Friday, March 29, 2013

What did you think of Sir Ken?

A former student asked me this earlier today. You see, Sir Ken Robinson visited GVSU this week (news story) and shared his message about the need for creativity to be infused in education - not just something added on. I told the student something like, "He was certainly inspiring. I left feeling passionate about being an educator and affirmed in my efforts to improve teaching."

(Watch this and see if you don't agree)

"But," I added, "I'm still thinking about how to implement the ideas he shared. What does it look like?"

The student responded, "You always ask that."

My colleague, John Golden, was also at the presentation and wrote this recap. He had the same question (no surprise for anyone who knows us). John focused on education in general, however, and I want to focus on a specific example Sir Ken gave about mathematics. There's currently no transcript or video of the complete talk so some of this is based on memory and notes which admittedly are a product of my own filter. So be forewarned.

Sir Ken talked about asking a math professor in London how the math department evaluated doctoral theses. The math professor explained that the math, obviously needed to be correct, but that this was not usually a problem. So it boiled down to two things. First, the work was something original that contributed to the current knowledge-base. And second, it was aesthetically pleasing. The math professor explained that math was a way of representing the beauty and truth of the world and that a dissertation needed to be able to demonstrate that connection. (If anyone remembers this differently, I'd be happy to make the necessary adjustments. Please leave your memories in the comments.)

As I thought about these requirements, it became clear that K-12 schools often focus on the initial point, correct mathematics, while ignoring originality and aesthetics. So what would this look like if we also incorporate Sir Ken's admonition that the later elements, associated with creativity, are not added on after the fact? I think standards-based assessments and problem finding activities are two sources to consider as ways to address these expectations, but I am open to other. What do you think?

Sunday, March 24, 2013

Which floor, please?

We were scheduled to present at the MACUL Conference early in the day, so I set my alarm to go off before sunrise. Once I was completely ready to go, I took some time to look out the hotel window across the Detroit River toward Windsor, Canada. I notice a few lights were already illuminating some offices in the tower to the right. Clearly, some people were getting an early start on their day. And then one of the lights moved, and I realized that it was one of the tower's exterior elevators. As I watched the lights move up and down, several questions came to mind. So I took some video to share the experience with you. (I apologize for the quality.)

Going Down
  • On average, how fast is the elevator going as it descends?
  • Is the rate of speed, as the elevator descends, fairly constant?
Going Up
  • Does the elevator travel slower going up?
  • How long would a trip to the top of the tower take?

At one point, there was a break in the action, and I noticed that the elevator cars stayed at their last location instead of going back to the ground floor. When they were called, it wasn't evident to me what determined which car answered which call.
  • If I was on the ground floor, what would be the average amount of time I would have to wait for a car to respond to my call?
  • What are the chances that a car would be waiting for me if I was on the ground floor? On some other floor?
Some of the questions above could be explored using the videos, but most would require further investigation. It has me wondering about the elevators in Mackinac Hall. Maybe some weekend or night I will conduct a my own experiment. 

Monday, March 18, 2013

What's the point?

Teachers act as if student interest will be generated only by diversions outside of mathematics. (page 89 of The Teaching Gap)
Some of my recent actions on social media can probably be directly related to reading the above words right before "pi day." For example:
I understand the desire to "make math interesting" but putting a decimal point between the month and the day of a certain date seems a bit of a stretch. I want people to have fun with math each-and-every day. This resulted in my creating a series of signs with this online generator.

While walking with my wife yesterday, we had the following exchange:

Kathy: How long are you going to do these signs?
Me: I don't know. How long does it take for something to become a meme (pause) or to become annoying?
Kathy: So you want other people to start making the signs?
Me: That was the idea. I want people to find math interesting daily.
Kathy: How many signs have you made?
Me: Three; so when does it get annoying?
Kathy: 3.14 (pause) and look at that, we're back to talking about pi.
Me: You might say we've come "full circle."

Today, I shared this sign.

Thursday, March 14, 2013

Where does it hurt?

Me: (after a fairly lengthy description of open questions) So what did you hear? What are you thinking?
Teacher: (long pause) I don't know what you want me to say.
Exchanges like this happen more often than I like. People have been trained to believe that when a teacher asks a question, he or she is looking for a particular answer. We want to be good students which means providing the expected answer. It reminds me of a book discussion on Diane Rehm about how patients and doctors fall into a routine that can result in mistaken diagnoses and unnecessary tests.

