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The Math Myth: And Other STEM Delusions
The “lively” ( Kirkus Reviews ), provocative, much-talked-about book that challenges the mandate for all students to master a full menu of mathematics, from the bestselling author When Andrew Hacker published an op-ed in the New York Times questioning the requirement of advanced mathematics in schools, it instantly became one of the paper’s most widely circulated articles. Why, he wondered, do we inflict algebra, geometry, trigonometry, and even calculus on all young Americans, regardless of their interests and aptitudes? In response to the controversy sparked by his ideas, Hacker fleshed out his arguments in The Math Myth , which Diane Ravitch has hailed as an “important book” that “demolishes some totally unrealistic policies that will prevent many students from ever receiving a high school diploma and leading useful lives.” In a book Howard Gardner calls “important and timely—and a great read,” Hacker offers a bold examination of widely held assumptions about the Common Core curriculum, the frenzied emphasis on STEM, and the type of knowledge that is—and will be—needed for most jobs. A mathematics professor himself, Hacker, in this “direct and clear” ( Kirkus Reviews ) “worthwhile read” ( National Book Review ), honors mathematics as a calling and extols its glories and its goals—yet shows how mandating it for everyone not only prevents other talents from being developed, but acts as an irrational barrier to graduation and fulfilling careers.
256 pages, Paperback
First published May 5, 2015
54 people are currently reading
719 people want to read
About the author
Andrew Hacker
34 books24 followersAndrew Hacker is an American political scientist and public intellectual.
He is currently Professor Emeritus in the Department of Political Science at Queens College in New York. He did his undergraduate work at Amherst College. This was followed by graduate work at Oxford University, University of Michigan, and Princeton University where he received his PhD degree.
Hacker taught at Cornell before taking his current position at Queens.
His most recent book, Higher Education? was written in collaboration with Claudia Dreifus, his domestic partner. Professor Hacker is a frequent contributor to the New York Review of Books.
He is currently Professor Emeritus in the Department of Political Science at Queens College in New York. He did his undergraduate work at Amherst College. This was followed by graduate work at Oxford University, University of Michigan, and Princeton University where he received his PhD degree.
Hacker taught at Cornell before taking his current position at Queens.
His most recent book, Higher Education? was written in collaboration with Claudia Dreifus, his domestic partner. Professor Hacker is a frequent contributor to the New York Review of Books.
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Displaying 1 - 30 of 84 reviews
May 1, 2016
I have a degree in mathematics, I work with technology, and I use math routinely in my job, so when I picked up Andrew Hacker’s anti-STEM manifesto, I expected to hate it. So I was actually surprised to find the overview section compelling. Hacker’s thesis is that STEM is over-emphasized in American education and that this does more net harm than good to students. I disagree, but I like to be challenged, and I was on board with this book for the first ten pages or so. I was eager to see his arguments.
Unfortunately for his cause, Hacker puts on an exhibition in fallacious logic, questionable reasoning, and outright dishonesty. His central thesis seems to be that math is just too darn hard, despite the fact that children in other countries don’t have the same problem with it as Americans. He never touches on possible reasons for this, be they cultural, genetic, or otherwise. Most of his “arguments” are laid out in speech bubbles as unsourced quotations. His analogies are often hilariously flawed. He asserts that being a strong swimmer wouldn’t help you as a lacrosse player—seemingly ignorant of the physical conditioning that underpins both. During a lengthy screed against Common Core (which is not uncontroversial, admittedly) he tries to delegitimize the Association of Governors advocating for it by complaining that only twenty-nine out of fifty governors showed up to the meeting. Most of them, in other words.
In fact, there’s anti-elitism throughout this book. He rails against highly selective institutions like Harvard for using stringent math requirements as part of their selection process. He builds this towards a chapter wherein—and I’m not making any of this up—he posits a cabal of elite mathematics scholars working to keep math in curricula but making sure it’s so hard that no one but themselves can excel in it, leaving them free to do research while grad students and TA’s handle the teaching work. He calls these scholars “mandarins”, because hey, if you’re going to be insulting, why not be a little racist too, I guess.
His solutions are just as bizarre. He advocates small group discussions over math problems. In his most egregious chapter, he suggests making the SAT a take-home exam to get around possible problems of sexism. And this chapter is where he does his most flagrantly dishonest work. In order to prove that the SAT is sexist, he takes PSAT scores for the state of Ohio and breaks them out by gender—only he doesn’t have the gender data, so he goes by first name. He excludes “ethnic” names and guesses on gender-neutral names using the ratios he already had as a guideline. And he admits that fully a fourth of the data fits these category. So when he ends up showing that boys have a 54-46 edge over girls, it’s hard to take that 8% difference seriously, because of the amount of guess-work that went into an already small sample.
But this isn't dishonest, just sketchy. For dishonesty, I would direct you to the chart of unemployment rates in specified counties expressed as a ratio of the unemployment rate in that county to that of the entire nation. This makes a county with a 9% (or so) unemployment rate show up on the chart at a head-slappy 134%. Elsewhere, Hacker identifies math as the leading academic reason for the 20% high school drop-out rate. While he (in one instance) admits that there are other, more significant NON-ACADEMIC reasons, but he never offers any real numbers about what those are. He just lets the reader see 20% drop-out rate attributed to math.
The fact that his stats are so atrocious is what makes this book contemptible instead of purely bad. To use misleading math to argue that math education is unnecessary? It’s almost like some bizarro reductio ad absurdum argument FOR comprehensive math education, because not only does he lie, but he lies pretty transparently. The secret message of this book could be: learn statistics so you won’t be fooled by books like this. In fact, I’ve changed my mind. Everyone should read this book purely as an inoculation against ignorance.
Unfortunately for his cause, Hacker puts on an exhibition in fallacious logic, questionable reasoning, and outright dishonesty. His central thesis seems to be that math is just too darn hard, despite the fact that children in other countries don’t have the same problem with it as Americans. He never touches on possible reasons for this, be they cultural, genetic, or otherwise. Most of his “arguments” are laid out in speech bubbles as unsourced quotations. His analogies are often hilariously flawed. He asserts that being a strong swimmer wouldn’t help you as a lacrosse player—seemingly ignorant of the physical conditioning that underpins both. During a lengthy screed against Common Core (which is not uncontroversial, admittedly) he tries to delegitimize the Association of Governors advocating for it by complaining that only twenty-nine out of fifty governors showed up to the meeting. Most of them, in other words.
In fact, there’s anti-elitism throughout this book. He rails against highly selective institutions like Harvard for using stringent math requirements as part of their selection process. He builds this towards a chapter wherein—and I’m not making any of this up—he posits a cabal of elite mathematics scholars working to keep math in curricula but making sure it’s so hard that no one but themselves can excel in it, leaving them free to do research while grad students and TA’s handle the teaching work. He calls these scholars “mandarins”, because hey, if you’re going to be insulting, why not be a little racist too, I guess.
His solutions are just as bizarre. He advocates small group discussions over math problems. In his most egregious chapter, he suggests making the SAT a take-home exam to get around possible problems of sexism. And this chapter is where he does his most flagrantly dishonest work. In order to prove that the SAT is sexist, he takes PSAT scores for the state of Ohio and breaks them out by gender—only he doesn’t have the gender data, so he goes by first name. He excludes “ethnic” names and guesses on gender-neutral names using the ratios he already had as a guideline. And he admits that fully a fourth of the data fits these category. So when he ends up showing that boys have a 54-46 edge over girls, it’s hard to take that 8% difference seriously, because of the amount of guess-work that went into an already small sample.
