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'nuff said.
Thursday, March 24, 2011
Someday
The National PTA partnered with experts on the Common Core State Standards to create grade by grade guides that reflect the Common Core State Standards. The site also has a brief powerpoint of additional materials for mathematics describing focus and coherence. Slide #5 caught my attention:
'nuff said.
'nuff said.
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19 comments:
wait!
I don't get it!
What does this slide mean?
Does that mean that they are explicitly sacrificing depth (someday) for breadth today?
Somehow if they give kids a shallow understanding of a lot of things, some magical day it will become Deep?
Really?
I must be missing something.
Since it was explaining the CCSI to parents, I took it to mean that "Someday" - when the Common Core is fully adopted and implemented, students will be taught to depth over focused topics.
I just found it hilarious that they labeled it "Someday" instead of "After CCSI Implementation" or "In two years" or "future" or something like that.
Kind of off topic, but I'm pretty sure I have the right group of people to appreciate it. I'm really wishing for a national curriculum right now--or at least a series of textbooks that goes K-10 instead of K-6 and another for 6-8.
I'm doing math with a friend's daughter. She's homeschooling, so I get to pick the book, and we're using a Singapore text. Our most recent section is converting units of area: cm^2 to m^2 and that sort of thing. So, I thought to myself, this is the US, we should also do problems with in^2 and ft^2--I'll go look through the elementary and middle school texts in my library (I have 2-3 full series of each sitting outside my office door at work). Guess what? None of the books teach the topic _at all_. Aargh! Everyone is assuming someone else is teaching it, and no one is.
OK,
I'm dong ranting now.
"I'm really wishing for a national curriculum right now..."
Keep in mind that there is probably a 50% or better chance that if we have a national curriculum it will be TERC or EM based rather than something close to Singapore Math.
Do you really want a nationwide K-12 TERC-ish curriculum?
-Mark Roulo
Lsquared - the problem is that this topic is now considered "science" not math, and isn't taught until high school, usually in chemistry and physics. A lot of students never see it with squared units (which they get in one of the first problems I assign), so kudos to you!
In my math boot camp for first generation college students, I teach these kinds of problems and they are often brand new to these college freshmen.
i'm still a little shocked
to encounter college students
knowing nothing of how areas
and volumes are measured.
"square" and "cubic" units
*must* have been shown them
many times of course; somehow
they've *given up* on ever
understanding this amazingly-
-simple concept.
they never get it from me either.
they'll fight like hell to stay
ignorant of it by this point, indeed.
"if i have to *change my mind*
about anything to succeed
in college, to hell with it"
summarizes pretty nicely...
i'm a really patient guy
(when i'm at work) so
i'll keep looking for a way
to make it clear for as long
as they'll stay with me.
seldom for long.
"but what's the *answer*?"
the *answer* is that
"way too late" is still
a lot better than "never"...
>>square" and "cubic" units
*must* have been shown them
many times of course;
Many teachers are verbal, not visual. Few have made the committment to teach with multisensory techniques in elementary or middle. They may talk about squares and cubes, but they don't show it. And sadly, ime, if the class is grouped such that the majority is working on 'basic', then the minority will not even get to this 'advanced' topic.
It is more than that -- in elementary school, they show squares and cubes, but they don't show the UNITS typically, so students don't understand that the conversion also has to be squared or cubed. By the time we get to them in college, it is too late for many of them to really internalize it. I've taught a few successfully, but it becomes really hard (especially when I'm hoping to move on and actually teach them some chemistry too!)
I dunno guys. Maybe these comments are true about some/many elementary schools, but they don't reflect my kids' experience. This is fresh in my mind because my son's fifth grade math class has been covering volume lately. The problems he get absolutely do include units, sometimes metric, sometimes customary. I rather liked one recent set of exercises, which gave lengths in meters and asked for volumes in both cubic meters and cubic centimeters.
I had the following brainstorm at an embarrassingly advanced age:
For a long time, I knew there were two formulas that were somehow relevant to circles, namely 2*pi*r and pi*r^2, but I could never remember which one was area and which one was circumference.
I finally realized that pi*r^2 must be the formula for area, because area is described in square units.
kcab - that's great that they are working with units! Trust me when I say way too many college students arrive without those skills.
However, be aware that being able to convert lengths and then get volume is very different from being able to interconvert volumes. The first skill is a lot easier, because you can just convert the meters to centimeters, then multiply the lengths. In the second case, you have to square or cube the conversion factor which isn't intuitive. Hopefully, your kids learned to do that as well, but I'd suggest you quiz them on it. (e.g. if they have a volume in cubic centimeters, can they figure out the volume in cubic meters?)
However, be aware that being able to convert lengths and then get volume is very different from being able to interconvert volumes. No kidding, especially if you're working in customary units. In metric, not so bad. Perhaps that was part of what I liked about that particular exercise, it led to a discussion of working with exponents. Also, that he had to think at all about what he was doing.
Anyway, I'm sure even kids who work with units in elementary or middle school will forget about them if teachers don't continue to stress the importance in high school math & science classes.
Keep in mind that there is probably a 50% or better chance that if we have a national curriculum it will be TERC or EM based rather than something close to Singapore Math.
Do you really want a nationwide K-12 TERC-ish curriculum?
I just wanted to repeat that -- it's important! National Standards, sure. Curriculum? No, not unless you can stomach it being the worst curriculum you've seen.
students don't understand that the conversion also has to be squared or cubed
right --- unit multipliers were a big help for me in grappling with this, which I was learning for the first time just a couple of years ago
(otoh, I didn't 'believe' that you **didn't** also square the units....I just had had essentially no experience whatsoever with unit converting squares to squares or cubes to cubes
btw - and this should be a post, not a comment - back when I first started writing ktm with Carolyn Johnston, she and some others explained unit multipliers
I had never heard of unit multipliers!
I loved them immediately, and used to teach and re-teach them to C. every year, more or less against his will. **Because it was against his will,** I never managed to teach unit multipliers to fluency.
Nevertheless, this year he is taking chemistry and he's suddenly doing very well because they're doing dimensional analysis.
All those years of teaching unit multipliers **pretty well** had a big benefit.
Even not-very-good teaching and not-enough-practice gives you a big leg up down the line.
I am against National TERC.
Needless to say.
In the second case, you have to square or cube the conversion factor which isn't intuitive.
Exactly.
Saxon teaches that, and it's not intuitive (or not for me).
Of course, no one ever mentioned "conversion factors" to me when I was a kid, either.
That was another Big Revelation.
I was educated by wolves.
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