out by the time they are expected to make the choice as to which mathematics path they wish to go down. Also, I am a bit surprised that an educator would even be of the mindset that a student needs to learn only the minimum for their career path.

Math education certainly needs to be improved, and I think the whole "citizen math" scheme would be much better implemented as say word problems/projects in a Algebra or Geometry course.

 

[bcrowell]

This is a very poor rationale, in my opinion, as it anticipates a person knowing their desired career path as a 9th grader at 14 years old.

I agree with everything in your #26 except for some reservations on this point. Most people at that age are accurate at evaluating their own interest/ability in math, and in academics in general.

 

[DelcrossA]

I agree with everything in your #26 except for some reservations on this point. Most people at that age are accurate at evaluating their own interest/ability in math, and in academics in general.

I'm not so sure as a reason there is conversation about math reform in the U.S. is due to the lack of understanding of mathematical concepts. Also, prior to HS most students have not been exposed to algebra and have zero exposure to using anything but arithmetic in physical science courses. I do not really think they are capable of making an informed decision at this point.

I couldn't quickly find any stats specifically about high schoolers but according to Penn State (https://dus.psu.edu/mentor/2013/06/disconnect-choosing-major/) 75% of students switch career paths and, perhaps more importantly, 20-50% of entering undergraduates enter as undecided. This does not speak to me that most people have a good grasp on their own interests.

 

[bcrowell]

I couldn't quickly find any stats specifically about high schoolers but according to Penn State (https://dus.psu.edu/mentor/2013/06/disconnect-choosing-major/) 75% of students switch career paths and, perhaps more importantly, 20-50% of entering undergraduates enter as undecided. This does not speak to me that most people have a good grasp on their own interests.

Such a switch doesn't mean they suddenly discovered they had a previously unknown talent for math. They could be switching from physics to chemistry, or from history to English.

 

[betadave]

There is a course on EdX titled "The Challenge of Global Poverty" that presents the results of an evidence based study on tracking. It found in India that tracking produced an overall gain. The better students went further and the weaker students went further. They suggested that the good students were held back by the weak and the weak were demoralized by the strong. The way we set up school programs has no tools for recognizing how to improve the system. My observation (tutoring mostly math for the last 20 years and having been on the planet for 71 years) is that we create a new program and put it in place with limited ability to correct any inherent errors. We leave it alone for 15 to 20 years, just enough for one generation to pass through and then we change the program with new vocabulary to show the next generation that we finally fixed the problem. In the case of CPM in California, they tested it on a set of selected students who did well so they launched the program. It was abandoned after 20 or so years as it failed to prepare students. The testing was flawed and corrections were not possible as the state owned the copyright for the texts and they had no desire to change.

Some of you have shown how the great support of your parents mattered and that supported how to make students succeed. Individual experience and personal anecdotes of how people succeed or fail are not useful. I, for one, got a poor early education. I flunked 8th grade and graduated from a weak high school that gave no chance to do calculus. As I recall there were 6 of us in the physics course and my class total was 49 students. I had to take a refresher course as a freshman in college because my math was weak. That poor start should predict a failure yet I hold a masters degree from MIT in Chemical Engineering. That story does not help one bit for fixing the system.

I hope we can get to the point where we actually test the programs and modify the programs based on supportable results. Until we do that, I doubt we have the ability to reach the goals of overall mathematical literacy. From my view, the problem is the lack of interest the educational system has in using evidence to improve. By the way, EdX also has a four part course on the problems with our educational system. It is so convoluted that we will not find the solution here.

 

[bcrowell]

There is a course on EdX titled "The Challenge of Global Poverty" that presents the results of an evidence based study on tracking. It found in India that tracking produced an overall gain. The better students went further and the weaker students went further. They suggested that the good students were held back by the weak and the weak were demoralized by the strong.

This is very interesting, but India has specific characteristics that don't translate to other places. Big parts of their educational system are completely dysfunctional (K-12 teachers who draw a paycheck but don't show up, business students in college who spend their classes chanting definitions of terms in unison). They also have massive corruption in educational admissions.

The US is nearly unique among industrialized countries in not doing more tracking, but there's a reason for that, which is that we have social fault lines that make tracking vulnerable to becoming a tool for discriminating against individuals based on their race and class. Compared to Europe, we have a lot more income inequality, our big cities have a lot more immigrants and a lot more linguistic diversity, and we have the legacy of slavery and systematic racism, including severe racism against Latinos. Where I live, in Orange County, California, Latino kids back in the 50s went to inferior, segregated schools, and the young ones worked as "ratones" (literally, "rats") climbing orange trees to pick the fruit that was inaccessible by other methods.

 

[houlahound]

What you guys think about standardised testing where staff careers are hinged on the results.

I am reading about how this has caused a lot of corruption and cheating due to performance pressure.

 

[Andy Resnick]

There is a broad consensus in the US that education is a public good. I'm using "public good" in the nontechnical sense: that education is widely believed to help society in general. There are several completely different ways in which education can be a public good:
<Snip>
Andrew Hacker's opinion piece cites poor numeracy in the US, and says that "We should be doing better," but he doesn't explicitly say why he thinks it's important that we do better. <snip>

I can't read Hacker's mind, but I propose a 4th reason why numeracy taught at the K-12 level is a public good:

4) Numeracy helps create an informed population.

My rationale is that numeracy, especially statistical numeracy, is an increasing feature in the news: surveys, public health studies, demographic studies, etc. These data are often used as 'inputs' into creation or modification of policy, yet average citizens who elect people to represent their interests are wholly unable to make sense of conflicting reports and are thus unlikely to be able to rationally represent their own interests. Examples abound.

Average citizens are increasingly reliant upon statements made by 'experts' even though those same citizens are generally unable to ascertain if that 'expert' is an expert or a crank. Again, examples abound. Cranks should not be responsible for policy.

 

[mathwonk]

this seemed to me like a well informed and well reasoned critique of hacker's book:

http://www.slate.com/articles/healt..._great_example_of_mathematics_illiteracy.html

 

[symbolipoint]

this seemed to me like a well informed and well reasoned critique of hacker's book:

http://www.slate.com/articles/healt..._great_example_of_mathematics_illiteracy.html

Basic Numeracy was too difficult for me to learn. Several weeks of remedial instruction and one year of beginning algebra in high school changed this for me. How is this change to be understood and why is this change so difficult to support?
( read some of the article but none of Hacker's report).