by Brian
My apologies to the gender police, but it
seems appropriate to borrow the title of Tolstoy's wonderful short
story to ask the question. Because as Pakhom tragically found out, we need far less than we think. The State Board of Education
has increased the amount of math needed to graduate from 2 to 3
credits for this year's incoming freshmen class. The requirement for
the class of 2013 is for every student to take Algebra and Geometry,
and pass an end of course exam in both. Then they will have to take
and pass Algebra 2, or take an alternative course after a conference
with their parents and an administrator approves of the plan. I teach
high school math. I generally try to avoid sarcasm, but what have
these people been smoking?
I have to answer the same question from my students every year: "When
are we ever going to use this?" There are two equally honest answers:
1-never, or 2-in your next math class. You will never solve a quadratic
equation by factoring or using the Quadratic Formula in your adult life
unless you become a math teacher. You will never do a two-column geometry proof
again; and if you try to use the same kind of logic to win an argument
it won't work. You won't create an amortization table for a loan;
you'll use the software on your computer (just like your banker). And
you will never have to calculate the volume of a pyramid,or a sphere,
or a trapezoidal sand box (that one was on the WASL).
So
why are we so concerned with teaching, and testing, math that people in
everyday life never use? It's a great mystery to me. I want all my
students to know how to understand and use fractions, decimals, and
percents in situations that they will encounter in their adult lives.
I want them to understand the power of compound interest, both in
saving and spending money. I want them to understand statistics so
they can make informed decisions on how much confidence to have in what
they read. And I want the ones who love math to be more challenged by
problems that no text book can use because they are too difficult. The
smartest student I ever had (800 on the math SAT when he was a
sophomore) told me recently that it was the math contests like MathCounts and the Math Olympiad
in middle school that really excited him about the possibilities in
studying math in college. Now he's a chemical engineer, with a minor
in math. Another student who participated in those contests is now an
aeronautical engineer, running the wind tunnel at the University of
Washington.
So let's get real about the math we want our high
school graduates to master. We need to provide a more rigorous and
challenging curriculum for the ones who will go on to be rocket
scientists. But we don't need that many rocket scientists. The
majority of our students need a curriculum that will make them
realistically numerate with the kind of math they will actually use.
So when they ask me "When are we ever going to use this?", I can
honestly answer: all the time!
The question remains How much math does a high school student need? Enough so that their understanding of economics, personal finance and statistics allow them to be active and critical citizens. Enough to open the gates to the future they envision for themselves. Enough so that they have room in their schedule to learn to think well in the modalities in which their strengths lie. Enough so that there is room for rigorous courses that foster the critical and humanities thinking that allows a person to PERCEIVE THE CULTURAL POLITICAL CONTEXT and POSE THE PROBLEMS that the specialist mathematicians and scientists can help solve.
As an art teacher I have caught the bruised students who for the past several years had been counseled ( and with the new requirement now will be required) to take more math than they need for their future.
What it does to many of them is to load their pockets daily with stones that impress upon them that their mind is substandard- that they cannot think.
And a subsequent year of a similar course work, will do what? Cement those stones into a wall that keeps them from that daring required to self launch into a career that would make them productive.
For some it is too much and they just drop out rather than try to face another forced march though a world arcing with parabolas, formulas, and proofs.
If the math requirements of today were in place when I was in high school I likely would not have seen myself as a smart kid who couldn’t do math, who applied confidently to a competitive college and did well. I would have bogged down and come to believe that I was some how defective and not allowed to take the enough of the classes that gave wing to my intellect and future…Art (many classes), Psychology, Honors History…
I see a nation of increasingly numbed citizens with dim horizons when I see how many kids are seeing a gate closed rather than opened when it comes to math requirements to get out of high school and through college.
If we look around the world at the problems that plague people, most of them are in need of solutions that are arrived at first through the humanities based skills of mutual respect, empathy, trust, vision, consensus. Without those how do we really know what the issues behind the problems are? How can we even attempt to deliver a solution without getting caught up in the conflict?
Once the issues are clear and the communication is open, the solutions brought by the specialists in math and science can do their best to equalize the distribution of resources, to stem the erosion of soils, invent the next…
Pertinent reading to this stream can be found in Harper’s Magazine Sept. 09 “Dehumanized – When Math and Science Rule the School” by Mark Slouka.
