# Discovery Doesn’t Work

I had trouble in ed school because (well, at least in my view of it) I openly disdained the primary tenets of progressive education. I am pro-tracking, anti-constructivist, and pro-testing, all of which put me at odds with progressives. Here is the irony: I mention often that I am a squishy teacher (squishy=touchy feely). I am not just squishy for a math teacher, I’m the squishiest damn math teacher from my cohort at the elite, relatively progressive ed school that made my life very difficult. My supervisor, who knew me first as a student in a curriculum class, was genuinely shocked to learn that I didn’t talk at my kids in lecture form for 45 minutes or more, given my oft-expressed disagreement with discovery. Even my lectures are more classroom back and forth than me yammering for minutes on end. (In fact, my teaching style did much to save me at ed school, but that’s a different story.)

Here is what I mean by squishy: My kids sit in groups, not rows. When I set them to practicing, which is usually 20-35 minutes of class, they are allowed to work independently, in pairs, or as a group of four. I often use manipulatives to demonstrate important math facts. My explanations are, god help me, “accessible”. I don’t just identify the opposite, adjacent, and hypotenuse and then lay out the ratios. No, I’ve been mentioning opposite, adjacent and hypotenuse for weeks, whenever I talked about special rights. I introduce trig by drawing a line with a rise of 4, a run of 3, and demonstrate how every right triangle made in which one leg is 3 and the other 4 (that is, have a “slope” of .75) must have the same angle forming it. I spend a great deal of time trying to think of a way to help kids file away knowledge under images, concepts, pictures, anything that will help them access the right method for the problem or subject at hand. (For more info, see How I Teach and The Virtues of Last Minute Planning.)

However, I am not in any sense a constructivist as progressive educators use it. I use discovery as illustration, not learning method. I don’t let kids puzzle over a situation and see if they can “construct” meaning. I explain, give specific instructions, and by god, my classroom is teacher centered. I am the sage on stage, baby. And that’s why I got in trouble in ed school, despite my highly accessible, extremely concept-oriented teaching style; I routinely argued against constructivist philosophy, and emphasized the importance of telling kids what to do.

Anyway. I was incredibly excited to read an article that openly states the obvious: Putting Students on the Path to Learning: The Case for Guided Instruction. This article is just so dead on right. To pick one of many great excerpts–click to enlarge, but why can’t I copy text from pdf files any more?:

Yes. Low ability kids like discovery; it is less work for them, yet they feel they are doing something important—but in fact, they aren’t learning very much. High ability kids tend to be “for chrissake, give me the algorithm”, when they would be better off puzzling through the math for themselves.

The article talks about the importance of worked-out examples. I read the article this morning and had a worked out example on the board the same day—step by step factoring of a quadratic. Here’s the weird thing: the kids who need the help with factoring had to be prompted to use the example, but the kids who got factoring were clamoring for worked examples in the area they had trouble with.

This would be a great thing for notebooks. But how do you get the kids who need help to keep the notebooks?

Great article, that changed my teaching immediately. How often does that happen?

#### 7 responses to “Discovery Doesn’t Work”

• Dave aka Mr. Math Teacher

So far, I find the (independent) discovery approach to be less effective than direct instruction for all levels of student ability. My preference is to blend what I call guided discovery by selectively leading students towards one or more “aha” moments, ideally related to conceptual understanding more so than procedural fluency; whether any, much less all or 80%, experience lightbulb moments is still difficult to determine on any consistent basis.

My scaffolded approach blends modeling and guided inquiry, sometimes starting with guided inquiry followed by modeling, other times reversing the two. My students seem to appreciate the blended approach, with a preference for modeling procedures, or problem solving. I have not attempted to isolate the contribution of either method, so I cannot speak to their individual efficacy, however, when mixed, they seem to engage more students more often than either alone. The extent to which these improve student learning is yet to be determined.

Keep up the good work!

• educationrealist

I don’t think the article is pushing for discovery in all cases for bright kids. But a carefully planned discovery lesson is going to be more useful on occasion for the brighter kids. I agree that the “aha” moment is important. I like my kids to remember that they saw, and understood, why something was the case–even if they forget the specifics.

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• surfer

When I was a kid, was introduced to sins and cosines via the unit circle. I (still) think of trig more this way rather than in terms of opposite over hypotenuse. To me, those big triangles seem like overgrown scaled up ugly confusing versions of the true unit circle. And then unless you are doing surveying or navigation or something like that, you’re really not using geometry so much. So the more algebraic, more analytic geometry concept of the unit circle works better for me (in physics, calculus, etc.)