But this isn't dishonest, just sketchy. For dishonesty, I would direct you to the chart of unemployment rates in specified counties expressed as a ratio of the unemployment rate in that county to that of the entire nation. This makes a county with a 9% (or so) unemployment rate show up on the chart at a head-slappy 134%. Elsewhere, Hacker identifies math as the leading academic reason for the 20% high school drop-out rate. While he (in one instance) admits that there are other, more significant NON-ACADEMIC reasons, but he never offers any real numbers about what those are. He just lets the reader see 20% drop-out rate attributed to math.
The fact that his stats are so atrocious is what makes this book contemptible instead of purely bad. To use misleading math to argue that math education is unnecessary? It’s almost like some bizarro reductio ad absurdum argument FOR comprehensive math education, because not only does he lie, but he lies pretty transparently. The secret message of this book could be: learn statistics so you won’t be fooled by books like this. In fact, I’ve changed my mind. Everyone should read this book purely as an inoculation against ignorance.
April 28, 2016
Let me get this out of the way right off the bat: This book has a plethora of semantics errors. The fact that Hacker does not have a background in mathematics education is obvious to anyone who does.
Now, that being said, there are many good, valid points in this book. He just doesn't know how to articulate what he means. I can decode his message, but my biggest fear is that others cannot. Perhaps others who are in the position of effecting change in the world of mathematics education. That's a bit scary to think about.
However, I hate the idea that what he's trying to say will get lost in the hubbub. The crux of his message is this: Hardly anyone has practical need of advanced mathematics, yet we require it of all our young people, which then creates an unnecessary barrier to success. Simply put, why should kids be forced to learn how to factor trinomials when they don't know how to do taxes, chose a health insurance plan, manage their finances, or even pick the lowest unit price of an item at the store? Even worse, we're denying them high school diplomas (or admission to college, or college diplomas) because of these math requirements, which are neither interesting NOR valuable to them.
Of course there's a part of me that wants to say that sometimes we have to do stuff we don't want to do and that it's for their own good even if they don't realize it. But honestly, that just doesn't sit right with me. I'd kind of be okay with that, except that they could be spending their time developing strong "numeracy" (quantitative literacy) skills instead. I honestly don't see what value it adds to force the every student to learn advanced math for math's sake when there are other ways of helping them become good problem solvers who are fluent with numbers. Plus, it causes obvious harm to those who can't successfully jump over the hurdle.
So, yeah. Also, I teach advanced math! I think there's a place for it. I just don't think it should be required of every student. Nor should we do away with math in school entirely. We just need to rethink WHY we're forcing advanced math upon ALL kids, and whether we can accomplish what we desire in a way that's more beneficial to the average student.
Now, that being said, there are many good, valid points in this book. He just doesn't know how to articulate what he means. I can decode his message, but my biggest fear is that others cannot. Perhaps others who are in the position of effecting change in the world of mathematics education. That's a bit scary to think about.
However, I hate the idea that what he's trying to say will get lost in the hubbub. The crux of his message is this: Hardly anyone has practical need of advanced mathematics, yet we require it of all our young people, which then creates an unnecessary barrier to success. Simply put, why should kids be forced to learn how to factor trinomials when they don't know how to do taxes, chose a health insurance plan, manage their finances, or even pick the lowest unit price of an item at the store? Even worse, we're denying them high school diplomas (or admission to college, or college diplomas) because of these math requirements, which are neither interesting NOR valuable to them.
Of course there's a part of me that wants to say that sometimes we have to do stuff we don't want to do and that it's for their own good even if they don't realize it. But honestly, that just doesn't sit right with me. I'd kind of be okay with that, except that they could be spending their time developing strong "numeracy" (quantitative literacy) skills instead. I honestly don't see what value it adds to force the every student to learn advanced math for math's sake when there are other ways of helping them become good problem solvers who are fluent with numbers. Plus, it causes obvious harm to those who can't successfully jump over the hurdle.
So, yeah. Also, I teach advanced math! I think there's a place for it. I just don't think it should be required of every student. Nor should we do away with math in school entirely. We just need to rethink WHY we're forcing advanced math upon ALL kids, and whether we can accomplish what we desire in a way that's more beneficial to the average student.
August 20, 2016
Hacker has an interesting hypothesis. He wants to change the instruction of mathematics in school. In fact he wants to emphasize arithmetic and have mathematics for STEM (science, technology, engineering, math) students. As a person who struggled in arithmetic but excelled in mathematics I find this interesting. Hacker claims math is the cause of many high school and college drop outs. He claims calculus is never used by the majority of people after leaving school.
As a scientist I had some problems with Hacker’s argument. I read the book because on some points I agree with Hacker. I have a problem with his unreferenced claims and he played games with his statistics to make them deliberately misleading. I think Hacker is correct that we should not try to follow the lead of Asia on rote learning. The United States in the 18th and 19th century lead the world with innovative education; we in fact educated all children not just those of the wealthy. We need to sit down and rethink education completely. I agree with Hacker that we need to teach more analytical and strategic thinking, encourage creativity and teach people to think out of the box. Hacker states that with the over emphasis on math we have segregated social science and the humanities to a place of lesser value. I have seen this happen and it needs to be corrected as these fields are of equal value to science, math and engineering. Hacker states we need to include in the regular course work art and music as both also use math and arithmetic skills and teach creativity. Hacker also recommends that arithmetic and math skills be taught to the level and job requirements rather than everyone in high school having to learn trig and calculus. He provides the example of a person unable to enroll in a cosmetology course because she failed algebra in high school.
To me education is providing an introduction of a wide range of topics, information and subjects in a stimulating and exciting way to grab the student’s interest and imagination to want to learn more. If one grabs the attention of a student in a topic so they want to make a career in that field, then that is success. I think more time and money should be spent on educating better math teachers and improving or creating better ways to teach math and arithmetic.
I read this as an audiobook downloaded from Audible. This book would be more effective if read in book format or download the PDF from audiobook publisher. Barry Press does a good job narrating the book. Press is an actor that also narrates audiobooks.
As a scientist I had some problems with Hacker’s argument. I read the book because on some points I agree with Hacker. I have a problem with his unreferenced claims and he played games with his statistics to make them deliberately misleading. I think Hacker is correct that we should not try to follow the lead of Asia on rote learning. The United States in the 18th and 19th century lead the world with innovative education; we in fact educated all children not just those of the wealthy. We need to sit down and rethink education completely. I agree with Hacker that we need to teach more analytical and strategic thinking, encourage creativity and teach people to think out of the box. Hacker states that with the over emphasis on math we have segregated social science and the humanities to a place of lesser value. I have seen this happen and it needs to be corrected as these fields are of equal value to science, math and engineering. Hacker states we need to include in the regular course work art and music as both also use math and arithmetic skills and teach creativity. Hacker also recommends that arithmetic and math skills be taught to the level and job requirements rather than everyone in high school having to learn trig and calculus. He provides the example of a person unable to enroll in a cosmetology course because she failed algebra in high school.
To me education is providing an introduction of a wide range of topics, information and subjects in a stimulating and exciting way to grab the student’s interest and imagination to want to learn more. If one grabs the attention of a student in a topic so they want to make a career in that field, then that is success. I think more time and money should be spent on educating better math teachers and improving or creating better ways to teach math and arithmetic.
I read this as an audiobook downloaded from Audible. This book would be more effective if read in book format or download the PDF from audiobook publisher. Barry Press does a good job narrating the book. Press is an actor that also narrates audiobooks.
