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Math Education: An Inconvenient Truth Related Videos
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http://wik.ed.uiuc.edu/index.php/Everyday_Mathematics
The title and links made me think of the Judge and Gore movies, though this isn't really have a direct connection. Still, interesting video.
the second method is certainly strange but it's building upon a higher abstraction of the problem.
But her claim that the books that scare her don't have algorithms is wrong, they all have algorithms but some just use abstract algebra.
But I do find it a bit wierd how they are getting students to think about such a simple thing as multiplication in terms of algebra before teaching them algebra.
But yes these methods can start to prepare students for some higher level maths thinking, but without it done in such depth to keep their little brains working then it's pointless.
Any standard maths education runs on the principles that you are taught the fundamental ways just to do problems and then you look back at how you did them later.
Within this video however I do not feel her as a trustworthy source on all these topics,
Firstly she's reading someone else's script constantly and then there's her recommendations. Oh and the who are you factor.
"A University professor told me students couldn't do 4x4" - Erm what? Reference or else I don't believe you.
If so, cool; if not, then the books should at least teach *those* methods...
Honestly, this is how I do problems like this in my head, and I certainly don't remember the algorythms we learned in school.
The other advantage of the cluster problems method is that it lets you get better at doing the problems. It is culmulative. With the "standard" method, no matter how good a math sense you get, it takes you x amount of time to solve the problem.
With cluster methods, if the only multiples of 6 you know are 6 x 10 and 6 x 1, you can still solve the problem in your head. But if you know 6 cubed, and 6 x 13 and other various and sundry information about 6, your ability to do problems grows. This is what I mean about building math sense.
When she kept adding 6 x 1 = 6 to her division problem it made me want to strangle her.
Now, this is not to say that she doesn't have any valid points. It is obvious that there are serious SERIOUS problems with the math books in question, but she seems to be fixated on the wrong part. Teaching students to use calculators is fine. Teaching alternative (better) algorythms is fine. Getting students to plan a world trip in math class? Not without a massive reorganisation of the entire curriculum, please.
When I was in elementary school, I went to a very unique private school for grade 2, 3 and 4. In that school, most of the subjects were condensed into a holistic approach to learning. Instead of social studies or science or art or music, we would spend a year studying "africa" or "the ocean". We learned history, geography, science, we studying all aspects as they related to the theme of the year. It was incredibly engaging and well thought out.
The exceptions were spelling and math, which we spent x amount of class time each week working on in the traditional way.
Is it possible that math could also be incorporated into a holistic approach to education. It is possible. I just don't see how it could be efficient. Math does apply to the real world. It is just that it makes more sense to teach a non-mathematical approach to the world to children, and develop their math skills seperately, so that when the time comes to look at the world in a more rigourous, mathematical view, their math skills will have (hopefully) developed to the point where they are able to apply math.
Bottom line, I think the lady in this video has a few good points, and the books may very well be crap. But she's completely wrong about the value of these algorythms.
I agree with her because I've seen the consequences of this alternative math education. It's a reaction to the "New Math" that was implemented in the 60s (in the US, and later in many other countries). New Math tried to teach formal math before giving students an intuitive background, with disastrous results. The "Everyday Math" approach does exactly the opposite -- it constantly resorts to intuition, and constantly delays formalization. Defenders of Everyday Math like to claim that formalization is just around the corner, but they never get to it.
I specially like her points because she's not a math teacher. She's someone with a background in science who noticed the problem and got interested in it. I'm an Electrical Engineering grad student, but I'm also working on becoming a licensed math teacher partly because of the disaster that math education has become in my country (Brazil).
In the long run, it is possible to teach elementary arithmetic and algebra using just about any approach, including Everyday Math. It's just not practical, and specially not in public schools where teachers have little time to allocate to each student. Math instruction must balance intuition and formality, and a curriculum which neglects one of these aspects will create deficient students. This deficiency can be overcome if kids are motivated enough to figure out the missing pieces, and if they have help from their teachers and parents, but this scenario is unrealistic in most cases.
I agree with her that math education sucks in many schools, but I think standard algorithms alone won't solve that. Some kids get so used to mechanical operations that they don't even know what the heck they're doing when they do it. They should at least be acquainted with dynamically reducing a problem to one or more simpler problems. That's the basis of almost all analytical thinking. I get freshmen in college who don't have a clue how to do mental long division or find the prime factorization of a number.