Saturday, August 31, 2013

Two Articles For Your Consideration

I recently read two articles that I would like to share with you...

The first is A Mathematician's Lament by Paul Lockhart.  This article showed up in my in-box from a student that I had in class last year.
Lockhart begins his article by suggesting that art and music education be mandatory for every student.  However, instead of giving them a blank canvas, we will make them sit through lectures and study colors and applicators.  The must work their way up the ranks from worksheets on the basics, to pre-paint-by-number, and finally paint-by-number.  Only a few exceptional students will be allowed to paint on a blank canvas.
He goes on to say that this is what we are doing in math education.  We are killing math.  Teachers tell students they have to learn the remedial stuff before they can do the real stuff.
I think he's on to something here.  Students need to see why it's important, yes, but they need to see how perfectly beautiful and fun it is too.

The second is The Case Against Algebra II by Nicholson Baker.  A few days after I received the first article, this arrived in my inbox from a fellow math teacher.
Baker suggests that schools no longer make Algebra II mandatory.  After reading this, I had to ask myself Is Algebra II really necessary?  Algebra II curriculum usually includes Complex Numbers, Factoring, Polynomials, and Nonlinear Expressions and Equations.  Can a person function in society without knowing these topics?
First, if school districts are going to eliminate the mandate to learn Algebra II, then Algebra I has to be an amazing experience for students.  Teachers have to be education rock stars, so that students see the importance and sheer joy of mathematics.  Students need to be inspired to take Algebra II, not forced to take it.  Refer back to the first article.
Now let's suppose that Algebra II is an elective.  The only students in the class are the ones who want to be there.  Now Algebra II will truly be Algebra II, unlike many districts where Algebra II is really a repeat of Algebra I will a few extra topics.  When we teach every student Algebra II it's not No Child Left Behind, it's Every Motivated Child Held Back.
Let's take a look at the students who want to take Algebra II.  They are now in a class that is rarely disrupted or slowed down to meet the needs of those who don't want to be there.  They can learn Algebra II in their Algebra II course.  They can learn Pre-Calc in the next course (rather than Algebra II again).  They can begin Calculus with a review of Limits rather than a review of Algebra I.  They can finally compete globally.
So what happens to the students who don't take Algebra II?  Will they become utter failures in society? I honestly don't think so.  Maybe if students aren't forced to take Algebra II, they won't hate math so much.  Maybe if they don't hate math so much, they won't hate school so much.  Maybe if they don't hate school so much they won't be absent as often.  Maybe if they aren't absent as often they won't drop out of school.  Maybe if they don't drop out of school they will become productive members of society.  Maybe if they all become productive members of society we will keep more jobs in America.  Maybe if we keep more jobs in America our unemployment rate will go down.  Maybe if our unemployment rate go down....
You get the idea.

See?  You can save the entire country just by making Algebra II an elective.

Seriously though, what are your thoughts?


  1. First, I'm sharing this post with my department.

    This is really good stuff-I teach in Chicago, and EVERY student is required to take Algebra 1, Geometry and Algebra II (I do mean every, including students in the severe and profound program). Our classes are leveled, partially so that students actually learn the content they are supposed to (at least at the higher levels), but lower level Algebra 2 contains almost no actual Algebra 2 curriculum.

    I think it would make students hate math less to not take Algebra 2, but I also worry about their preparation. In Chicago, a huge proportion of our students don't qualify for college level math and take up to three semesters of 0 level courses at community college first--so I would be worried that not taking Algebra 2 would put them even further behind. Maybe a different course? Maybe more options?

  2. I actually wrote a post very similar to this one but much less eloquent inspired by the same articles. I agree wholeheartedly. Algebra II is really only necessary if a student wants to continue to do pre-calc and calc. Many students stop after taking the mandatory, painful algebra II course and they leave high school thinking math is nothing more than a series of arbitrary procedures that needed to be memorized then forgotten. They never see the beautiful coming together of all of this discrete knowledge into the unified theory of functions that is calculus.

    I think though, that rather than requiring the march from Alg 1 to Geo to Alg 2 to Pre-calc to calc that will only be useful for a student wishing to pursue the hard sciences in college, we should require 3-4 years of math. Students should indeed take algebra and geometry because they won't know what they like about math until they've taken these two courses, but after that we should offer business math, the geometry of art, math history, non-Euclidean geometry, discrete mathematics. We should let them see that the math world is not one-dimensional: there are many branches they can explore that may be more suited to their interests than the standard march.

    Choice is powerful. Students will tend to like a course more just because they had a choice in taking it. They will also be able to explore the mathematics that directly relate to their interests.

  3. My school, for some reason only required two years of math. However, 97% of the students took math for four years. I told my kids that algebra was the spelling, grammar and sentence structure of math, and that they could read and write math in many areas (prose and poetry?) after that course.
    But Alg II doesn't have to be boring or dry! Kids respond to blood, guts and gore and occasional threats of violence! (If you tell me the square root of x squared plus y squared is x plus y, I'll have to chop off your pinky finger)
    We would use action verbs for out steps. We would have stupid variable names. I loved teaching that course, and then pre-cal, calc, physics, stats, trig....What a blast. Thirty five years was probably not enough!