Category Archives: Big Picture

What Color is Math?

For a long time, the battle cry among students was Relevance! to me, to my future. I taught algebra and geometry in a hospital setting to a group of emotionally disturbed high school students whose diagnoses were very serious: schizophrenia, severe depression, acute anorexia. Math was the last thing they wanted to study. How could I make it relevant?

First, I cleared a bulletin board and put a heading on it: Math in the News. My students laughed. I offered extra credit every time they brought in an article. After a few weeks, the board was filled and we had to start taking articles down to make room for more. The articles were mostly about mathematicians, theories, and curriculum. No rock star statisticians then. Eventually the students stopped laughing and started seriously discussing the articles.

Secondly, I appealed to them emotionally by explaining that unlike literature and history which are subject to interpretation, math is a discipline of certainty.  Figuring out the correct and only mathematical solution can give you psychological relief from other anxieties (the mental anguish that brought them to the psychiatric unit in the first place). According to psychologists, even small positive emotions associated with “I got it” situations can help de-stress.

Now we don’t need to defend math. STEM (science, technology, engineering, math) has become an education war cry, an area that receives millions of dollars for creative learning and assessment. Now we talk about teaching 21st century skills so students can get jobs. Relevance is a priority. Students don’t even have to raise the issue; educators, business leaders, and politicians are doing it for them.  Liberal arts is being pushed out of the curriculum.

You may say, no, no, it’s now STEAM with the “A” standing for the arts. But subject areas such as history, sociology, psychology, and entrepreneurship are not the arts. Fareed Zakariah’s recent article, “Why America’s Obsession with STEM Education is Dangerous,” in the Washington Post, makes a great argument for the value of a liberal arts education featuring quotes from leaders in the tech world.

So what would I say now to my students if I were teaching a liberal arts subject? First, I would ask them to find articles about liberal arts, to post on a class Tumblr, track reblogs and invite comments from fellow students.

Secondly, what about the interpretive aspects of the humanities and social sciences? Certainty can be confining at times. Living is not about absolutes. It’s messy and we need to be able to understand and communicate all issues. What would life be like without the ability to dream and explore beyond science, beyond reason? What color is math?

The difference between the sciences and liberal arts is not an either/or situation. It’s an age-old tug-of-war that resonates in all of us. It’s what attracts millions to Star Trek’s very human(ities) Captain Kirk and the logical Mr. Spock. The success of their adventures confirms for us that together they are stronger than each alone. As technology draws us into global complexities, we also need the liberal arts to understand and solve the problems that arise. We need Kirk-Spock solutions.

What’s in a Name?

Learning is a complicated process that is difficult to define. We all know it when we experience it. We also know when we don’t. We know the difference between passing a test because we pulled an all-nighter and passing because we really understand and have thought about the material. When I think of learning I think process: explore, discover, connect, invent.

Learning can happen formally in school or in an online course. We also learn through activities, social interaction, and just plain exposure. We can learn from a positive experience such as attending a play, or a negative experience such as getting mugged afterwards. Through learning, we become who we are and develop attitudes toward learning. As I look back, I realize that my love of learning was spurred quite randomly—by my last name, Diogenes.

Diogenes was a Cynic in Ancient Greece who scorned material things and those who owned them. Choosing to live in the marketplace, he slept in some sort of tub and engaged in personal acts in public explaining that one should not be ashamed of what is natural.

Diogenes defended morality, reason, and truth. When Plato defined man as a featherless biped, Diogenes supposedly plucked a chicken and tossed it into Plato’s lecture saying, “This is Plato’s man.” Plato changed his definition.

According to a popular story, Diogenes carried a lantern in broad daylight. When asked what he was doing, he said he was looking for an honest man. So people used to ask me, “Have you found an honest man yet?” I only answered yes once when I called a wedding planner about my ceremony and she asked. I answered, “Yes, and that’s why I’m calling you.”

The inquiries of strangers started me trying to find answers and eventually sent me to the library to do research on Diogenes. I even applied to college as a philosophy major. One professor, who was holding oral exams with each student, began our appointment by saying he had looked at his calendar and wondered if he was interviewing Diogenes about Descartes or Descartes about Diogenes.

Even today I dip into stories on Diogenes. Recently I read a great book, Examined Lives, by James Miller, because it had a chapter on Diogenes. That’s why I picked up the book, but, of course, I learned a lot more. It seems somewhat incredible to say, but it’s clear that I would be a different person if I had been born with another last name. And learning may not have become the enjoyable, gratifying experience it is for me if I were not a Diogenes.

Many people badmouth the use of electronic devices: “Children can’t focus on more than a few paragraphs” “They will never be able to think of anything on their own.” What if we look at it from another perspective? Now young people explore, discover, socially connect, and create through digital devices everyday. One could say that the processes of learning are embedded in their lives more than ever. And you never know which random stimulus can lead to a love of learning.

Are You Ready for Critical Thinking?

Definitions of critical thinking vary greatly. My feelings about critical thinking are reflected in a scene from the movie Rudy, the story of a working-class young man who has to overcome many obstacles to achieve his goal of playing football at Notre Dame. After yet another disappointment, Rudy asks the local priest for advice. The priest replies, “In thirty-five years of religious studies I’ve come up with only two hard incontrovertible facts, there is a God and I’m not him.”

We all agree that critical thinking exists and we know it is not repeating facts. After that, it’s up for grabs. My favorite part of critical thinking is creativity, building on what you are hearing, reading, or learning, and making connections, usually clever, enlightening, or imaginative.

Although educators say critical thinking should be encouraged, in reality, it is often discouraged, ignored, or put off so that educators can achieve their own goals. Saying “That’s interesting but,” “I will take questions at the end if I have time” “We’re going to address that in next week’s class” are all ways to delay spontaneous critical thinking.

As part of Jumpstart’s Read for the Record,  I read Loren Lang’s Otis about a heroic farm tractor to a group of preschoolers. The sound of the tractor, “putt puff puttedy chuff,” was repeated many times as he did his work.

After the reading, the teacher started singing “Old Macdonald Had A Farm:”  “On his farm he had a cow…with a moo moo, here, and a moo moo there…” Then she asked the children to call out suggestions for what was on the farm. One boy kept saying “tractor.” “After being ignored three times, he stopped. In a few more grades, he will probably not even bother to make a suggestion as teachers continue to ignore his critical thinking.

As critical thinking does, the boy’s thoughts stimulated mine. What’s on a modern farm?

A milking machine, with a chugga, chugga, here, and a chugga, chugga there

A harvester, with a tatata, tatata, here, and a tatata, tatata there

A banker, with a foreclosure, foreclosure, here, and a foreclosure, foreclosure, there

A frustrated farmer, with a fuck, fuck, here, and a fuck, fuck there

We need to be realistic about critical thinking if we are going to encourage it. Ironically, those who oppose it are correct when they stated that teaching critical thinking results in: “challenging the student’s fixed beliefs and undermining parental authority” (Texas Republican 2012 Platform, later retracted). See Stephen Colbert for critical thinking on that!

I support teaching critical thinking, but we need to think about how we will handle the consequences. Based on articles critical of general testing, my son Ross put his name on a middle-school standardized test and handed it in without answering any questions. His teacher called me; she was extremely upset about the “terrible” action he had taken. I thought, I guess this is not a good day for critical thinking.

Educators, if you are serious about critical thinking, start looking ahead, get ready to be made uncomfortable and to think on your feet.  Students who think critically will rock your world!