Back to main page.

Comments

"Maybe I've gone blind or lost my capacity to read, but I simply cannot tell whether the Saxon Physics Home Study Kit — "Offering 100 physics lessons, tests, answers, periodic table, charts, and more: all you need to teach a complete physics course" — also includes a Solutions Manual and an Answer Key & Test Forms."

I had the same questions and still don't know the answer.

Also take a look at science "standards" in Chicago and Illinois. http://instructivist.blogspot.com/

-- CharlesH - 12 Feb 2006

"Each year I would note that even the best math teachers in the public school where I taught were only completing about 42% of each math book prior to the start of summer vacation."

Maybe it is not necessary to complete a book because the topics keep spiraling from year to year. What wasn't taught in fourth grade can always be taught in eighth grade. I had eighth graders who couldn't calculate the area of a square!

-- CharlesH - 12 Feb 2006

I've had calculus students (engineering calculus) who couldn't calculate the area of a circle.

-- RudbeckiaHirta - 12 Feb 2006

good lord

ENGINEERING CALCULUS???????????

RH — had they forgotten?????

I mean, had they forgotten the formula????

Did they really not know????

Though it's pretty bad to have forgotten the formula, I must say.

When I worked through the Russian Math book last summer I was pretty close to remembering the formula, even after 30 years.

I remembered:
πr²

I half-remembered:
πd

-- CatherineJohnson - 12 Feb 2006

π

-- CatherineJohnson - 12 Feb 2006

That really doesn't look like pi, does it?

-- CatherineJohnson - 12 Feb 2006

Each year I would note that even the best math teachers in the public school where I taught were only completing about 42% of each math book prior to the start of summer vacation

The trouble is, I'm pretty sure that's not what she meant.

How are these books put together?

If each book has only....23% new content? Was that the figure?

Where is that content?

Is it 'sprinkled' throughout the book in the appropriate sections?

-- CatherineJohnson - 12 Feb 2006

&960;

-- CatherineJohnson - 12 Feb 2006

&03C0;

-- CatherineJohnson - 12 Feb 2006

damn

-- CatherineJohnson - 12 Feb 2006

&928;

-- CatherineJohnson - 12 Feb 2006

Π

-- CatherineJohnson - 12 Feb 2006

π

&#03C0;

-- CatherineJohnson - 12 Feb 2006

I don't know.

Those aren't too bad.

960 (small) :
π

928 (large):
Π

pi (small):
π

-- CatherineJohnson - 12 Feb 2006

The small pis look like pi to me. The big pi looks like the math symbol for repeated multiplication.

-- CarolynJohnston - 12 Feb 2006

They had forgotten -- or, rather, I'm assuming that it never really got firmly tucked into their brains in the first place. This means that at least one of the following is likely to be true:

1. They did few enough "find the area of this circle" problems in middle school that it was easier to look up the formula each time than it was to memorize (or better yet: remember) it.

2. They were allowed formula sheets on exams, to take the emphasis away from memorization. (Again, I'd rather have them remember than to memorize.)

I'm starting to form a mental list of all the ridiculous things that my students don't know. (Another item on the list: when the problem involves letters other than x and y, some of my students can't identify which is the independent variable and which is the dependent variable.)

-- RudbeckiaHirta - 12 Feb 2006

I'm starting to form a mental list of all the ridiculous things that my students don't know.

I'm hoping you'll do more than form a running list.

These things ought to be writtten down, recorded, AND REMEMBERED.

I'm wondering if we're seeing the results of YEARS of rejection of memorization.

I'm old enough to have spent quite a lot of time MEMORIZING STUFF.

STUFF I STILL HAPPEN TO REMEMBER ALL THESE YEARS DOWN THE LINE.

-- CatherineJohnson - 12 Feb 2006

some of my students can't identify which is the independent variable and which is the dependent variable

I don't think I ever learned that in math.....

I learned it in pscyology.....but not math

-- CatherineJohnson - 12 Feb 2006

oh!

I don't know that symbol (repeat multiplication)

What does the upside-down 'U' mean?

Is that the one you're talking about?

I've just recently discovered that all the kitty-corner U's seem to mean 'belongs to the set of'.....or something along those lines.

I'll use the little one.

-- CatherineJohnson - 12 Feb 2006

Christopher had to memorize a gazillion formulas for the area test.

I THINK that may be why he did relatively well when his friend did poorly.

His friend had also memorized the formula, but he'd stopped practicing as soon as he had them memorized.

We now make Christopher do practice problems for each test starting 4 days beforehand.

It's a kind of Crammed Overlearning.

It's not Real Overlearning; it's Teaching to Crammery.

But it's more than what you get just from studying until you've got something memorized.....

-- CatherineJohnson - 12 Feb 2006

ok, not a gazillion

but in that short a time frame, it was a challenge

-- CatherineJohnson - 12 Feb 2006

he learned the formula for trapezoids basically the same day he learned the formula for triangles

-- CatherineJohnson - 12 Feb 2006

ok, what I'm saying is: we made Christopher keep doing practice problems after the point where he could do them very quickly

we didn't make him do huge numbers

instead, we'd make him do 3 or 4 — just a handful — each and every day

we had him continue doing this after the point at which he could do it

his friend stopped doing practice problems after he had shown himself and his mom that he knew the formulas and could use them quickly and accurately

when you've JUST learned something, you absolutely can't count on continuing to remember it EVEN AFTER YOU'VE TESTED YOURSELF TO SEE IF YOU DO REMEMBER IT

-- CatherineJohnson - 12 Feb 2006

"some of my students can't identify which is the independent variable and which is the dependent variable"

I think they'll find it easier to identify the various variables if they are associated with input and output.

