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Friday, January 31, 2014

The Five Elements of Effective Thinking (Seeing the Flow of Ideas)

We're looking at Burger and Starbird's The Five Elements of Effective Thinking, chapter 4: Seeing the Flow of Ideas.

Summary: Ideas have history and lives of their own. Knowing where ideas came from can help us understand where they're going. Looking back and seeing the past can help us understand where to go in the future. All ideas are interconnected, and understanding those connections help us think more deeply about them. Understanding the interconnectedness of ideas also helps us integrate new learning into our current understanding of the world.

Critical Quotes:

"Innovators...recognize that each new idea extends a line that started in the past and travels through the present into the future. Successful and effective learners and innovators harness the power of the flow of ideas." (p. 95)

"...every advance can be the launchpad to far greater advances yet to be discovered." (p. 95)

"Every great idea is a human idea that evolved from hundreds if not thousands of individuals struggling to make sense of and understand the issue at hand. Thoughtful individuals moved the boundaries of our knowledge forward little by little;" (p. 96)

"They [teachers] know the meaning of the basic ideas, and they know how one idea leads to another. Students who duplicate that perspective grasp the ideas of any subject better than those students who view each new week as an entirely new intellectual mountain to climb." (p. 100)

"Effective students and creative innovators regularly strive to uncover the unintended consequences of a lesson learned or a new idea." (p. 106)

"We limit ourselves when we think that success is an end." (p. 109)

Ben's Thoughts:

I absolutely agree with the fundamental concept here, and I think the insight about how teachers view course material vs. how students view course material in the quote above is valuable to students who can leverage it. Teachers see the big picture and build the complexities out of a solid understanding of the fundamentals; we also see the connections between all the sub-sections, and how they work together to make a whole. This is often the thing that students fail to see, perhaps because they haven't fully grasped each piece, and so it is hard for them to put the pieces together in a whole. Good education gives students perspective, teaches them to see the "big picture", and helps them integrate everything.

There is one part of this chapter to which I take some exception. Personally, I'm a bit of a neo-Platonist, and I don't think of ideas as "human" (the way the authors describe them). I think of ideas as ethereal entities on their own out there in idea-land. When an idea passes through our mind, it represents an intersection between our physical reality and the ethereal idea-land where that idea resides. Some would argue that an idea that has never occurred to a human hasn't ever existed, but I prefer to think of it as out there in idea-land, just waiting to be discovered.

Thursday, January 30, 2014

The Five Elements of Effective Thinking (Raise Questions)

We're looking at Burger and Starbird's The Five Elements of Effective Thinking, chapter 3: Be Your Own Socrates.

Summary: Questions are one of the most powerful tools we have in critical thinking. Questions open us up to possibilities; they expand our horizons; they lead us down new paths. We need to learn how to form quality questions, and to tell more fruitful questions from less fruitful ones. Questions are how we explore ideas. We need to learn to formulate our own questions.

Critical Quotes:

"Constantly formulating and raising questions is a mind-opening habit that forces you to have a deeper engagement with the world and a different inner experience." (p. 74)

"Alternative perspectives lead to new sights and new insights." (p. 78)

"If you can't create the questions, you're not ready for the test." (p. 79)

"It's what goes on inside your head that makes all the difference in how well you will convert what you hear into something you learn." (p. 84)

"The real goal is for students to develop skills and attitudes that will allow them to independently think through the complications of life and find ways to learn for themselves." (p. 93)

"Ideally, the goal of education should be to develop critical thinking and communication skills and other such mind-strenthening abilities." (p. 93)

"The right questions can be incredibly powerful tools for understanding and learning. Great questions can lead to insights that will make a difference.... Questions give us a breath of inspiration and insight;" (p. 93)

Ben's Thoughts

A few years ago I went to a professional development day that was all about using the Socratic (questioning) method in the classroom. I didn't completely convert my classroom to this method, but it occurred to me that an authentic learning environment should be more about good questions than a stream of information. Before that day, a lot of my classes had revolved around me disseminating information, and then me generating questions, and my students trying to remember the information and apply it to my questions. This is a pretty standard methodology that is widely applied throughout the American educational system. But, as I reflected upon it, it seemed backwards. Really, the questions should come from a developing dialogue in the classroom; students should have as much input into the questions as I do, and we should be partners in seeking answers to questions, rather than me just spewing information at them.

