@epiphany I didn’t mean to yell. The caps were used to emphasize the points.
“BLANKET STATEMENTS make it hard to take your posts seriously.”
I’m sorry if that was miscommunicated…I’m not ‘message board savvy’. (I need to learn how to “bold” here.)
However my post was an attempt to help you to deliver your talking points more effectively.
Obviously you have strong feelings about current trends. Just realize that your blanket statements about the “past versus current state” is not necessarily true everywhere and detracts from your message.
Examples: “Finally, and most importantly, today’s high school students do not read.”<<<<not in my children’s experience…their reading lists have always been impressive, especially the summer reading lists.
“For one thing, logic was explicitly taught in public schools and then later (when I attended a private school for a couple of years) it was a required course of its own. Two, in publics, we were taught the elements of argument and were required to practice that regularly – both in analyzing texts and in developing our own arguments. Three, we were taught to identify categories as we made our arguments. Ideas belong to classes, and those classes belong to larger categories.”<<<<your experience, which you share as evidential proof that it was taught this way in the past…again, not in my experience.
“Wrong. I cannot find such instruction in any of their textbooks, with which I am well acquainted.”<<<my children worked with proofs extensively at their public high school.
Every time I read such blanket statements it makes me question the veracity of everything else you write.
You may find this brief explanation of qualifying statements interesting. https://spot.pcc.edu/~mdembrow/QUALIFYINGStatements.htm
In conclusion I was/am actually trying to be helpful, since I agree with some of your observations as worrisome trends. Sorry if you took it the wrong way.
And thanks…I did have a lovely evening. Life is good!
As an aside, I’ve seen several school districts examining/adopting whole/integrated math for HS. Geom as a separate topic/year-long course maybe going bye-bye.
The CC fora use (an annoyingly limited subset of) BBcode to show formatting. The three most useful for everyday purposes are the codes to make text bold, make it italic, and to offset it as a quote.
BBcode is very similar to HTML, except that it uses square brackets rather than angled brackets. So:
[list]
[]Writing [ b]bold text[ /b] results in bold text.
[]Writing [ i]italic text[ /i] results in italic text.
[li]Putting something between [ quote]quote tags[ /quote] results in text being offset as a block quote, as at the beginning of this post.[/li]/list
Note that some BBcode tags have effects on paragraph spacing and such, so if you’re playing formatting games it’s always best to preview your comment before submitting it.
It’s certainly worth pondering whether expecting students to learn more of certain subjects–such as math–might mean that they don’t learn any of it as well. I think I learned geometry pretty well–but it was in high school, and our math topped out at “Math Analysis,” which was basically pre-calculus. No calc at all.
I also wonder whether trends might be really different in large cities, small towns, affluent suburbs, rural areas, etc.
Although high school geometry back then emphasized proofs, it did not seem like that many students really retained the knowledge and skills and used them elsewhere, including non math contexts where logical thinking may help understand something.
No. You delivered it in the wrong way. Whatever you thought of my content, you communicated in a tone likely to antagonize, which it did. It was entirely unnecessary to become so histrionic that it affects – hmmm-- your credibility.
As to content, I could say the same thing about your statements about “your children.” That’s not projectable. It’s an example of a (happy) exception to a trend. I never denied there were exceptions. I never claimed absolutes or universals. Your replies, both now, shed heat, not light, on a national modern trend observed and reported on far beyond CC’s Parents Forum.
My children were and are also exceptions to a trend. So what? This thread is not about your children or my children. It goes without saying on CC that many of our own children do not always fall into the lowest common denominator of national trends, just as there are outstanding journalists who buck the contemporary trend of sensationalizing and sloppy prose. Ditto for filmmakers who resist appealing to the lowest tastes of the masses. Those journalists and those filmmakers are opposing trends.
Back to the other tangent we’d gotten onto … math education. I actually like all the emphasis on word problems in Common Core and other math education these days. When I was a kid in the 70s-80s, the textbooks certainly taught the standard algorithms, but didn’t teach what to use them for. There would be pages of long division, but few word problems that required the use of long division. I don’t think I saw a word problem the entire year I took Calculus. (My school didn’t have AP, so this may not have been universal.) I had no idea what calculus was for other than “find the slope of the line” and “find the area under the curve.”
Also, related to the 14 x 21 mental math, I think @xiggi might actually like some of the Common Core implementation at the elementary schools in our district. Several days a week the kids do ~10 minute “Number Talks” where the kids sit in a circle without paper and the teacher poses a grade-appropriate question such as 14 x 21. The kids have some time to think about how to solve the question mentally. They hold up fingers for the number of different ways they have thought of to solve the problem. Then the teacher calls on several kids to share on the board their ways of solving. This gets kids to really have a feel early on for things like the distributive property, breaking things into prime factors and remultiplying, and using numbers that are easier to multiply and then adding or subtracting as xiggi did in 6 x 49 = 6 X (50-1). It’s not always arithmetic problems; sometimes it is “what could the next number in the series be?” or other types of math questions.
I’m also in California, and both our old standards and the new CCSS standards include geometric proofs (whether the sequencing of math is integrated or separated as Alg I, Geometry, Alg II). It’s not as much proofs as when I was a kid and we proved each new theorem in Euclid’s order, but they did spend several chapters on proofs and formatted them the same way we did when I was a kid.
Also, the CCSS (and the new SAT I believe) includes more statistics throughout, which I think is an important part of math that is practical for everyday life and has gotten short shrift in the past.
@epiphany wrote about “…a national modern trend observed and reported on far beyond CC’s Parents Forum.”
Call for references, please, along with an explanation of their authority if those are popular-press discussions rather than, say, peer-reviewed studies of national educational trends.
Although improbable, this is what schools such strive to accomplish. A basic problem such as the 14 x 21 is a goldmine to develop mental agility and understand various concepts. There is an inherent beauty in HAVING to use mental math. The next step is to allow paper and pencil to weigh the differences between different methods, including the simple multiplication of 21 by 14 – which should also take only a few seconds.
How about “memorizing” the multiplication by 11? Split the 2 and 1 and add the sum for 21 x 11 and you have 231. How hard is to multiply 21 by 3? That is 63. Now you have 231 + 63 for the same 294! Indeed, it is more tangential or circular but it might fit the neurons of a group of kids. Others might find the direct method clearer.
The implications are endless. For instance, if one would ask which is greater 14 x 21 or 15 x 20 and NOT allow the students to process the numbers? Bridging arithmetic to … geometry DOES provide the answer as the operation with the closest number will always be the largest as it approaches the square form and departs from a rectangle. By the way using a very large set of numbers with 6 0r 8 digits works in the same way, and it has been a question on the older GRE.
The purpose of such gymnastics is not to have students memorizing obscure formulas but to teach them the value of reasoning FROM a base of knowledge. Since this is a discussion about the SAT, the last line is relevant. Many are confusing this type of mental agility with “tricks” and other pejorative terms. This could not be farther from the truth.
Our education system has simply forgotten to rely on logical processes and has rewarded thoughtless memorization in a growing pattern. We are paying the price for having people who struggled with the concepts of THINKING in charge of educating the next generations. This has been obscured by the unveiling of technology ranging for the HP12 or TI-83 and the ubiquitous presence of cell phones who can … calculate. Yet, next time you are paying at Walmart, throw a curve at the cashier by letting her looking at the screen that SAYS the change to a 100 bill is 79.13 and you propose to give her three quarters to avoid too many coins and bills!
(I need to learn how to “bold” here.)
