As Cognition Slips, Financial Skills Are Often the First to Go... NY Times
Early today I read the scary piece above from Saturday's business section of the NY Times about how age begins to affect your basic financial - and math skills. I went through the checkpoints and - phew - I passed. But having that big 70 in front of my age, I am nervous about slippage.
So this morning, glancing through yet another column on education no-nothing Nicholas Kristof, whose column I try assiduously to avoid, I noticed some math problems embedded in the column, Are You Smarter Than an 8th Grader?
So I tried to do this one without looking at the answer:
A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?
I went back to 8th and 9th grade algebra -- that's 1958-9, folks -- about 60 years before common core. And like they ask, I am going to show my work.
First step: I have 2 options here. Either trial and error - take a guess and see where it lands you. This is often a process I follow and do pretty well.
But I decide on option 2 -- dredge up my old algebra.
I must find the value of x.
[NOTE - I taught 4-6 grade self-contained classes and math was easiest for me to teach --- and even without common core -- taught my kids they must first identify the crucial thing they must do first -- solving these things has an order --- not always a rigid order -- but you must work from a plan. I did teach them option 1 - just make an educated guess.]
Let's solve for x in the equation: 2x -5 + x + 7 + x + 6 = 40.
Got that so far? If the total length is 40, then the 3 pieces must add up to 40.
My pre-common core teachers taught us that an equation was like a see saw that always must have both ends in the same position -- you can't let one side tilt. Did I ever take kids to a park and try it? Can't remember but I think I did use a balance scale -- the law says you if you put stuff in one side you must put other stuff -- not the same necessarily - in the other side so they are balanced. A great way to teach the concepts of what an equation is. And I would teach this in 2nd - and maybe even 1st grade just by letting kids play with these as toys.
Now let's solve for x.
My pre-common core teachers taught us that in solving for x you must isolate x on one side of the equation (see-saw) -- use do unto one side of the equation as you would do unto the other -- as basic and important a rule anyone needs to know.
So -- I do +5 and -7 and - 6 to both sides of the = sign.
Thus -- we have the numbers on the left side all cancel each other out and end up with 2x + x + x (4x)
while on the right side we get 40 +5 -7 -6 = 45 - 13 = 32.
4x = 32. Follow our golden rule and divide both sides by 4 to isolate the x and we get x= 8
Now that we know x we are ready to solve the original question:
The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?
Did I have to know the lengths were in centimeters instead of inches? A bit of a red herring but maybe kids need to see through the red herrings.
And also - why use "x" as a variable when X is also the multiply symbol? A bit of confusion I would say. I say that because I want to notate this as 2x4 =8 but using the x as a multiplier here is confusing.
So:
1st piece: 2 times 8 - 5 = 16 - 5 = 11
2nd piece: 8 + 7 = 15
3rd piece: 8 + 6 = 14
The longest piece = 15.
But let's always check out work - as those pre-common core teachers taught me using the old math in the 1950s - by adding up all the lengths to be sure they = 40.
11 + 15 + 14 = 40.
Voila.
And I want to make the point that through the 8th grade I struggled with math -- or arithmetic. It was the simple logic of algebra that opened my eyes mathematically in the 9th grade. [Just a message to the debunkers of the value of math - who argue kids should only be taught consumer math.]
In the 10th grade , geometry really shook up my brain -- a 98 on the regents.
11th grade Intermediate algebra and trig are less memorable.
12th grade Advanced algebra--- 100 on the regents -- the only one in an exceptionally bright senior class at the now closed Thomas Jefferson HS - where I did not feel very bright compared to the competition. That same year, calculus for me was a disaster - so I reached my limit. I tried to avoid higher math in my masters in computer science and then found I had an interest in artificial vision which required differential equations and beyond -- did you know your eye was doing calculus?
Hey, any teachers out there looking for a guest lecturer for their class? Just don't ask me about quadratic equations.
by BAR managing editor Bruce A. Dixon
Should we be wondering if the prosecution of cheating Atlanta teachers for racketeering was racist? Or should black parents and educators be leading a movement against high-stakes standardized testing as the gateway tool to privatizing public education in black and brown communities across the country?-----
Since at least 2001, when George W. Bush's conservative Republicans teamed up with Massachusetts Sen. Ted Kennedy's liberal Democrats to pass and implement the No Child Left Behind Act, it's been the policy of both capitalist parties implemented by the federal Department of Education to create, to provoke and to exacerbate a phony educational crisis. This program of crisis-creation has been backed by Wall Street, by banksters and hedge fund types, by giant corporations like Wal-Mart and powerful right wing interest groups like the US Chamber of Commerce as well as the so-called philanthropic tentacles of corporate America like the Gates, Broad, Heritage and Walton Family Foundations. The solution to the fake crisis has been the whole industry of testing experts, turnaround consultants, diploma mills for fake principals, lucrative charter school companies and their contractors, and the private but government sanctioned agencies that rate school districts. Even the agencies that rate school districts are staffed by the same “run the school like a business” experts approved by the US Chamber of Commerce who were employed to write President Obama's Race to the Top program, which punishes school districts that don't privatize or implement “run the school like a business 'reforms'” fast enough.