Is Algebra Necessary?
http://thedianerehmshow.org/shows/2012-08-29/algebra-necessary
Mastering algebra is widely considered a stepping stone to higher mathematics and college readiness. But last month, a political science professor touched off a debate when he challenged the value of algebra in American education. He argued we should remove algebra from high school and college curriculum, citing it is a key reason why kids drop out of school. But critics say the issue is not algebra – it’s how it’s taught. With more effective class instruction, the course can instill critical thinking and reasoning skills needed in everyday life. Diane talks with her guests about math education and why it matters.
Guests
Andrew Hacker
professor of political science at Queens College of New York. He is the co-author of "Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids - And What We Can Do About It."
Ed Nolan
program supervisor of mathematics in Montgomery County.
Jacob Vigdor
professor of public policy and economics at Duke University.
Judy Bolton-Fasman
a writer and parenting columnist.
Comments
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All persons can learn math. It's a matter of proven methodology and readiness levels for learning a concept. And access to support. And early success.
The Montessori method using manipulatives that help children effortlessly grasp basic concepts is like learning phonetics is to reading and writing.
Then, there is a proven logical, no whistles and bells, lots of review math text series written by John Saxon. There are schools who use his texts and their students score higher on standardized tests. However, most schools are stuck in Junk texts, seemingly all by McMillian Press?, utilizing the latest and greatest "research" from the educracy. Often with a highly inefficient hiatus between AlgebraI and 11 by geometry. Saxon integrates them.
My " expertise" comes from learning Algebra form an excellent teacher who taught using the same methodology that John Saxxon later documented, and homeschooling a son and daughter , observing the differences between the child who had more time in Montessori, and the child who dabbled in Saint Louis' West County elite high schools, and their overall success and satisfaction with John Saxxon Math. And their SAT scores. And I noted with interest I that did not Teach the second child division till she was 12----it was effortless. And then she took off running, loving math.
Of course, this is a study of 3........
I immensely enjoyed Algebra class, but I never learned how to use it beyond solving formulas. The teachers never gave us practical use for the formulas. So, what I learned was of no use to me in my adult life. It has been decades since I took those courses in 9th and 10th grade and I don't remember how to solve a simple formula now. Learning how to apply the math is far more important than memorizing the formulas.
I feel that playing with the mathematical formulas is what develops the critical thinking skills that are important. While there are other ways to develop such skills, I believe math is one of the best teaching tools. Furthermore, different students may require different teachers.
I would also argue that teaching algebraic thinking is more easily accomplished in Kindergarten and First Grade than waiting until Seventh Grade or beyond. I have been home educating my children, and our math has involved learning abstract concepts like negative numbers as young as four, when it is easy to make a game out of it and accept it as a natural concept. (I learned that particular concept much, much later and still have a difficult time truly understanding the logic of it all....)
Other countries are doing much better at teaching algebraic and abstract thinking much earlier. One example that comes to mind is the Mathematics Enhancement Programme in the UK (a course found as a free download online and which is based upon a Hungarian program) that has shown remarkable possibilities in helping children (mine included) learn to think mathematically and logically at younger ages, preparing them for higher mathematics in a way that allows the concepts to already be familiar and understandable in the upper grades.
Algebra encourages analytical thinking. Algebra is not difficult. Algebra is useful every day in many ways. Algebra should be taught to all students. I am horrified at the suggestion that we must "dumb down" yet another area of education.
As a society, we have dumbed-down our education systems to the detriment of the students. The solution here is not to get rid a valuable subject matter, it is to teach to the students, not to standardized testing.
Introduce algebra EARLIER. May sound crazy, but a simple Google search of "introduce algebra in elementary school" turns up several reputable reports that it could be a really good idea:
http://tuftsjournal.tufts.edu/archive/2001/november/features/index.shtml
http://blog.peaksmart.com/2011/04/algebra-in-elementary-school.html
How can he say that challenging children in school is bad for education and bad for learning!? If he thinks that algebra is too hard, then why not get rid of all subjects that are not passed at a 100% rate? Giving children a challenging subject or topic makes them think more critically and this practice of thinking critically is essential to growing up to be a more proactive and productive member of this society.
I'm disgusted that education is being attacked not only in the political world, but through these arguments as well. The greatest wealth for the future of our country and society is held in education and health.