January 15, 2022
Though now a bit out of date, this remains an essential text. It makes points that should be common sensical but are seen as anything but. They include
1. Not every child can be good at math.
2. Many, many children are facing unnecessary hardship because we're trying to force them to be good at math.
3. Being good at math can be a great advantage in the job market, but it's not a necessary one.
4. Policy choices can help students find better personal paths, but not if we keep trying to stuff every student into the same STEM box.
A valuable corrective and an interesting bit of polemic, recommended.
1. Not every child can be good at math.
2. Many, many children are facing unnecessary hardship because we're trying to force them to be good at math.
3. Being good at math can be a great advantage in the job market, but it's not a necessary one.
4. Policy choices can help students find better personal paths, but not if we keep trying to stuff every student into the same STEM box.
A valuable corrective and an interesting bit of polemic, recommended.
April 27, 2016
Good, little repetitive if one is used to consuming books and podcasts like Freakanomics.
Essentially lays out the case not to eliminate math, but just we shouldn't emphasize high level math so much in grade school and high school. High level in this case being beyond first year algebra.
One thing I appreciated it was the 'why do we just measure our educational success against STEM? What about fine arts, how do we stack up against other countries there?' sort of attitude.
Essentially lays out the case not to eliminate math, but just we shouldn't emphasize high level math so much in grade school and high school. High level in this case being beyond first year algebra.
One thing I appreciated it was the 'why do we just measure our educational success against STEM? What about fine arts, how do we stack up against other countries there?' sort of attitude.
May 11, 2022
Up front I must admit that I am a mathematics professor and, as such, cannot claim to be an impartial reviewer. In this book, Hacker makes several claims:
1. US High School mathematics is entirely geared for college preparation.
2. US College/University mathematics is the domain of “mandarins” whose entire goal is to protect the discipline’s status within education (both K-12 and higher ed).
3. The importance of STEM education, and Math in particular, has been oversold.
4. The vast majority of Americans do not need mathematics beyond an 8th grade (algebra) level.
5. Mathematics requirements at all levels of education are actively detrimental to majorities of students.
While I agree in large part with many of the above claims, I do not think this book presents a compelling case. This is for two reasons: first, the author clearly has an axe to grind and ignores that many of the issues he raises, while valid, are anything but exclusive to mathematics; and second, that these criticisms are much beside the point if you see the purpose of education as anything besides career-preparation, which I do.
To explain a bit more on the first reason, my essential rebuttal is that many of his arguments regarding mathematics in higher education could be made against almost any academic discipline, and certainly those under the umbrella of “arts and sciences”. The topics taught in an average college classroom are, strictly speaking, unnecessary and will never be used in the student’s lives after the class ends. Faculty are universally jealous of their areas of expertise and regard themselves as the ultimate authorities. If economics, for example, were a core part of K-12 education then university economics faculty would indeed have strong opinions about how it should be taught there.
A final mark against this book: Hacker’s style seems to be designed to appeal to readers with preexisting aversions to mathematics: tossing in scary-sounding mathematical words frequently (“azimuth” and “asymptote” are popular, presumably for the alliteration) and cherry-picking example problems (such as from the SAT or Common Core) which are notationally intimidating. His numeracy course detailed in the final chapter is the typical investigatory-learning pablum served up to the intelligent-but-math-phobic as “evidence” that you can learn math-adjacent stuff without all those worrisome equations.
1. US High School mathematics is entirely geared for college preparation.
2. US College/University mathematics is the domain of “mandarins” whose entire goal is to protect the discipline’s status within education (both K-12 and higher ed).
3. The importance of STEM education, and Math in particular, has been oversold.
4. The vast majority of Americans do not need mathematics beyond an 8th grade (algebra) level.
5. Mathematics requirements at all levels of education are actively detrimental to majorities of students.
While I agree in large part with many of the above claims, I do not think this book presents a compelling case. This is for two reasons: first, the author clearly has an axe to grind and ignores that many of the issues he raises, while valid, are anything but exclusive to mathematics; and second, that these criticisms are much beside the point if you see the purpose of education as anything besides career-preparation, which I do.
To explain a bit more on the first reason, my essential rebuttal is that many of his arguments regarding mathematics in higher education could be made against almost any academic discipline, and certainly those under the umbrella of “arts and sciences”. The topics taught in an average college classroom are, strictly speaking, unnecessary and will never be used in the student’s lives after the class ends. Faculty are universally jealous of their areas of expertise and regard themselves as the ultimate authorities. If economics, for example, were a core part of K-12 education then university economics faculty would indeed have strong opinions about how it should be taught there.
A final mark against this book: Hacker’s style seems to be designed to appeal to readers with preexisting aversions to mathematics: tossing in scary-sounding mathematical words frequently (“azimuth” and “asymptote” are popular, presumably for the alliteration) and cherry-picking example problems (such as from the SAT or Common Core) which are notationally intimidating. His numeracy course detailed in the final chapter is the typical investigatory-learning pablum served up to the intelligent-but-math-phobic as “evidence” that you can learn math-adjacent stuff without all those worrisome equations.
March 14, 2016
This book should be required reading for every teacher at every level of our education system. Arithmetic is necessary for an enlightened citizenry. Algebra and Geometry might make you a more critical thinker. Calculus could save you from intellectual rot. But requiring ALL prospective college students to be fluent in advanced mathematics is chasing millions of otherwise capable children from both high school and advanced degrees. It is just as likely that a banker will use Dostoevsky as differential equations. Just as a painter might use fractal geometry more than Foucault . An enlightened mind takes many forms.
June 11, 2016
Grade F Work
Hard to take Hacker seriously as an author when he has to resort to name-calling to try to make his point. Just because you don't understand calculus doesn't mean it's not worth a studying. Typical humanities reaction to math. I hope no educator in America is foolish enough to take this seriously. I would almost think this is an Onion parody, except it's not well-written enough. Don't waste your time on this piece of cr*p.
Hard to take Hacker seriously as an author when he has to resort to name-calling to try to make his point. Just because you don't understand calculus doesn't mean it's not worth a studying. Typical humanities reaction to math. I hope no educator in America is foolish enough to take this seriously. I would almost think this is an Onion parody, except it's not well-written enough. Don't waste your time on this piece of cr*p.
April 2, 2016
Hacker convincingly debunks the nonsensical assertions about the practical value of requiring all students to master higher-level mathematics, and persuasively explains why America's obsessions one-size-fits-all approach to schooling does a gross disservice to students and institutions of learning. Lively, provocative, and insightful.
April 26, 2016
Challenges prevailing thought and really gets you thinking.
October 19, 2022
It appears to me that Andrew Hacker had bad childhood experiences with math, decided it was way too hard, and set out to convince the world he's right. Unfortunately for him, his book is so riddled with errors, lies, and logical fallacies that I can't even begin to take him seriously. There are some good points that he started trying to make, and then he kept getting derailed by outrageous claims and ideas that undermined his arguments.
Before I get too far into this review, I'll admit that I am quite biased in favor of math education, since I have a B.S. in Mathematics and I work as a college math tutor. But I also work regularly with students who are struggling in math, and I'm sympathetic to their difficulties. There are lots of problems with math education and testing in the U.S., and this could have been a great book if it had focused on the truth!
An overarching problem throughout the book is that Hacker creates an artificial separation between "arithmetic" and "mathematics." He tells us on page 7, "Mathematics basically begins in high school," and that the math encountered in everyday life is pretty much all "arithmetic." He then spends the rest of the book calling algebra "advanced mathematics" that has nothing to do with everyday life. I don't think that basic algebra is advanced math! It requires an ability to think abstractly, which is why we don't teach it to first graders, but the vast majority of adults can learn beginning algebra, and it has many applications in everyday life. Hacker loses all credibility with me when he spends the whole book saying that "advanced mathematics" (i.e., algebra and geometry) is completely unrelated to most people's lives. (He actually admits early in the book that basic algebra is relevant to daily life, but then he seems to forget that for the rest of the book.) He also claims that math has nothing to do with coding. This seems like saying that flour and eggs have nothing to do with cake. He promised early in the book that later he would go into more details about coding and why it's unrelated to math, and I was looking forward to seeing how he could possibly try to back up that claim, but he never returned to the topic.
