kitchen table math, the sequel: Alternative Learning Theories to Constructivism

Friday, April 16, 2010

Alternative Learning Theories to Constructivism

Nothing is going to dislodge constructivism from its pedestal until a competing theory understands what's so appealing about constructivism.

Constructivism is a coherent way to understand ourselves and how we learn. Our intuitive experience of mastery is that we gain it through a highly inefficient process. Whether it's learning that letting go of something makes it fall, or that not all animals have teeth, our primary way of learning about the world is not from books or even from a master, but from our ambling around. first, by bumping into ideas/new concepts, where we don't even know what we don't know. Then, as we dimly start to figure out what the elements are to this new notion, we explore. Maybe we vary the conditions a bit. Maybe we play with things in our hands, build a model. If we finally get somewhere on this without giving up, we start to build hypotheses that can be tested and hopefully test them. If we hit upon a relatively correct one, we go with it, applying it to everything around (until we hit a problem again, and then we start over...)

Watching children learn to walk or to speak reinforces this notion of constructivism: kids just learn these things, quite inefficiently, but no teaching (outside of very rarefied conditions) would have helped. Kids do it at their own pace, with great variation, yet they nearly all arrive at the same place.

Constructivism is at its core, natural.

Ed school theories can articulate constructivism using a variety of words, but in the end, all of them posit a cycle, often with 4 stages.

One version is:
awareness --> exploration --> inquiry --> utilization -->awareness

Another is:
engagement -->exploration -->explanation --> elaboration -->engagement

These theories are coherent. But being a coherent theory doesn't make it right, and even if it is, it doesn't make it *the best way to help children* reach mastery. One reason it is viewed as best is because it is natural to our experience: why fight nature? The history of humans gaining knowledge of the world is clearly constructivist from fire and the wheel to geometry to public sanitation. Another reason is the theory can be taught in a lecture, from a textbook, and then by observation. It's easy to express. It fits our intuitive experience, at least in part. And what other theories compete with it?

Constructivism will never leave ed school until some other theory replaces it.

Lemov's taxonomy might work as a competing theory, if it were a theory. But it's more a proto theory of the interaction of student-teacher learning, and could still all be fit into the constructivist learning theory. Here's one example from Lemov's book:
There's a consistent progression to the lessons of the champion teachers who informed this book. It's best described as "I/We/You." This name refers to a lesson in which responsibility for knowing and being able to do is gradually released from teacher to student. It means beginning with "I" by delivering key information or modeling the process you want your students to learn as directly as possible, then walking your students through examples or applications. In the "We" step, you first ask for help from students at key moments and then gradually allow them to complete examples with less and less assistance on more and more of the task. Finally, in the "You" step, you provide students the opportunity to practice doing the work on their own, giving them multiple opportunities to practice

Many people might say that the above is explicit instruction/direct instruction. His "model directly as possible, walk them through examples" is to the well informed a vastly different model than constructivism.

But to the not-fully-versed-in-ed-school, it may not seem different at all. A constructivist would say it fits his model, too: first you introduce a carefully tailored environment for the awareness phase. The tailoring delivers key information. A student and teacher go through the exploration phase by walking through examples or applications, using them as focal points and areas for jumping off. Then, in the inquiry phase, you ask for help from students at key moments, gradually allowing them to complete a problem with less and less assistance, as you turn the inquiry from teacher-inquiry to student inquiry. And then the utilization phase is the practice opportunity phase, where you allow them to practice and reinforce as they interact with the world.

Cog Sci ala Willingham doesn't compete either, mostly because it's not coherent, and the individual elements can be shoehorned into constructivism. He calls for understanding the need for distributed practice, but certainly proponents of the cycle can argue that each time around the loop, you're getting another round of practice, each at a deeper level. He calls for recognizing the difference between how children learn and how adults do, but I think this supports the constructivists more: children, especially young children, have even more bumping-into-things to do. Constructivism supports giving kids more free range to do this bumping. Many would intuitively see that and think only adults can learn from books. He calls for getting the reward system tuned just-so, but that can fit if you build the environment correctly, and if the teacher does nothing but reward.

Engelmann and Carnine's work won't, because they created a theory of instruction, not learning. It doesn't concentrate on explaining how *we* get to mastery; it says how we teach *them* to get to mastery: isolate the necessary concept with enough positive and negative examples to disambiguate all possible misconceptions from this core concept. It is a method for *efficiency*, and rests on the notion that in order to help the low performing student to catch up, you will need efficiency. But in isn't focused on learning. Engelmann and Carnine argue the *number of examples* needed for a low performing child is exponentially more than for a high performer--they aren't at core arguing the low performer learns differently.