-- CharlesH - 13 Feb 2006

"Christopher had to memorize a gazillion formulas for the area test."

I think the formula for the circumference of a circle is one that lends itself totally to conceptual understanding. It should be possible to forget this formula at any time and reconstruct it from that understanding if that understanding is solid. I would use strings and a round table or other circular objects to illustrate that pi is a ratio of circumference to diameter.

-- CharlesH - 13 Feb 2006

I think the formula for the circumference of a circle is one that lends itself totally to conceptual understanding

Absolutely!

I was STUNNED to discover that the circumference is approximately 3 times the length of the diameter!

I learned NONE of this stuff.

I memorized formulas, practiced formulas to overlearning, and remember most of the formulas to this day.

I could be the poster child for what's wrong with traditional American math ed, as well as for what was right with it.

-- CatherineJohnson - 13 Feb 2006

The problems my calculus students can't do are word problems. Things like "Let G (measured in days) be the length of time before the food in the freezer goes bad. Let T (measured in degrees Fahrenheit) be the temperature of the freezer. G = f(T). What is the practical meaning of f(0) = 120 ?"

(This is not an actual problem but rather something I made up on the spot so that googling students don't find their homework here.)

Many of my students would say, "When the freezer is at 120 degrees, the food goes bad in 0 days."

Don't dare ask them the meaning of f'(10), what the units would be on f'(T), or whether f'(T) is positive or negative.

(However, they all know that the derivative of x² is 2x -- even though I haven't taught that yet.)

-- RudbeckiaHirta - 13 Feb 2006

Speaking of the formula for finding the area of a circle, several years ago we decided to solve the equation "pie = cake." It began when one of our girls had learned the formula at school that day and mentioned it at supper. That prompted the comment that "pi(e) are not squared, pie are round." From there, a discussion was had as to the shape of cakes. The next thing we knew, we were working on solving pi(e) = cake. -- KarenA - 13 Feb 2006

The "upside down U" ∩ denotes the intersection of sets. So the set C = A ∩ B would be the set all things that are members of both A and B, if that makes sense. Hopefully that displayed properly.

-- BenFromBelow - 13 Feb 2006

Hi BenFromBelow!

It did display properly. I have to check out how you did that.

-- CarolynJohnston - 13 Feb 2006

I just pasted the symbol from the character map. I wasn't sure if it would display because the font in the comment box is different from the rest of the page.

-- BenFromBelow - 13 Feb 2006

Hi Ben from Below!

R H — I can't wait til I get close enough to calculus to know EXACTLY what's going wrong with these students.

Right now I 'get it' in only a hazy way.....

-- CatherineJohnson - 13 Feb 2006

When you say they can't do word problems....does this mean they can't do what I've been calling 'applications'?

I may be asking that wrong.

-- CatherineJohnson - 13 Feb 2006

Yeah, they can't do applications.

I have some theories about what's going wrong.

None that are lending themselves to clever simplifications that will fit in a comments box.

If they knew algebra inside-out and backwards and forwards and could graph basic functions without the freakin' graphing calculator, they'd be WAY better off. Calculus is not hard for algebra ninjas. Add into the mix a healthy dose of executive function, and they'd easily be A students.

-- RudbeckiaHirta - 14 Feb 2006

Calculus is not hard for algebra ninjas.

Calculus is just algebra with teensy-weensy increments.

-- GoogleMaster - 14 Feb 2006

None that are lending themselves to clever simplifications that will fit in a comments box.

THAT'S OK!

WE HAVE LOTS OF SPACE!

WIT AND WISDOM!! DING! DING! DING!

Calculus is not hard for algebra ninjas.

-- CatherineJohnson - 14 Feb 2006

algebra with teensy-weensy increments???

good lord

-- CatherineJohnson - 14 Feb 2006

Wit and Wisdom

-- CatherineJohnson - 14 Feb 2006

you, too, GoogleMaster!

-- CatherineJohnson - 14 Feb 2006

so I'm getting the picture that Math Brains must be Word Brains, too

-- CatherineJohnson - 14 Feb 2006

"so I'm getting the picture that Math Brains must be Word Brains, too"

I would concur. We play a lot of word games, especially with math vocabulary, as a means of helping them learn and remember the language of math.

But when it comes to the arithmetic algorithms, I'm a devotee of "learning to automaticity."

-- KarenA - 14 Feb 2006

Capital Pi, Π (Table of HTML for Greek Symbols) is used for repeated multiplication just like capital Sigma Σ is used for repeated addition.

If you remember the Greek letter names and the math terms "product" and "sum" it actually makes sense. Products of series are just not as common as sums of series.

-- AndyLange - 16 Feb 2006

Hmm, the Greek characters just don't look the same in a sans-serif font as they do in a traditional serif font. Also, there's a lot more difference between capital and lower case sigma (Σ σ) than there is between capital and lower case pi (Π π).

Which is yet another vaguely math-related thing I didn't really learn until college math, physics and engineering courses - the Greek letters. (Not the alphabet, which I still don't know, but the names and how to draw most of them). Many of those fields tend to use Greek letters when they run out of Latin letters for standard notations for particular things, rather than Saxon's subscripts (which Cathernie mentioned in a different article).

-- AndyLange - 16 Feb 2006

Jeepers, I didn't even finish reading the table of ALL the HTML special characters - there are specifically named product and sum symbols (∏ and ∑) in addition to the Greek letters (Π and Σ). Plus lots of other math symbols, although no good (easy) way to compose them into equations with subscripts, superscripts, fraction bars, or oversized versions for things like intergrals.

-- AndyLange - 16 Feb 2006

the Greek characters just don't look the same in a sans-serif font as they do in a traditional serif font

I know.

It doesn't work at all.

-- CatherineJohnson - 16 Feb 2006