## Saturday, September 30, 2006

Formidably prolific Ken DeRosa of D-ED RECKONING has done a yeoman's job dissecting (in multiple installments) the purported Reading First scandal which, by all appearances, is a pseudo-scandal.

The intent of the law was to fund reading programs with a scientific research base and to weed out fashionable but worthless whole-language programs. OIG is barking up the wrong tree.

### Fuzzy math behemoth cracking?

Could the fuzzy math steamroller be showing signs of sputtering?

Teens and Tweens, a site devoted to "understanding-based" math education that gratifyingly beats TERC over the head, cites a letter from a math teacher in Detroit who reports that Detroit's public schools have jettisoned CMP (a widely used fuzzy math program for the middle grades) in favor of a more traditional program:

"The Detroit Public Schools have replaced CMP with normal textbooks from Holt-Reinhart-Winston. The first group of students to have CMP throughout all 3 middle school years (6-8) had horrible standardized test scores. Someone finally got wise. The new textbooks seem OK. I will, however, continue to teach students rather than a curriculum."
However, the last sentence is somewhat mysterious. What could this teacher be teaching the students if not a curriculum? The phrase harkens back to one of the progressive ed dicta: “teach the child, not the subject.”

How about teaching the child the subject?

## Tuesday, September 19, 2006

### Deep understanding

When learning operations with integers you could just memorize (rote learning?) that a negative number times a negative number is positive or you could go for deep understanding as presented by Dr.Frank Wang of Saxon fame.
This is a brief excerpt of a much longer explanation:

Using the field axioms, we can prove a variety of things that you likely take for granted such as

–(–a) = a

– (a + b) = – a + (– b)

and a x 0 = 0 x a = 0

Now, we finally get to the crux of our explanation (the same explanation as above). In a field, the distributive property must hold. That is, if a, b and c are real numbers, then

a x (b + c) = a x b + a x c

and

(b + c) x a = b x a + c x a

The distributive property ties together the different operations of addition and multiplication.

Now, we replace a, b and c with -1, 1 and -1 respectively.

That is,

(-1) x (1 + (-1)) = (-1) x (1) + (-1)x(-1)

On the left hand side we see that 1 + (-1) is equal to 0 since any number plus its additive identity is equal to 0. Any number multiplied by 0 is 0 (this can be proven from the axioms for a field). Therefore, replacing the lefthand side with 0, we get

0 = (-1) x (1) + (-1) x (-1)

Since any number times 1, the multiplicative identity, is itself, we can further simplify this equation to get:

0 = –1 + (–1) x (–1)

We now need to figure out what (–1) x (–1) is. Since a number added to its additive inverse is 0, (–1) x (–1) must equal the additive inverse of –1. This is simply 1 so

(–1) x (–1) = 1
Sometimes memorization comes in handy.

## Monday, September 04, 2006

A veteran teacher identifies patterns of how educational fads come and go:

1. They start out with an inital flurry of interest/activity, often based on the results of "recent studies" or surveys. We have to listen to the "experts" and keep track of the data they provide.
2. This is followed by a few people (usually someone in an "influential" position... not "just a teacher") in the district attending some sort of workshop/training to become an "expert" in this new approach.
3. This person often arranges to fly in some kind of "national guru" for an inspirational talk.
4. Interest spreads throughout the district thanks to a multitude of workshops/trainings on this great new approach.
5. Everyone signs up (not always willingly), takes the courses, and immediately starts using the "latest vocabulary" wherever they go.