Ira
Is Hacker for real? Or a plant by our enemies??? By reading "The Great Gatsby" a person can develop the same skills in problem solving as by learning algebra???? !!!!! Are you kidding me!!
Eliminating algebra in high schools would be one of the most destructive things we could do to our country. A very dangerous idea. Math is the basis of the progress of humanity.
True, not everyone is predisposed to math. But how do you know that you are good at it if you are never exposed?? I was a lousy high school student until I took algebra. I went on to receive both undergraduate and graduate degrees in math, eventually formed a high tech company that employed 3000 people around the world. I can guarantee you that if I never took algebra I never would have gone to college, and then who knows...?
Thank goodness the pinheads in Europe drove mathematicians such as von Neumann and Einstein out in the 30's or we would all be speaking German right now... And there would be no Diane Rehm on the radio. Diane, why do you give such people a voice???? I'm tuning you out for a while, until I calm down. (That's right, Einstein started as a mathematician well before physics.)
I failed algebra in high school - only got out because my algebra teacher passed me and made me promise to not take algebra again. Then when I was 39, I decided to go back to college. I knew my problem with algebra was that I did not understand the very basics of decimals and fractions. I taught myself these basics and some algebra I from old text books and tested into algebra II when I began college. I believe that not every child is ready to learn decimals and fractions as early as 4th grade. As a society, we cannot cater to every different child's ability, but if parents understand their child's limitations, tutoring at a later age would be very helpful.
Students are being set up to fail Algebra by the deliberate dumbing down of elementary school mathematics, in "new age" constructivist math programs adopted by the majority of our nation's schools over the past two decades. Students are no longer required to master basic arithmetic, foundation skills essential to advance into the study of Algebra.
Elementary teachers receive their training in our schools of education, where they are taught to support the "new approach," are not required to take rigorous math courses, but must take numerous methods courses in support of the constructivist programs!
The National Council of Teachers of Mathematics issued a game changing document for math education in 1989, calling for radical changes to math instruction that included the de-emphasis of the basic skills of arithmetic. The NCTM has influence over the development of school math programs, state standards and professional development Given this, it is not surprising that so many students struggle once out of gradeschool with more advanced math and science coursework, beginning with Algebra
The inherent value and future applications of Algebra in formal study, professions, and life, the education mandate for its study in school
are not questioned by our international betters. Higher performing nations in math and science hold the rightful assumption most students can and will learn Algebra (as well as more advanced math and science courses) achievement to which the majority of our country's children today are given no chance of aspiring.
Their secret: rigorous content rich programs, math knowledgeable teachers, the expectation math achievement, as in any discipline, will be difficult and require hard work involving skills building, practice, memorization, conceptual and problem solving. No excuses, no shortcuts.
We owe our children here at home the same, our children's futures, our nation's security and future prosperity depend on it
Students are being set up to fail Algebra by the deliberate dumbing down of elementary school mathematics, in "new age" constructivist math programs adopted by the majority of our nation's schools over the past two decades. Students are no longer required to master basic arithmetic, foundation skills essential to advance into the study of Algebra.
Elementary teachers receive their training in our schools of education, where they are taught to support the "new approach," are not required to take rigorous math courses, but must take numerous methods courses in support of the constructivist programs!
The National Council of Teachers of Mathematics issued a game changing document for math education in 1989, calling for radical changes to math instruction that included the de-emphasis of the basic skills of arithmetic. The NCTM has influence over the development of school math programs, state standards and professional development Given this, it is not surprising that so many students struggle once out of gradeschool with more advanced math and science coursework, beginning with Algebra
The inherent value and future applications of Algebra in formal study, professions, and life, the education mandate for its study in school
are not questioned by our international betters. Higher performing nations in math and science hold the rightful assumption most students can and will learn Algebra (as well as more advanced math and science courses) achievement to which the majority of our country's children today are given no chance of aspiring.
Their secret: rigorous content rich programs, math knowledgeable teachers, the expectation math achievement, as in any discipline, will be difficult and require hard work involving skills building, practice, memorization, conceptual and problem solving. No excuses, no shortcuts.
We owe our children here at home the same, our children's futures, our nation's security and future prosperity depend on it
This discussion is very disturbing. It is also revealing of the vast - truly vast - divide between science-literate individuals and laypeople.
