BatmansWife Posted March 17, 2012 Share Posted March 17, 2012 (edited) With all the tizzy going on over Beast Academy....I thought maybe I would investigate AoPS a little. Until recently, I had never even heard of it. So, I was looking at the prealgebra videos page. I scrolled down and picked one. Multiplying Fractions. The first example is 3/5 x 7. Right away I thought: Okay.....that's 3/5 X 7/1...multiply 3 X 7 for 21 and multiply 5 X 1 for 5. Answer: 21/5 He teaches it: 3/5 X 7 = (3 ÷ 5) X 7 = 3 X 1/5 X 7 = 3 X 7 X 1/5 = 21 X 1/5 = 21 ÷ 5 = 21/5 Ummm...that's the same answer that I got in a fraction of the time (pun intended). :blink: Next one: 3/5 X 7/2. Again, I think 3 X 7 is 21, 5 X 2 is 10. 21/10. Again, it seems like he drags it out and makes if more complicated than it should be. It makes me go :001_huh: . Near the end he says to multiply the tops and multiply the bottoms. I guess I don't get why they don't just do that to begin with. Don't get me wrong.....I don't mind the guy....he seems spunky enough. :001_smile: But, I just don't know if making things drawn out and more complicated is necessarily the best way to go. I'm not being snarky here or anything....I'm just trying to decide if I should keep investigating AoPS more or not. I realize this video is just a tiny part of AoPS....so, is all of it like this? Edited March 17, 2012 by ~AprilMay~ Quote Link to comment Share on other sites More sharing options...
stripe Posted March 17, 2012 Share Posted March 17, 2012 Ha, this is how proofs in math look. Lots of getting back to the definitions. It's complicated bc it explains. Otherwise people forget or mess up the rule and make mistakes. Quote Link to comment Share on other sites More sharing options...
8filltheheart Posted March 17, 2012 Share Posted March 17, 2012 With all the tizzy going on over Beast Academy....I thought maybe I would investigate AoPS a little. Until recently, I had never even heard of it. So, I was looking at the prealgebra videos page. I scrolled down and picked one. Multiplying Fractions. The first example is 3/5 x 7. Right away I thought: Okay.....that's 3/5 X 7/1...multiply 3 X 7 for 21 and multiply 5 X 1 for 5. Answer: 21/5 He teaches it: 3/5 X 7 = (3 ÷ 5) X 7 = 3 X 1/5 X 7 = 3 X 7 X 1/5 = 21 X 1/5 = 21 ÷ 5 = 21/5 Ummm...that's the same answer that I got in a fraction of the time (pun intended). :blink: Next one: 3/5 X 7/2. Again, I think 3 X 7 is 21, 5 X 2 is 10. 21/10. Again, it seems like he drags it out and makes if more complicated than it should be. It makes me go :001_huh: . Near the end he says to multiply the tops and multiply the bottoms. I guess I don't get why they don't just do that to begin with. Don't get me wrong.....I don't mind the guy....he seems spunky enough. :001_smile: But, I just don't know if making things drawn out and more complicated is necessarily the best way to go. I'm not being snarky here or anything....I'm just trying to decide if I should keep investigating AoPS more or not. I realize this video is just a tiny part of AoPS....so, is all of it like this? Quite simply, b/c in 3/5 x 7, 3/5 is 3 divided by 5 and 3 * 1/5= 3/5 Once a student firmly grasps the process, then simple multiplication of numerator by numerator and denominator by denominator is appropriate. But, the **why** is far more important to master at the pre-alg level than speed. Quote Link to comment Share on other sites More sharing options...