This false distinction between "arithmetic" and "advanced mathematics" is essential to Hacker's arguments throughout the book that we need to be teaching math differently. He believes (seriously) that there is a conspiracy among high-level mathematicians (he calls them "mandarins") to force students to study topics that are irrelevant and exceptionally difficult. He honestly thinks that math departments in colleges refuse to teach classes that relate math to real life experiences. This is just false! At the community college where I work, we have two common college-level math tracks: the standard algebra/trigonometry/calculus, and another track with a series called "Math in Society" and possibly continuing on to statistics. The Math in Society class covers topics like loans and interest, elementary statistics, voting, taxes, logic and logical fallacies, and reading charts and tables. It's commonly taken by non-STEM majors who don't intend to continue on to calculus. It's exactly the type of class that Hacker spends the whole book saying that we need (but the elite mathematics cabal supposedly won't consent to). My college has been teaching this course for as long as I've been working there (over a decade). I doubt we're that unique. It seems that Hacker just didn't do adequate research.
When he does present the results of research he has done, it is riddled with ridiculous errors. He frequently gives examples of questions that are supposedly samples of questions from maths tests and texts. By the end of the book, I had decided that he was making up many of these (if not all of them). Most of them aren't even valid questions (they omit critical information, are filled with typographical errors, give contradictory information, etc.). One example of supposed test questions was just quoting standards from Common Core - they would never be on a test in that format.
One example that I found particularly egregious was supposedly from a financial literacy class developed for a high school. Hacker said that he thought a financial literacy class was a great idea, but then claims that after seeing the lessons, he realized that they're just more of the elite forcing advanced math on students in ways they could never apply to real life. I'm not going to reproduce his entire example here, but it's on page 172 of the book, entitled Cell Phone Expenses. I would absolutely be appalled if this example were in a math lesson anywhere. It gives a function that supposedly describes the cost of a cell phone plan, but the function just doesn't make sense and would never be reasonably used to describe cell phone expenses. (One piece of the "split function" is "F(x) = 40 +0.35([x-750] + 1) if x > 750 and x is not an integer." It seems to be trying to use the "+ 1" to round x up to the nearest integer.) I highly doubt that this is a real example from any lesson. Hacker may have read a lesson, failed to understand it, and then made up something similar that didn't make sense because he lacks a solid understanding of the topic.
In contrast, I frequently tutor students in algebra classes who encounter problems about things like cell phone expenses. A problem might go something like this:
Cell phone plan A costs $50 a month for unlimited minutes. Cell phone plan B costs $20 a month plus 10 cents per minute. How many minutes would you have to use per month for plan A to be more cost-effective than plan B?
This is a straightforward math problem that's very relevant to real life. It's also an example of the type of question that is commonly found in algebra textbooks - the very books that Hacker believes are unnecessarily difficult and unrelated to everyday life. The problem seems to be that Hacker has no idea what algebra actually entails, since he can't even reproduce examples coherently.
Hacker sprinkles mathematical phrases throughout the book without any indication that he really knows what the phrases mean. His goal seems to be to make math sound difficult by using big words. It gets very annoying, like if I filled this review with French phrases in an attempt to sound fancy. (I don't speak French. What a faux pas!)
Many of the arguments Hacker makes could be just as easily applied to almost any high school subject. Why require students to study history, or science, or physical education? Are we likely to need to know the date of the Magna Carta in everyday life? How is it relevant in the average career to know whether Pluto is classified as a dwarf planet? I think English is probably the only subject that is absolutely necessary in most careers (in an English-speaking country). And even so, there's no need to study Shakespeare or other difficult literature. That's just an obstacle keeping students from getting their diplomas and degrees, right? Why make students study any of it?
High school and college educations are supposed to be more than minimal career training. They indicate that the recipients have been exposed to a variety of topics, that they have learned to think critically and abstractly. If we drop everything "unnecessary" from the curriculum, we could probably save a lot of time and just give students their diplomas after elementary school. Math teaches logical thinking and problem solving, in addition to the ways it directly applies to everyday life. Hacker says that we can teach those skills in other ways, and I agree - that's why we have classes in many different topics. But math has excellent properties that make it especially helpful in developing some analytical and critical thinking skills. Dropping algebra from high school requirements would weaken the meaning of a diploma.
The funny thing is that I actually agree with Hacker about many of the issues he identifies. Common Core has a lot of problems. Standardized tests are overused and biased in favor of certain populations. Math classes are major hurdles for many students and even derail some educational plans. Timed tests measure speed instead of understanding. A surprisingly high percentage of adults lack numerical literacy skills. But the solution is not to stop teaching algebra! (This reminds me of the joke where a patient tells his doctor that it hurts when he raises his arm, and the doctor tells him to stop raising his arm.)
An example of a way Hacker completely skews information to try to support his point occurs on pages 149-150. Hacker references a study that asked math teachers if they agreed or disagreed with the statement, "Some students have a natural talent for mathematics and others do not." Hacker claims that since 82% of American teachers surveyed agreed with this statement, "four in five of our mathematics teachers believe that success in their subject calls for special genetic endowments." What a misinterpretation of the data! I agree with the idea that some students are more talented than others, in math as well as other areas, but does that mean that success requires natural talent? Of course not! I would never suggest that we should only teach reading to children who pick up on it quickly, or only allow tall children to play basketball. "Natural talent" is NOT a requirement for success in basic high school or college math, and I think the majority of teachers would agree with me.
Maybe the most alarming part of the book is that Hacker has actually taught a college math class! He's thoroughly unqualified (he normally teaches political science), he's obviously not very good at math (as evidenced by all the errors in his book), and his description of the material covered in the class is appalling. For example, he has his students calculate the area of West Virginia by filling a map with dots and COUNTING the dots. He describes his students groaning at the prospect of counting thousands of tiny dots on a map - because this is a ridiculous activity! A major goal of math is to notice patterns that allow us to simplify problems like that. For example, I might overlay the map with a grid and count the dots in one square on the grid, then multiply by the number of squares completely contained within West Virginia. Then I would only need to count dots in border squares. Hacker also has his students "verify" the value of pi by measuring cake pans and aluminum cans - does this qualify as college-level math? This is the math of millenia ago, before we had more sophisticated methods. As far as I can tell, Hacker had his students merely following directions and performing simple arithmetic rather than attempting to do any mathematical thinking or problem solving. He led the class in some interesting discussions, but they sounded like the work of a political science teacher rather than a math teacher (i.e., having the class debate the meaning of the word "most"). I'm in favor of Hacker's point throughout the book that we need more education on math literacy in everyday life. But his class didn't seem like it taught the students how to actually use math to solve everyday problems. They certainly shouldn't be finding the area of anything by counting thousands of dots one by one!
In summary, while I'm sure there are some great books out there discussing the problems with mathematics education in the U.S., this book is not one of them. I cringe at the possibility that anybody is taking Andrew Hacker seriously.
Before I get too far into this review, I'll admit that I am quite biased in favor of math education, since I have a B.S. in Mathematics and I work as a college math tutor. But I also work regularly with students who are struggling in math, and I'm sympathetic to their difficulties. There are lots of problems with math education and testing in the U.S., and this could have been a great book if it had focused on the truth!
