Structured Internalization an Educational Theory

Beyond Constructivism –page 1 of 18

Beyond Constructivism

Published in the Fall 1999 edition of

Pennsylvania Educational Leadership

Richard M. Oldrieve, M.Ed

28359 Center Ridge Rd.

Westlake, OH 44145

Voice and FAX: 440-892-1994


Beyond Constructivism

As part of the process of developing his breakthrough theories concerning Light, Photons, and General Relativity, Albert Einstein framed his ideas into “thought experiments”. He would reduce a theory down to its simplest terms and think it through to see where the logical holes were. Einstein would often have no other choice but to use a thought experiment, because many of the experimental apparati necessary to test his theories had not been built and some still have not been built. Yet even if the lab equipment had been available, thinking and visualizing instead of doing undoubtedly saved Einstein time by helping him eliminate ideas that would have led to dead ends and allowing him to hone ideas without having to spend years in the laboratory.

Even though educational researchers have plenty of subjects to work with and don’t have many concerns about equipment, thought experiments should still be in their repertoire. Not only do dead ends cost educational researchers time and resources; dead ends cost communities and students time and money that are even harder to come by. I mention how to avoid dead ends in an issue of Educational Leadership that is devoted to constructivism, because I would like to propose a few thought experiments to explore the limits of constructivism and to suggest what conceptual philosophies and teaching strategies lie beyond constructivism.

First Thought Experiment

For the first thought experiment, please envision a 6-year old girl who started kindergarten in September and faces 13 or more years of schooling to graduate into intelligent adulthood. Then propose a curriculum that will help her construct the theory of relativity for her senior thesis.

Pause! Think! Give it a shot!

Did you happen to suggest that you would put the child in a room and she would learn how to read, write, do arithmetic, and construct the theory of relativity all by herself?

I doubt it. We all recognize that there are some limits to constructivism See Figure 1 for a diagram of a brilliant 6-year old trying to re-invent the theory of relativity. Besides, even if our kindergartner succeeded, she still would have undershot her potential. Why? Because Albert Einstein constructed the theory of relativity 80 to 90 years ago--with the help of his professors, his colleagues, and his first wife (a theoretical physicist herself who some have hypothesized to have been the real brain of the family). Consequently, a child with similar talent should have taken quantum physics even further than Einstein did. As the old saying goes, “There’s no point in re-inventing the wheel.” Or more appropriately to this article, “There’s no point in re-constructing the theory of relativity inefficiently.”

Sir Isaac Newton acknowledged this reality when he credited his formulating the laws of gravity and his inventing of Calculus to having stood upon the shoulders of the giants of science who had come before him. Four hundred years after Newton, our knowledge base is even greater, and it is asking a bit much to expect that students can literally construct what has taken millions of intellectuals thousands of years to discover, hypothesize, and prove true.

In a similar vein, long-time constructivist Erma Yackel (1999) made a stunning admission in her session at the April 1999 convention of the National Council of Teachers of Mathematics. In the San Francisco convention center, sh stated, “After ten years, I’ve finally come to realize that the teacher is not the ‘guide on the side’… the teacher is the teacher.”

Although not explicitly stated by Yackel, I take her statement to mean that she’s come to realize that teachers have an expertise that the students don’t. We can never forget or downplay the struggle that mathematical giants and teachers went through to construct the knowledge that students are being expected to learn. Remember, 4000 or 5000 years ago, no one even knew how to write down a name or date on the top of a piece of paper. If knowledge and concepts weren’t difficult to construct, then there would be no need for schools.

Yackel’s statement also implies that she now recognizes teachers must make judgmental decisions. Teachers must decide which student developed the best solution, which solution isn’t so good, what’s the most efficient and/or elegant solution, which solution works but takes too long to implement, and how can we help the student(s) understand who didn’t even come close to the correct solution.

A week later at a different convention down the road in San Diego, I discussed Yackel’s admission with a well-known reading professor. He gave a knowing smile and nod of the head, and said that he believed the old distinction between active and passive learning to be more useful than the concept of constructivism.

Second Thought Experiment

So let’s try a second thought experiment: Please construct a curriculum in which a kindergartner could be lectured to for thirteen years and come out understanding the theory of relativity.

Not even worth bothering to try is it? Maybe it’s possible, but I don’t believe many of us would want to put ourselves in the girl’s shoes. See Figure 2 for an idealized graph of how a good lecturer developing a smooth curve of thought from one point to the next.

Third Thought Experiment

For a third thought experiment, please try to compare and contrast an active learning curriculum with a constructivist curriculum.

Despite my regard for the reading professor, I don’t think he’s correct. I don’t think “active learning” always equates with constructive learning or even effective learning. Most of us have seen a class where students were obviously physically and even mentally engaged in a hands-on experiment, but that none of those active students had the foggiest idea what they were doing. Most have us have also participated during in-services where there was plenty of making and taking going on, but not much learning.

To me the concept of constructivism just makes far more sense than the concept of active learning. Trying to solve a problem seems to have more potential for generating neuron connections than just participating in an activity (see the January 1999 edition of Educational Leadership). Yes, a student might remember the experience of riding on a roller coaster, but the fact that the student remembers going around the loop de loop does not mean that the student has learned the concept of centrifugal force.

The challenge of teaching is to ensure that the student who is physically engaged is also mentally engaged, and that the student who is mentally engaged is also trying to solve problems.