Of course, part of any classroom needs to be instruction. There is always a time and place to demonstrate a technique or to convey a piece of critical information. But, from that point forward, I tried to become much more aware of my questions in the classroom, and to think about the kind of questions I was asking, and to try to use questions in my classroom as a tool to help lead students and to help them build their own understanding of a topic. When I taught Latin, my example was that I would teach students the critical translation questions to ask (Part of speech? Case? Number? Gender? Tense? Voice? Mood? etc.) so that they could learn to ask themselves those questions. Eventually, we got to a point where many students could parse the Latin on their own and craft a respectable translation.

Even now, as a math teacher, many students want me to solve their problem for them, and there's certainly a time to give students examples of how to work certain kinds of problems, but just as often, I step back and say, "What do you think? How would you solve this problem? What are your options?" This is much more difficult than just showing the student a solution, but it builds their ability to work at problems, which is more important than solving any particular problem.

Wednesday, January 29, 2014

The Five Elements of Effective Thinking (Fail to Succeed)

We're looking at Burger and Starbird's The Five Elements of Effective Thinking, chapter 2: Fail to Succeed.

Summary: Mistakes are the pathway to success. Mistakes help us refine our understanding. They help us imagine new possibilities. They help us understand "why". Freeing ourselves to make mistakes also frees us from the fear and constraint of "being wrong", which often stops people from taking critical steps in developing their thinking.

Critical Quotes:

"If you're stuck, a mistake can be just the thing to unstick you." (p. 48)

"Mistakes, loss, and failure are all flashing lights clearly pointing the way to deeper understanding and creative solutions." (p. 49)

"Success is about persisting through the process of repeatedly failing and learning from failure." (p. 57)

"Failure is a sign of a creative mind, of original thought and strength." (p. 71)

Ben's Thoughts:

Implicit in this element is risk taking, which seems to be a problem for a lot of people. Personally, I have a high risk-tolerance, and, in fact, do not often perceive as "risks" things other people think of as "risks". But I encounter my students (and even adults) who have a visceral fear of anything they perceive as a "risk". Students won't answer a question in front of their peers for fear of "looking stupid". This is one of the hardest preconceived notions to break, because for every time I tell students that it's okay to be wrong, and that being wrong is the first step on the road to understanding, popular culture tells them that being wrong is bad and that it makes them stupid.

This element ties in very nicely with Dweck's research on growth vs. fixed mindsets. Growth mindset individuals see failure as an opportunity to try again. They see potential for growth and learning, and so aren't afraid to fail, because they don't see failure as the end, but rather as the path. Fixed mindset individuals are afraid to fail, because they believe that their abilities and intelligence is fixed, and so if they fail once, then they believe they'll fail every time.

Somehow, we have to break this fear of failure. We're all going to get it wrong sometimes; that's part of life. If we use that failure to grow and learn, then we're the better for it. Nothing ventured, nothing gained.

Tuesday, January 28, 2014

The Five Elements of Effective Thinking (Understand Deeply)

We're looking at Burger and Starbird's text The Five Elements of Effective Thinking, chapter 1: Understand Deeply.

Summary: Advanced ideas are often built on a foundation of other ideas. It's important to understand the fundamentals clearly and deeply. One of the key skills here is stripping away the fluff to get to the core of the idea you're investigating. Don't be satisfied with your current depth of understanding, because you can always go deeper, you can always understand more clearly. Push yourself to increasing your understanding.

Critical Quotes:

"It is at the interface between what you actually know and what you don't yet know that true learning and growth occur." (p. 35)

"Commonly held opinions are frequently just plain false. Often we are persuaded by authority and repetition rather than by evidence and reality." (p. 36)

"Becoming aware of the basis of your opinions or beliefs is an important step toward a better understanding of yourself and your world." (p. 38)

Ben's Thoughts:

Not following this principle is one of the most common errors I see in the classroom. I remember one of my Latin professors in college telling us a story about her high school Latin class studying/translating Caesar's campaign against the Gauls, and one of the questions on the final exam was "Who was Vercingetorix?" and none of the students knew that he was the leader of the Gauls whom Caesar captured and brought back to Rome, which marked the end of his campaign. The students had translated Caesar's journals all year, but they got so lost in the intricacies of translation that they lost sight of the bigger historical picture.

