May 24, 2010

Induction is not Constructivism

(Update:  cleaned up a bunch of typos and reworded the post to clarify.)

Brian Rude asks a good question,

The induction model certainly makes some sense. But isn't it another name for constructivism?

I see how Brian got confused due to my oversimplified model, which conflates inductive reasoning with the inductive-like process of the learning metaphor I proposed.  And, since constructivism relies heavily on inductive reasoning, Brian's conclusion is a fair take-away.

So, let me clarify.  Take a look at this less over-simplified schematic.

The diagram shows how a learner converts an observation of some stimulus into a thought/memory. i.e., how the learner learns. I've re-labeled the induction process I was explaining in the previous post to a a sub-induction process and added on three primary super-processes of learning: direct memory, deductive reasoning, and inductive reasoning.  (Bear in mind that this is merely a hypothetical conceptual model, what is actually happening in the brain is still largely unknown.)

The point I'm trying to get across in the model is that the observed stimulus ALWAYS gets transformed as it becomes knowledge.  I could have used an alternate model and placed the sub-induction directly under the "direct memory" process and indicated that the "sub-inductive" process was subsumed in the "deductive" and "inductive" reasoning processes to get the same point across.  Something like this.

I think the first diagram is conceptually clearer.  The main take-away for either model is that there is no direct access into the brain.

The learning flow would go something like this:  1. learner observes stimulus, 2. learner processes stimulus via one of the super learning process, 3. learner  then the sub-learning process, and 4. then the extracted "knowledge" goes into the learner's memory.

How the observation is made or how the stimulus is presented to the learner determines what super-process the learner will use.  Let's look at some examples (now would be a good time to review these three posts on the nature of knowledge).

The teacher tells the learner the following fact (i.e., a verbal association): "The U.S. Constitution was written in Philadelphia."  The learner learns this fact via direct memory (I couldn't think of a better name, sorry).  However, the verbal statement does not merely get imprinted in the learner's memory verbatim (not that anybody seriously believes this in any event).  The fact gets abstracted by the sub-induction process into the learners existing knowledge, something like this:

The knowledge is the connection.

This knowledge could have been learned other ways as well.  Let's say the learner has been exposed to the following two facts: that "the U.S. Constitution was written at the constitutional convention" and that "the constitutional convention was held in Philadelphia."  From these two facts, the learner can use deductive reasoning to deduce that  "The U.S. Constitution was written in Philadelphia."

How about another one: learning a rule relationship.  Here's the rule: "the steeper the inclined plane, the less time it takes the ball to roll down the inclined plane." This rule can be learned deductively or inductively.

In the deductive method, the teacher might start off with: “The question is, Is there a connection between how steep an inclined plane is and how long it takes a ball to roll down it?”

The teacher then tells the student the rule-relationship (the steeper the inclined plane, the less time it takes the ball to roll down the inclined plane) and then show examples using inclined planes of different angles. These examples would confirm the rule. The knowledge of the rule is processed by the learner through the deductive reasoning process and then stored via the sub-induction process. (Sorry, no fancy connection map this time.)

In the inductive method, the teacher has the learner do an experiment by rolling balls down inclined planes of different angles, measuring how long it takes each ball to roll down, and then has the learner draw a conclusion.

This way requires more skills. (In the deductive method, the learner merely compares examples with the rule. “Yup, the ball takes less time when the angle is steeper.”) For example, the learner has to change the angles, measure the times, write the measurements, compare and contrast the instances, and figure out the connection. This means the teacher would have to teach these pre-skills before learners do the experiment.

The knowledge of the rule is processed by the learner through the inductive reasoning process and then stored via the sub-induction process. However, the learner takeaway is the same, that is, the connection mapping in the learner's memory is the same.

Which finally brings us 'round to constructivism.

Stripping away all the pedagogical blather, constructivism is merely a teaching pedagogy that favors learning through inductive reasoning as the preferred pathway.  Constructivists favor learning by experience or by doing. This means that the learner will be observing stimuli (examples and non-examples of something) and generating general ideas revealed by the examples and non-examples.  Hey, that sounds suspiciously like inductive reasoning.

Here's what I wrote about the inductive reasoning process that learners go through when they observe a stimulus during the learning process.

Knowledge is not directly transferred into a learner, but rather knowledge is acquired indirectly through an inductive process. Specifically, knowlege is typically acquired through an "inductive reasoning" process.

That is, the learner observes stimuli (examples and non-examples); (2) performs a series of logical operations on what it observes; and (3) arrives at (induces, figures out, discovers, “gets”) a general idea revealed by the examples and nonexamples.

In contrast, direct instruction relies more heavily on deductive reasoning pathway for teaching certain forms of knowledge, such as rule relationships. Using deductive reasoning, the learner goes from general (rule) to specific (examples). In the deductive method the teacher teaches the rule statement first. Then examples and nonexamples are then presented. Then the teacher tests all examples and nonexamples to see if the learner has learned the rule.

Constructivism can be faulted for many things, but its reliance on the inductive reasoning pathway of learning is not one of them. That is a perfectly valid pathway which proponents of direct instruction use (such as for teaching sensory/basic concepts). Constructivism's faults lie elsewhere -- over-reliance on the induction method of teaching and generally a failure to attend to the important minutiae of teaching for determining whether the learner has learned the intended knowledge and is retaining it. The latter is a self-imposed error based on ideology because constructivism makes it more difficult to get the minutiae right.


