Garfunkel's Syndrome, Part III
A question that I asked in Part II of this series was the following:
Anyway, one of the first recipes I looked up turned out to be a simple one--perfect for an eternal "beginner" like myself--and one that I've always loved: Zuppa Toscana (sp?) à la Olive Garden.
If this is what we want, then over time it would be reasonable--even important--at some point to ask, What are some better ways to teach this recipe? or, again if you like, How do people best learn this recipe? especially if we observe that (a) either the teaching or learning (or both) is, for some reason, not natural or easy, and (b) despite all the time, energy, and money we put into this hypothetical endeavor, our students consistently get their butts handed to them at international food competitions.
Asking ourselves how we can better teach a topic or subject (or better learn a topic or subject) is indeed important. But the question that I mentioned at the beginning of this post is one that we can ask first: What restrictions should we use to narrow our search for the answers?
We know there must be some restrictions. While all of us draw circles--for various reasons--that contain different ideas and methods and even questions within education that are thereby endowed with value, excluding others either partly or completely, for a short time or for a long time, there are certainly areas where we can see widespread agreement. For example, as open-minded as we are (or think we are), none of us would spend much time considering my shin-kicking proposal from the previous post. And, as iconoclastic as each of us might be, almost all of us would agree that one or both of the restrictions Mr Garfunkel mentions in his paper, research and precedent--what one might call the "what works" restrictions--are necessary.
In other words, given the universal set U (below) of ideas/methods/questions/etc., that could possibly pertain to better teaching and/or better learning, there is widespread agreement that elements like s, shin-kicking, should be excluded from consideration (i.e., they are not valuable).
And despite the fact that there may be no agreement whatsoever regarding the value of elements a, b, or c (or, perhaps, unanimity among the population that all three are worthless), there is nearly universal agreement that either Set P (the set of all elements that are connected to precedent and meet needs) or Set R (the set of all elements that are connected to published research and show positive effects) or both (either P &cap R or P &cup R) are necessary circumscriptions--even if we believe those sets are empty.
If we can indeed restrict ourselves to considering a limited set of approaches to teaching mathematics, then what restrictions do we use?
Soup Sequitur
Several months ago, I developed an interest in what you might call cooking--though you should know that it's difficult for me to describe looking up easy-to-follow recipes on the Internet, buying the ingredients, and following the instructions verbatim as "cooking."Anyway, one of the first recipes I looked up turned out to be a simple one--perfect for an eternal "beginner" like myself--and one that I've always loved: Zuppa Toscana (sp?) à la Olive Garden.
It's certainly one of a very small number of "keeper" recipes for me (and, more importantly, my family). I would suggest trying it with some fresh parmesan sprinkled on top and a good bread to lap it up with. If you don't like spicy, I think you can skip the crushed red pepper without dramatically affecting the taste.Instructions
Sauté 1 pound of ground Italian sausage and 1 and 1/2 teaspoons of crushed red pepper in a large pot. Drain excess fat and refrigerate while you prepare other ingredients.
Dice a large white onion and tear 4 tablespoons of bacon strips into pieces. In the same pot, sauté bacon, onions, and 2 teaspoons of garlic puree for approximately 15 minutes or until the onions are soft.
Mix together 5 chicken bouillon cubes and 10 cups of water, then add it to the onions, bacon, and garlic. Cook until boiling.
Thinly slice 3 large baking potatoes. Add potatoes to the pot and cook until soft, about half an hour.
Add 1 cup of heavy cream and cook until thoroughly heated.
Stir in the sausage.
Add 1/4 of a bunch of kale just before serving.
"And a Spaceship Lands."
Suppose we want to teach this recipe to people who have no idea about cooking; or, if you like, we want people who have no idea about cooking to learn this recipe. For this specific content (the recipe), that might mean that we want people to be able to recite it from memory and be able to prepare the soup to a certain level of quality unaided.If this is what we want, then over time it would be reasonable--even important--at some point to ask, What are some better ways to teach this recipe? or, again if you like, How do people best learn this recipe? especially if we observe that (a) either the teaching or learning (or both) is, for some reason, not natural or easy, and (b) despite all the time, energy, and money we put into this hypothetical endeavor, our students consistently get their butts handed to them at international food competitions.
Asking ourselves how we can better teach a topic or subject (or better learn a topic or subject) is indeed important. But the question that I mentioned at the beginning of this post is one that we can ask first: What restrictions should we use to narrow our search for the answers?
We know there must be some restrictions. While all of us draw circles--for various reasons--that contain different ideas and methods and even questions within education that are thereby endowed with value, excluding others either partly or completely, for a short time or for a long time, there are certainly areas where we can see widespread agreement. For example, as open-minded as we are (or think we are), none of us would spend much time considering my shin-kicking proposal from the previous post. And, as iconoclastic as each of us might be, almost all of us would agree that one or both of the restrictions Mr Garfunkel mentions in his paper, research and precedent--what one might call the "what works" restrictions--are necessary.
In other words, given the universal set U (below) of ideas/methods/questions/etc., that could possibly pertain to better teaching and/or better learning, there is widespread agreement that elements like s, shin-kicking, should be excluded from consideration (i.e., they are not valuable).
And despite the fact that there may be no agreement whatsoever regarding the value of elements a, b, or c (or, perhaps, unanimity among the population that all three are worthless), there is nearly universal agreement that either Set P (the set of all elements that are connected to precedent and meet needs) or Set R (the set of all elements that are connected to published research and show positive effects) or both (either P &cap R or P &cup R) are necessary circumscriptions--even if we believe those sets are empty.