Tag Archives: logic

Smarter Balanced: Lacking Smarts; Precariously Balanced

It’s a bit long, but it sure takes the lid off the CCSS. Read it now.

deutsch29

In this time of  “public-education-targeted boldness,” the Common Core State Standards (CCSS) has made the American public one whopper of a “bold” promise:

The standards were created to ensure that all students graduate from high school with the skills and knowledge necessary to succeed in college, career, and life, regardless of where they live. [Emphasis added.]

There is neither now nor never has been any empirical investigation to substantiate this “bold” claim.

Indeed, CCSS has not been around long enough to have been thoroughly tested. Instead, the above statement–which amounts to little more than oft-repeated advertising– serves as its own evidence.

However, if it’s on the *official* CCSS website, and if CCSS proponents repeat it constantly, that must make it true… right?

Keep clicking your heels, Dorothy.

Now, it is one issue to declare that CCSS works. It is quite another to attempt to anchor CCSS assessments to the above cotton…

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Common sense versus logic and math: Congruence again

I thought I would write a computer routine to check if two figures were congruent by the CCSS definition (rigid motions). One day I will post it.

The most important thing was to be specific as to what is a geometrical figure. You can read the CCSS document from front to back, back to front, upside down and more, but NO DEFINITION of a geometrical figure. For the computer program I decided that a geometrical figure was simply a set of points. My diagram may show some of them joined, but any two points describe a line segment (or a line). So a line segment “exists” for any pair of points.

The question is “Are the two figures shown below congruent or not?

congruent or not

I rest my case…..

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Filed under abstract, geometry, language in math

Fractions are parts of the same whole, part 3

When is a whole not a whole? (again)

When it’s two wholes (or more) :-

John eats 1/2 of his pizza, Mary eats 3/4 of her pizza. So between them they ate 1/2 + 3/4 of a pizza, or 5/4 of a pizza.

So which whole are we referring to ? John’s pizza ……. No.   Mary’s pizza ……. No.    Both pizzas …….. No.    John’s pizza and  Mary’s pizza and  both pizzas …….. No.

Conclusion: What we are referring to as “the same whole” is an abstract unit of one pizza, and the fractions are measurements using this unit. Wouldn’t it be a good idea to start off like this, with fractions as measurements, and avoid years of misunderstanding, stress and confusion.

Is this so different from adding whole(adjective!) numbers , as when  adding two numbers they have to be counts of the same thing (or whole(!) before it is chopped up).?

Fun arithmetic:        3 apples + 4 bananas = 7 applanas

Desperately fun arithmetic :  1/2 of my money + 1/2 of your money = 1/2 of our money

 

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Filed under arithmetic, fractions