I do not wish to call anyone names, only to point out that being in a position of authority does not legitimize your ignorance, or that being successful without so-called 'essential' skills does not make those skills therefore 'un-essential.' This is an arrogant, egotistical, and potentially dangerous way of thinking when other people are listening. To think that your particular avenue towards success should work for everyone!
I found Dr. Hacker's comments on questioning the value of critical thinking - as taught through algebra and other mathematical thinking - naive to the point of being absurd. To actually suggest that taking an anthropology course offers the same, or better educational value in the 'real world' as a math course is so profoundly sad and disheartening. This poor man actually believes what he's saying.
And why shouldn't he? What experience does he have to the contrary?
Check out the third graders learning algebra at Concord Elementary School near Glen Mills, PA
Thumbs up to this!
As someone who teaches math in college for a living, there is probably a slight overemphasis on Algebra (most students do not particularly need to solve for zeros of a third/fourth degree function), but there is an underemphasis on math in general. People definitely need to understand exponential and geometric functions for their applications in financing (a College Algebra topic, although it can be covered in other math courses), and they would benefit from seeing applications of math in other fields -- logic, geometry, statistics, probability, game theory, and some may appreciate special topics such as voting, number theory, and graph theory. They need to be able to recognize math in the world around it, and they need to be able to use math to address the problems and issues they come about.
In terms of the financial crisis/challenges we have, though, these are the sort of issues that demand people understand Algebra and Calculus. We may be able to get away with removing certain aspects of Algebra, but it is even more critical to emphasize its more immediate applications for students on non-STEM tracks. We need our citizens prepared not just for their jobs but for their civic duty of being voters.
I could not disagree with this premise more. Algebra is fundamental to almost every other field in mathematics, as well as science, social science.
In my day job I do data analytics and use machine learning to help people understand their business. I.use.math.a.lot.. Yet I earned D's in highschool algebra. I am dyslexic, I suck at arithmetic. While I could grasp the algebraic concepts, i could not for the life of me get through a test without making a calculation error, or forgetting a negative. It made me HATE math, and I wasted two years of college trying to figure out a major that would require the least amount of math. I finally just took it, and fell in love with it.
The real interesting problems, the problems of life, these are not problems one will be able to solve with just high school algebra. They are not problems that can or should be manually calculated. K-12 is like practicing for a soccer game for 12 years without ever playing a game. A simple calculator can perform everything you learn from k - 8. A scientific calculator can do 8 - 12. They try to spice it up by throwing in "story" questions, but who really cares about the train from Chicago any way?
the problem is the curriculum. It spends to much time having kids compute the solutions to meaningless (or boring) problems. Mathematics should be taught in conjunction with programming. With these two combined, relatively simple mathematical concepts and simple programming techniques can enable students to solve very complex problems,. I invite people to check out the statistics course on Udacity (MOOC), it is taught using this method and is absolutely fantastic.
The system is broken, but that does not mean the skill is not necessary, we just need to rethink how it is taught.
I jumped for joy when I first read Professor Hacker's piece in the NYT. I am an advocate for rigorous education and tough teaching. I have degrees from Wellesley College and U.C. Berkeley and write for the Financial Times.
However, algebra as taught to me was counterproductive and useless. I NEVER understood it, though managed to do well in it anyway, because I could see patterns. I use algebra daily, though as one guest on Ms. Rehm's show said, not by sitting down and turning tasks into equations. Algebra is NOT necessary for critical reasoning, absolutely not. In fact, if you do not grasp algebra in a deeper sense, what's the point? Only later on the job did I realize that I was doing "mixture" problems or developing my own mathematical solutions to my needs. This did not come from the study of algebra.
I am appalled at the intolerant attitude of people for whom the algebraic language comes easily. Algebra is like sitting through a class in a foreign language where the teacher just shouts in that language; louder whenever you don't get it. Math was taught by people who understood it, but were utterly hopeless at explaining it to someone who did not. There was a distinct lack of creativity in trying to explain the principles. Are people for whom poetry comes easily or who paint, or who are brilliant at writing a well-reasoned essay so dismissive as many of the commenters above are for those of us who struggled with algebra? Did they tough it out in English class, did they suffer through drawing or mastering important skills that are not economically remunerated in our society, the way they tell those who suffered through math to do?
Many have already expressed this thought, but it is still accurate.
