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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I'm not sure 8th grade is the right spot to start pushing Algebra. Somehow we bought into the idea that all kids need the college prep skills, even if they don't go to college. As a software developer, I've used algebra on a daily basis. My wife, an AP History teacher, barely uses math at all. However, she will be the first to admit that her difficulty with math in high school pointed her towards teaching History/Social Studies. Can you navigate and succeed in the world without Algebra? I would have to say so, assuming you are prepared to accept certain career limitations.
Our college is involved with a critical thinking program across the curriculum. Math teaches linear reasoning. This is one way of problem solving. But there are other creative ways that are nonlinear in nature that and are still critical thinking problem solving.
Would like to hear the guests comment with their feelings on education based on course mastery vs. grade level. For example, a child takes classes based on his/her individual ability rather than attained age.
Would like to hear the guests comment with their feelings on education based on course mastery vs. grade level. For example, a child takes classes based on his/her individual ability rather than attained age.
Agreed.
I use math and algebra so often and so many ways I'm not aware I'm using it.
And your cite of Mager, I learned a long time ago that it takes a second to learn something and a lifetime to unlearn it so it had best be gotten right the first time.
Does Prof. Hacker believe we should eliminate Civics classes since there are newspapers, cable news, Google, Wikipedia?
I am wondering if the panel can speak to the character benefits of sticking with algebra, despite its difficulty? While mastering algebra may not always translate into better reasoning ability in adulthood, sticking with something that is unpleasant and difficult and even failing can be a valuable life lesson. Dropping out of high school over one class seems to be a symptom of a larger problem. How will these students deal with a difficult, unpleasant task in the workplace? Will they just quit their jobs?
Algebra is the graceful art of understanding relationships among variables. With or without the aptitude that concerns Dr. Hacker, skill and adeptness at any exercise, physical or mental, can be improved. Aptitude at algebra certainly isn't NECESSARY to have a critical or able mind, but we live in a complicated economy and individuals will improve their financial and larger lives by being adept with the use of algebra. I beg to differ with Dr. Hacker on the mortgage question -- a simple or complicated mortgage can be drilled down to a few variables (interest rate, years to maturity, principal amount) and I don't think we'd be in the mortgage mess if people had understood that they were overborrowing relative to their incomes and land values. People who vote can and should understand the relationship between economic growth and macro interest rates versus their own mortgages and home values. They can use algebra to help them without the cost and inconvenience of hiring a financial advisor. By the way, I am a financial advisor.
To Mr. Nolan's comment about wanting to be an architect so he could spend his career sketching; I had a career as an architect for over 40 years. During that time, it was essential that I had an understanding of algebra so that I could perform many tasks, including structural analyses. Had I not undertaken to learn algebra (a subject I did not enjoy), I would have found it extraordinarily difficult to practice architecture or to become licensed in my state. Now that I'm retired, I can spend my time in art work, but my life is much richer because I have a basic understanding of math, and particularly of algebra. I couldn't have predicted any of this when I was a teenager faced with taking high school algebra.
Daniel
I do not have a high IQ but pushing myself though many years of algebra and trigonometry all the way to Calculus I in HS has really improved myself tremendously. Prof. Hacker is fooling himself if he thinks that mathematics do not radically improve one's critical thinking skills. Math is also the key to a stable and higher paying job in this economic climate.
No one is saying one has to get an "A" in algebra I and II to be a SUPER critical thinker. Algebra takes practice. Even college math professors make algebraic errors...
Dropping Algebra? Seriously? Does Prof. Hacker realize that his suggestion would also require that we drop ALL of the experimental sciences (since they all involve algebra)?
As a mother of twin girls who may attend public school in a couple of years, I am increasingly concerned that these type of discussions and propositions will end up lowering even more the quality of the education in America. I come from the developing world where I was fortunate enough to go to private school and I was truly surprised to see that what I thought were very basic skills acquired during my middle and high school times were superior to those of my peer classmates when I attended graduate school at Duke University. I would like to ask the panel to discuss how eliminating subjects like algebra from the curriculum because they are 'difficult' will end up decreasing the quality of education of the future American decision makers.
My children go to the school of Science and Math. Yes, we are learning other subjects but PE is only twice a month and no sports. That's the way the world is and that's fine. Oh, they love it! Yes, I home schooled my children and found out I love math and know how to do it! LOL Trig-Yikes but I am ready to tackle it!
my grandfather was an engineer. when i was i asked him how an airplane flies. he said the force pushing it up is stronger than the earth pulling it down. that was the first time i thought "algebraicly" .. algebra is not math, its logic. it just happens to use numbers to teach it.
