Common Core will limit calculator use

New tests linked to Common Core standards will limit the use of calculators on math tests, according to the Hechinger Report. It’s likely calculators will be banned for tests in grades 3 to 5. At sixth grade and above, calculators could be used in some sections, but not in others.

Those rules “are sure to influence regular classroom use of calculators, from the elementary ban to the ways increasingly sophisticated calculator use is assumed at the secondary level.”

“The old saw is, teach to the test, and that’s the reality,” said W. Gary Martin, a professor of math education at Auburn University in Auburn, Ala. “If [students] can’t use a calculator on the test, it’s effectively banished from the classroom.”

On the other hand, Mr. Martin and others praised the PARCC guidelines for high school, which call for the use of an online graphing calculator with comparable functionality to a Texas Instruments TI-84, a popular calculator in high schools.

Students often rely too heavily on calculators, said Brad Findell, the associate director of math-teacher-education programs at Ohio State University. The calculator “on” and “off” sections at grades 6 and above “represents a reasonable middle ground that potentially . . .  can bring us to a better place where students end up being thoughtful,” he added.

Smartphones, stupid people

Smartphones Mean You Will No Longer Have to Memorize Facts, argues David Pogue in Scientific American.

When my father was growing up, his father offered him 25 cents to memorize the complete list of U.S. presidents. “Number one, George Washington. Number two, John Adams …”

A generation later my dad made the same deal with me, upping the reward to $5. (The prize had grown, he explained, “because of inflation and because there are more presidents now.”)

This year I offered my own son $10 to perform the same stunt. My son, however, was baffled. Why on earth should he memorize the presidents?

Nowadays, he argued, “everybody has a smartphone” and always will.

Smartphones will outsell regular old phones in 2013, writes Pogue. “Having a computer in your pocket is the norm.”

Should we mourn the loss of memorization skills? “Having a store of ready information” could be more fundamental and important than other obsolete skills, he speculates. But, no, he decides.

. . . we’ve confronted this issue before—or, at least, one that is almost exactly like it. When pocket calculators came along, educators and parents were alarmed about students losing the ability to perform arithmetic using paper and pencil. After hundreds of generations of teaching basic math, were we now prepared to cede that expertise to machines?

Yes, we were. Today calculators are almost universally permitted in the classroom. . . .

In the end, we reasoned (or maybe rationalized) that the critical skills are analysis and problem solving—not basic computation. Calculators will always be with us. So why not let them do the grunt work and free up more time for students to learn more complex concepts or master more difficult problems?

And how has that worked?

With students freed from memorizing facts, maybe they’ll “focus on developing analytical skills (logic, interpretation, creative problem solving) and personal ones (motivation, self-control, tolerance),” Pogue writes.

And maybe winged pigs will play hockey on the ice in hell.

Calculators: Useful or not?

In response to Konstantin Kakaes’ Why Johnny Can’t Learn Without a Calculator, math teacher Paul J. Karafiol argues that Calculators in the classroom are useful.

Teaching math requires actually understanding math, and people who understand math have always been in short supply, in and outside of the teaching profession. So a different, simpler explanation for the failure of students to learn math is that there aren’t a lot of excellent teachers out there teaching math. Technology doesn’t enter into the picture.

Where it does enter the pictures is in a new and completely unexpected change in mathematics education. Excellent teachers who use technology can increase access to higher mathematics for students with poor computational skills, by allowing these students to reason about concepts without getting bogged down in computation. This year, my AB Calculus class included some students who couldn’t reliably add fractions. By the end of the course, almost all of them could explain what the derivative of a function means (in abstract and contextual terms), how it is calculated, and what it could be used for. They could do all this because they used calculators with computer algebra systems—calculators that give algebraic answers, not just numbers—to do the heavy lifting.

Finally, Kakaes never engages what is, to me, the central question that technology poses to the mathematics teacher, namely, what of the traditional pencil-and-paper mathematics is worth teaching?

“The argument should be about when and how often students should be taught to use their calculators,” Karafiol writes.

Kakaes responds here.

Do timed tests cause math anxiety?

One third of students end up in remedial math in college and “the level of interest in the subject is at an all-time low,” writes Jo Boaler, a Stanford math education professor, in Ed Week.  She blames timed math tests — solve 50 multiplication problems in three minutes — for causing math anxiety that cripples learning

Math has become a performance subject. Children of all ages are more likely to tell you that the reason for learning math is to show whether they “get it” instead of whether they appreciate the beauty of the subject or the way it piques their interest. The damage starts early in this country, with school districts requiring young children to take timed math tests from the age of 5.

Common Core State Standards, which call for math “fluency,” may encourage timed testing, Boaler worries.

Stress caused by timed testing can lead to changes in the brain, permanently hurting children’s ability to learn math, she writes.

There are many good teaching strategies for encouraging fluency in math, but the ones that are effective are those that simultaneously develop number sense—the flexible use and understanding of numbers and quantities—without instilling fear and anxiety. Strategies that involve reasoning about numbers and operations, such as the pedagogical approach called “number talks,” are ideal for developing fluency with understanding.

