<p>I feel somewhat vindicated. For several years, I fought tooth & nail to get a better math program into my kids’ middle/high schools. I lost. I also pulled my kids from the district & found a school with math a curriculum that prepared them for … well … MATH. Everything I predicted has come true. Wow, I’m clairvoyent. </p>
<p>I think the thing that really gets me in the article is this statement: “In many cases, high schools are trying to make up for what students should have learned in elementary and middle school, when there was no expectation that they would have to take such rigorous math courses.” No duh. The thing is, our district doesn’t believe in tracking, so the students were ALL recipients of the lack of expectation. I’d like to take this article and wave it in the faces of every administrator I talked to over the years … “I told you so!”</p>
<p>I’m not surprised. At least they were talking about Algebra I & II and Geometry. Our SD implemented the infamous Core Plus as the HS math curriculum, and the resutls were disastrous.</p>
<p>Actually, the integrated stuff is still acceptable under the new law, as long as the subjects are (theoretically) covered. My district JUST gave up on the integrated curriculum last year.</p>
<p>Just this weekend, I was talking about math education with friends who had been educated in Hong Kong and Taiwan respectively. The issue came up because one of the friends, an educator, had attended panel discussion about the respective merits of the Japanese and Singaporean math curricula compared to the American ones. All three friends agreed that for them, algebra had been easy compared to arithmetics because there had been an emphasis on both process (skill) and understanding (concept). The math wars in this country have pitted skills vs. concept. My educator friend reported that the panelist who made the most impression on him stated that it did not matter which curriculum was used; each had its good and bad points. What mattered were the teachers. My friends’ experience reinforced the conclusion reached by Liping Ma that in China (in this case Hong Kong and Taiwan, rather) teachers really focus on the fundamentals, whereas in this country, teachers are more process-oriented but don’t necessarily know why the process works, and thus are unable to explain it to their students.
Understanding fractions is important to doing algebra but this is something that far too many teachers fail to explain to their students (and often fail to understand themselves)</p>
<p>I have been appalled when I sub in high school math classes. The lack of very basic algebraic sense floors me. I have seen students who do not understand why numbers & variables need to be on opposite sides of the equal sign to solve an equation (for example, why 6x-3=15 needs to be changed to 6x=12 before one can attempt to solve). There is no way they can begin to understand anything even somewhat challenging without a very basic knowledge. When I try to explain about solving fractions, they shut down. Chemistry becomes a problem, as do other sciences. Now that MI also requires either chem or physics for every high school student, I’m thinking that kids will be retaking math & science classes until they’re 25.</p>
<p>I went to a conference last year where a teacher said in her state the way they get around the four-year requirement is to teach Algebra I three times: Alg I A, Alg I B and Alg I C, and then the kids take Geometry.</p>
<p>Not only have kids told me they need calculators for multiplication/division by 10 … I have also been asked what 3x4 equals, what 24 divided by 3 equals, etc. Many kids can’t look at an answer to figure out if it’s in the ballpark, either. For example, if they punch numbers into a calculator incorrectly (or forget that parenthesis are necessary when punching things into the calculator) & their answer is WAY off … they have no clue that the answer makes no sense. When I tried to show a group of kids the difference between punching a series of numbers/operations straight into the calculator & then with the appropriate parenthesis, they were awestruck that the answers were so different.</p>
<p>My mom is a high school math teacher. She has tried countless times to get the middle school teachers (and to a lesser extent, the elementary school teachers) to listen to reason: her kids are failing math because they have been mollycoddled through the past 8 years of their mathematical education. My mom has had to teach 10th graders how to multiply fractions, which is something I learned to do in 6th or 7th grade (and that was under that disgusting Chicago math program). </p>
<p>And as a student, even in my AP Calculus class, everyone except me and one other student whined and moaned about the non-calculator sections of the practice tests. My classmates could not do simple calculus (like, finding the derivative at a certain point) without a calculator. (I’m old-fashioned and I always think my calculator is lying to me, so I do it all out by hand.) People are not only losing the ability to do math in their heads, but they are losing the ability to do math by themselves.</p>
<p>Frankly, I’d like it if they banned calculators from all math classes up until the point where it becomes restrictive to not use them (i.e. trigonometry). Nobody <em>needs</em> a calculator for algebra or geometry. It is only in trig where memorizing all those sine and cosine decimal equivalents becomes impractical and where a calculator is needed.</p>
