They do what they do.
Thinking about schools and peers and parent-child attachments....I came across one of my favorite posts .
I now have a bookmark folder dedicated to articles like these.I'm trying to imagine what the rebuttal(s) would be from the constructivist camp.
"I'm trying to imagine what the rebuttal(s) would be from the constructivist camp."I haven't read the article, but a common rebuttal is that that activity/learning is not authentic.:-)-Mark Roulo
Where did they ever get the idea that every learning experience needs to be "authentic?" In my life, the authentic learning experiences (which I take to mean the ones where I get to bring all my existing knowledge together to create something new) are few and far between, and are supported by all the non-authentic learning experiences I plodded my way through to get the knowledge.
So the ones who had the will (or grit) to study and work hard did the best. Who'd a thunk?
In my life, the authentic learning experiences ... are few and far between, and are supported by all the non-authentic learning experiences I plodded my way through to get the knowledge.Ditto. Contrived "authentic" experiences just will not get you where you need to be when a truly authentic experience comes along.Lisa, the article is a little bit more nuanced than that. It compares students who study on their own to those who study with others, e.g., being quizzed by a friend. The lonely memorizers won out.
Hmmm. The lonely memorizers won out.Sounds like yet another good argument for homeschooling.
This probably won't change anyone's mind. It's just spelling. Drills and practice are OK in sports because it's just sports. It's OK in music, because it's just music. The Geography Bee is different since many of the facts relate to understanding, but most will lump it with the Spelling Bee as a rote exercise in memorization. Of course, expertise in the Spelling Bee requires a lot of understanding of languages, but most never get to that level.However, when it comes to critical thinkng and understanding, everything changes, apparently. I think the basic problem for them is drill and kill. If you don't want to play a sport, that's fine. If you don't want to play music, that's fine, but everyone has to go to school. They don't want to turn kids off with lots of drill. But how do you turn less into more? With pedagogical smoke and mirrors.They talk of balance, but when you approach mastery of skills thematically or from a top-down understanding direction, it never quite happens. This requires them to claim that skills really evolve from understanding. If you understand the concepts, you can figure out how to solve the problem. Mastery is only about speed, not understanding. If you really don't understand math, this viewpoint looks pretty good. They never seem to pay attention to the fact that the kids who do well in math are the ones who have mastered the basics (probably with help at home), and that mastery has a direct connection with understanding.It's not that a top-down or thematic approach to learning can't work, it just requires a lot more effort to ensure mastery of basic skills. This never happens.What I find interesting, related to this article, is that I've discovered most things while doing long homework sets alone at home. As soon as you start to work with someone else on a problem, the amount of discovery and learning drops. Someone might discover something, but it won't necessarily be you. The discoverer will attempt to teach you. You don't get the same chance to have the lightbulb go on. Most kids will end up being taught directly (and poorly) by other kids.I've long thought that they really aren't interested in discovery. They just want to see active learning going on in class, but they don't have a rigorous definition of what that means. If kids look engaged and motivated, then they are learning, right?
I've recently many teachers in our district are giving open book/open note math tests. Why in the world would anyone do that? A parent explained that this would free up the students from having to memorize math facts. I am speechless.
And here's another funny thing: the amount that you have to memorize in order to function well in math classes isn't that much. Certainly not as much as it takes to memorize the spellings of all the common words in English that vary from phonetic spelling. And certainly not as much time as students have to put in to practicing if they play an instrument, are on a football team, or even want to excel at some video games.
We had open-note, open-book tests in some of my most rigorous MIT engineering courses. They were the most dreaded of all our tests. You actually HAD to understand the material to make any sense at all of the test problems -- looking in the book, or your notes, wouldn't help you unless you knew exactly what formula (or whatever) you were looking for. That said, I'm sure elementary school tests are in a different league. :-)I truly don't understand why people think doing math (or spelling, or geography) is fundamentally different from sports and playing musical instruments.
spotted in the _notices_:http://www.ams.org/notices/201010/rtx101001303p.pdf(link to .pdf)"Teaching General Problem- Solving Skills Is Not a Substitute for, or a Viable Addition to, Teaching Mathematics "not *exactly* on-topic for this threadbut i've long since forgotten how tosign in and post "up front".ed-psych struggles to findits soul in math journals.who knew.
"ed-psych struggles to findits soul in math journals."Mavericks. It's a very simple analysis using a chess analogy, which is just one form of problem to solve. The only interesting thing about it is that it comes from the education community.Speaking of problem solving, other than "the Art of Problem Solving, Vols. 1 and 2", what other general math problem solving books or resources do KTMers recommend?
Steve,IMHO, it pretty much begins and ends with Polya.http://www.math.utah.edu/~pa/math/polya.html for the summary of method.http://www.amazon.com/How-Solve-Aspect-Mathematical-Method/dp/4871878309/ref=sr_1_1?ie=UTF8&qid=1287418166&sr=8-1 for Amazon's page of the bookFrom the product description ...."Solving problems", wrote Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.""Good examples for imitation and many opportunities for practice." ....... it's a constant surprise that edu-schools don't organise ritual book-burnings every year!!For resources, use the fantastic http://nrich.maths.org/public from Cambridge University. Or download a bunch of the many excellent national math competitions that are organised.http://www.mathcomp.leeds.ac.uk is a British Math competition and http://www.cemc.uwaterloo.ca/contests/contests.html is the Canadian version that hopefully gives you a taste of the international versions you may not have seen.Sorry for the lack of clickable links ..... I tried but my HTML wasn't perfect and I couldn't find the problem!!! Polya was not much help with this problem .....Richard I
Thanks for the links.Polya always seemed too general for me.I prefer a process that starts by finding the particular class or category of the problem and knowing what the governing equation(s) is (are). Is it a D=RT problem or is is a mixture problem or is it a combination or permutation problem. This would give you some direction when you draw the picture and start defining variables. I think Allison once talked about the need for this quick categorization ability. Some problems are obvious, but what about all of the subtle variations? Has anyone written up guidelines for problem identification?
OT, but is there a science/biology equivalent of KTM?Is there anyone doing for science what Singapore Math has done for math?
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