In my own classroom, I see it happen with concepts like differentiation. Students learn the limit definition of the derivative, and then they learn the Power Rule, the Chain Rule, the Quotient Rule, the Product Rule, etc. And I always start differentiation by showing the tangent line problem and visualizing taking a secant line with a diminishing delta "x" (as this sets up the limit definition nicely) until it becomes a tangent, etc. But still, when I ask: "What does it mean to take the derivative of a function?" I get blank stares, because my students failed to deeply understand the basic concept. I probably did the same as a student.

This, to me, is the real difficulty of being a teacher: a good teacher is one who has thought extensively and deeply about the truths and mysteries of her/his subject, and s/he is trying to introduce students to the fundamentals, but students just haven't put in the time to see the beauty of the underlying structure of the subject. And if they don't put in the time, they'll remain forever mired in the quicksand of shallow understanding.

Monday, January 27, 2014

The Five Elements of Effective Thinking (by: Edward Burger and Michael Starbird)

Last Spring I attended a lecture by Dr. Edward Burger (president of Southwestern University, and perhaps the most famous math teacher since Pythagoras), and received this book: The Five Elements of Effective Thinking (buy it here on Amazon) by Edward Burger and Michael Starbird. It's a quick read with lots of useful thoughts. It ties in nicely with the "growth mindset" research of Carol Dweck, which I've written about on this blog before (and I recommend you search it up). The five elements in the title correspond to chapters in the book, and so that's how I'll organize my blog posts. Each one will be a post with a summary, some critical quotes, and a little personal commentary. Below are links to my posts for each of the five chapters.

Chapter 1: Understand Deeply
Chapter 2: Fail to Succeed
Chapter 3: Raise Questions
Chapter 4: Seeing the Flow of Ideas
Chapter 5: Engaging Change

Edward Hopper and Beautiful Things

One of the themes I started on this blog a while back revolved around Beauty and its importance in the world and in our lives. I picked up a pseudo-random book from the library the other day (The Art of Travel by Alain de Botton). The book was just okay; it didn't contain anything I thought was worth sharing, but it had excellent illustrations that were selected to fit the mood of certain sections of the book. One of the sections used a couple of paintings by Edward Hopper, and I had forgotten how much I enjoy his work and was inspired to share a little bit of it here. So here's to putting a little beauty in your day!

This first selection is probably Hopper's most famous and most "spoofed" work, "Nighthawks". One of the recurring themes of Hopper's work that I enjoy is his exploration of "ordinary" American life. But the painting raises more questions than it answers: Who are these people? Why are they up late? Why are they at a diner? What's the story with the man and the woman in the red dress (because it seems that there must be some kind of story.)?

This is called "Apartment 3c". This was one of the pieces used in the book I mentioned above in a section on train travel. I'm not sure why I like this piece so much, but let me take a couple guesses: 1) the dominant color is green; this may seem trivial, but certain colors draw us in and set a certain kind of mood. 2) The young woman depicted is reading, and I love images of people reading, because reading is such a personal thing, it transports us to another place, and we become lost in whatever we read. And the idea of watching someone forget themselves and become engrossed in something is enticing to me. 3) There's a young woman, traveling alone on an overnight train (the sun is setting in the background and she doesn't look like she's getting off soon). What's the story there?! Again, Hopper leaves me with more questions than answers.

I'm going to let this one stand without commentary. It caught my eye and I like it. Enough.

Last, but not least, I thought I'd share one of his landscapes, because, although he's not known for them, Hopper has a way of taking a landscape and bringing it alive, of making me feel like I'm actually there. It's also fun to see him work his magic with a bright blue ocean and bright sea-scape, instead of the interior of a train. It just goes to show his versatility and skill.

Anyway, I hope you enjoyed this little share. I'm really going to try hard to update the blog more often. This year has been killer at school, and I just haven't had the kind of time for other pursuits that I used to.