But constructivism encompasses more than merely solving problems. My father was a NASA engineer and even when I was in Cub Scouts he tried to teach me about Bernoulli, Archimedes, and ion-powered rocket ships. Thirty years later, the pictures, models, and contraptions are still vivid, but the most enduring lesson he taught me was a mental process he didn’t explicitly teach or demonstrate. One evening while I was in eighth grade we were driving to a chess tournament in Hershey Pennsylvania and my father suddenly suggested that we practice by playing a game of chess in our heads. At first I was skeptical, but a few moves later I was just as suddenly thinking in a different way. Of course a few more moves later my skepticism proved accurate and our abilities collapsed on themselves. We no longer could ascertain where the bishops, rooks, and pawns were placed, but nevertheless my consciousness had experienced the possibilities of mental imaging and visualization. I was now better equipped to work out “thought experiments”, and to construct what S.I. Hayakawa calls maps of the territory--mental maps of how ideas, facts, and concepts fit together to form a coherent and sensible world view.

Fourth and Fifth Thought Experiments

Which brings us to our fourth and fifth thought experiments. For the fourth, please spend at least a minute trying to visualize your favorite (or least favorite) roller coaster. If you want to earn extra brownie points, try writing down a description of your roller coaster ride.

For the fifth thought experiment, please think of the concept of centrifugal force. Now visualize and feel the roller coaster ride.

(Centrifugal force is the force generated by an object wanting to keep going straight even as it goes through a circle. On a turn, your body wants to keep going straight, so you feel like you are being thrown off the side of the roller coaster. On a loop de loop, the centrifugal force makes you want to keep going straight through the bottom of your seat--which holds you upside down as you go through the top of the loop.)

If you’re like me, the difference in visualization between the two rides is tremendous.

Sixth Thought Experiment

Now for a sixth thought experiment, think of what it takes to devise and implement a good constructivist lesson. For a story-starter, I’ll suggest the concept of place-value.

Did you visualize letting the children free play? Or did you think of the sheer intellectual brainpower and creativity it takes to devise a lesson in advance and to ensure it is carried through to the spirit--if not the letter. In these two visualizations and this particular essay as a whole, I’m trying to build a map of a more coherent educational philosophy. And since I firmly believe in the importance of the prior giants, I don’t think that constructivists can ignore what our educational forebears have discovered. One, B.F. Skinner found that it is easier to teach something if it is broken into parts, and two, Jerome Bruner suggested that structuring a curriculum and/or a lesson makes it easier to follow.

In the above examples of thought experiments four and five: I imposed a structure of visualizing a roller coaster ride. By breaking the visualization down into a visual and a physical component, the ride became more intense. With more time and effort I could have begun the journey by having readers visualize the smells and sounds of an amusement park. To turn the visualization into a definitely nasty experience, I could have started with a visualization of the sights and sounds of a carnival, then tossed in a visualization of eating curly fries, elephant ears, and cotton candy, and then brought in the visualization of the roller coaster with centrifugal force.

Final Thought Experiments and Conclusion

My whole point in this essay is to bring out the concept that constructivism is not the end all and be all of education. In fact, isolating constructivism from other educational movements dooms constructivism to failure. I believe combining structured lessons with lessons broken down into smaller parts with visualization with engaged problem solving with guided feedback with standing on shoulders of giants leads to what I see is the future of constructivism: “structured internalization”.

Yes, constructivism is a great concept, but the constructing must be structured so students can make a series of mini-leaps of conceptualization that lead to the knowledge we know that they must acquire. Yackel realized that the teacher is the teacher, but what is also important to remember is that the curriculum writer is the curriculum writer. Just like the good old or bad old days, a broad overall scope and sequence needs to be laid out, and then lessons need to be written that flow from one to the next. There must be small leaps within each lesson and small leaps between lessons.

The teacher’s job becomes to perfect lessons so students can make as many of the leaps without assistance as possible. And the teacher’s job becomes to help students understand important concepts they couldn’t construct for themselves.

In our sixth thought experiment: think of Meryl Streep, John Grisham, and Spike Lee. If you were a multi-billionaire interested in financing the next blockbuster movie: Who would you want to write the screenplay, direct the movie, and play the starring role?

The Difference Between Writing and Delivering the Script

Somehow the billionaire would know that among other various heavy weight projects John Grisham wrote “The Firm”, Spike Lee directed “Do the Right Thing”, and Meryl Streep starred in “The Bridges of Madison County.” And if the billionaire didn’t know such things, he or she wouldn’t invest any money in the project. With millions of dollars at stake, Hollywood investors don’t seem to get confused by the fact that it’s the job of the screenwriter to compose the overall plot and the general flow of lines that actors will speak. Nor do they forget it’s the job of the director to bring life to the overall vision. And certainly they don’t lose sight of the fact it’s the job of the actor to bring life to the individual characters and lines.

Somehow in our zeal for constructivism, not only did educators overestimate what students could construct for themselves, we have forgotten that most teachers are actors and not screenwriters. Teachers are great at bringing life to their characters and lines. They know how to make lessons come alive and they know how to help students. Most teachers can not possibly come up with great constructivist lessons day in and day out--especially elementary teachers who must teach four or five subjects a day for essentially five hours straight. Even if they have the talent, most teachers have neither the time nor the energy. Yet give teachers a good core curriculum to work with and they can unleash the potential of students.