How do you do or understand statistics without algebra?
So what! They can't do math. So, I can't draw or play any instruments, or write any poems. Does that mean, we should stop teaching music or english or art, because it makes me feel and other people like me feel inadequete. This logic does not make sense.
I have been teaching math at a community college. I have seen that students who struggle with algebra is not because of algebra but more because of negative numbers, fractions and exponents. Students who know the arithmetic usually get the algebra even if it takes them hard work. But students who always need calculators to get the correct answer for (2-3) are the ones who do bad and never get algebra. So my belief is that there is nothing wrong with algebra but the way arithmetic is taught in elementary schools and the early use of calculators in schools.
I'm 67 and have two masters degrees, and have had a long, successful career as an educator. I took two years of Algebra in high school (9th and 11th grade). I made it through the rest of high school and a B.A. without taking any more math. I only passed Algebra 2 because a friend told me to think about it as thinking skills. I could never relate the x, y, z's to the real world. I had to take statistics for both of my Master's degrees, but enjoyed it because it related to what I needed to know to do my job and my research. I now work with math teachers and help them to relate what they are teaching. It is hard for many math teachers to answer the simple questions: "What is the enduring understanding of your subject that your students will need to know for the rest of their lives?" I usually get silence from the math teachers, then one brave teacher will start his/her answer with, "If the students are going to be engineers...." My reply, then, is how many of your students will become engineers? I'm not against teaching Algebra and higher math, BUT it has to be made relevant and has to connect to the real world uses. I teach teachers to use inquiry, problem and project based learning in order to connect learning to what students need to know forever and to make learning relevant and connected to the real world. I'm convinced that if you want students to have higher order thinking skills, these skills need to be embedded in ALL content areas. I'm also convinced that we need to make learning relevant in ALL content areas. Students need to learn the math they will need forever. We also have to consider readiness. Students have to have basic math skills before they take Algebra. Again, I'm not against taking Algebra, but readiness and relevance are critical.
I don't think we should remove the math requirement, but we do need to change the way it is taught. Currently it seems we're doing a disservice not only to those who are not mathematically minded, but also to those who are. My son struggled all last year in 3rd grade math and we struggled to figure it out since he is very intelligent and mechanically minded. We had him tested and figured out the problem--he is exceptionally intelligent and the teacher was dumbing down the math so much in order to reach everyone that his bored and frustrated mind would check out. We got him into the gifted and talented class and he is excelling because they are gearing the learning to his level of thinking. Something needs to change or we're going to lose on all sides of this battle.
Jennifer in Texas
There are so many ways to counter Dr. Hacker's arguments....
a. In fact, one does need math skills to do anything of any interest in woodshop. Think about design work, building things that function well for humans...think about engineering....
b. Madame Bovary would have benefited by knowing math...good grief, has he read the book?
c. As an anthropologist, I can tell you that math, including algebra and geometry, are essential tools in my field as well.
Does he not know how broad our discipline is and how many ways we incorporate math in studies of human populations/genetics and on and on? Even if we don't have to do the math, we have to be able to understand what's being said in articles we read.
I think Dr. Hacker is way off base....and doesn't really understand what doors are shut to young people if they aren't required to learn things they'd rather not.
I would gladly have skipped algebra if given the choice...I am so glad I did take it AND wish I had been required to do much more math and science!
I have been teaching math at a community college. I have seen that students who struggle with algebra is not because of algebra but more because of negative numbers, fractions and exponents. Students who know the arithmetic usually get the algebra even if it takes them hard work. But students who always need calculators to get the correct answer for (2-3) are the ones who do bad and never get algebra. So my belief is that there is nothing wrong with algebra but the way arithmetic is taught in elementary schools and the early use of calculators in schools.
It is important to discuss why we teach Algebra instead of succumbing to a knee-jerk reaction that once we delete Algebra, Biology and English may be next (all of which I firmly believe would be extremely detrimental to our society and economy, but, let's keep that aside). Critical thinking skills is certainly one reason to keep the subject but so is basic logic. The logic that can solve 3x=9 (answer: x=3) can also determine how much money is left after rent and bills are subtracted from a monthly income. The same logic is necessary to evaluate the cost of a pair of jeans on sale and if they're worth buying versus a movie ticket. Moreover, from a voter literacy standpoint, I cringe to imagine a American public who cannot access current events like climate change research because they are intimidated by rates of change over time.
This day and age is confronted with innumerable, massive complex issues that require an educated public and, as a society, we don't expect enough of our kids. They're capable and they can handle it (as a high school math tutor for 3 years, I've seen it). Let's not lower the bar further nor handicap the future of this country by removing Algebra from our skill set.