I think you’re right Clix, though I think there may be some diminishing returns past geometry (and into Algebra II). Geometry and algebra exercise different parts of the brain, while advanced alegbra…Algebra II, seems excessive for typical students, just as not all students should take advanced sciences or advanced literary studies…the common core course serves them well enough so they can pursue more specialized interests elsewhere.
Clix: I do calculus problems for fun. I use logic that I first learned in Geometry a long time ago when I negotiate with my district. But what I’m arguing against is the idea that everybody is like us. To require Algebra, Geometry and Algebra 2 for graduation from high school just does not make sense for every student. I had a student once who said she really liked math until they invited the alphabet to join.
I don’t know that I agree. Math gets more and more abstract the deeper you get, and it stretches your brain in ways that other disciplines don’t. I know that I’m a better writer for having taken geometry class – not because I use the two-column proof table in my writing, but because I know to check to see where I’ve jumped to conclusions or glossed over significant details.
I don’t see the evidence that making students take the same math over and over will help them master anything. It bores them. School is boring enough. Plus, at least in my state in the last 13 years, the focus has been on literacy. Most professional development is about literacy. Even the math teachers are expected to teach reading and writing, but I don’t see it go the other way.
There doesn’t seem to be much creativity, excitement, or growth in how we teach math to students. Boring them certainly isn’t going to help, nor is forcing them to take math they don’t see in their daily lives. All students need to learn to read and write effectively, yes, but we allow them to read and write about things that connect to their lives and their interests. Why can’t math departments have a little freedom to do the same with their courses?
J Broekman gets it! Kudos and best wishes. I suspect others do also.
And how many who are now upside down in their mortgages never took personal finance?
I totally agree with the idea of statistics in place of Algebra 2.
Four years of gym or three years of math is a false dichotomy; why not both?
And I don’t think last year’s economic bust was caused by not understanding the math. The people on Wall Street who created that all took Algebra 2.
I am curious as to Bob’s background. He conveys that “I’m going to inspire every kid that walks through my door” attitude that I entered teaching with and was then quickly slapped in the face with the reality of the daily classroom.
I think kids should have to take 3 or even 4 years of math, but make it math that will be useful to them. Personal finance, econ, computer programming, carpentry, etc….
Mark, this is what the State Board of Education provides as a rationale for Algebra 2:
Why Algebra II is important
Algebra II is a gateway that prepares students for success. Students who have taken Algebra II and another math course in high school are the ones most likely to place into a credit bearing mathematics course in a community, technical, or four-year college or university. In fact, four-year schools require at least Algebra II for entrance.
They are a interpreting a statistically meaningful correlation as a cause and effect relationship, and that’s a poor use of mathematics.
Bob, I admit that I do not know which math concepts any specific student will need during life. But I believe life is long, and high school is not the only opportunity people have to get the education they need to fulfill their dreams. One of my best friends failed algebra in high school, and absolutely hated it. She graduated, got married, had 2 beautiful daughters and got divorced from their father. She was supporting them as a custodian in a school, and decided she wanted to be a teacher. With that motivation she took algebra again, and passed with flying colors. She became a wonderful English teacher.
I do know, from 57 years of living and 25 years of teaching, that the vast majority of my students will never use most of the math that I am teaching them. I think it’s wrong to require students to master subjects they may never use in order to graduate from high school. I want to teach them math they will use.
“And you will never have to calculate the volume of a pyramid,or a sphere, or a trapezoidal sand box (that one was on the WASL).”
Unless you’re trying to figure out how much sand to buy for a hand-me-down or built-in sandbox that doesn’t come with handy instructions…
Should math classes use more realistic problems? Sure! Should students leave high school with four years of gym and fewer than three years of math? No way! I’m not sure that Algebra II is necessarily the best use of that third year. I’d rather see statistics as the third requirement, in the probably vain hope of getting young citizens to question the use of statistics in propaganda.
However, I do know people who are not math teachers who use Algebra II and even Calculus concepts on a daily basis. They’re not physics teachers, either: they’re financial analysts and computer programmers. If we’re going to base our society on complex computer applications, we need people who understand the math behind them, or we’ll just keep repeating last fall’s bust.
As far as I know, Algebra and Geometry have always been required…the state now requires a third year: Algebra II.