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Mr. Nauton said...

So some details may be more difficult, but we want the induction model, right? There may be more rubber balls bouncing all over the classroom, but we want our students to experience/acquire knowledge in a manner that "requires more skills" -- and won't that learning create more thought/memory connections for future learning?
Great blog, I'm going to dive into your past posts until my head explodes...

Anonymous said...

I think the difficulty in discussing constructivism stems from the fact that there are two kinds: Constructivism, the theory of education psychology that holds students learn by actively constructing their own understanding, and constructivism, the teaching practice that relies heavily on manipulatives. Teachers who use constructivism do not always use Constructivism.

kieran@coredogs said...

My understanding of constructivism is different. It isn't just about induction. It's broader, and includes some of the things you have talked about.

Here's how I understand it - all knowledge is constructed. It doesn't matter if the learner is "given" info directly (e.g., an expository lecture) or induces it. The learner's perceptions are interpreted WRT existing knowledge.

The concept map you gave is a good example. The learner interprets the sentence "The constitution was written in Philadelphia" and makes connections. If the learner doesn't know that Philadelphia is a city, s/he might make a link to cream cheese. So what the learner already knows (and doesn't know) affects how the sentence is interpreted.

Construction happens whether there is induction or not.

Learning by induction is perhaps better understood as active learning. Learners learn more during discovery. For example, in the ball-down-a-ramp experiment, they might learn that increasing the height of a right triangle while leaving the hypotenuse fixed, increases slope. They may have already learned this, but practical experience reinforces the connections. And because learners have to generate the focal connection - slope and ball speed - that mental connection will be stronger and less likely to be forgotten than the same connection learned through reading.

There are costs to induction, like the errors you mentioned. We know that once an erroneous connection is made, it can be difficult to undo.

Another cost is time. It takes time for learners to do experiments. And, as you point out, to learn the prerequisite skills to be able to do the experiments.

The active learning literature recognizes this. It recommends teaching fewer concepts in more depth. This avoids the "mile wide and once inch deep" problem - students might cover a lot of concepts in a class, but learn each one so shallowly that strong connections are not built up. They forget quickly. An alternative is to learn fewer concepts more deeply, so they actually remember something.

Note that I am not an education expert, though I have been teaching for a long time. I learned about constructivism, active learning, and related stuff so I could do a good job on a virtual textbook about Web tech.

I could be talking out of my nether regions. But I don't think so.

Unknown said...

Kieran has it exactly right. I came to the comments section to say something quite similar. I'm a scientist and educator who is also now an entrepreneur and working in exactly this space.

The constructivist approach simply recognizes that people don't learn in a vacuum. Prior stored information affects their perception and so affects what they can learn accurately.

The Philadelphia Cream Cheese example illustrates this concept so well that I cannot improve on it.

Induction forms a cornerstone of science, much of which consists of making and classifying observations. It asks the question, "What do all of these data mean?"

Deduction has an important role too. It asks, "What can this new rule, formed by induction, tell us about things we may observe in the future?"

Direct memory should not be a part of science because it presumes to accept authoritative information on faith. For example, Einstein says that nothing travels faster than the speed of light. Until you've analyzed this statement yourself, reviewed the evidence, and read other opinions, you're not ready to accept this statement as (tentative) fact. It's merely an opinion.

In learning science, students have a basic problem alluded to by Kieran. (Teachers have the same problem in designing learning.) How much induction can you shoehorn into a short time when you have so much required information to learn?

How many experiments can you perform when you know that doing more will, if they're well designed, provide for more and better learning? These experiments must be real. Simulations won't do, not because they're useless to learning but because they cannot be the object of the investigation, only a supplement to it at most.

Traditional experimentation takes lots of time. Often, it also requires lots of preparation and money as well. More experimentation means more opportunities to learn to think scientifically and to understand the nature of science. It means that you will encounter more situations with ambiguous data or with data with inherent errors that prevent a clear-cut conclusion.

I believe that technology can allow students to do more experimentation. As an example, a high school in Long Island City assigns all of their science students homework consisting of real science labs done online. By so doing, they've increased their Regents science pass rate from 50% to 66%. That's a 32% increase in pass rate from a single cause: more real science experiments.

This high school is a general-admission school with a 60% poverty rate.

Unknown said...

Kieran has made an excellent comment that covers the concepts that I came to the comments section to make myself.

I particularly like the idea of Philadelphia Cream Cheese as explaining constructivism as I've learned it through extensive study.

I'm a scientist, technologist, and educator as well as an entrepreneur. My concern, which I've been working on for a decade, is how to improve science education.

Constructivism makes that point that you must relate learning to pre-existing knowledge in the students' minds.

Induction forms the cornerstone of science. Scientists have spent lots of time collecting and organizing data just so that they can use the inductive method.

Deduction takes existing rules and applies them to guide further data collection.

Direct memory has no role in science. Just because Einstein says that nothing travels faster than the speed of light does not make it so. Scientists must verify to their own satisfaction such statements by authority. They do not take them on faith.

In science education, we must provide more authentic science experiments that are inductive and not deductive. Yet, time prevents and untrained teachers avoid enough authentic experiments.

Technology holds the promise of fixing this problem, and it's the area in which I've worked for over a decade.

In one poor school (60% poverty), it raised the Regents science pass rate from 50% to 66% without any other changes being made.