Education ∪ Math ∪ Technology

Month: August 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.

Five recommendations for teachers

Here are some recommendations that I think, if you aren’t doing, can really impact your teaching next year.  Please post any other recommendations in the comments below. I have been using all of these (aside from #1 which I only just implemented this year) for the past few years in my own teaching practice and I find they have really helped me improve my teaching.

1. Spend lunch time with your fellow teachers whenever you can, relationships are more important than 30 min of work.

Your colleagues at school need you. You need them! As a profession, we need to step outside of our classrooms for at least part of each day and interact with other adults.

2. Follow the 10 minute rule. If you talk for more than 10 minutes, expect no one to be listening to you.

Adult learners, when really motivated, can focus their attention on someone speaking for between 15 and 20 minutes at most. Your student’s attention span is even less. If you talk too long, your students, your peers, they will tune you out and start daydreaming. So don’t speak continuously for more than 10 minutes at a time, break up your lesson into smaller chunks. Try and speak to the entire class for as little time as possible, and try to spend more of your time engaging with your students 1 on 1 or in small groups.

3. Don’t assign homework, work on sensible projects, assign deadlines. Let students choose what they take home.

None of us likes it when we have work that it is assigned to us that must be done at home. We hate it. Our students hate it. However, most of us will quite happily do some work at home when we are entirely in charge of the direction of our work. Students should have the same opportunity to develop self-direction in their homework. Can you check that they’ve done something? Sure, but try and let them come up with the "what" and try not to make the process punitive. I personally feel that is less important that students do exactly 20 minutes of homework every night from your class and more important that they learn how to take a project and finish it on their own time.

4. Share class notes for your course, even if you require all students to take notes.

The first reason for this recommendation is that it will help your students to improve their own note-taking. They will have a better idea of what they are aiming for because they will have a good model to look at. Without feedback about how well we are doing, we cannot improve what we do!  It is also important to remember that for many of your students, note-taking is a mentally exhausting and difficult process. They literally cannot both takes notes AND understand what you are saying at the same time.  Your students will eventually come up with strategies that will help them learn effectively on their own. For some of your students, they will take notes on everything you do and it will help them. Some of your students will listen extremely carefully, and learn more this way. You can support their ability to retain the knowledge by providing some supporting information aside from their careful attention.

I would share these notes electronically if at all possible, and I would use whomever in the class produces the best notes (or even better, have students produce the notes as a collaborative exercise). Alan November, for example, recommends assigning a few students to the role of scribe, and using Google Docs to allow them to collaborate to build one set of "perfect" notes.

5. Use an online shareable calendar for your lesson planning and share it with our students.

Your students should have access to your lesson plans. They should understand how these are created and be able to look back and see an overview of what you have covered during each unit. Ideally you should have these lesson plans up in advance so you can give students a preview of what is coming. This can also be a great way of ensuring that students who are absent one day have access to the same information that everyone in the class has. These don’t have to be incredibly detailed, but should include enough information that a substitute teacher could follow the lesson plan if necessary.


What does the relationship between higher grades and “success” in life mean?

I’m not really worried about my students’ grades. I might only be concerned if I could establish a clear connection between the grades I assign my students, and their success later in life. I’m much more concerned that my students are successful, so this might the only reason I would change my grading practices.

It’s important here that by successful that I don’t really mean by my standards. I want them to be successful by their standards and to be able to look back on their lives and say, "I lived a good life", whatever that means to them.

I don’t see how what grade I gives them will reflect in their future success. It’s possible that I may close some doors if I give a grade which is too low, or that I may open up unlikely futures if I give a grade which is too high, but at the end of the day it’s not a grade I want to give, it’s the ability to learn.

There are studies which attempt to show a relationship between a student’s grades and their future success in life, as defined by society. It’s my opinion that at best these studies can show that students who receive higher grades achieve a higher level of success as defined by a capitalist system AND even that isn’t a causal relationship, it’s almost certainly just two variables which are both in a causal relationship with a whole another set of variables.

Students who get high grades are probably good at studying, maybe because they get good family support. They may be good at memorizing information, or very carefully following instructions of teachers.  There are a lots of other reasons why they get good grades. Many of these reasons are also things which lead to future success which can be measured.

There are lots of types of success which cannot be easily measured. For example, if someone becomes a fire fighter and is responsible for saving the lives of hundreds of people, I think that person is successful in life. Someone who volunteers their time and helps people find places to sleep and food to eat; they are successful in what they do. A mother or father who knows how to speak kindly to their children and involve them in decisions or a baker who makes the best cupcakes around; these people are successful, but you can’t measure their success with any standardized metric.

It is arrogant of us to assume that we as teachers have that much influence over our student’s lives. While I’ll agree that the influence of a good teacher is significant, there are so many other factors at play as well; we are just one factor among many. We should continue to push our students, and to help them learn and become good people; all of these are still important, but I think we should relax about their grades. They really don’t make that big a difference.

Eight Videos to Help Teachers Get Started Using Twitter

Here are eight videos to help teachers get started with using Twitter. The idea for these videos is to make them short and to the point and provide specific instructions on how teachers can use Twitter.

How to sign up for Twitter

Verifying your email account with Twitter

Customizing your profile on Twitter

How does Twitter work?

Installing Tweetdeck

Customizing Tweetdeck

Finding people to follow on Twitter

Participating on Twitter


You might be a hardcore Twitter user if

You might be a hardcore Twitter user if:

  • you look at 2000 followers as "getting started"
  • you think 5,000 tweets was a long time ago
  • you’ve ever tweeted with people in the same room as you (conferences don’t count)
  • you’ve considered unfollowing your partner because "they don’t post enough useful stuff"
  • you’ve ever spent 24 consecutive hours tweeting
  • you’ve ever tweeted BEFORE calling 911 when witnessing an emergency
  • you use 4 or more different twitter clients on the same computer
  • you’ve tweeted while: parachuting, swimming, skating, spelunking, etc…
  • you recognize when someone is back to Twitter, because "hey, that person is tweeting again!"
  • you miss your Twitter friends after an hour offline
  • you’ve ever attended multiple Tweet-ups in the same week
  • your Twitter withdrawal symptoms, on those rare occasions when they do happen, only take a few minutes to appear
  • you post a question on Twitter and get 500 responses within minutes in 3 different languages
  • you think the definitions on the sidebar of looked better at the top of the column rather than the bottom, and you tweet about your opinion
  • you’ve ever written your own Twitter client because the ones you use "don’t work right."
  • you automatically add hashtags to everything you say in real life (at least in your head)

Please add some more ideas in the comments below and I’ll incorporate them into this list.

Most effective teacher in my friend’s school

My friend, whom I met when I worked in an international school in Bangkok, worked in a bilingual school in Thailand before the school where I met him. He said it was an interesting job, but he was glad to be working at a school with a different emphasis.

The school he worked at had pretty good test results, some of the best in the country. Students would consistently score well on the state standardized tests held all over Thailand. So my friend went to observe the best teacher in the school, as measured by how well her kids did on the standardized tests.

He told me that he watched 2.5 hours of this teacher reading out answers from previous standardized tests. She did nothing else! She didn’t ask any questions, she didn’t check for any understanding from the students, she spent 150 minutes going through questions and their solutions on a multiple choice exam.

What type of education system do you want? Is this what we want to emulate? Time and time again I remind myself how grateful I am to work in the International Baccalaureate framework where the only year I have to worry about a standardized test is at the end of 12th grade. Fortunately the exams at the end of the IB program are at least well written.