<p>I’m not disagreeing about what’s “required” on the AP free response answers or in a “good proof”. I’m disagreeing about how best to “get there”. My son didn’t need the practice of writing about math that you and Tokenadult seem to believe necessary for your children’s development. </p>
<p>I’m not denying that such coursework/practice best for some kids. I am not stating that it was unnecessary for yours kids. I am stating that it is not the best approach for all - and that it may actually harm some.</p>
<p>I completely concur with the necessity of all students learning to write. I don’t see this as the case for the OP.</p>
<p>In the last analysis, I don’t find elementary teachers always able to see gems of writing in fewer words, and most seem to be of the mindset that “more is better”. On our state tests, the higher scores on open response questions are almost 100% of the time bestowed upon the student who writes the MOST, not the one who writes clearly and consisely, and perhaps produces less print.</p>
<p>More is sometimes MORE, and not better. Kids are often given the message that verbosity is often preferred to clarity, and that is wrong, IMO.</p>
<p>“He responded that he did not think he could make a good teacher because too many things were so obvious to him that he did not think to explain them.”</p>
<p>Yep. I ran into this problem when I was expected to help other kids learn to spell. How do I spell so well? Beats me. Working to memorize the spelling of a word makes about as much sense to me as working to memorize the pronunciation. I just know the word. And as for proofreading, I can spotlight mistyped words because their wrongness leaps off the page at me. For me, it’s as though misspelled words on a page are written in red ink. So how in the world do I teach someone else to find them? They can’t see the red ink.</p>
<p>Some kids have the equivalent of mathematical X-ray vision. Teachers need to be flexible with those kids, just as they’d be flexible with an LD kid who couldn’t grasp the problem.</p>
<p>I still get angry when I think about the years of my life that were wasted on those foolish educational projects. In seventh grade science, twenty people spent two class periods scattering colored jelly beans in the grass and then picking them up again. Do you think it will be easier to find RED jelly beans in green grass, or GREEN jelly beans? Let’s test the theory empirically. Argh! Think of the public good you could do with the 40 man-hours we wasted. That was the year I started skipping school.</p>
<p>My eighth grade science teacher constantly told stories, like about how one of his professors in college put a fish in liquid nitrogen and then shattered it on the table. (Which is really bizarre and I don’t know what that was illustrating that needed to be illustrated). Anyway he gave the SAME test each time, with one question added on (we took it like once a week or so). So at most if you memorized the test you got ONE question wrong, if that. But the kicker was if you went to the teacher and said “I don’t understand this problem”, he’d tell you the answer. So basically everyone got 100% every quarter. Then he put “receives accommodations” on the report cards, because he thought it was a GOOD thing. So they had to reprint all the report cards.</p>
<p>That class was at least amusing though, and luckily I have no aptitude for science whatsoever apparently, so I was all right. My english teacher was a man who’d been a retired a few years and came back the year before when the other teacher got pregnant. This guy wrote a textbook back the '60s. He didn’t go for any of the “make a book illustrating verbs!” that the GT team class was doing This was still an “honors” class (for regular kids), but it was better than almost any of the HS english classes I’ve had. They don’t really teach grammar anymore; this guy did.</p>
<p>So I would have failed too, huh :-p? When do schools start introducing negative numbers? I might be safe with that “proof” if third graders haven’t…</p>
<p>“So I would have failed too, huh :-p? When do schools start introducing negative numbers? I might be safe with that “proof” if third graders haven’t…”</p>
<p>Ahh- brings back memories of the pre-school teacher who, when told by my (math-gifted) 3 or 4 year old that 5-7 = -2, said that she didn’t believe in negative numbers.</p>
<p>The Algebra Project launched by Robert Moses aims to introduce algebra concepts, in particular the idea of negative numbers in 6th grade. But many kids grasp the idea of negative numbers much earlier. I know quite a few of my S’s classmates did well before then.</p>
<p>We officially learned it in sixth grade. I don’t think it was introduced very well. Also it seems like people are promoted missing a basic understanding of things like this and no one really identifies it. I tutor kids struggling in algebra 1 and some of them don’t have the concept of negative numbers, which is half of the problem. Obviously they are getting most answers wrong by not knowing those basic operations. By now I don’t assume that anyone knows that, basic as it seems…I go over the problem like they haven’t even been introduced to the concept of adding negatives. They usually seem grateful since often this is where the
“hole” is, but I suspect that with the prior help they’ve gotten, someone has just repeated the algebraic concept of “subtract from boths sides” (or whatever) while assuming they must know how to work with the negatives.</p>
<p>I had an online conversation about this once with a thoughtful mom from Louisiana. I said that kids in Minnesota pick up negative numbers from an early age by dealing with below-zero temperatures. She replied that she had never seen a below-zero (Fahrenheit) temperature in her entire life.</p>
<p>The Miquon Math program introduces negative numbers, multiplication and division, fractions, the number line, and many other cool ideas in a thought-provoking way, all by third grade, much of the cool stuff by first grade. That program is by far my most recommended math program for bright young people. The Singapore Primary Mathematics series is a good follow-up program after getting through most of Miquon Math. </p>
<p>Interesting. The Algebra Project, which began in Cambridge, MA, introduced negative numbers by getting students onto the subway, with Central Square Station as O. Going in one direction was positive, in the other direction was negative. When the Project was transferred to Mississipi, they had to rethink it a bit because there was no subway. So they decided to use bus routes instead.</p>
<p>Sports are an easy way to introduce negative numbers. Center ice, 50 yard line, whatever sport you choose. Controlling the ball or puck and moving to score on your opponent is positive. Your opponent moving toward your goal to score is negative. ERAs, batting averages, all the stats in sports — fantastic ways to teach kids the basics.</p>
<p>Wait … your schools bother to teach the “concept” of a negative number? I recently found out how our local high school teaches negative numbers. The students apparently get to high school with no idea of what the heck a negative number is. To deal with this, they are taught the following: If there is a negative number and a positive number, and it’s an addition or a subtraction problem, simply subtract the smaller number from the bigger number. Then give the answer the sign of the larger number. Problem solved.
Who cares what it all means, as long as they can get the answer, I guess.</p>
<p>Kelsmom I’m not sure how unusual that is. Most of us posting here probably aren’t/don’t have kids who would miss such a significant concept regardless of where or how it’s taught because of the supplemental education or simply ability they have available. But like I said, I was amazed to find out that most people who were struggling with Alg 1 missed this concept. I showed it on a number line to one boy. He understood then. Everyone had told him some sort of “formula” to know it and he was trying to repeat it to remember but it wasn’t working. He knew how to solve an equation but he was making mistakes with the signs trying to do some crazy formula without the number line understanding. </p>
<p>As a last resort, I teach them where the negative key is on the TI-83 (it’s assumed people know this too). You can use them on most any standardized exam, so while it kind of avoids the problem, it’s better than nothing. You can type the numbers you’re working with right in. Same with complex numbers, there’s an “i” key and it’ll change the sign appropriately for you.</p>
<p>The Algebra Project puts a huge emphasis on teaching the concept of negative numbers. Some sixth graders were rolling their eyes. Some had learned it already through the idea of owing money. In earlier grades, the class had a “bank” where the students could borrow or deposit money.
After they’d gone on the subway, they came back and drew a line representing the subway line, with the stations numbered plus or minus depending on their location vis-a-vis Central Square.</p>
This was still an “honors” class (for regular kids), but it was better than almost any of the HS english classes I’ve had. They don’t really teach grammar anymore; this guy did.</p>