An overarching problem throughout the book is that Hacker creates an artificial separation between "arithmetic" and "mathematics." He tells us on page 7, "Mathematics basically begins in high school," and that the math encountered in everyday life is pretty much all "arithmetic." He then spends the rest of the book calling algebra "advanced mathematics" that has nothing to do with everyday life. I don't think that basic algebra is advanced math! It requires an ability to think abstractly, which is why we don't teach it to first graders, but the vast majority of adults can learn beginning algebra, and it has many applications in everyday life. Hacker loses all credibility with me when he spends the whole book saying that "advanced mathematics" (i.e., algebra and geometry) is completely unrelated to most people's lives. (He actually admits early in the book that basic algebra is relevant to daily life, but then he seems to forget that for the rest of the book.) He also claims that math has nothing to do with coding. This seems like saying that flour and eggs have nothing to do with cake. He promised early in the book that later he would go into more details about coding and why it's unrelated to math, and I was looking forward to seeing how he could possibly try to back up that claim, but he never returned to the topic.
This false distinction between "arithmetic" and "advanced mathematics" is essential to Hacker's arguments throughout the book that we need to be teaching math differently. He believes (seriously) that there is a conspiracy among high-level mathematicians (he calls them "mandarins") to force students to study topics that are irrelevant and exceptionally difficult. He honestly thinks that math departments in colleges refuse to teach classes that relate math to real life experiences. This is just false! At the community college where I work, we have two common college-level math tracks: the standard algebra/trigonometry/calculus, and another track with a series called "Math in Society" and possibly continuing on to statistics. The Math in Society class covers topics like loans and interest, elementary statistics, voting, taxes, logic and logical fallacies, and reading charts and tables. It's commonly taken by non-STEM majors who don't intend to continue on to calculus. It's exactly the type of class that Hacker spends the whole book saying that we need (but the elite mathematics cabal supposedly won't consent to). My college has been teaching this course for as long as I've been working there (over a decade). I doubt we're that unique. It seems that Hacker just didn't do adequate research.
When he does present the results of research he has done, it is riddled with ridiculous errors. He frequently gives examples of questions that are supposedly samples of questions from maths tests and texts. By the end of the book, I had decided that he was making up many of these (if not all of them). Most of them aren't even valid questions (they omit critical information, are filled with typographical errors, give contradictory information, etc.). One example of supposed test questions was just quoting standards from Common Core - they would never be on a test in that format.
One example that I found particularly egregious was supposedly from a financial literacy class developed for a high school. Hacker said that he thought a financial literacy class was a great idea, but then claims that after seeing the lessons, he realized that they're just more of the elite forcing advanced math on students in ways they could never apply to real life. I'm not going to reproduce his entire example here, but it's on page 172 of the book, entitled Cell Phone Expenses. I would absolutely be appalled if this example were in a math lesson anywhere. It gives a function that supposedly describes the cost of a cell phone plan, but the function just doesn't make sense and would never be reasonably used to describe cell phone expenses. (One piece of the "split function" is "F(x) = 40 +0.35([x-750] + 1) if x > 750 and x is not an integer." It seems to be trying to use the "+ 1" to round x up to the nearest integer.) I highly doubt that this is a real example from any lesson. Hacker may have read a lesson, failed to understand it, and then made up something similar that didn't make sense because he lacks a solid understanding of the topic.
In contrast, I frequently tutor students in algebra classes who encounter problems about things like cell phone expenses. A problem might go something like this:
Cell phone plan A costs $50 a month for unlimited minutes. Cell phone plan B costs $20 a month plus 10 cents per minute. How many minutes would you have to use per month for plan A to be more cost-effective than plan B?
This is a straightforward math problem that's very relevant to real life. It's also an example of the type of question that is commonly found in algebra textbooks - the very books that Hacker believes are unnecessarily difficult and unrelated to everyday life. The problem seems to be that Hacker has no idea what algebra actually entails, since he can't even reproduce examples coherently.
Hacker sprinkles mathematical phrases throughout the book without any indication that he really knows what the phrases mean. His goal seems to be to make math sound difficult by using big words. It gets very annoying, like if I filled this review with French phrases in an attempt to sound fancy. (I don't speak French. What a faux pas!)
Many of the arguments Hacker makes could be just as easily applied to almost any high school subject. Why require students to study history, or science, or physical education? Are we likely to need to know the date of the Magna Carta in everyday life? How is it relevant in the average career to know whether Pluto is classified as a dwarf planet? I think English is probably the only subject that is absolutely necessary in most careers (in an English-speaking country). And even so, there's no need to study Shakespeare or other difficult literature. That's just an obstacle keeping students from getting their diplomas and degrees, right? Why make students study any of it?
High school and college educations are supposed to be more than minimal career training. They indicate that the recipients have been exposed to a variety of topics, that they have learned to think critically and abstractly. If we drop everything "unnecessary" from the curriculum, we could probably save a lot of time and just give students their diplomas after elementary school. Math teaches logical thinking and problem solving, in addition to the ways it directly applies to everyday life. Hacker says that we can teach those skills in other ways, and I agree - that's why we have classes in many different topics. But math has excellent properties that make it especially helpful in developing some analytical and critical thinking skills. Dropping algebra from high school requirements would weaken the meaning of a diploma.
The funny thing is that I actually agree with Hacker about many of the issues he identifies. Common Core has a lot of problems. Standardized tests are overused and biased in favor of certain populations. Math classes are major hurdles for many students and even derail some educational plans. Timed tests measure speed instead of understanding. A surprisingly high percentage of adults lack numerical literacy skills. But the solution is not to stop teaching algebra! (This reminds me of the joke where a patient tells his doctor that it hurts when he raises his arm, and the doctor tells him to stop raising his arm.)
An example of a way Hacker completely skews information to try to support his point occurs on pages 149-150. Hacker references a study that asked math teachers if they agreed or disagreed with the statement, "Some students have a natural talent for mathematics and others do not." Hacker claims that since 82% of American teachers surveyed agreed with this statement, "four in five of our mathematics teachers believe that success in their subject calls for special genetic endowments." What a misinterpretation of the data! I agree with the idea that some students are more talented than others, in math as well as other areas, but does that mean that success requires natural talent? Of course not! I would never suggest that we should only teach reading to children who pick up on it quickly, or only allow tall children to play basketball. "Natural talent" is NOT a requirement for success in basic high school or college math, and I think the majority of teachers would agree with me.
Maybe the most alarming part of the book is that Hacker has actually taught a college math class! He's thoroughly unqualified (he normally teaches political science), he's obviously not very good at math (as evidenced by all the errors in his book), and his description of the material covered in the class is appalling. For example, he has his students calculate the area of West Virginia by filling a map with dots and COUNTING the dots. He describes his students groaning at the prospect of counting thousands of tiny dots on a map - because this is a ridiculous activity! A major goal of math is to notice patterns that allow us to simplify problems like that. For example, I might overlay the map with a grid and count the dots in one square on the grid, then multiply by the number of squares completely contained within West Virginia. Then I would only need to count dots in border squares. Hacker also has his students "verify" the value of pi by measuring cake pans and aluminum cans - does this qualify as college-level math? This is the math of millenia ago, before we had more sophisticated methods. As far as I can tell, Hacker had his students merely following directions and performing simple arithmetic rather than attempting to do any mathematical thinking or problem solving. He led the class in some interesting discussions, but they sounded like the work of a political science teacher rather than a math teacher (i.e., having the class debate the meaning of the word "most"). I'm in favor of Hacker's point throughout the book that we need more education on math literacy in everyday life. But his class didn't seem like it taught the students how to actually use math to solve everyday problems. They certainly shouldn't be finding the area of anything by counting thousands of dots one by one!