Beyond the fear and anxiety, timed tests also convey strong and negative messages about math, suggesting that math ability is measured by working quickly, rather than thinking deeply and carefully—the hallmark of high-level mathematical thinking.

Children can learn math skills and concepts in tandem, writes Barry Garelick on Education News.

Reformers criticize traditional math instruction as “skills-based,” implying “students who may have mastered their math courses in K-12 were missing the conceptual basis of mathematics and were taught the subject as a means to do computation, rather than explore the wonders of mathematics for its own sake.”

Students have struggled with math for a long time: If one dinosaur eats two cavemen per hour, how many cavemen can four dinosaurs eat in 30 minutes?  When I was in elementary school in the ’50s, before calculators or timed tests of math facts, many kids were anxious about math because there were right and wrong answers. We didn’t tackle the lowest common denominator to appreciate math’s beauty or explore its wonders. We though the point was to “get it.”

“New math” came in a few years later, when my brother was in first grade. In trying to teach concepts, it made kids even more anxious.

My daughter did timed tests of addition and subtraction problems in first grade — 25 years ago! They probably did multiplication in second grade.  She thought the tests were fun. Of course, she was good at it. But Boaler says math anxiety is worst for high-ability students.

The dangers of education technology

Technology is undermining math and science education, argues Konstantin Kakaes, a New America Foundation fellow, on Slate. Fancy gizmos and software shortcuts waste money and weaken learning, he writes.

When Longfellow Middle School in Falls Church, Va., recently renovated its classrooms, Vern Williams, who might be the best math teacher in the country, had to fight to keep his blackboard. The school was putting in new “interactive whiteboards” in every room, part of a broader effort to increase the use of technology in education. . . . It is beginning to do to our educational system what the transformation to industrial agriculture has done to our food system over the past half century: efficiently produce a deluge of cheap, empty calories.

. . . Williams doesn’t just prefer his old chalkboard to the high-tech version. His kids learn from textbooks that are decades old—not because they can’t afford new ones, but because Williams and a handful of his like-minded colleagues know the old ones are better. The school’s parent-teacher association buys them from used bookstores because the county won’t pay for them (despite the plentiful money for technology). His preferred algebra book, he says, is “in-your-face algebra. They give amazing outstanding examples. They teach the lessons.”

The modern textbooks, he says, contain hundreds of extraneous, confusing, and often outright wrong examples, instead of presenting mathematical ideas in a coherent way.

Technology can help students learn concepts, advocates claim. In practice, that doesn’t happen, Kakaes writes. Students are even more likely to arrive in college with little understanding of math. The graphing calculator has done the work for them.

A science teacher demonstrated the superiority of her interactive whiteboard by showing him a music video featuring a Rube Goldberg machine. He wasn’t impressed. Then she showed a drawing of an electric circuit in which wires connect a light bulb to a battery. Close the circuit and the bulb lights up.

Her students like it when the bulb lights up, she says, because it reminds them of a video game. But this shortcut is dangerous. Learning how to visualize—as required when an electric circuit is drawn on a blackboard—is vital for developing the ability to think abstractly. You also have to make students manipulate real circuits with real batteries, with real wires that connect them and sometimes break. Showing them a toy circuit in computer software is an unhappy middle ground between these two useful teaching exercises: You neither learn how to trouble-shoot in the real world, nor do you think clearly about how electrons work.

Math and science require hard work, practice and perseverance, says Williams. There are no shortcuts.

Brits ban calculators in primary school

Britain will ban calculators in elementary school to give children time to learn arithmetic.

Schools minister Nick Gibb said: “Without a solid grounding in arithmetic and early maths in primary school, children go on to struggle with basic maths skills throughout their school careers.”

Nearly half of British adults have the numeracy skills expected of children aged nine to 11, according to a government survey. They have difficult comparing prices and paying bills.

The quiz measures skills expected of the average 11-year-old:

The Government's maths quiz: How does your maths compare with the average 11 year old? average 11 year old?

Why math tutors prosper

Many elementary students never learn basic math facts,  writes Lynne Diligent on Dilemmas of an ExPat Tutor.  They end up in remedial math classes in college. She advocates drill on math facts, more homework and no calculators till 11th grade.

I no longer teach Grade 3; I am now a private tutor. Unfortunately, I am now running across a number of 14-year-olds who are using calculators to add 5 + 3, or 7 + 6, or 9 + 2.

 Diligent also calls for requiring students to learn concepts before moving on, instead of  “spiraling” through the same things year after year.   

And she believes teachers should “instruct and explain, and then follow up with practice to master the skills,” rather than putting students in groups and telling them to figure out problems on their own. But group work is great for math tutors, she writes.


The calculator crutch

On Community College Spotlight, a dean wonders what to do about calculator-dependent students who can’t pass low-level math classes that require them to do their own arithmetic.  Should college instructors allow calculators?