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<p>When my S saw this thread he commented, “It took centuries for mathematicians to figure out some of this stuff.”</p>
<p>My dad was a civil engineer, and he was very precise with his calculations.</p>
<p>I prefer that my children know how to calculate a precise answer rather than poke all around the edges hoping they get “close enough” with their answer. Perhaps I am thinking like the daughter of a civil engineer?</p>
<p>In the 5th grade I was part of a small group that was being taught math in some sort of new way. I remember using a bunch of colorful, different sized block and needing to draw straight lines, (I remember the teacher saying, “Patty, that line is not straight, USE YOUR RULER”). I never figured out what the math was that we were supposed to be learning.</p>
<p>I’m someone who got a masters degree in math. Just tell me what you are talking about, don’t try to dress it up, that just puts another level of abstraction between me and the concept.</p>
<p>On the upside the Seattle area just exhibited the surprising good sense to get rid of the WASL, so when this fails in a few years maybe we’ll get rid of it too.</p>
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<p>You’re not the only one who doesn’t understand it. </p>
<p>Also, at the risk of sounding like a broken record, I still don’t understand why so many people are fixating on “basic math facts” in a thread about algebra and geometry. And why multiple people seem to have equated deriving concepts and axioms through pattern recognition with “singing kumbaya”, which is a complete straw man. If your kids are actually sitting around talking about how they feel about addition problems in math class, and I would certainly believe that it happens, then yes, you have a problem. But that doesn’t seem to be what this discussion was originally about.</p>
<p>Perhaps the “Discovering” books actually <em>are</em> inferior. I’ve never used them, I wouldn’t know. But I haven’t yet seen a satisfactory explanation as to <em>how</em> they are inferior.</p>
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<p>I don’t think the students are expected to figure the math concepts totally on their own. Eventually, the teacher has to step in and say: “Okay, here is how you should do it, and here is the solution.” This is true even if the students have figured it out already. As I mentioned in a post, this step is important to reinforce learning.</p>
<p>I agree completely that teachers are key, no matter what the curriculum is. A big problem in k-8 education is that teachers are generalists, and very often, they focus on reading rather than math pedagogy. By the time the kids get to the point were they encounter specialists, they have been taught math and science badly and have huge holes in their knowledge. It does not matter which method is used. </p>
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<p>In my 11+ exam (right after 5th grade), we were handed blank sheets of paper in which we would be writing our essays, do our math, science, etc… So the first step was to draw straight lines. Even with a ruler it was a nerve-racking experience, as it was a race against time. Focusing on drawing neat, parallel lines took time away from actually doing the exams. But penmanship was also a component of the exam. I can still have nightmares about it!</p>
<p>Our school district started out with “everyday math” in the elementary school, but supplemented it with basic math facts starting about mid year in the first grade. So many parents objected to what they called “fuzzy” teaching that that the year my son was in fifth grade they let parents pick a track for their kids, either traditional math or the everyday math. Through middle school they could jump back and forth between the two, but in High School they had to pick a track and stick with it. After about eight years of doing this they found that there was almost no difference in the test scores of the two groups of high school kids. There was one group who did score slightly higher, the group who had bounced between the two programs in middle school. </p>
<p>I think this underscores Marite’s contention that we would be better off if every teacher was familiar enough with a number of teaching methods to use them in combination to get the best results from each individual kid. ( Which in my experience is what a good teacher does, regardless of the “approved curriculum”)</p>
<p>I went through the “Discovering Math” textbooks in my education. The very specific ones being referred to in this discussion. There might be some validity to the approach, but the textbooks are horrible. My friends–all of whom were among the gifted and talented—managed to scrape by with them, but hated it. We all hated it. We made fun of it. Those textbooks were the butt of a lot of our jokes. We’ve spent many hours discussing how bad they are. Those textbooks are synonymous with “dreadful.” </p>
<p>“I didn’t do well on this assignment.”
