Tuesday, March 14, 2006

Critical Thinking in the Classroom

As a member of the Critical Thinking PLC I have been doing a great deal of thinking about how to get my students to question, infer, and apply the knowledge I teach in various ways. Lindsay Donaldson and I have had various discussions about rigor, and high expectations and what these look like in our classrooms. How do we challenge students to not only study and memorize the content, but really engage them in using the content to help them become better problem solvers and thinkers. I always reflect back on the saying, "give a child a fish and feed him for the day, teach a child to fish and feed him for his life." Yes, the facts and vocabulary are essential, but I think my end goal is to teach them to fish (or so to speak). I would like to give my students tools they can apply to all aspects of their lives, tools that expand beyond foreign language, and far beyond my classroom. So my question becomes HOW? How do we teach/grade thinking? How do some of you do it?

Monday, March 13, 2006

My Ears are Ringing

Does anyone else think that high school-aged kids should know when they need to be places without bells ringing throughout the day? A bell ringing every hour does not help prepare kids for life. When was the last time an adult at his or her job (other than those of us in education) had to respond to a bell? It doesn’t matter if you’re a plumber or CEO, being on time is a vital piece to success… and after high school nobody is going to be ringing a bell to remind you to get somewhere. I propose high schools around the country post clocks and daily schedules in their hallways, then get rid of the bell and expect students to show up on time!

Thursday, March 09, 2006

Knee of the Curve

One of the issues I think we need to look at as educators is the accelerating pace of change. I’m reading a book right now that makes a compelling case for the amazing changes that are going to happen in the lifetimes of our students (and, more specifically, within the next 30 or so years).

The books spends some time talking about exponential growth. For those of you who may have forgotten some of your algebra, a simple example of exponential growth is doubling. Start with 1 of something, then double it and you have 2. Double it again and you have 4. And so on. The famous exponential growth example in technology is “Moore’s Law”, where an industry executive predicted that the “speed” of computer chips would double every 18-24 months. The thing with exponential growth is that at the beginning, the growth doesn’t look all that spectacular. While it’s true that going from 1 to 2 is doubling, the absolute increase is only 1. And from 2 to 4 is doubling, the absolute increase is only 2. In fact, at the beginning exponential growth is barely distinguishable from linear growth. The author makes the case that humans are conditioned to view things as growing linearly, because we naturally take a fairly short-term view of things. But the thing about an exponential curve (when you graph it), is that suddenly the curve seems to shoot up – almost vertically. The author argues that we are currently in the “knee of the curve” and that even though we give lip service to the idea that things are changing rapidly, we don’t really have a good intuitive sense of how quickly and how much things are about to change. So, for example, if you have 1 million of something and now double it, you have 2 million – or an absolute change of 1 million.

If we are in the “knee of the curve,” then we are about to see explosive changes in just about everything because of the capabilities of technology. My daughter is in Kindergarten. By the time she graduates from high school, the typical household computer will probably be at least 100 – and maybe as much as 1,000 - times faster than current household computers (and most likely one-tenth of the cost). The Internet – in terms of mass use of it and also broadband access – is still in its infancy. It’s already had a massive impact on all areas of our lives – and we’re still just figuring out how best to use it. Imagine what it’s going to look like in 12 years. At the current pace, the fastest computers will be able to simulate the human brain in 2013. He predicts that between 2025 and 2030 we will be able to upload ourselves into computers. This sounds like science fiction (and there's much more in the book - especially the nano technology stuff), but he has shown a remarkable ability to predict change in the past.

Even if you don’t buy all the predictions, I think there’s no question that the pace of change is itself increasing (that would be the second derivative for all you math folks), and that should have a powerful impact on what and how we are teaching our students. Do you believe that school as we have typically defined it is going to prepare our students adequately to be successful in the 21st century? As David Warlick says:

Never before in the history of the world has a generation been better prepared for the industrial age.
Or, from Tim Wilson:

    • Old teaching methods don’t work with today’s kids. I raised a few eyebrows when I suggested that the act of a teacher consciously deciding not to use advanced technology with his or her students might be considered educational malpractice.
    • The value of factual knowledge is plummeting. I showed how quickly basic facts can be accessed with Google and looked ahead to a day within ten years when all students will carry an Internet-connected computing device with them 24×7.
    • We are in a relevance race. If we fail to utilize new technologies, we risk alienating our students. It won’t be many years before students can homeschool themselves and earn a high school diploma without setting foot inside a traditional school. If schools as we know them are to survive and prosper, we’re going to have to adjust to a world where we’re not the only game in town.
I tried to come up with some choice quotes to leave with the group. Here are two that seemed to go over well:

If your work can be automated, it will be.

And the question of the day:

What are you doing right now to prepare your students to collaborate seamlessly across cultures in jobs that probably don’t yet exist?

So, what are you doing right now to prepare your students?

How Much is Too Much?

Being the math geek that I am, I recently attended a CALCULATOR CONFERENCE! How exciting huh? The conference was held in Denver this year, so it was a great opportunity to be able to attend T cubed.
These sessions gave me an understanding of how to teach using a constuctivist approach and a calculator. One particular session brought up the relentless question of how much "technology" use is too much technology use?
unfortunately, in some of my classes I ask the students to add 19 and 12 and the first thing they do is grab their calculator. I don't know how many times students have come to me and said, "Ms. Korn my calculator doesn't have a fraction button so I cannot do this problem. Or, well my calculator said that that was the answer, it MUST be right!"
I'm stuck between a rock and a hard place. I want to utilize the thought provoking technology lessons and live in the 21st century, but I don't want to give my students the understanding that they don't have to think for themselves. Do any of you have any suggestions as to how much is too much?


I'm curious to know to what extent other departments are cross-curricular. The recent push is for all departments to read and write within their content area. I see great benefit for students to be able to express themselves mathematically. For someone to be able to teach or explain a math concept clearly, they really have to know that concept at a higher level. As a math teacher, if I give a writing assignment, I'm a little out of my comfort zone in grading this in the same way a language arts teacher would grade it. Instead, I look for understanding of the ideas, not so much the punctuation, spelling, structure, or other elements of writing. Honestly, I have a hard time with expressing myself concisely and elegantly (as you can see from this post).

Mathematics naturally lends itself to using science applications or historical references, even music, as a theme for a lesson. But, to what extent can other departments use math in their lessons. I know that at the college level, social sciences use high level mathematics to model data. I just don't think most high school teachers would be comfortable using math at a high level, just like I'm uncomfortable grading a written assignment. How much are we expected to do? Is it enough to just have the students write (or do math) outside of their normal settings?