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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Why does Professor Hacker oppose Algebra instruction?
In the interest of full disclosure, would he disclose his own results in algebra classes that he took?
And he claims that no evidence supports the utility of algebra for students and future workers. Does Prof. Hacker fear the available statistics due to confusion or avoidance of math?
I am an artist with a MFA and teach university art – in a field where math aversion is a common practice. Yet I totally disagree with not presenting a student with algebra. I believe that a sound general education is important in any field - and surprisingly enough my students use algebra in the programming language used in one of my design classes. You never know where the logic and skills presented to you will come in handy.
I use algebra everyday in my career as a veterinary technician. I wouldn't be able to do my job without dose/concentration= volume.
Even if you do poorly in mathematics, you still took it. I meet all types of people in my line of work and you can definitely tell the people who took algebra than the people who didn't.
IMHO this guy Hacker has a horrible attitude about education.
First, he dismisses math as a thinking aid being easily replaceable by reading - as if humans aren't capable, and worthy, of using all methods of improving their brains and themselves.
Second, he apparently thinks education is solely for the purpose of finding a job. Screw the idea of learning anything that's not of immediately apparent benefit to a particular occupation!
I'm a very non-violent person, but I would pay good money to see Neil DeGrasse Tyson - or Danica McKellar - beat the snot out of this guy.
The Poly Sci professor just said that girls out perform boys until the multiple choice tests! He just made the point for the one Math Professor: that we need to solve open ended problems AND that girls can be successful!!
Jodi, EdingtonMath.com
This is a good show about the need for Algebra in the classroom. While I would disagree with those who would call "Algebra as stupid". I would like to see a panel with Math teachers and Math professors having a reasonable dialogue about this subject. In full disclosure I should add that I am a teacher and enjoy teaching and tutoring students in Algebra. The question should not be about whether we require students to take Algebra or not. But if you are going to remove - say a musically gifted student from an Algebra class - you need to be willing to be able to supplement that students curriculum with a class that would necessarily provide him/her with the reasoning skills provided in an Algebra class. My experience has been that many young girls have been discouraged from taking Math in general and Algebra specifically simply because they 'don't have the ability' to do Algebra. If we don't have the students taking at least a basic course in Algebra, we are relegating all High School graduates to positions in rudimentary jobs. This discussion needs to continue but Dr. Hacker is after all a professor from the 'soft sciences' - if you want more Psychologists, Sociologists etc then perhaps no Algebra is needed but if we want to produce more Engineers, Scientists, etc. then we certainly DO need Algebra.
I use algebra almost every day... while changing a recipe, drawing or adjusting sewing patterns, deciding how much paint to buy or to understand the yield on my investments, or where the deficit comes from.
It is probably the most useful thing I learned in school, but I learned my most of my math in Canada where it was taught more like a foreign language and it wasn't subdivided into geometry, algebra, calculus, etc. I was quite good at math, was able to help my peers after the teacher showed us how to do it.
In the US we were supposed to go home and "discover" math on our own which very few were able to do. I couldn't and wound up fluent in several languages instead, but math is still my secret love.
Imagine sending kids home to learn German, French, Latin or Russian by discovery.
Astrid in Lorain, Ohio
I thought I hated math, but turns out it was arithmetic that I hated.
If algebra (which I didn't enjoy) hadn't been required, I never would have discovered the art of geometry and calculus.
How can we assume that a child might not be successful if you don't ask them to try these 'higher' math topics?
Your guest from Duke just identified the key - tailoring the teacher to the students learning. I love math, have always been adept at math. I tutor high school and college math and I have a child learning math in elementary school. I have seen students quite capable in math really struggle because they never mastered a fundamental early in their private school education. WHY??? The way math is taught must be reconstructed to adapt to the way students learn. This is not a suggestion about dumbing down the subject but about presenting it in an engaging way and in providing the training wheels until students "GET" it.
Different personality types, for example Myers-Briggs, have a bearing on algebra abilities and preferences. Myers-Briggs Sensors are less likely to be pleased with algebra, while Myers-Briggs iNtuitives are more likely to like and excel in math subjects. Similarly, Myers-Briggs Feelers are less comfortable math, whereas Myers-Briggs Thinkers more likely succeed at the subject. So, perhaps different teaching techniques for Sensor and Feeling-preferring students versus those for iNtuitive and Thinking preferring individuals would assist most students to better learn mathematics.
