K-12: The Math You Need Is Not the Math You Get
Learning school subjects should be like learning anything else in life. You start at the beginning, proceed step by step, master more difficult aspects, and become skilled. Isn't that how we learn to drive a car, build a doghouse, play the piano, surf, or operate a computer? Of course. That's how we humans do it.
But our Education Establishment does not approve. Those in the Education Establishment insist on doing everything in inefficient, likely to fail ways, something like taking a child to a busy street and saying, Now, let's see you parallel park. Lots of adults, with years of experience, avoid parallel parking. But our schools (this is the essence of Common Core) put a 15-year-old in this stressful situation on the theory that he will be able to handle stress better in the future. No, many are scarred and never try parallel parking again.
Public schools (and Common Core) consistently embrace counterproductive methods. For example, "[t]he first standards gave a strong call for a de-emphasis on manual arithmetic in favor of students' discovering their own knowledge and conceptual thinking."
Their own knowledge? Is that a clever way of saying wrong answers? And what is manual arithmetic? Is that when you jot down 27 and 68 and get 95? Why would you want to de-emphasize a quick way to get the right answer?
Another summation adds: "Reformers do not oppose correct answers, but prefer to focus students' attention on the process leading to the answer, rather than the answer itself. The presence of occasional errors is deemed less important than the overall thought process."
Occasional errors? You see that the insanity is built in. Reflect on these two quotes, and you will not be surprised that PISA (Program for International Student Assessment) places the U.S. near 30th among the nations, despite vastly greater budgets.
Here is another summing up where elementary arithmetic is transmogrified into high school physics: "Problem-solving is a process – an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypotheses, testing those predictions, and arriving at satisfactory solutions."
Wouldn't it be more useful to teach students to generate correct answers? But no, our educational pretenders prefer lots of wasted energy.
The Standards mandate that eight principles of mathematical practice be taught:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Seriously, shouldn't this be called Ph.D. (Piled Higher and Deeper) humor? Has anyone now reading this ever done these steps? Arguably, all of them are contrived distractions intended to keep children away from actual arithmetic.
Here's another obstacle: what these people call a problem is mislabeled. Normally, we would call it a riddle, a thing intentionally designed to be difficult and irritating, at least for a few minutes. Furthermore, the English is not at an elementary level, thereby guaranteeing that poor readers will be further alienated from simple arithmetic.
Here is a preposterous fourth-grade question that became famous for symbolizing every bad tendency in Common Core: "Juanita wants to give bags of stickers to her friends. She wants to give the same number of stickers to each friend. She's not sure if she needs 4 bags or 6 bags of stickers. How many stickers could she buy so there are no stickers left over?"
The Independent Journal Review concluded: "The question can NOT be answered as asked." They produced a funny video where four adults grapple unsuccessfully with this inane question. Yes, but not funny when your kid asks you to solve the problem.
Let's turn away from gobbledygook and look at the real problems real people routinely deal with.
A man drinks four sodas every day. How many six-packs does he need to get through the month of September?
You go on a 600-mile trip. Your car gets 20 miles to the gallon. The price of gasoline is steady at three dollars a gallon. How much money do you set aside to cover fuel?
You get a job (in June) where you can make $100 a day (no days off), but the employment agency gets 10% commission. So what do you take away?
You plan to open a business at a certain location. You count passing cars for five minutes: 95. How many, more or less, would go by in an hour?
Everyone should be able to solve these in their head or on paper in 10 to 15 seconds. The first step is knowing the multiplication tables and other math facts. But guess what: memorization, like mastery, is disparaged. So every problem is the same sort of deep mystery over and over.
Common Core wants you to "to reason abstractly and quantitatively." What could that mean? Public schools do not teach fundamental skills, so students, after years in the classroom, can't do life's simple problems. Instead, they can "use appropriate tools strategically." Does anybody know what that would be? Oh, maybe they mean a calculator. That's pretty much the way all the kids end up: calculator-dependent.
"Parents, educators and some mathematicians opposing reform mathematics complained about students becoming confused and frustrated, claiming that it was an inefficient style of instruction characterized by frequent false starts." Confused and frustrated. That's exactly the problem. What we want students to feel is confident and comfortable.
It's a total bait-and-switch, just like sight-word reading. School officials promise to teach you superior methods that turn out to be vastly inferior. Then you realize you've wasted years; at the end of it, you can't do simple arithmetic (just as you can't read). Focus on the tsunami of waste for a few minutes, and you'll start to scorn our professors of education.
What they do in the public schools now is push kids into the dark woods before they know how to survive in the backyard. There is a real perversity throughout public school education, but you especially see it in math, where they have children crying over what traditionally was easy homework.
The most recent PISA results, from 2015, placed the U.S. an unimpressive 38th out of 71 countries in math and 24th in science. Among the 35 members of the Organization for Economic Cooperation and Development, which sponsors the PISA initiative, the U.S. ranked 30th in math and 19th in science.
Math is a story of endless failure. "This pattern that we're seeing in mathematics seems to be consistent with what we've seen in previous assessments ... everything is just going down," said Peggy Carr, acting commissioner at the National Center for Education Statistics.
As this is the situation year after year, we can reasonably conclude that the Education Establishment wants this result. All the bad practices are so readily fixed if there were the will to do so. Seems to me the public is forced to choose between two verdicts: sabotage and unbelievable incompetence.
First step: Abolish Common Core (or Commie Core, as some joke). What is Trump waiting for?
Teach efficiently. That should be the new mantra. Ask homeschoolers and private schools what they're doing. I bet their worst methods are better than Common Core's best.
Bruce Deitrick Price's new book is Saving K-12: What happened to our public schools? How do we fix them? He deconstructs educational theories and methods at Improve-Education.org.