We hear a lot about test scores, how U.S. students have fallen far behind other countries when it comes to math and science.
This is no longer surprising because it has been in the news for quite a while. Yet, it is no less alarming.
In previous eras in this country, campaigns to improve literacy hit us hard.
“Could you read and write?” said Allen Sanderson, an economics professor at the University of Chicago.
Those who could not found themselves crippled financially, socially and emotionally.
“The counterpart to that today is how good is your mathematical literacy and quantitative reasoning,” Sanderson said. “There is no turning back from that just as there is no turning back from reading and writing.”
Sanderson offered an example of an auto mechanic. Any novice used to be able to pop the hood of a car to tinker with a problem.
“Now you take it to the dealer, where it’s plugged into a machine, but the auto worker has to be sophisticated to work with that,” he said.
Many who go far in today’s world are savvy in technology or finance.
“The basis is mathematics,” Sanderson said.
But to succeed in math, a strong sense for numbers and the ability to manipulate them must come by the time a child finishes kindergarten.
“No child fails algebra because they don’t know math facts,” Angela Andrews, a retired National-Louis University math education professor, said in December in a presentation for the Metropolitan Math Club of Chicago titled Why Children Fail Algebra: It Begins in Kindergarten.
Kids can memorize facts, but they miss the big picture without an ability to reason.
“We teach them to count to 100 and we think we’re done,” Andrews said.
A child must learn to count by twos, threes, fives and 10s. Andrews referred to it as a strong mental number line. A child, she said, must be able to jump along the number line.
For first-graders, the cheapest screening for math skills is to have the child count backward from 15, Andrews said, adding, “If they can’t they need an intervention.”
The Common Core State Standards currently being adopted in most of the U.S. are intended to help children reason and manipulate numbers. Some educators and parents find them frustrating because they are radically different from traditional U.S. teaching methods that move quickly through a lot of material and because the transition has been rocky.
Common Core emphasizes hands-on activities to help students visualize and solve problems.
“Typically, U.S. teachers use tools to explain something,” said DePaul professor of math education Akihiko Takahashi. “But the tools should be for the students.”
We like to get answers quickly, but countries that top the U.S. focus on a process, Takahashi said. “Algebra is not just an answer. It’s how you do a graph, how you manipulate the equation.”
In her December talk, Andrews gave fascinating examples of educators confusing elementary-school students. For instance, a teacher who puts loops in her 2s is bound to have students confuse that number with 6.
Students are led to believe that an equal sign means an answer is coming when in fact it indicates balance.
When American students are asked how many 10s are in 374, many will incorrectly reply seven, Andrews said, because place value is misunderstood (the correct answer: 37). Other countries call this “the American disease,” Andrews said.
The confused kids, lost at a young age, face a vexing problem that forever plagues some.
They cannot catch up.