Math, like English, is critical and algebra is an integral part of math. I use algebra every day and I do not teach math, nor am I a scientist. I use it in my job (sales) at home with my family, and in my hobby (woodworking).
To not teach it would be criminal. If we don't teach algebra because it is difficult for some, do we allow those who struggle with English to skip out on those classes?
Every subject will have some who struggle with learning it. To provide them a way out, by just not taking the class, is wrong. There are certain basic subjects that need to be learned by everyone. Even if some struggle to understand, they are still learning part of it.
Perhaps it is also partially the teacher and not the student.
.. sorry I was not able to call in during the airing of this show.
My contention is that the student who fails to grasp a difficult topic is not a failure. The failure is the education system itself.
Algebra is not a problem for me; however, literature was a mental black hole to me. I could read literature and tell you every detail therein - color, size, shape, names, dates, places, ....; however, unless the text specifically stated emotions, motives, ...., they were not within the text I had read - period.
I have argued teachers and administrators to death challenging them to either show me the text or teach me how to determine what they claim the work of literature contained.
No educator ever rose to the challenge - probable because they were algebra phobic.
I didn't hear the whole show, but I did hear Andrew Hacker say that only 5% of the jobs out there require algebra. Give me a break! I can think of many professions just off the top of my head that require algebra... engineers, accountants, financial planners, actuaries, computer programmers, architects, pharmacists, doctors, optometrists... I'm sure there are many others. I am a research microbiologist, and I use algebra on a daily basis. Any other research scientist in the natural or physical sciences would also need to know algebra. In junior high and high school, have most students determined their future career paths? I doubt it! Allowing students to opt out of algebra would certainly prevent them from pursuing all of the careers I mentioned above. I would imagine that even nonscientific fields use algebra at times... say chefs and graphic designers. I agree with the other panelists on the show-- better methods must be employed to effectively teach algebra. But allowing students to opt out is simply not the answer.
I tutor my cousins and children (which total about 17). I have noticed a downfall of math being taught and an increase of readership and writing. The reasoning behind this is that the kids can now read the books at a younger age and teach themselves.
While this sounds like a good idea, it is infact backwards. Math is universal, reading is man made, and came from math. Kids need the basics to build a good foundation. Then reading can become easier to them. When they come across new material they can use the reasoning skills they learned in math and translate it to reading. (for example when teaching how to read and write, E's have 3 horizontal lines, or the difference between I's and T's, or tool and toll, and bass and base)
While reading is also important, it focuses more on memorization then thinking. Math teaches the kids HOW TO THINK on their own with deductive reasoning. Math is more than numbers it opens another part of your brain. This could be why Algebra is so difficult now.
Take Algebra out? How many years can you teach 1/4 + 1/4 equals 1/2 before it's enough? I am so against the dumbing down of our schools. Lowering the bar is not the answer, just because something is challenging doesn't mean we need to make it optional. KIDS will most likely opt for the easier class to not jeopardize their graduating then actually choose a class that really challenges them.
I have excellent critical thinking skills and ability to synthesize information. I stunk at algebra. I am a highly successful adult. Phooey to that nonsense about needing algebra.
I won't discount the value of math. I even like the idea of algebra! But being a female with dyslexia, I was totally intimidated by math and failed miserably. Yet I ask, aren't there other (discounted) subjects that are equally or perhaps more valuable? I can think of philosophy, ethics, logic, ecology, communication skills, and oh yeah, the arts! I never felt my right brain received an equal workout in school and to this day feel cheated because of it. Easily can we predict a person's job skills potential;shouldn't society, place a child at an early age,in learning situations where they can soar? We need new models to create a new world and while economics and technology are driving forces today,math just isn't for everyone. The real need for education (which we have missed for centuries), is to teach us how to get along.
I use basic algebra all the time: I need to buy carpet, paint and do other things using algebra. However, the algebra I use is not very complex relative to what is currently required of students. At a certain point, algebra becomes too complex to be needed by everyone and is then a specialized subject. My simpler algebra is often called "pre-algebra", and the analytical skills espoused by algebra proponents are probably achieved by my being engaged with this math. Do I really need excessively complex math to gain these analytical skills? My answer is "no."