This is a good show about the need for Algebra in the classroom. While I would disagree with those who would call "Algebra as stupid". I would like to see a panel with Math teachers and Math professors having a reasonable dialogue about this subject. In full disclosure I should add that I am a teacher and enjoy teaching and tutoring students in Algebra. The question should not be about whether we require students to take Algebra or not. But if you are going to remove - say a musically gifted student from an Algebra class - you need to be willing to be able to supplement that students curriculum with a class that would necessarily provide him/her with the reasoning skills provided in an Algebra class. My experience has been that many young girls have been discouraged from taking Math in general and Algebra specifically simply because they 'don't have the ability' to do Algebra. If we don't have the students taking at least a basic course in Algebra, we are relegating all High School graduates to positions in rudimentary jobs. This discussion needs to continue but Dr. Hacker is after all a professor from the 'soft sciences' - if you want more Psychologists, Sociologists etc then perhaps no Algebra is needed but if we want to produce more Engineers, Scientists, etc. then we certainly DO need Algebra.
two points:
1) I tell my students i would have them study say, calculus (insert your favorite mathematics class here), for the same reasons i would have them read Hamlet, or memorize the opening lines of The Canterbury Tales. Contained therein are beautiful and subtle ideas of lasting interest to people of all eras.
Curriculum seen from this point of view offers us the opportunity to see the The idea of 'revenge' in Hamlet as no more, nor less timeless than the inverse square law in mechanics. That the force of gravity between two bodies is directly proportional to the product of their masses and inversely proportional to the square of there distance apart is timeless, subtle, and beautiful in many of the same ways as a work of art.
2) If a piece of information is practical (one can build or blo up bridges with it), aesthetic (it makes you smile), or intellectual (harder to explain ... in art: does the artist use his or her materials to evoke the intended emotions? in mathematics: does the information follow from given assumptions?) ... then by all means study it.
by closing the doors to mathematics to a percentage of our students, we effectively deny access to a huge percentage of human thought.
no thanks.
I think math is developmental. If students don't 'get it' in middle school because they are not developmentally ready, they do get a negative attitude about math which can continue into adulthood.
if k = all kids
e = education curriculum
a = algebra
ke = kids with education
ke > k(e-a)
Fascinating topic. I think this debate will have to continue as there appears to be little standardized research with control groups to argue either side. With that said the anecdotal evidence appears to support what neuro and psychological sciences are proving that not all brains are created equal just as any other organ that is limited by the dictations of their genetic code... otherwise, I would have become a basketball player instead of a psychiatrist with as hard as I applied myself to both passions. Darn muscles aren't as fast as my brain. So maybe some people should be allowed to skimp on the meat of algebra, but again more research will be needed to identify those individuals. I myself and my soon to be born son will engage in algebraic math because of its empowerment and enrichment in my life and the worldly confidence that comes with that.
Very Respectfully,
Jether
This. Well put.
I would like to suggest that Professor Hacker is unable to separate himself from his algebra background. The If-Then statements he must employ in his critical thinking skills, the logic skills he relies upon, these were doubtless enhanced by practice in algebra. The fact that algebra as another language is inadequately presented to our youth should not be the basis for eliminating its teaching to a portion of our students. I received a fabulous math education in algebra starting at Nathaniel Scribner Junior High, yes, as early as 7th grade (in the 1970s)! We wrote poetry and music to pi, we learned algebra as enmeshed in our social lives. I truly pity the adults I hear saying they don't have a "math brain". Yes, there are people who will fail at any subject. But they will gain for having tried.
I taught 7-9 grade math in the seventies and noticed that the students were often missing basic math skills. We start teaching math too young. In the 1930's Piaget determined that children don't understand Conservation of Matter and other important math concepts until age 7-8. Perhaps we need to wait and have math teachers instead of generalists teach math to children in elementary school. Algebra is especially difficult if you don't have basic math skills.
"Algebra" means MORE than one single thing. Yes, some algebra is used every day. Some algebra is almost never used unless you are in a highly specialized field.
Why is this all being lumped together? For example, why do all students in Michigan need to pass Algebra 2? I am a highly skilled, highly intelligent person. I get numbers very well. I did fabulously in most of my math classes. Heck, I was one of only two people in my nearly 400 person senior class who got to the second round of the Michigan Math Prize Competition test.
I have never used anything from Algebra 2 outside of that class.
The problems elementary school kids get where "5 + (box) = 9" are algebra. That's an essential skill. This should NOT be lumped in with "2Xcubed - 8Xsquared + 4X -10=23Y.
Furthermore, asking students to do any of this before they are cognitively ready to do this DOES hurt them. If you fail to understand something over and over again, you DO shut down. We go on and on about how every student is different, but we refuse to acknowledge it in practice. Instead, we lump the kids together by date of creation, rather than their cognitive development.
Look him up and find his CUNY rating results. HE offered his courses and was rated quite easy (3.3 our of 5.0)....
I'd say that he doesn't think we should ask - and expect - students to bear down and LEARN subjects... even if they (the subjects) are difficult for them...
Dan
I use algebra almost every day... while changing a recipe, drawing or adjusting sewing patterns, deciding how much paint to buy or to understand the yield on my investments, or where the deficit comes from.
