by Scott77 76 Replies latest social current
I am a mathematician. No, seriously. A real mathematician. Maths has only a passing connection to numbers. Maths is just logic, and it is great fun, and an opiate too.
However, my chosen opinions here are:
Mermaids Prefer the AlgeBra.. (OUTLAW)
Who invented Algebra? A Clever x-pert (jam)
And my own offering:
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Focus
("Intleejint??" Class)
Breakfast of Champions -I'm taking Calculus right now. . . .
And you would think where I'd get hung up is in all that fancy calc stuff like derivatives, and derivatives of derivatives . . ..
But nooooooo. . . . . . all of those concepts I've got down pat.
Where do I always screw up? In the friggin algebra!
Drives me absolutely mad!
I know what you mean. Took algebra in HS, just slipped through one year, did pretty good with Algebra II for some reason the next, but struggled again with it as an undergrad in college.
I did not take calculus until I became a grad student. Since I get the concepts of calculus, (such as limits, and what they mean), I had no problem whatsoever getting an A, even in advanced calc and several courses dealing with calc and stats. But the algebra part of it still drives me batshit crazy.
d4g
I like algebra, geometry, and trig. I had excellent teachers for all of them. I like calc I. That was also an outstanding teacher. My calc II teacher wasn't so good, so I suffered through that, as well as the following math classes that finished the sequence. My experience leads me to conclude that teaching is a part of the problem.
I question the merit of the argument of that article. (Why am I not surprised that it was a political science professor that co-authored a book about how colleges are crap.) The title can be easily rewritten with any subject. "Is ____ Necessary?" Insert "English", "History", "P.E.", etc. For that matter, is eduction necessary? Why read when everyone can just watch TV? Instead of all those hard classes, just have two classes: One class entitled "popular culture" where everybody talks about what they watch on TV. The other class entitled "political science" where everybody talks about how they'll never get a job after graduation unless it's teaching the class "political science."
Should the whole thing be scrapped and just send the kids home? I don't think so. But I think something needs to change. I think it's terrible that so many kids are having such a hard time with math.
Math is about patterns, and to some people they are beautiful when they see them. But more importantly, math is about problem solving. And, I think, problem solving is pretty darn important in the real world.
When I teach an elementary school math lesson, it is always introduced as a real world problem. We make connections to the real world, connections to mathematical properties and we reach for the Big Ideas, for example, equivalence, or the fact that fractions and percentages are two different ways of representing the same thing, that is parts of wholes.
If students don't understand these things then no amount of formulas and calculations will ever make sense. They will simply exist as algorithms that can get you the right answer, but true mathematical reasoning will not be taking place.
I have taught functions in first grade and the distributive property in third grade. Functions can be taught with a problem solving "What's my rule?" method. The distributive property can be taught with manipulatives built into an array of 28, 7 long and 4 wide. Then, cut the array in two parts along the side with 7, say into 5 by 4 and 2 by 4. Then you have two groups which are the same size as the original group.
Ask the student if these two groups are equal to the original one. They will say yes. Ask them how many was in the first array. It was a 7 by 4 array of 28. Ask how many was in each of the smaller groups. A 5 by 4 array of 20 and a 2 by 4 array of 8. So, do you think you could add the two smaller arrays which were 20 and 8 and you would get 28? Well, count and see! When they agree you can show them that 20 + 8 =28. Then you can go back to the names of the arrays and show them that (7 × 4) = (5 × 4) + (2 × 4). And, they can learn it! They can also use this for calculation in multiplication for difficult facts like the sevens. We just did that . We broke that 7 down into a 5 and a 2. 5×4 and 2×4 are much eadier to compute mentally than 7×4. Why? For the fives, you skip count by fives and for the twos you skip count by twos.
I could go on, but suffice it to say, if these concepts are taught early enough and developmentally appropriately, then young students can really learn what otherwise might seem to be difficult concepts.
I'm glad to see this thread revived and I look forward to more comments from others. Mathematics was my first love, and it will remain an integral part of me until I die. I love teaching it, particularly at the high school level where I have had many happy experiences; and I have continued my own personal research in it. I can understand the pain and frustration those posters have who shared their feelings in this thread and I have to agree with Billy the ex-Bethelite that teaching is a large part of the problem with math-phobia in this country.
Quendi
Math has great subjects, will serve you well later. Teachers must Love, be exited about their subjects. how many are really ? what with science thought of as freaky? If teachers are struggling, how do we expect the students to flourish?
focus, that was funny, and off subject, which was Algebra not geometry,
of the Pythegroean class.
Grreatteacher: Math is about patterns, and to some people they are beautiful when they see them. But more importantly, math is about problem solving
Amen to that!
As several have commented, the quality--or lack thereof--of the teachers we had make a huge difference in how well many of us embraced and learned a particular subject. Often many of us learned in spite of our teachers, not because of them.
As a teacher, I am dedicated to not only knowing my subject well, but also to improving my methods of teaching. I want to ensure that my students are as engaged as possible and that my explanations are clear and easy to follow.
That being said, a person can read every book there is on "How to Teach" and still be a crappy teacher if they cannot make a personal connection with their students. Pedagogy aside, good teaching comes down to two basic things:
As a science teacher, I do use and teach math concepts as they relate to the particular concept at hand. But it's obviously not my main focus. Since we're on the subject of math, maybe our two math teachers, Quendi and GrreatTeacher, could weigh in on these points.
Differentiate between MATHEMATICS and ARITHMETIC. The way I explain it to my students (in simple terms is that MATH is about concepts and applying them to problem solving, whereas ARITHMETIC is number-crunching). I saw an excellent TED talk a while ago where the speaker made the point that machines are good at crunching numbers, but it takes a human to know how to input those numbers and to formulate the algorithms for solving the problem. His point was that teachers should focus on teaching problem solving techniques and how to use a computer as a tool for the heavy lifting and not waste inordinate time having kids do simply rote calculations.
Your comments, please!
GrreatTeacher: When I teach an elementary school math lesson, it is always introduced as a real world problem. We make connections to the real world, connections to mathematical properties and we reach for the Big Ideas ...
Excellent point!
I was recently talking with a friend of mine that is an electrical engineer. He commented that it wasn't until he was taking physics in college that he made the connection between algebra and science (his "real world").
He said, "Oh, so you mean when I have the problem f = m/a that's an algebra problem!" Woohoo, a light when on in his head. He asked me why none of his math teachers made the connection between algebra, which to him was presented as a complete abstraction, and real-world problems. Obviously I couldn't answer that.
But I assured him that I tried to make these connections with my students. So when they whiningly ask me, "Mr. Oubliette, when am I ever going to need to use this _________?" I see that as an opportunity to explain the importance of what we are learning and make those real-world connections.
It doesn't make the problem any easier to solve, but it does make it relevant, and that can make all the difference.
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| I'm glad to see this thread revived and I look forward to more comments from others. | |
| Quendi |
Hi Quendi,
You can 'shepherd' visiting posters on this thread through the discussions. One possible option would be to identify relevant,similar or differences as to each poster's experiences with math both as a passion and as a profession. Here you go.
Scott77
I had trouble with Algebra. It wasn't that I couldn't get the answer, I just usually got the answer in a different way. I didn't understand why I had to follow the specific formula. I had some D-bag teachers too, that didn't help. For some reason I kicked ass in Geometry. Go figure (pun intended)...
DD
