By Doug Ward

Angelique Kobler offered an uncomfortable question about education last week.

Kobler, assistant superintendent for teaching and learning at the Lawrence school district, met with the KU Task Force on Course Redesign and explained the steady expansion of blended learning in Lawrence public schools.

To illustrate the need for new ways of engaging students, she said, she asks her staff a question that can make even the most experienced teacher squirm: Has teaching occurred if learning hasn’t?

Education is never that cut and dried, of course. Learning depends on a wide range of factors that have nothing to do with an individual teacher. Kobler knows that. She uses the question to spur discussion about the need for change.

blended learning graphic
Wikimedia Commons

Today’s students are different from those a generation ago, as are their needs in an era when laptops and smartphones offer access to nearly unlimited amounts of information.

Fifteen years ago, Luc E. Weber, a professor of public economics at the University of Geneva, made an observation that has grown only more apparent today: “Teachers will have to accept that their role is changing,” Weber wrote in Challenges Facing Higher Education at the Millennium. “They will be decreasingly information providers and increasingly animators and commentators in charge of giving context and in-depth understanding of an area.” (p. 10)

Blended classrooms force teachers to heed that call for change. Many teachers are responding. Lawrence public schools started with a pilot program of eight blended classrooms in Spring 2013. By fall of this year, the district plans to expand that number to 150.

Kobler defines blended as “somewhere between traditional and virtual.” Students in blended classes can use whatever means help them learn: Some choose textbooks. Others work through assignments online. Sometimes students work alone. Other times, they reach out to peers to help them understand a topic or a concept.

In all those scenarios, the teacher keeps tabs on students and meets with them individually or in groups to keep them on track.

This approach isn’t easy to pull off. Teachers have to be willing to experiment, to make mistakes in front of students, and to talk with students about those mistake, Kobler said. Blended classrooms can seem chaotic as students go in several different directions at once, something that doesn’t also sit well with teachers who demand order.

Parents, on the other hand, have been enthusiastic about the blended approach, sometimes asking that their children continue in a blended classroom because the approach works well for them.

On the other hand, high-achieving students sometimes struggle in a blended environment, something I’ve found in my own classes. High achievers often thrive within a tightly structured, traditional model of “tell me what I need to know and I’ll tell it back to you on a test.” A blended, flipped or hybrid environment strips away this neat order and pushes students to find their own structure and to pace their own learning. That’s a far more difficult task, but it’s also far more meaningful in the long run.

Let me put a twist on Kobler’s earlier question: Can education survive if educators don’t adapt to the needs of students?

That question may make us squirm as well, though it’s also a bit easier to answer.

“If we don’t keep up, we will become irrelevant,” Kobler said.


Doug Ward is an associate professor of journalism and a fellow at the Center for Teaching Excellence. 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?”

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.