By Doug Ward

True learning has little to do with memorization.

Benjamin Bloom explained that with enduring clarity 60-plus years ago. His six-tiered taxonomy places rote recall of facts at the bottom of a hierarchical order, with real learning taking place on higher tiers when students apply, analyze, synthesize, and create.Education matters logo: Recent news, research, trends and thoughts about education

Deep learning, project-based learning and a host of other high-impact approaches have provided evidence to back up Bloom’s thinking. A study from the Programme for International Student Assessment adds even more evidence. It found that students who memorized mathematics material performed worse than those who approached math as critical thinking, Jo Boaler writes for The Hechinger Report.

Boaler, a professor at Stanford, says the United States has among the highest percentage of students who approach math as memorization. That’s not surprising, she says, because the teaching of math in the U.S. stresses memorization and speed of calculation for standardized tests. That not only narrows thinking, she says, but creates barriers to students who don’t learn well with memorization. Approaching math as problem solving, modeling, and reasoning expands thinking and expands math’s appeal to students.

“We don’t need students to calculate quickly in math,” Boaler writes. “We need students who can ask good questions, map out pathways, reason about complex solutions, set up models and communicate in different forms.”

That’s good advice for all disciplines.

Need a professor to respond? Try a sticky note. Really.Yellow sticky note with Professor, please take care of this. The sticky note survey says you will.

Experiments by Randy Garner of Sam Houston University found that professors are twice as likely to respond when a request is accompanied by a personal message on a sticky note, Harvard Business Review reports.

Writing for the Review, Kevin Hogan speculates on the reasons this approach works: It’s hard to ignore. It’s personal. And it creates a bit of neon clutter that the brain wants taken care of.

I’ve always considered duct tape a magic solution to most problems. Looks as if I’ll have to expand my toolkit.

Looking at K-12 as the key to raising college graduate rates

Michael J. Petrilli makes a good case that college graduation rates aren’t likely to improve significantly until students come to college better prepared.

Writing for the Thomas B. Forham Institute, he cites statistics showing that the percentage of “college prepared” students (35 percent in 2005) nearly matched the graduation rate of those students eight years later. He says that indicates that most students who are well-prepared for college eventually graduate.

“But until we start making significant progress at the K12 level — and get many more students to the college-ready level before they land on campus — our dreams for significantly boosting the college completion numbers seem certain to be dashed,” Petrilli writes.

Briefly …

The percentage of students needing remedial math courses at Colorado colleges and universities has declined for three years in a row, Education News reports. Among students who started college in 2013, 34.2 percent needed remedial math, down from 40 percent in 2011. (Rates in other states vary widely.)  … Eduardo Porter of The New York Times asks whether the federal government shouldn’t get a share of profits from federally financed research ventures in academia. He cites Tesla, Google, GPS, and touch-screen technology as examples of projects that emerged from taxpayer-supported research. … Google has made recordings of its Education on Air event available for viewing. One caveat: All the sessions have separate links but are part of a single video file of more than five hours. That makes skipping among the sessions a challenge.


Doug Ward is the associate director of the Center for Teaching Excellence and an associate professor of journalism. You can follow him on Twitter @kuediting.

By Doug Ward

If you want to find a quick answer to a question, where do you go?

Google, most likely.

If you want to help students from half a dozen disciplines understand how the elements of linear algebra apply to them, where do you go?

Again, Google. But this time, think outside the search box.

That’s one of the tricks Erik Van Vleck, a professor of math at KU, uses to help students learn linear algebra. Students in all disciplines use Google to search for information. Van Vleck pushes them to look at the search engine in mathematical terms, though, asking: “What does Google do when you put in search terms?”

Eigenvectors
The matrix transforms its eigenvectors (represented by the blue and violet arrows) to vectors pointing in the same direction. “Eigen” translates to “characteristic.” Interestingly, for a while after WWII, the use of “eigen” was replaced by “characteristic” in the British scientific literature. (Image via Wikimedia Commons.)

This semester, Van Vleck coordinates two dozen sections of Calculus I and teaches a freshman seminar in the computer age and computational mathematics. Students in the classes come from majors like biology, physics, engineering, computer science and, of course, mathematics. Each of those disciplines applies math to its own types of problems, but students need the same basic understanding of concepts like derivatives, matrices and eigenvectors.

To help students grasp those abstract concepts, Van Vleck looks for problems and examples that apply across disciplines.

“I’m trying to give them examples that everybody knows,” Van Vleck said.

That’s where Google comes in.

He gives students an article that explains how Google’s bots troll the web, gathering information about pages and determining how they are connected to one another. From there, Google’s computers construct matrices and eigenvectors that ultimately determine what shows up on the results page of a search.

Only Google’s engineers and computer scientists know all the elements of the company’s search algorithm. But by relating those abstractions to everyday life, Van Vleck not only engages students in problem solving but helps them learn better, as well.

“Part of my belief is that if people are comfortable with context, it’s easier to understand things,” Van Vleck said. “Abstraction is great, but often we map back to context we’re comfortable with or familiar with.”

Van Vleck learned this firsthand when he was a new faculty member. He and other recent mathematics Ph.D.s attended a seminar where they received equivalent mathematical problems. One of the problems was phrased abstractly, the other in terms of drinking beer.

You can guess where this is going.

“All the math Ph.D.s did better in the beer example because we could see how to solve the problem even though it was the same as the abstract problem,” Van Vleck said.

Van Vleck uses other techniques to help students learn, including a flipped approach in which he gives students pre-class assignments, builds on those assignments in class, and then has students follow up with related assignments out of class.

He has also boiled down a 400-page textbook to 20 pages of notes with hyperlinks to additional information for students who want to go beyond the essentials.

“If students can master those 20 pages,” he said, “they can pass the class.”

All of Van Vleck’s strategies are part of a pedagogical approach known as “just-in-time teaching,” which aims to make the most of classroom time by focusing on what students need most.

Here’s a link with more information about the just-in-time strategy.

You can also search Google, as long as you’ve done your math homework first.


Doug Ward is an associate professor of journalism and a fellow at the Center for Teaching Excellence. You can follow him on Twitter @kuediting.