Education ∪ Math ∪ Technology

Day: August 31, 2010 (page 1 of 1)

Videos About Problem Based Learning

I asked a question asking if anyone had videos explaining problem based learning or demonstrating it in practice. Within a couple of minutes I had the following responses.


The Avalon School in MN practices student-led PBL. Here are some resources: #edchat

My Project Based Learning (PBL) page (includes rubrics, checklists): #edchat

@davidwees Here you go a PBL Video #edchat

@davidwees Yes – plugging my own blog, but I really love how Susan @ Akron Inventor’s School described PBL #edchat

@davidwees A great video of work we’ve done at our school which touches on some PBL themes. Teachers TV link: #edchat

@davidwees #edchat

"Complete Guide to Project-based Learning" (but links include problem-based learning, too): #edchat

I’ll check these all out more later, but looks like a great collection of PBL videos! Thanks PLN.


The Language of Technology

I was helping out a teacher today who had been excited because he had learned how to do something new on his computer and he got stuck. He thought all of his work had been lost, so he came to me and asked for some help. It turned out it wasn’t lost, he just didn’t know that a small triangle like this one circled below meant that you could click on it and see more information. He was pretty pleased that his problem had a simple solution but a little embarrassed he didn’t know the solution.

He shouldn’t be embarrassed. He is just in the midst of learning a new language.  Technology has a language. The language is represented by the icons we click to open and close windows, the underlined text that tells us something is a hypertext and thousands of other similar nuances. Without knowledge of that language it can be really hard to navigate the technology jungle out there.

This type of problem I’m sure happens all the time. People are embarrassed to ask for help, they think they should know it, they don’t understand why someone can do stuff with technology so easily and they struggle. So the moral of the story is, if you are helping someone out with technology, take the time to teach them the language they will need to work with it.

Every educator should experience being a bad student

Last weekend my wife and I went and took the Seabus across the water in Vancouver to North Vancouver because she heard that someone was offering free Cha-cha-cha dance lessons. We were both excited on our trip over because both of us really like to dance. We brought our son because he likes to dance as well and we thought it would be a good experience for him to learn about a different type of dance.

As the class began I was hopeful and ready to learn. I was actively participating in the lesson and trying to get my feet to move the way the instructor intended. Unfortunately this is when the problems began. After only 3 or 4 minutes showing us the first step, which I knew was no where near enough time for this man with two left feet to learn the move, the instructor moved onto the next step.

I started to feel panicky. Then my son wanted to join us, and suddenly we were improvising steps I had learned yet. Everyone else seemed to be learning at hyper-speed! I was the only one who wasn’t having fun. I was embarrassed. We covered nearly 7 difference dance moves in 30 minutes which was 6 too many for me. I told my wife I wanted to sit down and take a break. I felt inadequate because now I was stopping her from having fun as well. I felt like a failure.

I realized later that I was having the same experience that many of our students have. They often experience failure like this on a daily basis. I can remember many of them entering class with a grin on their face thinking, "this will be the day I master this class." 

I think it will help me become a better educator as I analyze my own learning with a more critical lens and recognize that all of the characteristics of my learners are in me as well. We should think about the experiences we have had as learners and use them to understand the mindsets of our students better.

The Death of the Amateur Mathematician

Knowledge has always been advanced in human culture based on the ideas of others. Our entire knowledge structure today is based on what we, as a species, learned in the past. Each generation learns what the previous generation already knew, and then expands upon this base of knowledge for the next generation.

A problem with this system is that the amount of knowledge one must know before one can make an original contribution to the existing knowledge base increases with each generation. In other words, each generation spends more time than the previous generation learning about existing knowledge before adding their knowledge to the pool.

One way we have already begun to combat this problem is with increasing specialization. Instead of trying to learn everything from the previous generation, each individual learns only what is necessary in order to be able to advance the knowledge base and most individuals do very little to advance the knowledge base themselves, but instead provide the necessary support for our knowledge based society.

Here’s an example of the problem with specialization based on the field of mathematics. It used to be that almost every mathematician was an amateur without a lot of formal university training. Euclid’s Elements was a textbook for mathematicians for about 2000 years. Why was this possible? Well because quite simply, there wasn’t enough mathematics to be learned that you couldn’t contain a significant chunk of it in one book. So being an amateur mathematician was possible because you could read a few books about mathematics and suddenly be able to produce original ideas.

Now there are hardly any successful amateur mathematicians although many people still dabble in their spare time in mathematics.  In this case, I define a "successful" mathematician as someone who has in some way advanced the pool of mathematical knowledge.  The lack of amateur mathematicians is largely due to the fact that in order to be able to advance mathematics, one has to know quite a lot of mathematics, more than is really possible for the typical person. I can’t pick up a few books and suddenly be at the edge of what is known, instead I need years of training before I will reach that point, especially in the field of mathematics.  Most of what we teach at the high school level, for example, is mathematics that was invented more than 300 years ago.

We have essentially hit the limit for what an amateur mathematician is capable of producing. We should expect only highly specialized mathematicians will produce new knowledge in the area of mathematics for the rest of our future as a species. This limit will eventually increase so that eventually no one will be able to add to the field of mathematics.

Increasing specialization can only take us so far in allowing us to keep increasing the knowledge base. Humans are an insatiably curious species, so it is far to assume that for most of us, increasing what we know as a species is a worthwhile goal.  So what are we to do when it consumes an entire human lifespan just to learn enough to be able to add a small piece of knowledge to what we understand?

There are still a few areas where one can begin to add to existing knowledge without an enormous amount of investment in time learning the existing knowledge base. Interestingly enough, one of these is education itself. If we measure the complexity of a subject by the average number of years one needs to go to school before one can add to the existing knowledge base, then the field of education would be considered fairly simple. You can go to school for a mere 5 or 6 years after high school and be able to enter a classroom and learn about how people learn first hand. Add a year of learning about how to do research in the field of education and suddenly you can become someone who adds new knowledge to the pool of what is known about education.

Why is this true? Well, quite simply, as a species we are still mostly in the dark about how we learn, and what the best methods are for helping students learn. We have many theories about how learning works, and how to best apply it, but none of them has emerged as a definitive "best" theory.

Our ignorance as a profession of how people learn is astounding to me. It simply amazes me that we are still having a debate about whether having groups or not is best for learning. We still wonder if the introduction of technology in the classroom is worth it. Should kids be streamed or not? Is assigning homework right? How much homework is best? Home-schooled or not? Remember that we are the same species which is capable of sending someone off of our planet and then bringing them back, and that we did that more than 40 years ago! Why can’t we figure out how to make our education system work for everyone?

Another way to improve the odds of any individual person adding to the knowledge base besides increasing specialization is to greatly improve the efficiency of their education. Even a small improvement in the speed at which people learn the existing knowledge base could lead to years of extra time as a productive mathematician for example. If we knew more about how people learned, we should be able to translate this knowledge into improved opportunities for learning more about how the universe works, simply because we would be providing more time for specialists to work in their chosen field.

Furthermore, many people never have the opportunity to even consider adding to the pool of knowledge because they end their own education out of boredom! How many geniuses have we lost because of the way we constrain people so much in our system of education? Just improving graduation rates and allowing more personalization of education could do a lot to improve the efficiency of education.

We should be investing in our education systems more. We should invest heavily in research in education because that is an area where we can actually make an enormous improvement in the quality of education and eventually in how much we know as a species. A small gain in improved efficiency of our education system could lead to a large gain in end research because of the exponential effect of knowledge acquisition.