I've changed my mind. Before I get to my take-down of constructivism, I want to throw a few more things on your plates to mull over.
In this installment I want to discuss how knowing stuff benefits students.
Knowledge helps students in three critical ways:
- it makes it easier to learn new information,
- it makes it easier to remember new information, and
- it improves their ability to think by circumventing the thinking process and by freeing up space in working memory.
Knowing stuff makes it easier for you to learn new stuff
Comprehending or understanding something you hear or read demands background knowledge because language is full of semantic breaks in which knowledge is assumed and, therefore, comprehension depends on making correct inferences. Thus, one way in which knowledge aids the acquisition of more knowledge lies in the greater power it affords in making correct inferences. If the person conveying the information assumes that you have some background knowledge that you lack, you'll be confused when he explains or teaches that information.
Let's take an example from Willingham:
Suppose you read this brief text: "John's face fell as he looked down at his protruding belly. The invitation specified 'black tie' and he hadn't worn his tux since his own wedding, 20 years earlier." You will likely infer that John is concerned that his tuxedo won'’t fit, although the text says nothing directly about this potential problem. The writer could add the specifics ("John had gained weight since he last wore his tuxedo, and worried that it would not fit"), but they are not necessary and the added words would make the text dull. Your mind is well able to fill in the gaps because you know that people are often heavier 20 years after their wedding, and that gaining weight usually means that old clothing won'’t fit. This background knowledge about the world is readily available and so the writer need not specify it.Here's another:
When you read "tux," the cognitive processes that are making sense of the text can access not just "a formal suit of clothing," but all of the related concepts in your memory: Tuxedos are expensive, they are worn infrequently, they are not comfortable, they can be rented, they are often worn at weddings, and so on. As the text illustrates, the cognitive processes that extract meaning also have access to concepts represented by the intersection of ideas; "tux" makes available "clothing," and "20 years after wedding" makes available "gaining weight." The intersection of "clothing" and "gaining weight" yields the idea "clothing won't fit" and we understand why John is not happy.
Suppose that later in the same text you read, "John walked down the steps with care. Jeanine looked him up and down while she waited. Finally she said, 'Well, I'm glad I've got some fish in my purse.'" Jeanine's comment might well stop the normal flow of reading. Why would she have fish? You would search for some relationship between carrying fish to a formal event and the other elements of the situation (formal wear, stairs, purses, what you'’ve been told of Jeanine and John). In this search you might retrieve the popular notion that wearing a tuxedo can make one look a little like a penguin, which immediately leads to the association that penguins eat fish. Jeanine is likening John to a penguin and thus she is teasing him. Sense is made, and reading can continue. Here, then, is a second and more subtle benefit of general knowledge: People with more general knowledge have richer associations among the concepts in memory; and when associations are strong, they become available to the reading process automatically. That means the person with rich general knowledge rarely has to interrupt reading in order to consciously search for connections.How about one from Hirsch:
This is fun. Let's take one more from Hirsch:Consider the following sentence, which is one that most literate Americans can understand, but most literate British people cannot, even when they have a wide vocabulary and know the conventions of the standard language:Typically, a literate British person would know all the words in the sentence yet wouldn'’t comprehend it. (In fairness, most Americans would be equally baffled by a sentence about the sport of cricket.) To understand this sentence about Jones and his sacrifice, you need a wealth of relevant background knowledge that goes beyond vocabulary and syntax--—relevant knowledge that is far broader than the words of the sentence. Let's consider what we as writers would have to convey to an English person to make this sentence comprehensible.
Jones sacrificed and knocked in a run.
First, we would have to explain that Jones was at bat. That would entail an explanation of the inning system and the three-outs system. It would entail an explanation of the size and shape of the baseball field (necessary to the concept of a sacrifice fly or bunt) and a digression on what a fly or a bunt is. The reader would also have to have some vague sense of the layout of the bases and what a run is. By the time our English reader had begun to assimilate all this relevant background knowledge, he or she may have lost track of the whole point of the explanation.What was the original sentence? It will have been submerged in a flurry of additional sentences branching out in different directions.
Take, for example, this passage from my book What Your Second-Grader Needs to Know:Hopefully, these examples make it clear why it's easier for someone with a lot of background knowledge to learn new information even when he knows quite a lot of information already. Conversely, it is the novice who knows very little that finds it more difficult to learn new information, even though he has much more to learn.
In 1861, the Civil War started. It lasted until 1865. It was American against American, North against South. The Southerners called Northerners "Yankees." Northerners called Southerners "Rebels," or "Rebs" for short. General Robert E. Lee was in charge of the Southern army. General Ulysses S. Grant was in charge of the Northern army.