The argument that students "might" need it in the future is silly when there are so many other courses that fit that description. Additionally, there are courses that already exist that ALL PEOPLE need, or should use to be more successful. An often sidelined course in this category is something like Theatre Arts. While many see courses in this area confined to those few who have talents in the area, I see it as a course that should be required of ALL STUDENTS. Why? Because in this course, essential communication skills, presentation skills, tools for altering space and appearance are explored--the exact skills needed by nearly anyone in any field, including parents.
Ultimately, it should be decided at what level math becomes complex enough to be categorized as a specialization, relegating such courses to electives. In my mind, since I have, and most of my friends and acquaintances have, never, never, never ever used long strings of polynomials in their fields or in life, I would call for a stop at pre-algebra so students can then be allowed to take more relevant courses to their lives and careers.
One significant point is that though many of these professions may use algebra, very few of them use long strings of polynomials. They are using what most would call "pre-algebra", which is where I think students should be able to stop and take more relevant courses to their interests and careers.
Listening on Wednesday night (we have a delay on KAZU) to one of your guests say that a person would never sit down at the kitchen table and work out a mortgage. This is exactly what happened to us. We had a mortgage with a holding company & bank for many years. At one point - this was about 10 or 15 years ago - it occurred to me that it should have been paid off. I sat down and calculated the mortgage with the agreed upon rates and then went over the bank's statements and accounting and discovered they were not calculating correctly. As I recall they were not applying a decrease in interest with the decline in principle or something - basically they were not doing their algebra correctly. Once I explained the error and how it had come about the banker apologized profusely and offered me a job. No I didn't take it. But if I had not sat down at my table with a calculator we would have been out tens of thousands of dollars.
My kids began learning algebra basics in 5th and 6th grade and had no problems even through calculus. One is now in science the other two are jazz musicians.
Dear Mr. Hacker: Like Karl Rove, who has spent his entire life trying to compensate for being beaten up by a girl once over Barry Goldwater (look it up), you apparently had a problem with math, and are wasting your career and tenured position trying to avoid it and get others around it. While the Constitution (a logical document, gasp) guarantees free speech, someone with a docctorate should afford themselves that right by having something meaningful to say. The New York Times, your publisher, and even Diane Rehm have given you well over your allotted 15 minutes of fame on this one. You did get to "simply ask a question." You have gotten the answer - repeatedly - it is NO. In all your experience, and earning a Doctor of Philosophy nonetheless, no one has apparently been able to get you to understand the word, logically or not. Perhaps it is this lack of comprehension of logic and its usage that has led you to be unable to grasp this idea of no? Because you can ask a question does not give you the right to impress your assumed rhetorical answer upon the entire population. Please, Mr Hacker, take your seat. Or, as a teacher once teased me, "I don't care if you go away mad, just go away..." Better yet, go sit in the hall until you have something meaningful to add to the class. That is all.
Of the many fallacies of Hackers this is perhaps the most insidious, glaring error: Hacker is using a basic technique of algebra (and of all philosophical thought for that matter) to pose his question of whether we need algebra and logic to function in our daily lives. When learning a new concept, the first question next posed is "what if this is NOT true." While in opposition to mandatory teaching (and usage of) logic, algebra, etc. he all the while is using the same to pose the question. I wonder if he is aware of his hypocrisy. Inherent in his suggestion asking us to roll back society to times before Socrates and Plato, who posed logical questions, oops. I for one, happen to like traveling by car, not sandaled foot. Likewise, Hacker should recognize that logic, algebra, in fact of modern life, benefits from a basic (and yes, mandatory) understanding of algebra.
Second, I would like to see how you can teach a history of mathematics without understanding the very mathematics you are talking about. Do you think you could teach about the WWII Holocaust without an understanding of religion, prejudice, economics, and geography? Come on!.
Finally, I would like to know how only 5% of the working population will use algebra or other advanced mathematics, as he claims GWU has found. You mean to tell me 5% includes all seamstresses, surveyors, engineers, mathematicians, physicists, chemists, architects, economists, bankers, brokers, marketing and advertising professionals, teachers, lawyers, accountants, bookkeepers, etc. etc. will only be 5% of the entire future workforce? Perhaps Hacker should resign his position and join his children or grandchildren serving me as they push the french fry button (with a cash register that counts out its own change, no mathematics needed at all). That is where he is suggesting (and wants us) all working, apparently.
Anyone who doubts that algebra/math is a necessity in everyday life has not heard this conversation:
http://verizonmath.blogspot.com/2007/08/original-recording-of-verizon-cu...