In summary, while I'm sure there are some great books out there discussing the problems with mathematics education in the U.S., this book is not one of them. I cringe at the possibility that anybody is taking Andrew Hacker seriously.
December 19, 2019
Coming from STEM and majoring in Economics, I am no stranger to the inefficacies and the troubles involved in the process of guaranteeing the general student population a high degree of mathematical literacy. I am for reform in education when it comes to Math and Science; the way we are teaching isn't cutting it. All these words to say that I wanted to like this book. Sadly, I didn't.
Mr. Hacker posits -- correctly -- that a high number American students are subjected to mathematical courses entirely too difficult for their abilities or aspirations, thus affecting their grades and preventing them from enrolling in college.
Unfortunately, that's where the interesting part ends: after that, we're presented with some hilariously bad analogies, leaps in logic and, frankly, intellectual dishonesty.
Mr. Hacker's problems are with the educational system, the privatization of universities and the labor market -- but unfortunately, he doesn't know that because he doesn't know math. Mr. Hacker uses STEM education as the be-all-end-all reason for all problems in America: everything from the drop-out rate to sexism. Whenever he's self-aware enough to claim that there might multiple variables behind the problems he's describing, he quickly jolts over them and never provides any empirical insight, which is a big neon sign of intellectual laziness.
Mr. Hacker also advocates for eliminating abstract mathematics -- such as algebra -- from the schools' curriculum and replacing it with simple arithmetic, because that's what the average American ever needs (I'm paraphrasing). This is something I have a hard time agreeing with for a multitude of reasons, the primary one being because I'm not an idiot. I would argue that mathematical thought improves our problem-solving efficiency, helps us visualize things in a more abstract plane, and, overall, it deepens our reasoning ability, but alas! Mr. Hacker has already preemptively refuted my claims with one of his remarkable arguments:
My favorite part about this book is definitely how bad the statistics are. Mr. Hacker clearly does not understand them. In fact, he's so bad that, for a moment, I thought I was reading satire. He is literally using misleading and under-analyzed mathematics to argue against math education. Make of that what you will.
It's a very silly book.
Mr. Hacker posits -- correctly -- that a high number American students are subjected to mathematical courses entirely too difficult for their abilities or aspirations, thus affecting their grades and preventing them from enrolling in college.
Unfortunately, that's where the interesting part ends: after that, we're presented with some hilariously bad analogies, leaps in logic and, frankly, intellectual dishonesty.
Mr. Hacker's problems are with the educational system, the privatization of universities and the labor market -- but unfortunately, he doesn't know that because he doesn't know math. Mr. Hacker uses STEM education as the be-all-end-all reason for all problems in America: everything from the drop-out rate to sexism. Whenever he's self-aware enough to claim that there might multiple variables behind the problems he's describing, he quickly jolts over them and never provides any empirical insight, which is a big neon sign of intellectual laziness.
Mr. Hacker also advocates for eliminating abstract mathematics -- such as algebra -- from the schools' curriculum and replacing it with simple arithmetic, because that's what the average American ever needs (I'm paraphrasing). This is something I have a hard time agreeing with for a multitude of reasons, the primary one being because I'm not an idiot. I would argue that mathematical thought improves our problem-solving efficiency, helps us visualize things in a more abstract plane, and, overall, it deepens our reasoning ability, but alas! Mr. Hacker has already preemptively refuted my claims with one of his remarkable arguments:
'Of course mathematics' teachers and professors have to claim that what they do sharpens your thinking skills and makes you generally a better thinker. There is no evidence at all that people who have done a full menu of mathematics are any more thoughtful than the rest of us. I looked around for research to show that people trained in mathematics are smarter, more logical and couldn't find any. So I did a study of my own: at my college, every student takes a math test in order to get in. So, I took an incoming freshman who opted to take an introductory course in History. Then what I did was I lined up their math scores and their grades in the History course. Guess what? Zero correlation. Some people who did well in Math did well in History, and some who did well in Math bombed in History.'Great study, bro, very legit. On top of trying to pass this hilariously bad methodology as valid reasoning, Mr. Hacker also claims STEM education is one big conspiracy and the professors are behind it.
My favorite part about this book is definitely how bad the statistics are. Mr. Hacker clearly does not understand them. In fact, he's so bad that, for a moment, I thought I was reading satire. He is literally using misleading and under-analyzed mathematics to argue against math education. Make of that what you will.
It's a very silly book.
February 11, 2017
I knew I would have disagreements with this book before I started, but I was willing to give it a shot.
That ended on page 5, where the author cites what is supposed to be an example of a question students will answer on a Common Core exam:
"Use the properties of exponents to interpret expressions of exponential functions. For example, identify percent rate of change in..."
Wait a minute...this isn't a question at all! This is, in fact, the word-for-word standard F-IF.8.b from the Common Core. Students will never see this. It's used to inform the content taught in math classrooms. Already we see an outright lie. Either the author is so ignorant of mathematics education that he can't identify a math content standard, or he is willing to blatantly lie to his audience.
He continues his tirade about mathematics by slicing down the argument that being proficient in math will make you an expert in other areas; an argument I've never once heard before. I wish he had cited where he got that from.
What I took greatest exception to is the chapter where he discusses mathematical competitions and shows that the top ten countries in the 2013 Math Olympiad contained North Korea, Iran, China, Russia, and Vietnam. "So what can we conclude about mathematics, when it's brand of brilliance can thrive amid onerous repression?" Apparently the same thing we can conclude about the Olympics. Didn't you see that Russia is second in medal count? What can we conclude about athletics when it seems to thrive under such repression!?
This faulty logic, deliberate misinformation, and clear misunderstanding or deliberate misuse of mathematics is being used to prop up arguments that aren't even against math itself. Most of the arguments boil down to "math is hard" and "standardized tests don't work." This book isn't worth the paper it's printed on.
That ended on page 5, where the author cites what is supposed to be an example of a question students will answer on a Common Core exam:
"Use the properties of exponents to interpret expressions of exponential functions. For example, identify percent rate of change in..."
Wait a minute...this isn't a question at all! This is, in fact, the word-for-word standard F-IF.8.b from the Common Core. Students will never see this. It's used to inform the content taught in math classrooms. Already we see an outright lie. Either the author is so ignorant of mathematics education that he can't identify a math content standard, or he is willing to blatantly lie to his audience.
He continues his tirade about mathematics by slicing down the argument that being proficient in math will make you an expert in other areas; an argument I've never once heard before. I wish he had cited where he got that from.
What I took greatest exception to is the chapter where he discusses mathematical competitions and shows that the top ten countries in the 2013 Math Olympiad contained North Korea, Iran, China, Russia, and Vietnam. "So what can we conclude about mathematics, when it's brand of brilliance can thrive amid onerous repression?" Apparently the same thing we can conclude about the Olympics. Didn't you see that Russia is second in medal count? What can we conclude about athletics when it seems to thrive under such repression!?
This faulty logic, deliberate misinformation, and clear misunderstanding or deliberate misuse of mathematics is being used to prop up arguments that aren't even against math itself. Most of the arguments boil down to "math is hard" and "standardized tests don't work." This book isn't worth the paper it's printed on.
