Difference between rote knowledge and inflexible knowledge

From Daniel Willingham's Inflexible Knowledge: The First Step to Expertise

Much of what is commonly taken to be rote knowledge is in fact not rote knowledge. Rather, what we often think of as rote is, instead, inflexible knowledge, which is a normal product of learning and a common part of the journey toward expertise.

• Rote knowledge is memorizing without meaning.
• Inflexible knowledge is memorizing with meaning. It can be described as concrete and superficial.
• Knowledge is flexible when it can be accessed out of the context in which it was learned and applied in new contexts.  It can be described as deeper and abstract.
• Inflexible knowledge is the unavoidable foundation for expertise.

When encountering new material, the human mind appears to be biased towards learning the surface features of problems, not toward grasping the deep structure that is necessary to achieve flexible knowledge.

An important goal of education is expertise, which can be defined as "understanding the deep structure of a large domain".  However, before expertise is achieved, there is a large middle ground where students must acquire inflexible knowledge.  Acquiring and working (including practice) with inflexible knowledge are vital steps in the educational process.

To many of us it appears that the educational establishment has a bias against inflexible knowledge, leading schools to skip over a vital step in the learning process.   They often push to teach critical thinking skills before students have sufficient knowledge of the topics about which they are supposed to be thinking critically.  My own enduring example of this is the assignment of a research project on global warming or overpopulation in the fifth grade.  It can be a fun, engaging assignment, but the results I've seen make me question its educational value.  Among other things, it usually consumes huge amounts of precious time, requires excessive parent involvement, treats topics in a superficial manner because some critical science fundamentals (inflexible knowledge) have not been taught beforehand and leaves the student with a better understanding about creating dioramas than about the underlying concept.  Rote learning, anyone?

Daniel Willingham's advice to educators:

Appreciate the importance of students' growing knowledge, even if it's inflexible: Don't be reluctant to build students' factual knowledge base. Some facts end up in memory without any meaning, and other facts have meanings that are quite inflexible, but that doesn't mean that teachers should minimize the teaching of facts in the curriculum. "Fact" is not synonymous with rote knowledge or with inflexible knowledge. Knowing more facts makes many cognitive functions (e.g., comprehension, problem solving) operate more efficiently. If we minimize the learning of facts out of fear that they will be absorbed as rote knowledge, we are truly throwing the baby out with the bath water.

Remember that inflexible knowledge is a natural step on the way to the deeper knowledge that we want our students to have: Frustration that students' knowledge is inflexible is a bit like frustration that a child can add but can't do long division. It's not that this child knows nothing; rather, he doesn't know everything we want him to know yet. But the knowledge he does have is the natural step on the road to deeper knowledge. What turns the inflexible knowledge of a beginning student into the flexible knowledge of an expert seems to be a lot more knowledge, more examples, and more practice.

Related:  A working definition of mastery
              Wikipedia co-founder argues for the importance of 'memorizing facts'

Wikipedia co-founder argues for the importance of 'memorizing facts'

Larry Sanger, co-founder of Wikipedia, explains in an EDUCAUSE essay why he disagrees with the notion that "the instant availability of information online makes the memorization of facts unnecessary or less necessary".  He appears to be channeling Daniel Willingham in promoting the idea that a rich base of knowledge is the foundation for critical thinking and creative problem solving.

Sanger's essay also includes his thoughts on group learning and constructing knowledge (fodder for future posts), but in this post my focus is his view on the topic of memorizing facts.   I should note it's been my observation that when "educationists" and others object to "rote" learning, much of the time they are really arguing against the need to practice.  They seem to be in denial of the unfortunate reality that practice is often a "dull" but unavoidable exercise in the acquisition of knowledge.

Whenever I encounter yet another instance of educationists' arguments against "memorizing," the following rather abstract yet simple thought springs to my philosopher's mind: Surely the only way to know something is to have memorized it. How can I be said to know something that I do not remember? So being opposed to memorizing has always sounded to me like being opposed to knowledge. I realize this argument likely seems glib. The thing educationists object to, of course, is not the remembering or even the memorizing but rather the memorizing by rote — that is, by dull repetition and often without experience or understanding.

In a December 2008 interview, Don Tapscott, a popular writer on the subject of the Internet and society, argued that the Internet is now "the fountain of knowledge" and that students need not memorize particular facts such as historical dates. …This view is common enough among the Wikipedia users I have come across; they sometimes declare that since the free online encyclopedia is so huge and easy to use, they feel less pressure to commit "trivia" to memory....

But to claim that the Internet allows us to learn less, or that it makes memorizing less important, is to belie any profound grasp of the nature of knowledge. Finding out a fact about a topic with a search in Wolfram Alpha, for example, is very different indeed from knowing about and understanding the topic. Having a well-understood fact ready to recall is far different from merely getting an unfamiliar answer to a question. Reading a few sentences in Wikipedia about some theories on the causes of the Great Depression does not mean that one thereby knows or understands this topic. Being able to read (or view) anything quickly on a topic can provide one with information, but actually having a knowledge of or understanding about the topic will always require critical study. The Internet will never change that.

Moreover, if you read an answer to a question, you usually need fairly substantial background knowledge to interpret the answer.… 

Since an ever-expanding amount of information and research is frequently updating our understanding of disciplines, there is no reason to insist on memorizing facts and figures — and no reason to insist on a core of basic knowledge and books that should be mastered.

But this argument seems fallacious. It implies that the new information has either replaced or made trivial the old information. And this is obviously not so in most subjects.… And to return to my point, unless one learns the basics in those fields, Googling a question will merely allow one to parrot an answer — not to understand it.

It also won't do to make the facile reply that there is no such thing as "the basics."... But in most fields, there is certainly a body of core knowledge.

To possess a substantial understanding of a field requires not just memorizing the facts and figures that are used by everyone in the field but also practicing, using, and internalizing those basics. To return to my "glib" argument, surely the only way to begin to know something is to have memorized it.

"Test-taking cements knowledge"

Taking a test . . . actually helps people learn, and it works better than a number of other studying techniques.

It works better than studying and it works better than concept mapping, which is described as "having students draw detailed diagrams documenting what they are learning . . . prized by many teachers because it forces students to make connections among facts."

The Purdue study supports findings of a recent spate of research showing learning benefits from testing, including benefits when students get questions wrong. But by comparing testing with other methods, the study goes further.
“It really bumps it up a level of importance by contrasting it with concept mapping, which many educators think of as sort of the gold standard,” said Daniel Willingham, a psychology professor at the University of Virginia. Although “it’s not totally obvious that this is shovel-ready — put it in the classroom and it’s good to go — for educators this ought to be a big deal.”
Howard Gardner, an education professor at Harvard who advocates constructivism — the idea that children should discover their own approach to learning, emphasizing reasoning over memorization — said in an e-mail that the results “throw down the gauntlet to those progressive educators, myself included.” 

Don't think of it as testing, think of it as "retrieval practice".  After reading a passage, students wrote an essay about the passage from memory, re-read it and then took a test on it.  This group of students scored higher than the other groups who studied or who concept mapped.  The writing seems to have been important, but the critical part was retrieving the information.  Why it works is unclear, but it is speculated that "by remembering information we are organizing it and creating cues and connections that our brains later recognize."

How can schools incorporate these new findings in a way that can raise achievement levels?  What can parents do?

To Really Learn, Quit Studying and Take a Test - NYT