“After failing to move a runner past first base for the entire game, the Giants sent Davis to the plate with the potential tying and winning runs in scoring position. Unfortunately, he hit into a 6-4-3 double play to end the game.”
- How many outs were there when Davis came to bat?
- To whom did he hit the ball?
- Describe the kind ball he hit (pop up? Line drive? etc.)?
- What was the final score of the game?
- How many runners were on base?
Being able to answer each of these questions requires a few things. You need to be able to decode English text. You need to have some basic general reasoning ability (mostly deductive reasoning). You need to know the relevant baseball content knowledge. And, you need know some declarative facts about baseball to answer some of the questions. (There's probably lots of other basic stuff (like basic math skills) you need to know as well, but I'm going to ignore those for simplicity sake.)
Notice how there isn't any baseball-specific reasoning ability needed to answer these questions. There's a good reason for this: there is no such thing as baseball-specific reasoning ability. Rather, the kind of general reasoning ability needed to solve these questions, as well as the vast majority of questions most people will encounter in their lifetimes, is well within the ken of a preschooler.
Now, don't get me wrong, sometimes more advanced forms of reasoning (such as formal logic reasoning) are required to analyze a problem and those more advanced forms of reasoning should be learned because they are occasionally needed. However, those advanced forms of reasoning are hardly 21st Century variety as some would have you believe.
So where do the 21st Century skills come into play?
They answer is simple. They mostly come into play when you lack the requisite baseball background knowledge because the first place you are likely to turn to in your quest to acquire missing knowledge is the Internet. You'll google, twitter, blog, and facebook your way to an answer. And, when those sources are lacking, you'll fall back on your pre-21st Century knowledge acquisition tools.
But, let's step back a second and discuss how knowledge is acquired generally.
First, go read my eponymous post on this topic from back in April so you'll know what I'm talking about.
Now, think about how you acquired your baseball knowledge. If you're like me, you probably acquired your baseball knowledge using most, if not all, of the ways I set forth in the post. For example, I played little league and softball (and many other baseball-like sports (wiffleball, stick ball, handball, halfball, baseball videogames)) which predominantly involves learning many rule relations, procedures and underlying facts inherent in the game. I also watched many baseball games (and listened to the announcer commentary) and read many articles about baseball and baseball games. This tends to be fact-heavy learning and involves inductive learning.
For example, I learned the meaning of the unknown concept of "in scoring position" by observing runners and listening to the announcer say the fact "in scoring position." Eventually, I induced that this term means a runner on second or third base, but didn't include a runner on first base or at home plate. I could have learned the concept much easier by being told the relevant fact up front.
It's hard to say I inured any benefit from learning this concept the long and laborious way through induction and lots of examples, instead of the simple way of being told the fact directly and memorizing it. In both cases there would have been at least one, and most likely many other, connection stored somehow in my brain linking fact/concept "scoring position (baseball)" and the fact/concept "runner(s) on second and/or third base." (Similarly, I just selected and used the word "inure" in this paragraph without being able to verbalize the precise definition of the word (before I Googled it to confirm), but being sufficiently familiar with the word and knowing it was appropriate in the context of the sentence with imperfect knowledge. Who knows how I learned the connection of the word "inure" and the connection with the vague concept "to gain an advantage from"?) There are many ways to skin a cat. However some ways are more efficient than others. Efficiency is the main difference between constructivist and instructivist pedagogies.
In contrast I had to Google my way to an answer for the "6-4-3 doubleplay" question, mainly because I never learned the position numbering scheme for baseball. I knew such a scheme existed, I just didn't know how exactly the positions were numbered. With this critical fact missing from my knowledge baseball I was unable to answer the question, until I acquired the knowledge by looking it up. Now I know -- at least temporarily, and can use the connection. I could have easily learned that knowledge by being more observant and thinking while watching televised baseball games. But, of course, that's more cognitively demanding, and, I choose not to engage in such a cognitively demanding task and, as a result, failed to learn the connection.
There are a few take aways from this post.
There are many ways to acquire the same bit of knowledge.
The ability to reason generally is a trivial skill that most people know how to do.
Not knowing relevant knowledge (or not knowing it sufficiently) will often inhibit (or diminish) your ability to use your general reasoning skills.
Improving your general reasoning skills often won't compensate for a lack of knowledge when that knowledge is needed.
Many 21st Century skills are generally relevant only when you lack knowledge in the first place.
When you represent 'knowledge' as 'answering questions' you get a trivial, stunted version of knowledge.
And it's funny, how you just repeat this same sort of example, over and over and over - as though it might convince some of the people who were not convinced the last time you used this type of example.
Of course - you're fact driven - so 'type of example' is an example of that fuzzy critical reasoning you dislike to.
I can't find anything to disagree with here! (sorta a new experience).
But your points can be extended per Russell Ackoff, in his recent book with Dan Greenberg, "Turning Learning Right Side":
"An ounce of information is worth a pound of data.
"An ounce of knowledge is worth a pound of information.
"An ounce of understanding is worth a pound of knowledge.
"An ounce of wisdom is worth a pound of understanding."
"Data consist of symbols that represent the properties of objects and events. . .
"Information consists of data that has been processed to make it useful. . .
"Knowledge consists of answers to 'how to' questions; it is contained in 'instructions.' To say that New York is 92 miles to the north and slightly east of Philadelphia is to provide information. To say that one can get from one to the other easily by car using the Pennsylvania and New Jersey turnpikes is to instruct; to provide knowledge--'how to' get from one place to another.