Potentially, this passage is usefully informative to a second-grader learning about the Civil War--but only if he or she already understands much of what'’s addressed in it. Take the phrase "North against South." A wealth of preexisting background information is needed to understand that simple phrase--going far beyond the root idea of compass directions, which is simply the necessary first step. The child needs a general idea of the geography of the U.S. and needs to infer that the named compass directions stand for geographical regions. Then a further inference or construction is needed: The child has to understand that the names of geographical regions stand for the populations of those regions and that those populations have been organized into some sort of collectivity so they can raise armies. That's just an initial stab at unpacking what the child must infer to understand the phrase "North against South." A full, explicit account of the taken-for-granted knowledge that someone would need to construct a situation model for this passage would take many pages of analysis.
Knowing Stuff makes it easier to remember new stuff
Knowledge also helps when you arrive at the final stage of learning new information--remembering it. Knowledge makes it is easier to fix new material in your memory when you already have some knowledge of the topic. Many studies in this area have subjects with either high or low amounts of knowledge on a particular topic read new material and then take a test on it some time later; invariably those with prior knowledge remember more.
This is because a rich network of associations in long term memory (LTM), i.e., deep structure, makes memory strong: New material is more likely to be remembered if it is related to what is already in memory. Remembering information on a brand new topic is difficult because there is no existing network in your memory that the new information can be tied to. But remembering new information on a familiar topic is relatively easy because developing associations between your existing network and the new material is easy.
Knowing stuff helps you think
As we discussed in a previous installment, background knowledge allows you to "chunk" information. The ability to chunk helps free up working memory (WM). That freed up WM is now available to attend to other tasks, such as recognizing patterns in the material.
Most of the time when a student is listening or reading, it'’s not enough that he understands each sentence on its own--he needs to understand a series of sentences or paragraphs and hold them in WM simultaneously so that they can be integrated or compared. Doing so is easier if the material can be chunked because it will occupy less of the limited space in WM. Chunking, however, relies on the existence of background knowledge.
It'’s not just facts that reside in LTM; solutions to problems, complex ideas you've teased apart, and conclusions you’ve drawn are also part of your store of knowledge. The student who does not have the distributive property firmly in LTM must think it through every time he encounters a(b + c), but the student who does, circumvents this process.
It's also not sufficient for you to have some facts for the analytic cognitive processes to operate on. There must be lots of facts and you must know them well. The student must have sufficient background knowledge to recognize familiar patterns (chunks) in order to be a good analytical thinker. Consider, for example, the plight of the algebra student who has not mastered the distributive property. Every time he faces a problem with a(b + c), he must stop and plug in easy numbers to figure out whether he should write a(b) + c or a + b(c) or a(b) + a(c). The best possible outcome is that he will eventually finish the problem--but he will have taken much longer than the students who know the distributive property well (and, therefore, have chunked it as just one step in solving the problem). The more likely outcome is that his working memory will become overwhelmed and he either won'’t finish the problem or he'’ll get it wrong.
So, now we know that a deeply structured LTM full of relevant knowledge, such as facts, background knowledge, and solutions to problems, helps in all stages of the learning process. In the next installment, we'll learn why learning by problem solving frequently does not and why it typically hinders the learning process.
Go to part five now.
It sounds very commonsensical and plausible that background knowledge is needed for comprehension. It's amazing that educationists don't get it and continue with their neurotic aversion to content. Instead, pupils are taught endless "strategies" for reading comprehension in a futile attempt to circumvent domain knowledge.
"In the next installment, we'll learn why learning by problem solving frequently does not and why it typically hinders the learning process."
"Problem solving" must be a term of art in the mouths of educationists. Solving problems has been a part of math (and physics, etc.) instruction since time immemorial. How educationists can claim a monopoly on "problem solving" baffles me, unless they give it a specialized meaning.
What they mean by "problem solving" is making students solve problems without first giving them the proper tools and/or skills to do so. The theory goes that the less teacher delivered instruction the better.
Great posts, Ken. I just finished reading The Knowledge Deficit by Hirsch, and it is really well done. It's good to include it as a reference here. It's interesting to me to relate a lot of what Hirsch says about reading comprehension to mathematics comprehension.
As regards "problem-solving", mathematical problem-solving in our state schools has evolved into a purely formalistic exercise in memorizing this list of "prompts": Restate the Question, List Important Information, Pick a Strategy, Solve, Label the Answer, Verify. It looks good on paper, but in practice, the teachers do not teach children how to solve whole classes of problems. The teachers do not constructively address inefficient strategies and wrong solutions as they naturally arise over the course of a year's assignments in problem-solving, which are to prepare children for the state tests separately from the regular curriculum.
They are teaching kids to generate a high word count in response to each of the six prompts in order to generate high scores on the state mathematics problem-solving test. Regardless of whether a strategy was good or an answer was correct. Teachers know which side of the bread is buttered, and it's on the side of words, words, and more words. You'll see more of this as your son ascends into the higher grades...
I'm going to give a bibliography at the end to all the articles I've borrowed and stolen from.
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