Lauren Watka
A.M. Brown University 2012
I am a PhD graduate student at the UMD in College Park. When I was in 11th grade I swore off all math and science because it was hard. I went to school to play golf and wound up taking Chemistry as my one "required" science elective. The teacher I had taught chemistry a way in which nobody else had related the subject to me. I found out I really enjoyed chemistry and have been chasing this passion every since. However, my biggest regret during that entire time was that I had to go back and relearn things like algebra because I wasn't taught it well in school. Science was able to give mathematics a context which helped me understand the usefulness of it in a whole new way. Mathematics is at the core of all sciences and if you don't have a solid foundation in it, you will always struggle with any aspect of science. You get rid of algebra and you are destroying the foundations of science.
The problem isn't with algebra it IS how it's taught. Lately, however, there are newer teaching methods. Are the guests on today's show familiar with the free online Khan Academy on Youtube? One school I'm aware of has been using that very successfully as an adjunct to their math courses? The improvement in math skills for the students was markedly improved.
A working knowledge of calculus and statistics is necessary to understand and predict even the most basic natural and social phenomena. Every subject includes quite a bit of math, if you wish to understand your preferred subject at its most fundamental level. This includes both anthropology (radiocarbon dating, statistics, etc.) and political science. We have agreed, as a society, on a basic set of educational skills we should all know. This links us as a society, and in an increasingly divided one, alienating a section of the population by not giving them the skills they need would further this problem. Teach statistics earlier, introduce algebraic concepts conceptually early and make it more engaging. Also, have a tiered approach to teaching math like they had at my middle school (tested into algebra in 7th grade). PLEASE do not advocate reducing a section of the population as beyond hope when it comes to such important concepts as algebra and its related fields. This is insulting to them and to all of us as a nation.
I am shocked that anyone could think that a basic knowledge of algebra is a disposable skill. The example given with Toyota actually points out the huge lack of skill in that local workforce...so much so that Toyota realized that they better pay for additional training! Machine tool mathmatics involves simple algebra but before focusing on bit speeds, feed rates and material properties (the meat and potatoes of machining) time had to be spent to establish basic math skills.
If we want a skilled workforce in America then we must challenge our children and math is the foundation upon which our modern society is built.
Each subject should be taught when the student is ready for it, not simply when the child graduates from one grade to the next. As a whole I feel that the way we teach has fallen behind students capabilities and most students are simply bored. When a student can do the highly advanced computer games and win, but can not read or write tells everyone that the student has a capability, but the teaching method or approach is incorrect.
The argument that algebra is the only way to produce a critical thinker troubles me. As a social studies and literature teacher, I assert these courses do their part as well. Asking questions, finding avenues to information, evaluation of sources of information, synthesizing information, application, predicting outcomes all in context (including the human condition) . . . these are interdisciplinary skills that all educators should help students develop.
This is a great discussion!
I believe that the problem is NOT in the requirement of any subject (including algebra -- and geometry, which is also a problem for many, and requires very high level thinking skills for kids who may not be ready, either). The problem, in my opinion, comes from the same thinking as our country's obsession with being first -- the RAce to the Top, No Child Left Behind -- and the pressures that encourage everyone to be above average. We don't live in Lake Wobegon, and in fact, value diversity.
We need to think about teaching so that JOY and WONDER, not mastery and perfection, guide our practices. In classrooms where kids work together, aren't afraid of failure, can move at their own paces and see all subjects through applications that are exciting and relevant.
Algebraic thinking is important. Geometric visualization is important. All should be exposed and enlightened, not scared into mastering the same concepts that society is putting out there for us to attain.
Michigan began requiring that students pass Algebra 2 to graduate from high school. This is a huge mistake because the content in Algebra 2 truly is too hard for some students and should not be the reason they don't graduate. Ask any math teacher - some kids simply will never master Algebra 2 skills. But I do believe all students must have the basics of Algebra 1 to graduate, whether they take it when they are 13 or 17 because it teaches the beginnings of logic, problem solving and daily math issues like calculating sale tax, clothing discounts or why your property tax went up.
I work as a scientist in industry and also teach algebra and physics as an adjunct instructor at a technical school. I think that Dr. Hacker proceeds from a false assumption: that it is algebra in particular that is causing students to fail, rather than a general inability to reason quantitatively or think in a disciplined way. In my experience the students who cannot master factoring quadratics have an equally hard time with very basic, "practical" topics like calculating interest. They are the same students who, when they are taught F = ma in introductory physics, cannot deduce that a = F/m. Surely every student can pass if we don't ask them to do anything difficult, but the result will be that students are less prepared for the modern world, not more so.