Proud parents with Dr. Hilary at MSU COM graduation
This book came to mind when the teacher responded as she did. You see, I have tried to get in the habit of asking questions I do not know the answer to; it ensures that I avoid falling into an educational rut, and it makes my job as a teacher much more interesting. I tried to explain to the teacher that my question was an attempt to gather some information about what she had attended to in order to make a decision about our next steps. I said something like, "Think of me as a doctor trying to make an accurate diagnosis of your 'health' in regards to understanding of this topic. It's like I'm asking, 'Where does it hurt?'" She laughed and then went on to describe what she had understood about open questions. As the discussion went on, I would stop every now and then to ask, with a smile, "Where does it hurt?"

This is one of the ways we might use warm-ups more appropriately (see last week's post for my perspective on this problem). We could treat it as a way to diagnosis the readiness of the learners to move on or determine what issue we might need to address. (Here is an example of the latter.)

I saw an example of this earlier in the week. Students worked on some scale drawing questions, and after giving the answers the teacher asked if there were any of the questions students needed help on. A student called out a number. So far, so good. However, instead of doing more of a diagnosis, the teacher fell into the rut of showing the student how to find the answer. After a couple of minutes, the teacher stated, "That means the answer is 1/2 an inch. Okay?"

Fortunately, the student responded, "So 6 centimeters, right?"

Now the teacher could do an accurate diagnosis. The problem was not in finding the answer - it was interpreting the answer. "This is 1/2 an inch (holding his thumb and index finger close together). 6 centimeters would be more than two inches (expanding the distance between his thumb and finger). I wonder - were you thinking that 6 inches is half of a foot, so half of an inch is 6 centimeters? (She nods yes.)"

How often do we jump into treatment before doing an accurate diagnosis? I know that it seems inefficient to spend time listening to the student explain "where it hurts," but is it? Drs. Kosowsky and Wen found that it was important for physicians to take more time listening to their patients in order to get their diagnoses and treatments right. The same could be said for teachers.

Thursday, March 7, 2013

Am I getting warmer?

In The Teaching Gap, Stigler and Hiebert examine the details of typical lesson designs found in German, Japanese, and U.S. math classes from the Third International Mathematics and Science Study (TIMSS). A table found on pages 30 and 31 describes three specific lessons and notes whether or not each lesson's features represent the overall teaching in that country. The U.S column looks something like this:

  • Teacher asks students short-answer review questions. (Typical to begin with "warm-up" activity.)
  • Teacher checks homework by calling on students for answers. (A common way to check homework.)
  • Teacher distributes worksheet with similar problems. Students work independently.
  • Teacher monitors students' work, notices some confusion on particular problems, and demonstrates how to solve these. (Typical for teacher to intervene at first sign of confusion or struggle.)
  • Teacher reviews another worksheet and demonstrates a method for solving the most challenging problem.
  • Teacher conducts a quick oral review of problems like those worked earlier.
  • Teacher asks students to finish worksheets. (Unusual to not assign homework.)

My work with teachers brings me into a lot of secondary math classrooms, and I can say that not much has changed in the typical math lesson since the printing of The Teaching Gap in 1999. However, I want to focus on just one aspect of the U.S. lesson, the warm-up.

Because of my own interest in engagement, teachers often ask me to focus on when students are engaged (or on-task) during a lesson and what to do when they are not. Probably the most off-task period during many lessons is the first part of the lesson, the warm-up.  This might be for any number of reasons but I have a few ideas.

First, the students find little purpose in this activity. It is rarely collected, usually graded only as a consequence for causing a disruption, and often disconnected from the overall lesson. Without some purpose, it is difficult for students to engage in a task.

Next, there are times when the task is an extension of current work rather than a refresher. It would be like running a race without warming up. Consequently, some learners do not see themselves as having the potential to be successful with this initial task - a tough way to begin a lesson.

Finally, by sixth grade students are familiar with the design of most math lessons. They know that someone will at some point provide the answers to the warm-up. So some students do not work on the warm-up (off-task) but copy down the answers when they are shared (on-task). Others, work on the warm-up (on-task) but pay little attention to the answers because they already have them (off-task). Either way, this seems like an inefficient way to start just about every lesson.

What do you think? Have I accurately portrayed what is going on during the warm-up in many math classes or is this a straw man? If you agree that the warm-up is in need of a makeover, then perhaps in a future post we can discuss the alternatives. Otherwise, I do not want to waste your time any further - going over something that is not really a problem has no purpose and does not make any sense to me.