As large educational organizations have taken larger and larger pieces of control over your child’s education, the math skills seem to have fallen by the wayside. Although behind a paywall, this Wall Street Journal piece, describes what math is like… It isn’t the same as you and I learned…
Draw a picture to divide 2/3 by 3/4?
All mathematicians say: WTF?
Who needs to learn how to draw something that stupid? Have you done it yet? Go ahead, try it.. Sounds simple, doesn’t it? Just draw it… Make a circle and cut out a third, and then, divide what is left, into three fourths. Notice, I didn’t say into fourths and shade in three of them. I said divide that 2/3rds by 3/4th….
So … did you get 8/9ths? But wait, isn’t 8/9ths larger than the original 2/3rds… Why yes, it is. You see what you were thinking of was multiplying two thirds by three fourths… That would have given you 6/12ths or one half, which is indeed, an amount less than two thirds.. But when you divide by whole numbers you are determining how many of those fit into the dividend… Therefore when you are dividing by fractions, which are smaller than whole numbers, you are also trying to determine how many of those fit into a dividend… and since they are smaller than whole numbers, there would have to be more of them, than the amount you are dividing into…
Is your head spinning? Then ask yourself, why this is on a Common Core 5th grade test? As for drawing a picture of this problem? As a theoretical physicist, I can’t see how. Working backwards (from using the old trick to figure out the answer in my head), I would draw a circle and divide that circle by nines, and color in 8 of the them. Out of those eight, I would then split them into fourths… Knowing each of those fourths would be decimally close to 2.2 sections of the original diagram, and three of them would be close to 6.6, which is decimally close to a row of 6’s stretched to infinity, or the dividend 2/3rds. There is no practical application of this model that jumps to mind. So why are we tying up 5th graders time in doing 12 grade math?
Because this problem is easy to do, based on teaching a pattern, something Common Core is loathe to do, such as: when you divide fractions you multiply the numerator of one with the denominator of the other… the exact opposite of fraction multiplication… As adults, we get paid for finding simple answers out of complex problems… Common Core, takes something ingeniously simple, and makes it incongrously hard and complex. Won’t this put American students even further behind? Every corporate executive I know, says: “absolutely”.
But this diagramming is all over Common Core. Here are some from the Wall Street paywalled piece mentioned above.
“the teacher required that students draw pictures of everything: of 6 divided by 8, of 4 divided by 2/7, of 0.8 x 0.4, and so forth. In doing so, the teacher followed the instructions: “Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for 2/3 divided by 3/4 and use a visual fraction model to show the quotient . . .”
“This requirement of visual models and creating stories is all over the Common Core. The students were constantly told to draw models to answer trivial questions, such as finding 20% of 80 or finding the time for a car to drive 10 miles if it drives 4 miles in 10 minutes, or finding the number of benches one can make from 48 feet of wood if each bench requires 6 feet. A student who gives the correct answer right away (as one should) and doesn’t draw anything loses points.”
“Here are some more examples of the Common Core’s convoluted and meaningless manipulations of simple concepts: “draw a series of tape diagrams to represent (12 divided by 3) x 3=12, or: rewrite (30 divided by 5) = 6 as a subtraction expression.”
“This model-drawing mania went on in my grandson’s class for the entire year, leaving no time to cover geometry and other important topics. While model drawing might occasionally be useful, mathematics is not about visual models and “real world” stories. It became clear to me that the Common Core’s “deeper” and “more rigorous” standards mean replacing math with some kind of illustrative counting saturated with pictures, diagrams and elaborate word problems. Simple concepts are made artificially intricate and complex with the pretense of being deeper—while the actual content taught was primitive.”
GonzoEcon points out the double whammy this causes….
- First, the pictures will probably not help many of the students who are math-challenged.
- Second, more importantly, drawing pictures wastes the time of students who are adept at math.
So Common Core is doubly harmful.
“Some Common Core exercises emphasize the use of “friendly numbers.” I have never understood what makes one number friendlier than another. But I have a guess. Numbers that have pointy, sharp corners (7, 5, 4) are unfriendly. Numbers that are nice and round (3, 6, 8, 9, 0) are friendly. I don’t know what to do with 1 and 2. I hope someone who knows Common Core can help me with this classification issue.”
Parents should take heart. Wall Street just last year was pushing Common Core very hard. For the Wall Street Journal to allow this to be published, a very damning indictment of the Common Core math curriculum, means Wall Street has shifted its bets on Common Core … to selling it short… If even Wall Street is solidly behind it’s demise, Common Core is going to fail… The fight for parents everywhere is to now educate their individual state’s legislators and their voters, so no one else across the nation, does in children as did Delaware’s own, Greg Lavelle, crony Senator from the 4th District….