July 3, 2018
This book is far too alarmist for the quality of arguments it contains. Of the arguments it presents, the two I agree with is that not everyone needs to learn advanced math depending on the type of job they want (there's no reason for a dance major to need to prove proficiency in advanced calculus), and that the number of qualified domestic STEM majors more than outpaces the number of vacancies for such positions even though companies will claim H1B1 visas are the only way to get the skills they need (it's called training and/or paying better wages, both of which they are loath to do). I also partially agree that the focus on STEM is diminishing to other disciplines (while I support having more women in STEM, I also think it'd be great if we valued the work women do in other fields just as much). The rest is very meh. It's a bit weird to say that it's bad for math to be the subject that causes most students to fail; some subject has to have that title and it happens to be math. The idea that this is bad because math is an esoteric subject is also a bit odd. Math is challenging to many because it's tends to be a different way of thinking, and different ways of approaching problems is exactly what should be taught. Oh, and while I don't use the advanced math I learned in university in my day-to-day job as an engineer, I also don't use history or American geography or...yet I still learned them, so why is math the one being called out as superfluous?
May 16, 2016
Most of us have never used even a sliver of the High School math that we were taught. Most occupations do not require it. But all students must display a proficiency in Algebra, Trig, even calculus to graduate from HS, and most students who go on to community college end up taking remedial math because they already have forgotten all the maybe knew.
This book asks if this is really all necessary. Should we be require to take math that is essentially irrelevant to all but a few. Does it cause perfectly good students to give up on HS and college when their talents are elsewhere? Isn't this a real waste of human capital? We bar thousands of people yearly from going to or graduating from college by demanding they learn an arcane subject that will never again come up in their lives.
This is the author's thesis, and he makes a lot of sense. He argues for numerical literacy so that we can function at a high level in daily life, and only the higher math that is relevant and necessary to become an engineer, scientist or mathematician (although who know what the hell they actually do!) etc.
When I think of all the hours I have spent solving quadratic equations and mastering integral calculus--What a waste of time.
The author, btw, is a college Professor of Mathematics.
This book asks if this is really all necessary. Should we be require to take math that is essentially irrelevant to all but a few. Does it cause perfectly good students to give up on HS and college when their talents are elsewhere? Isn't this a real waste of human capital? We bar thousands of people yearly from going to or graduating from college by demanding they learn an arcane subject that will never again come up in their lives.
This is the author's thesis, and he makes a lot of sense. He argues for numerical literacy so that we can function at a high level in daily life, and only the higher math that is relevant and necessary to become an engineer, scientist or mathematician (although who know what the hell they actually do!) etc.
When I think of all the hours I have spent solving quadratic equations and mastering integral calculus--What a waste of time.
The author, btw, is a college Professor of Mathematics.
February 10, 2017
Interesting idea that we need less not more math, or more applicable vs theoretical math. I like that idea that the things you learn can and should be usable. Some good arguments. I am curious what a math teacher thinks of this premise.
Disagree with author's belief that Common Core has higher math standards. Whatever its initial intent, I have seen Common Core dumb down ambitious, challenging curriculum. When I read an Algebra 2 common core course description that weighs math essays heavier than problems and states that the right answer is not as important as the explanation, I choose not to use that curriculum. The right answer always matters in math and as it applies to science. The wrong number in engineering and medicine could have severe consequences.
Getting more citizens math smart, math literate, in order to think critically, understand measurements, statistics, and graphs is important. More important than higher math for fewer people. Good book for thought food.
Disagree with author's belief that Common Core has higher math standards. Whatever its initial intent, I have seen Common Core dumb down ambitious, challenging curriculum. When I read an Algebra 2 common core course description that weighs math essays heavier than problems and states that the right answer is not as important as the explanation, I choose not to use that curriculum. The right answer always matters in math and as it applies to science. The wrong number in engineering and medicine could have severe consequences.
Getting more citizens math smart, math literate, in order to think critically, understand measurements, statistics, and graphs is important. More important than higher math for fewer people. Good book for thought food.
May 3, 2016
This is among the most interesting books I have read on education today, and possibly the most important. As a journalism teacher I have questioned the emphasis on higher math in recent years. Hacker explains why we should question it, and question why math gets half the value or more in advancing in American education the book is highly readable and rich with both statistical and anecdotal evidence that the STEM movement has sold us a bill of goods.
July 18, 2016
Definitely a thought-provoking book. I agreed with some ideas, and would argue against others. I especially enjoyed reading about the discovery versus discipline styles of teaching, as well as the "voices" quotes included in various chapters.
October 3, 2016
The manifesto I have been waiting for since the second grade. Andrew Hacker deserves a medal.
May 9, 2016
Everyone needs numerical literacy, but teaching more/higher level math serves as a barrier.
June 18, 2016
Decision makers and educators fail to carefully and continually reconsider what it is that we teach and why and that does our society a grave disservice. There is simply no good reason to maintain our programs of study in their current form other than tradition, which no longer serves. This is the central point that Hacker makes, one that I share in my own book, Engage! Setting the Course for Independent Secondary Schools in the 21st Century. When we require that all students attain a certain bar in one field, we discount their varied talents and we fail to benefit from the many ways that they could contribute to society.
STEM is the buzzword in private and public schools around the country. We are told that STEM occupations are the future and that higher math is the key to STEM. Hacker finds both to be fraudulent. The government's labor statistics do not portend an increase in STEM fields. Foreigners are hired on H1B visas not due to lack of our own people to fill the positions but because they are cheaper and require fewer benefits, since they cannot leave a company without being forced to leave the US. The math required, even in engineering, involves number relationships that are quite specific to an individual field, almost never calculus and differential equations.
Math is proven in several studies to be the number one cause of attrition in both high schools and college, even when there is no reason for the requirements to be as they are. In 1982, 55% of high school graduates had a course in algebra, today 76% have had 2 years of it, but 20%-30% of all high school students drop out and 40% drop out of college due to failing math. Higher mathematics courses are used as arbitrary means to winnow the pool of applicants for university or professions and raise their level of prestige. There is zero evidence that mathematics trains the mind any better than any number of other fields, nor is the type of thinking that math engenders transferable. There is zero correlation between math scores and history grades, for example. The claim that mathematical "modes of reasoning can enrich our understanding of the entire human and social condition," also seems suspect in view of the provenance of champions in the elite math competitions from repressive countries like North Korea, China, Iran, and Russia.
Further, the foxes are in charge of the henhouse. When university programs like Biology or Engineering attempt to create their own math courses specific to their disciplines, the math mandarins take issue and shut them down. When math standards are up for assessment in public schools, again, the math mandarins charge set them high for no good reason other than to establish their own fiefdom and reinforce their prestige. Instead, Hacker affirms that we should be focusing on the kinds of mathematics that we use every day, as well as a basic understanding of statistics.
As a longtime educator, as much as I support much of what the author affirms, I do take issue with some of Hacker's proposals. Giving students exams to take home does not work because outside help from parents, tutors and others is widespread in many communities. As for his opposition to ability grouping, there is considerable research for and against and I am squarely in the pro- camp.
This book is surely worth a read by educators on the K-12 and college levels. It's time that we reconsider our requirements.
STEM is the buzzword in private and public schools around the country. We are told that STEM occupations are the future and that higher math is the key to STEM. Hacker finds both to be fraudulent. The government's labor statistics do not portend an increase in STEM fields. Foreigners are hired on H1B visas not due to lack of our own people to fill the positions but because they are cheaper and require fewer benefits, since they cannot leave a company without being forced to leave the US. The math required, even in engineering, involves number relationships that are quite specific to an individual field, almost never calculus and differential equations.
