Hello, all! I'm back!
Instead, I'm going to touch on something a little more prosaic: the math wars.
I follow Barry Garelick (author of Letters from John Dewey/Letters from Huck Finn and Teaching Math in the 21st Century
) and Katherine Beals (author of Raising a Left-Brain Child in a Right-Brain World
) because my own experience has led me to sympathize with their instructivist point of view. From 2006 to 2012, my Virginia county's school board backed the reformist Investigations in Data, Number and Space as its elementary math curriculum, and from my vantage point, the result has been an overall decrease in conceptual understanding and fluency and a corresponding increase in calculator dependency. When an otherwise bright fifteen-year-old reveals - as one did the other day - that he's never learned his times tables, that, for me, raises a blazing red flag.
Of course, the reformists aren't wrong to note that students often skate through our still largely traditional high school math curricula without fully absorbing the material. I think, however, that they fundamentally misunderstand the reasons why this happens and consequently propose the wrong solutions. We don't need more time-consuming constructivist exercises in which students are asked to "discover" the principles of mathematics on their own; on the contrary, we just need to be smarter in how we deliver direct instruction.
In my county, high school math is taught in a very disjointed way. Individual topics are covered in isolation in brief "units" and then, for the most part, are never brought up again until it's time to take the state's End-of-Course assessments. Our standards documents do allude to the vital connections between concepts and courses, but as far as I can tell, only a few exceptional teachers are pointing out those vertical articulations to their students. This needs to change. In order for teens to "get" math, they need to see how it all fits together -- and they need regular cumulative assessments of their understanding to combat forgetting. A few class periods of discussion and a few nights of practice simply won't cut it for most.
It would also help if teachers routinely threw monkey-wrenches into the works to force teens into more abstract modes of thought. Our state's algebra curriculum does this already with linear equations when it demands students solve an equation like (ax-b)/c = d for x, but we could do that with other concepts as well. For example, after giving students a firm grounding in the quadratics unit, ratchet up the difficulty level: ask them to solve 2(x+3)2-(x+3)-6=0 for x and see what happens. And as for "explaining your reasoning," why not bring back the traditional two-column proof? 'Tis simpler and far more elegant than an undirected group discussion.
Lastly, I think we need to approach math education with a good heaping dose of humility and not allow perfection to be the enemy of the good. In truth, no math program is going to successfully educate everyone because no math program can fully control the extra-academic factors that influence math achievement. We can do our best to motivate our kids by challenging them and building their competence, but in the end, some students will remain unreceptive. We can work hard to battle the American perception that math is something only brilliant nerds can master, but some folks will refuse to be convinced. We can preach at-home reinforcement 'till we're blue in the face, but some parents - for a multitude of reasons - will not step up. This is our reality; it sucks, but we have to face up to it. Revolutionaries have gotten into trouble before for presuming to upend entire systems to fix their "flaws." Let's read their failures as cautionary tales and not let starry-eyed technocratic schemes short-circuit our wisdom.
) and Katherine Beals (author of Raising a Left-Brain Child in a Right-Brain World) because my own experience has led me to sympathize with their instructivist point of view. From 2006 to 2012, my Virginia county's school board backed the reformist Investigations in Data, Number and Space as its elementary math curriculum, and from my vantage point, the result has been an overall decrease in conceptual understanding and fluency and a corresponding increase in calculator dependency. When an otherwise bright fifteen-year-old reveals - as one did the other day - that he's never learned his times tables, that, for me, raises a blazing red flag.Of course, the reformists aren't wrong to note that students often skate through our still largely traditional high school math curricula without fully absorbing the material. I think, however, that they fundamentally misunderstand the reasons why this happens and consequently propose the wrong solutions. We don't need more time-consuming constructivist exercises in which students are asked to "discover" the principles of mathematics on their own; on the contrary, we just need to be smarter in how we deliver direct instruction.
In my county, high school math is taught in a very disjointed way. Individual topics are covered in isolation in brief "units" and then, for the most part, are never brought up again until it's time to take the state's End-of-Course assessments. Our standards documents do allude to the vital connections between concepts and courses, but as far as I can tell, only a few exceptional teachers are pointing out those vertical articulations to their students. This needs to change. In order for teens to "get" math, they need to see how it all fits together -- and they need regular cumulative assessments of their understanding to combat forgetting. A few class periods of discussion and a few nights of practice simply won't cut it for most.
It would also help if teachers routinely threw monkey-wrenches into the works to force teens into more abstract modes of thought. Our state's algebra curriculum does this already with linear equations when it demands students solve an equation like (ax-b)/c = d for x, but we could do that with other concepts as well. For example, after giving students a firm grounding in the quadratics unit, ratchet up the difficulty level: ask them to solve 2(x+3)2-(x+3)-6=0 for x and see what happens. And as for "explaining your reasoning," why not bring back the traditional two-column proof? 'Tis simpler and far more elegant than an undirected group discussion.
Lastly, I think we need to approach math education with a good heaping dose of humility and not allow perfection to be the enemy of the good. In truth, no math program is going to successfully educate everyone because no math program can fully control the extra-academic factors that influence math achievement. We can do our best to motivate our kids by challenging them and building their competence, but in the end, some students will remain unreceptive. We can work hard to battle the American perception that math is something only brilliant nerds can master, but some folks will refuse to be convinced. We can preach at-home reinforcement 'till we're blue in the face, but some parents - for a multitude of reasons - will not step up. This is our reality; it sucks, but we have to face up to it. Revolutionaries have gotten into trouble before for presuming to upend entire systems to fix their "flaws." Let's read their failures as cautionary tales and not let starry-eyed technocratic schemes short-circuit our wisdom.
No comments:
Post a Comment