Archive for the ‘education’ Category

New Teaching Blog!

I have decided to start a new teaching blog called On Learning Curves.  Don’t worry.  I’ll still post for the Crockett because Cody Brown is too awesome.  But this isn’t the right forum for my thoughts on the day to day life of a new teacher.  subscribe and enjoy!


Economists in the Classroom

As a future teacher, and a fan of the dismal science, I love the recent Freakanomics post about the BASIS charter school is n Arizona.

The BASIS Educational Group, run by two economists, requires every 8th-grade student to take a year’s worth of economics.  Many BASIS students, who are all required to take at least six AP exams before graduation, go on to take AP Economics in 9th grade, and average a 4 (out of 5) on their AP exams.  ”Our students learn to love economics early on, and we hope that passion will continue long into life.”

And my favorite part:

BASIS also offers incentive-heavy contracts to teachers; and all staff members are on one-year contracts.

You do not have to be an economist to recognize the benefit of school competition.  I believe that a firm command of economic reasoning greatly improves human capital.  I find it encouraging seeing a school does too.  But the beauty of school competition is that I could be wrong.  Perhaps when everything is said and done an Art History heavy curriculum from some other charter school beats out BASIS.  Perhaps studying economics early does little good for students when they enter the work force.  So what? These kids have gotten a fair amount of college credit, and policymakers learn more about what curricula create the most human capital.  Doesn’t the world just feel better when we find Pareto efficient outcomes?


The difficulty of teaching math

From an article by Elizabeth Green:

Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it. Then they need to take each mind from not getting it to mastery. And they need to do this in 45 minutes or less. This was neither pure content knowledge nor what educators call pedagogical knowledge, a set of facts independent of subject matter, like Lemov’s techniques. It was a different animal altogether. Ball named it Mathematical Knowledge for Teaching, or M.K.T. She theorized that it included everything from the “common” math understood by most adults to math that only teachers need to know, like which visual tools to use to represent fractions (sticks? blocks? a picture of a pizza?) or a sense of the everyday errors students tend to make when they start learning about negative numbers. At the heart of M.K.T., she thought, was an ability to step outside of your own head. “Teaching depends on what other people think,” Ball told me, “not what you think.”

Lockhart’s Lament (Seguin’s response)

I just read Meusebach’s post on Lockhart’s paper on mathematics education.  As someone who will be teaching high school math in the near future I feel like I should make my critique.  In many ways I agree with Lockhart.  Mathematics education as I remember it sucks all of the creativity and artistry out of mathematics.  I hated math class all through middle and high school and I never excelled in the subject like I did with History and English.  It was not until college forced calculus on me, did I actually enjoy the subject.  I realized that math was not a spirit crushing exercise in monotony.  In my classroom, one of my overarching though nebulous goals is to show that math is not a game of following directions, but as creative as poetry, art, and music.

However I disagree with Lockhart on a number of points.  First he asserts that the true value of mathematics is its artistry.  This is wrong.  Mathematics is valuable because it is extremely practical.  The labor market makes this fact painfully clear.  Simply compare the salaries of mathematicians, engineers, statisticians, economists, and actuaries to careers that do not require the same quant skills.  The market rewards quantitative reasoning very well.  In fact one of the most accurate predictors of lifetime income is the number of math courses a person has taken.  Math may be beautiful because it is the art of reasoning, but it is valuable because it can do a lot of good to the world around us.

Furthermore, Lockhart doesn’t understand the challenge of teaching, or teaching math specifically.  He writes:

Teaching is not about information.  It’s about having an honest intellectual relationship with
your students.  It requires no method, no tools, and no training.  Just the ability to be real.  And if
you can’t be real, then you have no right to inflict yourself upon innocent children.
In particular, you can’t teach teaching.  Schools of education are a complete crock.  Oh, you
can take classes in early childhood development and whatnot, and you can be trained to use a
blackboard “effectively” and to prepare an organized “lesson plan” (which, by the way, insures
that your lesson will be planned, and therefore false), but you will never be a real teacher if you
are unwilling to be a real person.

Lockhart demonstrates the common misconception that teaching is simply an exercise in engagement.  Teaching is damn hard.  Students do not walk in as eager pupils ready to learn for the pure sake of learning.  The vast majority do not want to be there, and would leave at the drop of a hat if given the chance.  One of the most difficult challenges for teachers is not figuring out how to “be real” but getting control of their classrooms.  Lockhart’s brand of teaching describes an organic discussion where topics are introduced as they are discovered.  It sounds great and very Dead Poets like, but it is completely unworkable in a real classroom.  To say that all lessons are to be improvised  is like saying an essay should be written as a stream of consciousness.  In fact, the data is very clear that the best teachers meticulously plan lessons.  Lesson plans are effective because they provide order to an extremely chaotic situation.

I think, in my very limited experience, that the best teaching model will merge the current curriculum with many of Lockhart’s recommendations.  I agree that math, as it is taught now, fails to engage many of our most creative students.  But teaching in the real world requires much more than a passion for math.

Lockhart’s Lament

Here’s a paper we had to read for my number theory class.  It’s rather long, but if you read the first four or five pages you’ll get the general point.  Basically, Lockhart has a major problem with how math is taught in our school system.  He feels that math is taught mostly by showing people how to follow specific rules.  In grade school and undergraduate classes, those who excel at math are those who can follow these rules the best, not those who exhibit the best independent and creative thinking.  According to him, success in mathematics beyond this is predicated on the ability to think critically and independently.  More importantly, he argues, people are not exposed to this side of math and therefore aren’t aware how interesting it really is.  Although much of it sounds like he’s just bitching about people not knowing what he does for a living, there’s surely some truth to it.  But how would one go about implementing lesson plans that follow these guidelines?  He rails against standardized testing, but is there a way around using them to ensure some basic competency?  In the end, he raises some very interesting questions, but provides few answers.  I thought this might be especially interesting to anybody who might be teaching a math class in the near future.