The thing is, I don’t think requiring Alg II is “making sure people know how to use them before leaving public schools.” The grocery store math you mention, Bob, is not Algebra II. The stellar work your granddaughter must have done to master high-school-level geometry to graduate middle school is not the same as Alg II. And remember, we’re talking about the minimum requirement being Algebra II. Most 9th graders who enter are simply ready for Algebra I…and the math-based physics you mention in freshman science is part of the reason why 9th grade science tends to be the most-failed class in the 9th grade (not that the math shouldn’t be included, but more evidence that most students are not entering ready for it).
As for the premise that Alg II will somehow equip students to be more “math aware” in their future… I graduated with Calculus from high school and didn’t really grasp economics and personal finance. You may think, how could someone who got an A in Calculus not understand the basics of economics and personal finance? Well, that wasn’t taught in Calculus. I enjoyed the math class, I believe it forced my mind to bend and stretch in ways that primed it for other thinking, but no, I will never use Calculus. Nor will I use the concepts in Algebra II. Geometry and Algebra I, sure, I use them all the time for home improvements, etc., but I don’t think that Algebra II is a really “necessary” level of math to achieve for the kinds of kids who are struggling just to meet the minimum core graduation requirements.
As for “how does Brian or anyone know which match concepts any specific student will need during life?” No one can possibly determine what a given student will use…it is possible that a kid will graduate and never again have to write a paragraph–ever. Or, they might become a professional writer. The premise that we should add the requirement because we don’t know what the future has in store is a difficult premise to support. So does that mean we should require all students to take chem and physics and calculus “just in case”? Hardly. Chances are, if a kid is struggling with high school geometry, their future career in the field of mathematics is already in jeopardy–unless they CHOOSE to pursue it further and invest the effort to keep that option open for their future. No one is saying kids shouldn’t be able to choose to take upper division math, it just doesn’t make sense that it should be a minimum requirement for high school graduation.
Add this as well: requiring another year of math will mean kids have one fewer class of electives (or more if they have to re-take the math class repeatedly, thus supplanting more credits)…we’re not talking underwater basket weaving here, we’re talking arts, vocational programs, personal finance, technology, etc. That, to me, is an even bigger issue.
Interesting premise, Brian. I mean these comments respectfully.
How do you or does anyone know which math concepts any specific student will need during life? Assessment people have tried to answer that question for over a century. It seems to follow, “And who’s responsible when they encounter a math related something and they don’t know how to handle it?”
As for requiring algebra and geometry for high school graduation, it’s about time. I have met few people who could not do so with adjusted instruction.
Yes, Linnea, instructors and instruction may have to adjust to make sure all students pass. That’s what we contracted to do as teachers.
Ways exist, as the principal apparently knows, so that “all” (however operationalized) do pass these tests.
My grandaughter and her age peers had to pass algebra and geometry tests “to graduate” from public middle school and enter a below average public high school. (Some private high schools start their freshman science curriculum with math based physics. And, no, they don’t just cherry pick students.) My sons learned to use these same math fundamental principles in preschool and implicitly still use them everyday, including at the grocery store.
I wonder, what’s the big deal about making sure all people know how to use them before leaving public schools?
My friend was the starting principal at Jackson High School. When she told my husband and me (both math teachers) that all students would be required to pass Algebra in order to graduate, we said, “But what about those that don’t? What math program will you provide for them?” She said, “Not a problem. They will take it a second time.” We said, “But what about those who don’t pass it the second time around?” She looked at us bemused and said, “But, of course, they will.” She was an intelligent, compassionate, well-meaning educator and sincerely believed in what she was saying. She had never taught math.
My favorite math class was Senior Math, the last chance for those who needed a math credit to graduate. I taught budgeting where students discovered they couldn’t afford to move out, own a car, stereo, TV, etc. on minimum wage jobs. We explored paying on time where one young man thought he was doing the problem incorrectly because he ended up paying twice as much for the TV set on monthly payments than if he had paid cash. We balanced checkbooks. We explored saving a little money and watching it grow with time. We looked at the realistic probability that we would hit it big with the lottery. We determined how much paint we needed for their bedroom, how much fertilizer for their lawn. They saw how they would use math (and how they could use a calculator when they doubted their own manipulations.)
So I believe that the powers that be are intelligent, well-meaning individuals. But I don’t believe they made the right decision for the majority of our students.
What is the rationale behind the Alg II requirement? Is it just the premise that “more is better”?