“Bah. I’m sure you did better on that assignment than whoever wrote this textbook did at writing it.” </p>
<p>etc.</p>
<p>The friends who liked math took courses with teachers who didn’t use them(secretly). . I felt fairly lost for most of my math education. I got A’s on exams, but I couldn’t tell you what I was doing or how I got there. I hated math, even when I was getting A’s in it and didn’t find it difficult. </p>
<p>My experience went as thus:
There would be a story problem. As the story went on, I’d scrawl on the side an equation I figured out on my own and solve the answer to the problem.</p>
<p>Then I would realize that my answer as the answer to questions “e” and “f” and then have to make up fake answers for a through d. I didn’t need help “discovering” the answer. I knew the answer intuitively when I looked at the question because I’m just good at math. So I aced all my exams because I intuitively guessed my way through on how to solve things.</p>
<p>When I listened to my teachers try to explain things, I got confused and would do worse on exams. So I learned to bring other homework to class and tune out everything they said. Once I did that, my scores improved significantly. </p>
<p>Unfortunately, most of my classmates weren’t as lucky to have the same intuitive understanding of math at this level, and didn’t understand what on earth was going on in a through d and still couldn’t figure out e and f and were just lost and failed. </p>
<p>“What does this question have to do with…anything?”–very common question. </p>
<p>The average final grade of my honors pre-calculus course, which used this textbook, was a 50%. The average total grade for the calculus classes for a good while the year I took it was an F and the calculus teachers complained that the problem wasn’t that we weren’t smart enough. Out of curiosity they gave us tests to assess our knowledge in previous coursework from trig and pre-calc…and we failed them. We weren’t prepared. at all. </p>
<p>“You do the stuff we’re teaching you just fine…but the moment you encounter a part in the problem that involves anything from past courses, you just leave it blank. Didn’t you learn any of it?”</p>
<p>No. Not really. </p>
<p>I don’t know how valid this new method it is. It’s a shame, though, because even if it is, those textbooks are just bad. I feel sorry for the next group of kids who has to go through them.</p>
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By the way, it’s not just in math that this happens. In law school and on the bar exam, we were told that it didn’t matter whether we got the “right” answer; they were interested in our thought processes and how we got there. In practice, guess how many times a client walked in and said, “I don’t care if we win this lawsuit (if you negotiate a good deal, etc.); I just want to know that your thought processes were good”?</p>
<p>I spent many years with our son on just talking as a form of instruction. Asking him questions and seeing his answers. I spent some time doing this with our daughter too using AOPS as a base. You can travel all over the place with this approach and it provides a small forum to develop the ability to understand common sense and analysis.</p>
<p>It’s pretty clear that there has to be a balance between the concrete and the abstract and perhaps schools go overboard to both extremes.</p>
<p>Our school district uses Everyday Math (hard to pass the state assessments with any other program). Two schools supplement with traditional methods and one doesn’t. The one that doesn’t doesn’t perform as well as the other two schools. The district is trying to fix that (the teachers in the two schools do this on their own in addition to district curricular guidelines).</p>
<p>These days I have discussions with my son on computational complexity which spans the worlds of estimation and the concrete.</p>
<p>justbreathe: Thank you for answering my question (whether that was actually your intent or not).</p>
<p>When I learned high school geometry and trig (I was in high school from 1999-2003), it was largely through proofs and derivations, except for maybe the analytic geometry units. Very useful stuff, I thought. I don’t know how standard that is, either in the “traditional” approach or the ones we’re talking about in this thread.</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.</p>
<p>To my mind, this is analogous to writing an essay and having to explain* why* you used that preposition/adjective/semi-colon.
Dyslexia affects sequencing & a story problem in mathematics is not written sequentially, part of the challenge is to determine in which order to calculate the solution.</p>
<p>If you have already mastered the strategies, then you can go on to more difficult problems, but trying to do too many things at once, will confuse and frustrate the student and even if they intuitively are able to calculate the answer, if they aren’t able to explain how they know, the answer is still incorrect.
Seems much more time efficent to teach the problems without the verbiage before going on to requiring the explanation.</p>
<p>I’m reviving this thread to post the link to the following article. It does not matter what curriculum is used if teachers themselves are bad at math. In the past, this lack of math knowledge was disguised in the global score. With disaggregated scores, it is clear that nearly 3/4 of MA elementary teachers are incompetent at math. And that is in one of the highest performing states in the country!</p>
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<p>[Math</a> section of state’s licensing exam foils aspiring Mass. teachers - The Boston Globe](<a href=“http://www.boston.com/news/education/k_12/articles/2009/05/19/aspiring_teachers_fall_short_on_math/]Math”>http://www.boston.com/news/education/k_12/articles/2009/05/19/aspiring_teachers_fall_short_on_math/)</p>
<p>unfortunately that did not surprise me- in General- elementary teachers do not go into the classroom if they like and understand mathematics.</p>
<p>My D’s 5th grade teacher even told us at Parent night that she didn’t like math, that they would not emphasize it and would spend more time on creative writing.</p>
<p>It seems to be a circle- elementary teachers struggle with math- a few teachers can inspire students in middle and high school to higher level math, most of those people don’t become teachers, but others who struggled do and go on to teach the next generation.</p>
<p>“If you look at transcripts of some applicants for elementary school teaching positions, it’s possible you could see a transcript without anything math related. Someone could have last taken a math class in high school.”</p>
<p>^^^^^^^^^Why I like distribution requirements</p>
<p>I must say however- that both my kids- while they have learning differences that make lower level math more difficult, love science and kids and have been finding ways to improve their math comfort level.</p>
<p>Indeed, and that’s why so much of the math wars is irrelevant because it focuses on curriculum instead of teacher training.</p>
<p>Ironically, my S’s second grade teacher, who did amazing things with science and math, was a graduate of a state teachers’ college with a degree in education. Among the honors she earned were the State Teacher of the Year, a NASA fellowship, and the Millikin Family Foundation award. She did rocketry, had a weather satellite on the roof of the school with a monitor in her classroom, participated with her students in a long term environmental monitoring project called Gaia Crossroads, and all sorts of other things too numerous to mention.</p>
<p>But she was the exception that proves the rule: a dedicated teacher who went to “teacher’s college” when that was what you did to become a teacher, who was the very model of a “lifelong learner.” </p>
<p>In general, I’d strongly agree that many elementary and middle school teachers are not particularly inspired by math or well trained in teaching it. I have the impression that the Everyday Math teacher training tries to address that, but since many school systems skimp on teacher training to save money…</p>