They violate constructivism because it isn't *natural* to push for efficiency. It doesn't speak to how we go around making sense of our own world. And in our post-baby boomer world, we're all about ourselves and how we experience the world.

Are there competing theories to this? I'll address one in the coming days.


SteveH said...

I think there are two ways to look at what goes on in schools; theory and reality. Whenever I try to connect ed school theory to my son's classes, it falls apart. At best, I see their idea of natural learning and "guide on the side" with spiral curricula like Everyday math, but is it really this philosophy that drives what schools do?

What I do see are some simple little ideas. The first is that they don't want the teacher in front of the room with all kids paying attention to him/her. That kills any constructive method where the teacher guides the process. Teachers might lecture a little to get everyone started, but I saw little work at the end in getting kids brought back to the same page. They want people to walk by the classroom and see active, engaged learners, whatever that means.

Second, they want a wide range of abilities in one class, and they want the student groupings in class to include this wide mix.

Due to parent complaints, their own guilt, or reality, they came up with the idea of differentiated instruction try to fix this classroom model. It's a fix, not a main philosophical driving force. Even after many years, my son's school still tries to convince parents (and themselves) that it will work. What ends up changing is that they now group more often by ability. I made a comment once about how you can create mixed ability classrooms and differentiated instruction just by removing walls.

Mixed ability also means that they track by age and must come up with some way to justify sending kids along to the next grade when there is little reason for doing so. They do this by redefining what (K-6) education is all about. Constructivism, understanding, and critical thinking are all just cover for doing this. They really don't care about those things. What they really care about is pumping kids along.

Well, they might really care about constructivism, but only to support what they want to do in the classroom, not learning. Since they make the goals of K-6 education very fuzzy, maybe there is no difference. They see little linkage between mastery and understanding.

What can you do to create a change in K-6 education when they can't really define what their goal is beyond minimal state cutoff standards? I think K-6 teachers need much more content knowledge (like with Msmi?) before they can begin to understand what they need to do philosophically.

Anonymous said...

Allison, I'm looking forward to your next post. Part of this muddle, to me, is that "constructivism" as a foundation for K-12 education, mis-apprehends the proportion of any child's education that is/can be accomplished through exploration/discovery, and it also mis-apprehends the timing that best accomodates those constructivist experiences, which you and I agree are in fact a part of anyone's intellectual growth. They get the proportion wrong because they don't have a good grasp of how much skill develoopment and background knowledge are necessary in the academic subjects before valid "constructivist" experiences can be useful to the student; and they get the timing wrong in that they don't have a good sense of how long it can take to get to that juping off point. I think a good illustration is learning to cook. You have to master a lot of basics (with maybe a little experimentation along the way) before you can be a creative, innovative cook and manage to make a huge meal for a lot of people that's cheap, tasty, healthy, and varied. It's hard to apply constructivist principles to the early stages of learning to cook in a way that moves the students forward at all. And that is why good culinary schools don't use constructivist methods until the students are almost graduated.

Anonymous said...

Excellent post, Allison.


Allison said...


I completely agree. I think they make that mistake because of their fetishization of what they perceive as natural, and the importance they assign to it.

They believe learning is natural, and learning should be natural. But this is not true. Our brains are built for language acquisition and motor skill acquisition. It doesn't mean our brains, on average, are built for reading or mathematics.

Take reading: some kids learn to read by reading the way they learn to walk by walking. Therefore, reading instruction should be as natural as possible, and the child will naturally learn to crack the code sooner or later. If it's too much later, why, something must be wrong with their learning cycle--they must have a learning disability. Guided reading/whole language--these are perceived as natural because they are how adults read. Synthetic phonics? That's the definition of unnatural.

The same applies in math. Teach symbols, definitions, proofs? Unnatural. Teach fractions by analogy? Natural.

The idea that *learning these things efficiently is unnatural* is not present.

If they got the balance right between skill building and experiential learning, they might better see that the unnatural part, the inauthentic learning, is a step on the path to authenticity. Natural is what you get AFTER you've learned, not before.

Anonymous said...

Allison, they also misinterpret what's going on during school activities that are hands-on, exploratory, etc. For younger children, these experiences, while important and valuable, do not lead to "constructing knowledge" in any significant way. They are useful as a way of exposing children to topics and fields in a way that calls the senses into play, and as a motivator. But for the most part at this level (let's say K-4 or 5) there is not really any new knowledge or skills being built. Exposure is not the same as understanding. Once in a while, constructivist experiences can actually build skills and knowledge, but not nearly as often as constructivists think.

Erin Johnson said...