BatmansWife Posted March 17, 2012 Author Share Posted March 17, 2012 Ha, this is how proofs in math look. Lots of getting back to the definitions. It's complicated bc it explains. Otherwise people forget or mess up the rule and make mistakes. Quite simply, b/c in 3/5 x 7, 3/5 is 3 divided by 5 and 3 * 1/5= 3/5 Once a student firmly grasps the process, then simple multiplication of numerator by numerator and denominator by denominator is appropriate. But, the **why** is far more important to master at the pre-alg level than speed. Well....I get that it explains it and is showing the why behind it. But, I guess I'm wondering now if they are to show the entire process each time for every problem?? Of, is this just an initial teaching of the why and then for the problems you just do it (the quick way)? Quote Link to comment Share on other sites More sharing options...
Julie of KY Posted March 17, 2012 Share Posted March 17, 2012 With AoPS, you can always do it "the quick way". Oftentimes more than one solution is given to show more than one way to the same answer. Quote Link to comment Share on other sites More sharing options...
BatmansWife Posted March 17, 2012 Author Share Posted March 17, 2012 With AoPS, you can always do it "the quick way". Oftentimes more than one solution is given to show more than one way to the same answer. Oh, ok. Thank you. Quote Link to comment Share on other sites More sharing options...
joannqn Posted March 17, 2012 Share Posted March 17, 2012 Ha, this is how proofs in math look. Lots of getting back to the definitions. It's complicated bc it explains. Otherwise people forget or mess up the rule and make mistakes. :iagree: One of the things I love most about AoPS is the fact that same questions are explained in mathematical proof fashion. You do this because of this or that definition. Not only do I love the why being explained, but by the time an AoPS student gets to proofs in geometry, it should be a piece of cake. Quote Link to comment Share on other sites More sharing options...
melmichigan Posted March 17, 2012 Share Posted March 17, 2012 Ha, this is how proofs in math look. Lots of getting back to the definitions. It's complicated bc it explains. Otherwise people forget or mess up the rule and make mistakes. AoPS begins each lesson through discovery of the formula or rule by doing problems. The beginning videos on each topic often reinforce how one gets there. They build the foundation and then expand from there. Quote Link to comment Share on other sites More sharing options...
Momling Posted March 17, 2012 Share Posted March 17, 2012 Also, keep in mind that this isn't the first introduction to the topic. By pre-algebra, the kids should already know how to do this sort of problem the quick way that you and I were taught. The point of a lot of AOPS Pre Algebra seems to be more about the conceptual reasons why it works, not the quick procedure of the algorithms. Quote Link to comment Share on other sites More sharing options...
Julie Smith Posted March 17, 2012 Share Posted March 17, 2012 Ohhh, I like how he explained it. It makes so much sense. :001_smile: let's just hope my kids, when they get the feel the same way about it. Quote Link to comment Share on other sites More sharing options...
Meriwether Posted March 17, 2012 Share Posted March 17, 2012 I think this explanation is also a great start to explaining dividing fractions. I've tried and tried to get Dd8 to understand why it works to flip and multiply. She did LoF Fractions last summer and I've been remediating all year.:glare: Quote Link to comment Share on other sites More sharing options...
Ariston Posted March 17, 2012 Share Posted March 17, 2012 I (briefly) taught high school math. The problem with focusing on teaching the procedure for solving these problems (i.e. 'first you multiply the numerator, then you multiply the denominator') is: a.) this makes the knowledge completely arbitrary since the students don't understand WHY this 'trick' works, they only understand THAT it works. This makes students hate math eventually because they view it as an endless amount of tricks and formulae that they have to memorize and apply correctly in order to get the right answer. It makes math a pointless and arbitrary exercise. They don't 'get' it. b.) Because they were taught procedurally, they will inevitably forget what they are supposed to do and not be able to figure it out. They might end up adding or dividing instead of multiplying, beacuse, really, what's the difference....they know it was something like that.... My goal for my kids is not just that they can solve problems and get the right answer, but that they really partake in mathematical thinking (like the AoPS video you linked.) THAT is REAL math--its not just the ability to get the right answer. ELena Quote Link to comment Share on other sites More sharing options...
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