It is probably the most useful thing I learned in school, but I learned my most of my math in Canada where it was taught more like a foreign language and it wasn't subdivided into geometry, algebra, calculus, etc. I was quite good at math, was able to help my peers after the teacher showed us how to do it.
In the US we were supposed to go home and "discover" math on our own which very few were able to do. I couldn't and wound up fluent in several languages instead, but math is still my secret love.
Imagine sending kids home to learn German, French, Latin or Russian by discovery.
Astrid in Lorain, Ohio
The simple fact is that millions of young people are now not learning Algebra yet go on to develop all kinds of wonderful higher level cognitive skills. Everyone should have the opportunity and time to develop the cognitive skills that are suited to their particular individuality. My own experience with Algebra was highly positive, and I was a top student in math--yet I do not feel that it gave me confidence or even some critical thinking skills that I needed to have. My eyes were opened more in a history course in college to critical thinking than any math course that I had aced up to that point. Maybe that was due to inadequate math teaching but that is what we have--and I was one of the very high ACT/SAT math scoring females who supposedly mastered the subject.
One of my unschooled children, now an adult, became very math aversive through adolescence, after excelling in basic math as a younger child. She liked word problem types of work but could not deal with numerals as an adolescent. Because of our unschooling she was allowed to sample Algebra as much or little as she liked, which ended up being "very little." She went on to higher education in a creative theater program and took Logic for her math requirement. When she entered graduate school to study Orientation and Mobility for the Blind she was told she was the "smartest student" they had ever had in the program. I feel that by spending time on her creative pursuits in adolescence, she developed some of the phenomenal skills she has today that enable to her to write, produce, and direct original plays. I think forcing Algebra on her would have been detrimental.
If the way in which students are taught math is a key component in their success, it seems to me we should focus on recruiting and training teachers in math and science. However, if a person is skilled in math and/or science h/she is not likely to pursue a teaching career because the pay is so incredibly low compared to what s/he can earn in private industry.
Why is this aspect of the problem not being addressed?
A familiarity with algebra, as well as 'liberal arts', should be a predicate for any certification of ability. A high school diploma or a college degree should indicate at least a minimal ability to do basic skills, of which algebra is only one...maybe an 'award of attendance' should be given to those that went to school but failed to accomplish the rudements.
I first took Algebra in 7th grade and found it to be wonderful. I continued with Algebra 2 and 3 throughout Junior High. My teachers brought math to life through practical examples- encouraging the development of my critical thinking and problem-solving skills. Years later (at age 39), when I began working toward my Ph.D. I had an excellent base toward studying the statistics necessary for my research. Until I hit my freshman year in college, my math teachers did not treat girls as having lesser abilities than boys.
Patricia in Greensboro, NC
Is there any chance of putting students on a math "track?" The career path of my choosing was to be an Art teacher. I excelled at geometry because I had high spatial intelligence. I wouldn't have minded taking more geometry, but algebra was a constant struggle, and I don't feel I have become a better or smarter person for having wrestled with it. What about putting students on a mathematical track to suit the leanings of their intelligence?
Sure, you don't know when you're 14 if you are going to be an architect or scientist. But struggling with math and often having to have extra tutoring and assistance might prevent a young person from time to pursue those other areas of their cognitive development and inhibit development of genius in other areas. If it teaches them they are "dumb" because they aren't good at "critical thinking" they are being done a disservice when they could have learned they were smart, creative, and good at reasoning if they had pursued other areas of interest more suited to their individuality.
Sure, you don't know when you're 14 if you are going to be an architect or scientist. But struggling with math and often having to have extra tutoring and assistance might prevent a young person from time to pursue those other areas of their cognitive development and inhibit development of genius in other areas. If it teaches them they are "dumb" because they aren't good at "critical thinking" they are being done a disservice when they could have learned they were smart, creative, and good at reasoning if they had pursued other areas of interest more suited to their individuality.
I failed my second year of High school and after repeating this whole year I got a love for math, which was one of the subjects I failed the previous year. I used to think what was algebra good for, now I have a clear comprehension in my baking career, that the use of fractions and geometric figures is what facilitates my recipes and cake creations. These classes had a great impact in my life and now I get it clearly!
I have taken algebra, & statistics and think that both are necessary. I think we need to think about how higher math & algebra is used in daily use. We use these skills daily in shopping, cooking, business, etc..
Someone earlier mentioned a woodworker not needing algebra skills. I beg to differ, a woodworker, mechanic, etc. is going to use a wide variety of higher math and algebra in creating patterns and working with angles, and adjusting measurments and machinery.
We have already had a drastic decrease in our acedemic performance both nationally and internationally. While part of this is the advancement of education in other countries. However, a large part of this is because we continue to reduce our educational goals. I think we need to continue to strengthen our educational goals, and the creative methods in which we can use to teach our kids. Not every method is right for each person, but we need to identify the method that works best for each student.