<p>Ah, another untested doctoral thesis? Education is incredible for acopting someone’s theory of teaching which they needed to develop in order to get their doctorate. These theories are largely untested. And some of the OP’s above are right - there usually is a lot of good in these theories - the hope to improve things. The biggest problem, however, is that education, when embracing new theories “throws the baby out with the bath water.” There are many good things now, and they should be kept, and enhanced with new theories. Thank heaven my D’s math teacher believed in the “old” way of teaching in terms of memorizing the tables - they had to pass a quiz of so many problems in just a certain amount of time, or they couldn’t go on to the next lesson. She made sure they all knew them. And she did incorporate some of the new methods, as well, but not until her kids have a sound basis. Her kids performed better than other students in years to come - I wonder why? Perhaps a better foundation?</p>
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<p>Admittedly, I wasn’t alive yet in the '70s, but according to what I’ve read about New Math, it supposedly focused a lot on set theory, functions, graphs, logic, modulo arithmetic, inequalities, thinking in bases other than base 10. What’s so bad about that? As a computer scientist, I think that sounds fantastic! I wish that my elementary school classes had focused a bit on some of those things! Was the problem that they focused <em>entirely</em> on those things and didn’t bother with arithmetic? Or that teachers were teaching it incorrectly? Or something else?</p>
<p>Honestly, what the OP is describing doesn’t sound so horrible to me either, though I’m not sure that it would work for all kids. It doesn’t sound <em>anything</em> like “How do you feel about 2+2=4?” It sounds like learning certain math concepts through pattern recognition. And pattern recognition is a useful skill.</p>
<p>I wouldn’t want arithmetic to be taught that way - with arithmetic, there really is merit to just memorizing the facts, I think - but we are not talking about arithmetic, we are talking about algebra and geometry, and you don’t teach those by rote anyway.</p>
<p>I am in agreement with sptch.</p>
<p>The problems arise with an exclusive focus on concepts and a neglect of learning basic math facts.</p>
<p>Unlike in “our” day, students now have no “need” to learn math facts because they can always use a calculator.</p>
<p>Personally I think learning the math facts contributes to having a feel for mathematics and computation.</p>
<p>Figure into this mix the fact that some kids have a natural aptitude for math and will not suffer by it being taught in a suboptimal fashion.</p>
<p>I learned to read using the method alluded to above (with the switch over to normal spelling in 3rd grade) and my spelling is very strong. I suspect my reading and spelling outcome would have been the same, regardless of the method used to teach me these subjects.</p>
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I loved the old new math, though I only had it in 4th and 5th grades (actually late 60’s). </p>
<p>My biggest problem with the new new math is that my older son kept losing points for not explaining the obvious and my younger son occasionally got bollixed up by being told too many ways to do things. You could actually lose points on the state tests with the right answer if you didn’t draw a picture or explain in words why 2 oranges + 3 oranges = 5 oranges. I basically liked the TERC approach - it gave my younger son good number sense and an ability to do a lot of things in his head that I can’t do nearly as easily. All his teachers also made sure he knew their multiplication tables and the like.</p>
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<p>But the OP’s post isn’t about “basic math facts”. It’s about algebra and geometry textbooks! By the time you get to the point where you need those, you should already know basic math facts.</p>
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<p>Heh, that also sounds like what Kentucky does (did?), though in their case the motive seemed to be that they wanted to improve student writing ability, which they did by turning every subject into writing class, and testing students on writing ability rather than knowledge. It irritated me to no end. Terrible implementation of decent ideas.</p>
<p>Maybe that’s the problem with many educational reform efforts - the ideas may be good, but the implementations are bad.</p>
<p>The focus on the conceptual side of math, with the total exclusion of teaching process, has been a disaster for D. The teachers at her school somehow thought that students would learn how to do problems on thier own - but it did not work. </p>
<p>So in high school, a clearly brillinant student struggles in AP Calc b/c because she can’t manipulate fractions quickly, or know basic math facts. </p>
<p>Teaching conceptual math is fine, but it needs to be followed up with teaching and drilling on how to actually come up with the answer. </p>
<p>Teacher’s groove on the conceptual high-thinking part, but are bored by basic math drills - get over it! Teachers are paid to teach student, not to get their jolly’s at the taxpayer’s expense.</p>
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<p>Apparently your teachers didn’t “groove on” punctuation, forming the plural, or other basic writing skills. Or could it be that they tried to teach you, but you simply didn’t absorb it?</p>
<p>Of course not. Teachers are all lazy idiots looking to get their jollies at taxpayer expense. :rolleyes:</p>
<p>Interesting, my son went through some wierd, strange math in upper elementary school. I didn’t know it had a name and I ended up teaching him the conventional methods/formulas/etc. simply because I couldn’t believe the school wasn’t. He struggled with math starting that year although kept passing into the advanced classes and to this day stuggled in his required college math classes although again passing out of the remedial entry level stuff. He has only learned to “despise anything math related” sad to say. The school dropped it sometime between one and two and my other two boys had the more conventional (read: the way we learned) math. I’m not sold on this conceptural stuff as the norm.</p>
<p>I have a math question: If a money manager takes in $50 Billion, pays out 12.6% per annum for 25 years and less thereafter, what is his minimum rate of return after 30 years?</p>
<p>For teaching purposes I can see value in all systems noted above. But where does critical thinking get taught?</p>
<p>Only thing I know is that I don’t want to be travelling over a bridge where the designer learned geometry by estimation. LOL ;)</p>
<p>Basic math facts and algebra. </p>
<p>When people talk about basic math facts, they usually mean arithmetics: addition, subtraction, multiplication and division. Even at that level, according to Liping Ma, American teachers are not good at explaining; they fall back on teaching the procedure but cannot explain why students should follow it. And too often, they get it wrong.
