Tom Hoffman‘s perspective on Rhode Island’s summative graduation exam is worth your time:
Another question I thought was typical showed two spinners that would give you random numbers from 1 to four. It wanted to know the probability that the sum of the two would be a prime number. I drew a complete blank, until I realized I could easily write out all 16 combinations and just circle the ones that resulted in a prime number. That more clearly took mathematical reasoning, problem solving and content knowledge.
I like the question, and I like the direction it should push math curriculum. But I’m also aware that if even if kids have been taught probability, if they haven’t been taught it in a way that encourages flexible and resourceful problem solving — rather than pulling numbers out of stereotypical word problems and following procedures — they will be completely screwed.
I’m glad parents, policymakers, and stakeholders are taking these exams (or shortened versions of them) and reflecting on their results. But again we should be careful not to write expansive prescriptions for what we teach kids based on the test results of grownups. The proposition, “A middle-aged bureaucrat hasn’t used algebraic expressions in three decades and turned out fine therefore we shouldn’t teach algebraic expressions to fourteen year-olds” has yet to be nailed down for me.
Tom HoffmanMarch 20, 2013 - 6:03 am -
I’d say in this case the adult reaction wasn’t so much “That’s stuff I learned in school but have forgotten,” as “WTF was THAT?”
Jared CosulichMarch 20, 2013 - 10:36 am -
It’s not that we shouldn’t teach algebraic expressions because most of the population gets by just fine without them, it’s that we should call in to question the idea that there is some extensively prescribed curriculum (including algebra) that is necessary to being successful in life.
The real lesson that I see from these experiments (and I’m very happy to see them happening) is that much of what we consider requirements in school are divorced from any true requirements in real life.
Should we expose students to algebra? Sure, why not.
Should we not let them continue their education until they’ve mastered it or even limit their future opportunities because they struggle with it? Absolutely not.
There are an infinite number of paths that a young person can take to create a successful life for themselves as can be seen by the diversity of paths and knowledge that exist with adults that lead successful lives. We need to encourage the diversity of possible paths, not get hung up on whether someone can solve algebraic problems (or problems from any number of subjects) specifically.
Don HillMarch 20, 2013 - 12:24 pm -
I agree Dan, I don’t feel there is weight to the notion that the results of adults taking these tests should somehow prescribe what we should be teaching kids. I do believe that the results are more indicative of the fact that the material on these tests does not reflect the skills needed to be successful in the real world. If we are requiring students to pass a test with proficiency, in order to graduate high school career and college ready, then the skills being assessed ought to be skills used in those environments. If 60% of the adults taking the NECAP do not use these skills (i.e., can’t answer the test items correctly) why are we asking 100% of our students to be proficient in these areas in order to graduate? The results of these tests can be used in a myriad of other ways beneficial to education, why make it a graduation requirement?
IsaacMarch 20, 2013 - 12:42 pm -
Don, one part of your comment makes me a bit leery.
“Skills needed to be successful in the real world” =/= “Skills used in those environments”.
I’m not sure that either of these should be equated with the goal of education, but even assuming for purposes of argument that “skills needed to be successful” is the goal, are we equating “success” with median actual behavior?
My own opinion was rather nicely summed up by Randall Munroe here (particularly in the mouseover text): http://xkcd.com/1050/
MikeMarch 20, 2013 - 5:24 pm -
Following up on some of the other comments, could you explain exactly why:
‘The proposition, “A middle-aged bureaucrat hasn’t used algebraic expressions in three decades and turned out fine therefore we shouldn’t teach algebraic expressions to fourteen year-olds” has yet to be nailed down for me.,
WilliamMarch 20, 2013 - 6:47 pm -
> It’s not that we shouldn’t teach algebraic expressions because most of the population gets by just fine without them, it’s that we should call in to question the idea that there is some extensively prescribed curriculum (including algebra) that is necessary to being successful in life.
Plato might respond thus: “Yes, I said, but for [a practical] purpose a very little of either geometry or calculation will be enough; the question relates rather to the greater and more advanced part of geometry–whether that tends in any degree to make more easy the vision of the idea of good; and thither, as I was saying, all things tend which compel the soul to turn her gaze towards that place, where is the full perfection of being, which she ought, by all means, to behold.” (Republic, VII)
Is there a place for the tradition and culture practice of mathematics in molding students to seek the good?
Jared CosulichMarch 20, 2013 - 7:34 pm -
William: Absolutely. Let’s focus the requirements on the few skills that are necessary in the real world (reading/writing/communication, basic math, etc), skills that any reasonably successful adult could demonstrate.
Then we can spend the rest of the time exploring the history/tradition/beauty of more advanced subjects. We can focus our efforts on facilitating a deep love of learning, not just for practical purposes, but because learning even esoteric subjects can be a challenging and deeply enjoyable activity with benefits beyond what we can measure in a practical manner.
Dan MeyerMarch 21, 2013 - 3:58 am -
@Mike, two reasons:
One, I learned lots of valuable things and had lots of valuable experiences in school. Even though I’ve now forgotten their specifics, they’re part of my character.
Two, as a grownup, I’ve specialized myself to the degree that I don’t now need a lot of what I learned in school. I’m pretty much a math person, now. But that doesn’t mean that young-me should have only been taught math. Young-me had no idea what he’d eventually do.
GarthMarch 21, 2013 - 9:29 am -
Some people are getting close to figuring out the Higgs Boson. It may be possible from there to do a whole bunch of interesting things with gravity. Where would those people be without algebraic expressions? 99% of people do not need 99% of the math we teach in high school. Those 1%ers make the discoveries that change the world..
Jared CosulichMarch 21, 2013 - 9:44 am -
Garth: Computer programming is not required or even really taught at all in many K-12 schools. Despite this fact, millions of people have mastered programming and gone on to do amazing things with the skill.
We don’t have to require 100% of students to master something like Algebra to ensure that the 1% that really needs it has access to it.
We should strive to expose students to all of these subjects (algebra, computer science, etc) and make learning the subjects as accessible, interesting, and useful as possible.
We can even make it clear to students that the world currently will pay more for certain skills. Just give them the information necessary to make these decisions and make the learning as accessible as possible.
We don’t need to hold back students or make them think they are not capable of being useful contributors to society in order to ensure that those that will embrace and do great things with a certain skill set get access to that learning.
JoeMarch 22, 2013 - 9:39 pm -
Building on Dan’s reply to Mike:
Algebra is the high school math that most fundamentally addresses functions. Properly taught algebra will build a functional perspective into that child. We can hope that the perspective will remain even after the context it was taught in (algebraic expressions) has been forgotten.
Algebra is a vehicle for teaching a perspective about the world.
crazedmummyMarch 24, 2013 - 12:24 pm -
We’ve had a lot of time where most young adults were not “required to “learn algebra” to finish high school. For a couple of years now, we’ve had a system where most young adults have to at least find someone prepared to lie about their proficiency in Algebra.
I argue that this just makes society more cynical.