<p>Google Books has portions of Michael Spivak’s calculus book online. Chapter 1 covers the basic properties of numbers. If middle-school and high-school teachers could understand the material in the first chapter (meaning that they could do five or ten problems in the chapter), then I think that we’d be on our way to math teachers being able to explain algebra I to their students.</p>
<p>This is an admirable goal, but Spivak’s book is probably way above all but the very, very best middle school and high school students. To fully understand even the first chapter requires some pretty deep math experience. The concepts and the problems presented there are appropriate for the beginning of an introductory abstract algebra class for college undergraduates.</p>
<p>kelsmom, ur wouldn’t you want to change that to 6x=18? ;)</p>
<p>Years ago I read T*he Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom *. </p>
<p>From the Amazon review:
</p>
<p>It was very interesting, but it was pretty clear to me the problem is less with our books and more in the way we present the curriculum. One very telling moment. The math teachers are observing an American video and in the middle of a math lesson the PA system comes on to make some sport related announcements. The non-American teachers are appalled. Their schools would never, ever interrupt teaching time for announcements.</p>
<p>I actually felt our elementary school (which moved to the much hated TERC/Investigations curriculum) taught math very well. Math regularly was voted their favorite subject by the fifth graders (at least according to their yearbook). My kids got good number sense, could do all sorts of operations in their head, thanks to their ability to change equations to friendly numbers - i.e. 998+6 gets changed automatically to 100+4.</p>
<p>^ When I was in college, I was invited to give a talk to some high schoolers. I traveled quite a bit to get to the high school. Less than 30 minutes into my presentation (accompanied by slides carefully selected) the PA system came on and droned and droned. That was the end of my presentation.</p>
<p>Mathmom: Was math taught well using TERC/Investigations? Just curious because of the flack this curriculum has received. Our school used it, but S did not as he was always ahead of his grade.</p>
<p>I had no problem with the TERC curriculum. The teachers were well trained and seemed to be sold on the curriculum. All of them felt that they needed to do a bit more drilling on the side to get things like multiplication tables memorized and did so. They were definitely allowed to make these adjustments. I do feel the students get a good math sense - there was a lot of emphasis on making sure your answers made sense. For example when taught multi-digit addition they made sure that kids knew that 359 + 33 should be close to 390, if you got a four digit number you’d done something wrong.</p>
<p>That said, my younger son, who has trouble with memorizing and some auditory processing was the absolute last kid in his class to memorize his multiplication tables and he claims he still doesn’t really know them. Because of his memorization difficulties he might have been better off just learning ONE way to do something, but he seems to be coming into his own now that he’s in high school. He’s quite good at math, but runs out of time sometimes because he’s forgotten the shortcuts, or he’s double checking that 8x8 is 64 by doubling addition. He’s been known to rederive geometry formulas on the fly. His current math teacher (not honors because of a scheduling conflict) thinks he’s outstanding. He’s not a kid who eats up math like his older brother (who would do fine with any curriculum), but I do think some natural ability is there which was masked when he was younger by the LDs.</p>
<p>How successful the program is district-wide is harder to say. Partly because the state report cards are confusing. They say 100% of students met accountability measures - but I’m not sure what that means given that not all the kids pass the grade level standards. The elementary kids score better than the state averages on the state mandated tests. 75% meeting state standards in 5th grade and 10% meeting them “with distinction”. Obviously not everyone is doing so well however. It falls off in middle school where only 68% met the standards with 11% with distinction. I can’t even speak to the high school report card which is incredibly confusing.</p>
<p>My problem with the way math has been taught is the ‘trendyness’ of it. Every few years administrators come into school districts and bring in a new math “program” just for the sake of change (or for the sake of justyfying their salaries.) Most of these programs are experimental and iffy at best, and they often limit teachers rather than enable them to teach the material. A good, well trained teacher (and many aren’t but that’s another story) will use a variety of methods to teach math. These “programs” often do not allow for that kind of flexibility. And they can certainly hamper parents’ efforts to help their kids with their homework. I’ll never forget one mom who got so frustrated with trendy, inconsistent math instruction at her son’s school, that she walked into the district office and demanded a math BOOK. A basic algebra book she could use as she taught her sons the skills she felt he wasn’t getting in class (this was about ten years ago, before the availability of online materials.) The boy in question is now at Harvard – not studying math, by the way, though he has solid math skills for which his mother should get quite a lot of the credit. :)</p>