Constructivism will never leave ed schools because there is no reason for it to leave. Ed professors are not responsible for enabling students to learn (and thus their theories are never subjected to a reality check). They are responsible for justifying why an education degree is superior to a subject matter degree in providing the foundation for a qualified teacher.

Even if someone came up with an alternative learning model, why would any ed professor embrace it?

Additionally, there are student learning examples that are "natural" and consistent with constructivism (e.g. vocabulary acquistion with reading an abundance of narrative texts), and thus these few examples will always provide support for over-generalizing the theory to all school learning.

Robin said...


Did you read John Sweller's "Instructional Implications of David C Geary's Evolutionary Educational Psychology"?

He does a great job of talking about the implications to instructional design of Geary's distinctions between biologically primary information like speaking and walking where immersion works well.

He talks about how math and reading are biologically secondary knowledge and generally must be explicitly taught. Motivational encouragement must also usually be supplied.

To Sweller, Geary's distinctions explained why constructivist techniques sound plausible but actually perform poorly.

Allison said...

Nope, haven't read it. I'll try to find it.

Peter Warner said...

Thank you for that article, Allison, I'm looking forward to its sequel.

One point you bring up is especially welcome: you mention that a theory of learning is NOT the same as a theory of teaching. I first encountered that insight while reading Professor Plum's critique of constructivism, and I'd like to get a stronger sense of that distinction. I'm glad to see that you mention Engelmann as well, I'm fascinated by his insights.

My focus is on beginning reading instruction, in my case teaching Japanese students to read and write the (English) alphabetic code. Many teachers are committed to the view that learning to read is (or should be) a 'natural' process, and they strongly resist an explicit instruction approach. Many of them strongly resist the suggestion that reading is not a natural ability.

This 'learning is (or should be) a natural process' theme is very accepted, but (I think) not supported by actual experience. Your articles encourage a more honest and educated view. Thank you.

Best regards, Peter Warner.
Nagoya, Japan

Anonymous said...

Wow. Very nice post, Allison. I'm definitely staying tuned.

le radical galoisien said...

My Singapore math teacher was very unwittingly guide on the side.

The thing is, she had classroom control. She knew what was productive.

The first thing was getting every problem right. I think I've described this process several times now: You're assigned HW, you do it. You get it back -- if anything's wrong, you correct it green pen until it's right. There are twists on this -- sometimes you correct the other person's work and try to explain why what they did was an incorrect approach. You never lose any points on HW as long as you ultimately correct everything -- you lose them on exams.

Singapore Math as implemented in the classroom is very exploratory in my memory. Every week or two we'd suspend normal lecture and have competitions between groups and we'd write our submissions on transparencies and submit our answers.

Surprisingly it was during the PSLE period that exploration even increased more: we'd have remedial sessions (technically called "remedial" in order to justify funding: everyone who did not have a 100% had to attend) where we'd try to collectively piece together how to approach "unconventional" heuristics problems on the PSLE.

My math teacher was often very directly involved, yet not. Often she was just the loud mouthpiece for different students, rephrasing what other students' said. (Like seriously, we would draft new strategies in class.) At other times she just lectured but back then it never felt like a lecture.

Catherine Johnson said...

A constructivist would say it fits his model, too: first you introduce a carefully tailored environment for the awareness phase.

It's partly that (i.e. there are similarities between Lemov's taxonomy and what constructivists do) and partly that people hear what they want to hear.

Here's an excerpt from letters to the TIMES about Lemov:

I totally agree with Doug Lemov: clearly, a strong grasp of the content being taught is a must, but as I have learned in the past, the ability to “drop the lesson plan and fruitfully improvise” when needed is a far more important skill as we strive to focus on individual students’ needs. Improved student learning is not accomplished by stressing standardized assessments, structured curriculum and rigid lesson plans. It is found in the connections teachers make with students when they grasp the way different students learn.

March 15, 2010

That passage is the opposite of what Lemov actually says.

Catherine Johnson said...

I'm not sure Lemov's approach isn't based on a theory. Allison probably read, on the DI list, that there was a period during which teacher effectiveness research was being done -- back in the 70s and 80s, I think.

I've been poking around in that literature & it looks like the theory (or at least concept) underlying explicit instruction is called "information processing."

There's a new book out on constructivism that has a good introduction on this.

Constructivist Instruction: Success or Failure?

Barak Rosenshine is one of the main people in the field.

Catherine Johnson said...

What can you do to create a change in K-6 education when they can't really define what their goal is beyond minimal state cutoff standards?

major moment at the BOE meeting the other night

A couple of parents were pushing the board & administration to increase student achievement beyond meeting the state standards.

The board president said (paraphrase), "A lot of factors that go into student learning are out of our control."

Well, then.

Let's have another tax increase!