Tag Archives: meaning

CCSS and Standardized Testing – Who shall pass and who shall fail ?

This excerpt is from the following:


by Anthony Cody, and you should read it.

The Department of Education in New York convened a panel of educators to set cut scores on the new Pearson Common Core-aligned tests. This article  http://www.lohud.com/story/news/education/2014/07/26/common-core-cut-scores-examined/13219981/  spilled the beans about the process.

Tina Good, coordinator of the Writing Center at Suffolk County Community College, said her group produced the best possible cut scores for ELA tests in grades 3 to 6 — playing by the rules they were given.

“We worked within the paradigm Pearson gave us,” she said. “It’s not like we could go, ‘This is what we think third-graders should know,’ or, ‘This will completely stress out our third-graders.’ Many of us had concerns about the pedagogy behind all of this, but we did reach a consensus about the cut scores.”

The result was that this panel of professional educators provided the state of New York with the cut scores that meant only about 30% of the state’s students were ranked proficient.

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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

What is an equation? . . . . .What is NOT an equation?

Before starting, a definition: Any combination of numbers and letters and arithmetical operations (including   =   <   >   <=   >=) with more than three symbols is an algebra “thing”.  So, in passing, observe that a “number sentence” is an algebra “thing”.

Equations are neither true nor false: Some examples –

x + 10 = 45
x + 2y = 8
x^2 + y^2 = 4
y = x^2 + 5x + 7
x^2 + 5x + 7 = 0
x = 35
ax + by + c = 0

In each case the equation specifies the value or values of the letter quantities

x + 10 = 45
The value of x is such that if I add 10 to it I get 45

x + 2y = 8
The values of x and y are such that twice the y value added to the x value gives me 8

x^2 + y^2 = 4
The values of x and y are such that the square of the x value added to the square of the y value is equal to 4. This and the one above specify pairs of values.

y = x^2 + 5x + 7      You do these two
x^2 + 5x + 7 = 0

x = 35
The value of x is specified to be 35
and lastly,   ax + by + c = 0
Then we have identities, sometimes called equivalence statements.
These are ALWAYS true.

3 + 2 = 5
4 = 1 + 3
8 = 11 – 3
(x + 1)^2 = x^2 + 2x + 1
2x(4 + 7) = 2×4 + 2×7 (where x is multiplied by)
6/8 = 3/4
Later on, in algebra, we get definitions:

f(x) = 3x + 2
This means “The rule for the function whose name is f and whose input is x is multiplythevalueofhteinputxbythreeandaddtwotoit”
or “The value of the output of the function f for input x is the value of 3x + 2”.

y = f(x)
This means “The value of the output of the function f for input x is to be given the name y”.
These are NOT equations and they are NOT identities.
The whole current mess arises from the use of the equals sign for “gives” or “makes”, or “we get”, as in “3 + 5 makes 8”, or  “If we multiply 4 by 6 we get 24”, and we write

3 + 5 = 8, and 4 x 6 = 24
3 + 5 is 8 and 4 x 6 is 24 would be better.

The newfangled term “number sentence” appears to have been invented in order to avoid dealing with the correct mathematical jargon, but I see it as making things EVEN worse,


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Filed under algebra, arithmetic, language in math, teaching

“Number sentence”, what is this?

Being in complete agreement with  Dan Meyer on the term “Write an expression” I take exception to the vague instruction “Write a number sentence”.

Multiple choice question – Which of the following is a number sentence?

a) 3 + 2 = 5
b) three + two = five
c) three and two makes five
d) 2 + don’t know = 7
e) seven is 5 more than 2
f) they gave him 20 years
g) Mary gave three of her sweets to Jane and was left with 5
h) none of these, although they all have a verb

Answers on a postcard please, addressed to Santa Claus, North Pole

and next time I have much to say about “equations”


Filed under algebra, arithmetic, humor, language in math