"'Understanding'is contained in 'explanations, answers to 'why questions'. . . Explanations consist of the 'reasons' for behavior or properties. Reasons are of two types, retrospective and prospective: identifying what produced the behavior or properties to be explained, or what that which is to be explained is intended to produce. . .To say that a boy is going to the store because his mother sent him is a retrospective explanation. To say that he is going to the store to buy food for dinner is a prospective explanation.
"'Wisdom' is qualitatively different from [the above]. . . It is captured in Peter Drucker's distinction between doing things right (efficiency) and doing the right thing (effectiveness).
"Wisdom is not something that can be taught in a course (or even in through the lectures of a person we acknowledge to be wise). . .To be wise is to own wisdom, as yours, not as someone else's, and to do that one must constantly be faced with situations that call for the practice and application of wisdom--in school, at work, and throughout life."
You're being pedantic now, Stephen.
I wrote "answering questions" because that's what Pondiscio's example required as the demonstration of the reader's knowledge. I also alluded to this when I wrote "You need to know the relevant baseball content knowledge. And, you need to know some declarative facts about baseball to answer some of the questions."
I'm not sure what you mean by "a trivial, stunted version of knowledge." Knowing the declarative fact(s) required to demonstrate one's knowledge to others is often an important part of the person's knowledge base. Not knowing the declarative fact often means that the reader doesn't knw the relevant content knowledge. In the instant example, the declarative facts needed to answer the questions are trivial if the reader possess the unerlying content knowledge. (3 answers require a number as the answer; only one requires knowing a fact.)
There are some who are enamored with their own theories of knowledge that simply ignor all evidence and are beyond convincing.
In a world with many suitable examples that can be classified differently the expression "type of example" is an accurate descriptor.
If I'm being pedantic, it's because you're just repeating the same basic argument over and over. What's the point of that?
Yikes! The National Council of Teachers of Mathematics has a new publication, "Focus in High School Mathematics: Reasoning and Sense Making."
You have to buy the book at a hefty $34.95 for non-members. But it's clear from the blurbs and sample copy that the NCTM views reasoning and sense-making as teachable. That NCTM clings to this view when many kids aren't being taught the rudiments of arithmetic represents proof that reasoning and sense-making are in short supply in NCTM.
I thought there was some value-added from this post, not just a mere repeat.
The example clearly shows the interplay of general reasoning and content knowledge, not just the mere recall of facts.
I also used it as a stepping stone to show that knowledge is more than just a collection of facts. I also wanted to get across the point that a knowledge connection can be known and yet the nodes of the connection may not have been retained. (I'm not sure that point came across in the final version.) For example, a learner might learn a fact-based definition, yet not remember the definition, but still retain the knowledge that enable him to discriminate examples and non-examples of the definition.
So, the point is not merely to repeat or to convince you necessarily. often it merely advances the argument in small way and might merely lay the foundation for a better argument down the road.
Often it's merely a way for me to work through the argument in a different way and to get some feedback from critics. The exercise at a minimum often clarifies my understanding. That is the value of a blog.
Dick, and they wonder where we get the idea that "content knowledge" gets short shrift from the 21st Century folks. Because it's so easy to make sense and reason in high school math without knowing the underlying content knowledge.
The NCTM book presents a common theme in its unwavering advocacy of constructivism. The desire is to teach high order concepts without first providing a encompassing definition of the concept. Instead it leaps directly to having the students come up with examples from which the student must derive the general idea that is hopefully embedded in the examples.
If there is an asdvantage to teaching this way, it's neer been demonstarted to exist for novice learners. Also, it heightens the risk that the learner does not learn the general idea.
What ultimately is learned is simply content knowledge and there are many ways to teach that effectively. If anyone can explain how this excerise enhances reasoning ability, I'd like to hear it.
Ken says, "it's so easy to make sense and reason in high school math without knowing the underlying content knowledge."
That is evident in reading the sample Chapter 6 "Reasoning with Functions" and the topics in chapter on "Reasoning with Statistics."
The math-ed folks have acquired the underlying content knowledge, and they presume that kids who lack their information will view the instruction the same way the experts do. This error has been made over and over again since the "new math" of the 1960's.
I thought the Math Advisory Panel's report last year provided a good foundation to build on. But all of that has been dismissed by the "21st Century," "Core Standards," and NCTM camps. Not "Change We Can Believe In"--Not even change. Just aspirational-driven persistent commitment to failed instruction.
I like the way the reasoning with functions excerpt claims that there are "numeric reasoning," "graphical reasoning," and "algebraic reasoning" supposedly being used and developed in the examples.
What they really mean is that the student must know the underlying content knowledge, such as certain domain specific procedures, concepts, rules, and facts, and recognize how the example problems fit into one or more areas of the knowledge already known by the student. Then the student must apply deductive and/or inductive reasoning to find whatever answer is sought.
It's all semantics. I'd characterize it as follows: building content knowledge via the most indirect and obscure route possible in a vain attempt to appear as though content knowledge isn't been learned. There's some hyperbole in that definition, but not much.
Well, it's all rhetorical reified- abstractions rather than "semantics," but your characterization NCTM's treatment of the matter is apt.
The thing is, the instruction that would be involved in delivering the aspiration is a very tall order. The instructional time involved is huge. It's very questionable whether the cake would be worth all the ingredients.
Meanwhile, NCTM would have teachers and kids chasing "numeric reasoning," "graphical reasoning," and "algebraic reasoning."
Stephen Downes, I asked you before in a comment on one of Ken's posts if there is any evidence that could convince you that content knowledge is necessary for thinking. I suppose I was too late and you were no longer reading the thread, I'll try again here, running the risk of course that you might no longer be following the thread.
Is there any evdiecne that could convince you that content knowledge might be necessary for reading and critical thinking?
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