Math is proven in several studies to be the number one cause of attrition in both high schools and college, even when there is no reason for the requirements to be as they are. In 1982, 55% of high school graduates had a course in algebra, today 76% have had 2 years of it, but 20%-30% of all high school students drop out and 40% drop out of college due to failing math. Higher mathematics courses are used as arbitrary means to winnow the pool of applicants for university or professions and raise their level of prestige. There is zero evidence that mathematics trains the mind any better than any number of other fields, nor is the type of thinking that math engenders transferable. There is zero correlation between math scores and history grades, for example. The claim that mathematical "modes of reasoning can enrich our understanding of the entire human and social condition," also seems suspect in view of the provenance of champions in the elite math competitions from repressive countries like North Korea, China, Iran, and Russia.
Further, the foxes are in charge of the henhouse. When university programs like Biology or Engineering attempt to create their own math courses specific to their disciplines, the math mandarins take issue and shut them down. When math standards are up for assessment in public schools, again, the math mandarins charge set them high for no good reason other than to establish their own fiefdom and reinforce their prestige. Instead, Hacker affirms that we should be focusing on the kinds of mathematics that we use every day, as well as a basic understanding of statistics.
As a longtime educator, as much as I support much of what the author affirms, I do take issue with some of Hacker's proposals. Giving students exams to take home does not work because outside help from parents, tutors and others is widespread in many communities. As for his opposition to ability grouping, there is considerable research for and against and I am squarely in the pro- camp.
This book is surely worth a read by educators on the K-12 and college levels. It's time that we reconsider our requirements.
August 30, 2020
I agree with some of Hacker's opinions. I really do. Teaching of mathematics could be improved, both in my country (Spain) and in the USA. Many syllabus are outdated or simply they aren't suitable for today's society.
But I didn't like his approach to the topic. At all. He has decided his opinion many years ago, then he has been looking for arguments to support it. That's not the scientific method, in fact it's just the opposite. He simply dismisses studies and data that he is not interested in or even ignores them, for he doesn't explore other possible motives or explanations when they don't say what he wants, even if they clearly exist.
Besides, his argumentation is not well constructed, full of logical fallacies and questionable reasoning. He even uses a bunch of mathematical examples... with a lot of mistakes!! And it bothers me especially the use he makes of "voices", unsourced quotations he puts in speech bubbles. It doesn't matter if you put one or a hundred of those, they mean absolutely nothing in a reasonable argument. Literally nothing.
I didn't like either so much insistence on the utilitarianism of secondary education. For pages and pages it seems that almost the only objective of education is to train workers, my own beliefs are far from that.
And some of his analogies are hilarious, like when he asserts that being a strong swimmer wouldn’t help you as a lacrosse player. That's not true at all!! Professional athletes often practice or borrow exercises from other sports.
Hacker has some interesting ideas, but in the way he presents them, this book was a waste of time.
But I didn't like his approach to the topic. At all. He has decided his opinion many years ago, then he has been looking for arguments to support it. That's not the scientific method, in fact it's just the opposite. He simply dismisses studies and data that he is not interested in or even ignores them, for he doesn't explore other possible motives or explanations when they don't say what he wants, even if they clearly exist.
Besides, his argumentation is not well constructed, full of logical fallacies and questionable reasoning. He even uses a bunch of mathematical examples... with a lot of mistakes!! And it bothers me especially the use he makes of "voices", unsourced quotations he puts in speech bubbles. It doesn't matter if you put one or a hundred of those, they mean absolutely nothing in a reasonable argument. Literally nothing.
I didn't like either so much insistence on the utilitarianism of secondary education. For pages and pages it seems that almost the only objective of education is to train workers, my own beliefs are far from that.
And some of his analogies are hilarious, like when he asserts that being a strong swimmer wouldn’t help you as a lacrosse player. That's not true at all!! Professional athletes often practice or borrow exercises from other sports.
Hacker has some interesting ideas, but in the way he presents them, this book was a waste of time.
April 14, 2016
An effective argument that advanced math should not be required of all students. I did not expect to agree with the him so fully, but he won me over. He points out the destructive consequences to students of requiring all of them to take Algebra 2 and above in order to get a high school diploma, enter many universities or even study at some 2-year colleges for certification to enter fields that require nothing more than arithmetic. All too often colleges, universities and employers use these math requirements solely as a filter to cut down the applicant pool. Higher math is not needed, the author points out, by those employed even in most STEM fields. I enjoyed higher math (when I was in high school, less than 30 students took 4 years of math, and it was a well ranked high school), but it shouldn't be a gatekeeper to all students' academic progress, credentials or job aspirations. The author has hard words for those in the academic mathematics establishment who promote these high standards (which help fill and fund their departments) but do not take responsibility to present math to undergraduates in such a way that they can master the material.
May 30, 2016
5 stars for being thought provoking and original. As to his main points, the devil is in the details. While I agree that much mandated advanced math in high school (and college) will never be used later or even needed by most of those students, it could be argued that most mandated material will never be needed. As a computer programmer I didn't need any of the chemistry, physics, biology that I had to take. Or poetry for that matter. I have an advanced math degree, so am not biased against that field. Did mandated chem, physics, bio and poetry enrich my life? Sure. But, as Hacker points out, math seems to be an insuperable obstacle for too many students. His examples, e.g. a would-be nurse who couldn't pursue that career because she couldn't satisfy advanced math requirements is society's loss. On the other hand, students in many (most?) other industrial countries seem not to have as much difficulty with math. I lean towards accepting most of his premise.... but would like to see further research (followed by applicable curriculum changes) by educators with respect to validating his points. Everybody responsible for curricula in education should read this book.
April 11, 2016
As someone who had to take 3 calculus courses as a biology student in college, I totally agree with the author that not all high school (nor college) students need to take advanced math, especially in the form of advanced algebra.
Unfortunately, after the first few chapters, the author keeps beating the same points, and the text gets a bit redundant. I did like the examples of questions given from SAT and common core exams: My first thought was, yikes, I can barely remember this stuff (binomials?) let alone answer any of the problems(!). I think most students would be best served with more practical math (probability and statistics (what is sampling error of a political poll? what does it mean if a blood test has a 5% false negative rate for a disease that has a 1 % incidence?), exponential growth, how interest is calculated on a 30 mortgage, etc.).
Unfortunately, after the first few chapters, the author keeps beating the same points, and the text gets a bit redundant. I did like the examples of questions given from SAT and common core exams: My first thought was, yikes, I can barely remember this stuff (binomials?) let alone answer any of the problems(!). I think most students would be best served with more practical math (probability and statistics (what is sampling error of a political poll? what does it mean if a blood test has a 5% false negative rate for a disease that has a 1 % incidence?), exponential growth, how interest is calculated on a 30 mortgage, etc.).
December 12, 2016
I mostly agree with Mr. Hacker's main points, central of which is that STEM is not the cure-all to american educational decline (whatever that's supposed to mean) and that math department and educational system requirements are out of step with the math skills ultimately needed by most students, even for most so-called STEM degrees and careers. Unfortunately, this book is about twice as long as it needs to be to make the point, and did not offer any solutions as to how to rectify this system-endemic problem. Bit of a dissapointment.
January 6, 2020
Hacker makes two very valid points; math courses in high school should not be requirements in professions that don't use it, and math classes should focus on useful applications in everyday life. Unfortunately Hacker goes about making these points with misleading statistics, unnecessary jargon, and logical fallacies. Disappointing when the premise is ripe for insightful discussion.
July 8, 2016
Wow! Don't push algebra!!! Hacker feels that the big math push punishes students and adult learners. He emphasizes that most jobs do NOT require the higher math that the STEM push loves. Liked this title.
March 28, 2016
Political garbage after the second half...tiresome and long disproved.
July 6, 2016
Excellent book and one every parent, math teacher and school administrator should read.
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