Many students can be good at arithmetics simply by memorizing.<br>
Algebra, however, requires different skills. This is why it is such a threshhold and why there is such a debate as to whether it should be introduced in 8th grade. Many American teachers argue that most 8th graders do not have the maturity to learn algebra, even though this argument flies in the fact of foreign countries’ experiences.
But for students to be good at algebra, they have to be good at fractions–something that American teachers are often terrible at explaining, again according to Liping Ma.
I also think that to be good at upper-level math, a student has to be good at logic.
I have seen students who were terrific at advanced math but could be stumped by simple arithmetic calculations. I have also seen students who knew their math facts cold but did not do well in algebra and beyond.
Obviously, knowing one’s math facts is crucial. As in the Whole Language debate, a good math teacher will combine the teaching of math facts with a more discovery-based approach. When my S was taking math enrichment classes, I loved seeing the way young kids lit up with a “Aha” grin when they found the solution to the problem posed by the teacher. His basic role was to pose the problem and to keep the discussion from straying too far afield.
I also remember the look of pure panic on my S’s regular teacher when my S came up with a different way of solving a problem. Hers was straight from the textbook"s teacher’s manual; she had memorized the solution, but I do not know whether she truly understood it.</p>
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<p>I’m with you!</p>
<p>I was scared recently when my university discussed, as a cost-saving measure, reducing the requirements for graduation. My first reaction was I didn’t want to drive over a bridge designed by a civil engineer who hadn’t taken the bridge-design course because it was no longer required!</p>
<p>My younger daughter has attended Seattle Public schools since 3rd grade- where various workbooks of new-new math were used.</p>
<p>The curriculum is big on story problems & for my daughter who is dyslexic this posed an obstacle- because the written explanation was given more credit than if the answer was correct.
Much of the time- we couldn’t even figure out what the question was.
I feel it is one thing to have materials based math in elementary school- but in high school, where they need to be prepared to go on- how can they go on, if the curriculum didn’t even cover things like long division in upper elementary?</p>
<p>NCLB stipulated for testing to evaluate student progress- because of poor performance in math- Seattle has not required passing of the math portion for graduation.</p>
<p>Almost 29,000 Washington High School Students Cant Pass Math WaSL</p>
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<p>[Seattle</a> SD recommends inferior Discovering Algebra curriculum](<a href=“http://www.wheresthemath.com/blog/]Seattle”>http://www.wheresthemath.com/blog/)</p>
<p>It really is puzzling why the district chose this course.</p>
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<p>Yeah, that’s a real knee-slapper. :rolleyes:</p>
<p>As I said before, my (brilliant) chemical engineer father was the one who impressed me with the importance of being able to estimate using large numbers. To my knowledge, none of the plants he designed all over the world have blown up yet. 
He was also scornful about teaching that depended on memorizing formulae. He said that if you needed to use it frequently you would remember it, and if not you’d look it up. Being able to DO something with it was more important than memorizing it. He also used to pose math problems for us to do in our heads during dinner. :D</p>
<p>Engineers are not “learning geometry by estimation.” But I can imagine a situation in which they might use their knowledge of loads and weight-bearing ability of certain materials to estimate costs of certain design alternatives before working out all of the details. Just as an example.</p>
<p>I guess I don’t understand why so many parents equate memorizing math facts and solving problems only using a single “approved” method ordained by the teacher with good math education and good math skills. Perhaps it is because that is all THEY can understand?</p>
<p>My objection would be expecting students to intuitively figure out mathematical concepts through observation and discussion.</p>
<p>For some people, it’s just not gonna happen. And it could be slow and painful for everyone to try and drag it out of them.</p>
<p>In the long run, it’s probably more efficient and less frustrating to teach the concepts.</p>
<p>I doubt very seriously that your brilliant engineer father learned math by estimation :rolleyes:</p>
<p>Of course it’s good to be able to estimate, but to use estimation as a benchmark in a math curriculum is just not sound. IMO</p>
<p>And frankly, as a parent who has had to either tutor her children in math, or hire tutors, because the teachers, and/or the “approved” method of teaching was suspect, I believe that some basic math facts, taught at an early age is a more appropriate method of teaching than having everyone get in a circle, sing kumbaya, and come up with their own methods and definitions. ;)</p>
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<p>I agree. Some will figure out but most will not. However, getting the students to observe and discuss is a good idea as long as the discussion is not allowed to drag out while it is clear that the students are not figuring out the concept on their own. It is important for the teacher to underscore what the students have learned on their own.
My S taught math to young children and this was a key thing that he was told to do. Even when most if not all of the class “got it,” it was important for him to go over the problem and spell out the procedure and solution in order to clarify, and inscribe it, so to speak, in the students’ mind.</p>
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<p>Probably, but too often, the teacher is just parroting what s/he has read in the text and is not actually explaining the concept, why it works and when it should be applied. So that when a student goes astray, the teacher is not able to bring the student back onto the proper path to a solution. It’s not as if the traditional method has been so successful. If it had, there would not be all these attempts at improving math teaching!</p>
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<p>My husband taught highschool for years, and is now a school board liason for the reading and approval of textbooks. In his opinion, the reason there are all these “new attempts” at teaching methods in math and English are so that educrats with PHD’s can publish and legitimize their paid positions, and so that textbook companies can make a buck.</p>
<p>^^Guess how many students ever learned algebra in previous decades? How many ever got to calculus? Is it a tribute to traditional math?
I’m not saying that reform math is superior. But those who advocate going back to traditional math pedagogy should also bear in mind the failure rate with this approach. It was probably just as high if not higher.</p>
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<p>If the teachers are only capable of parroting the text, it will be a complete and total disaster if these same teachers are expected to lead students in a discussion to figure out mathematical concepts on their own.</p>