Education ∪ Math ∪ Technology

Month: March 2013 (page 1 of 2)

We cannot underestimate the importance of context

My youngest son recently learned how to walk. He’s certainly not an expert by any means, but he can now toddle around for 10 to 12 steps at a time and not fall down. I noticed something strange about his walking though – he makes no effort to avoid obstacles in his way.

This is strange because I remember when he first learned to crawl a few months ago, he had the same problem, but he fairly quickly learned how to crawl around the obstacles on the floor and therefore avoid them.

There are two possibilities – he knows about the obstacles and chooses not to avoid them because he wants to focus on keeping his balance, or he doesn’t notice the obstacles at all. The first possibility seems unlikely to me since he normally hesitates in his walking when he seems uncertain and he does not even look at the obstacles at the floor. The second possibility seems more likely to me.

How is it that he can not notice obstacles while walking that he avoids easily while crawling? My theory is that there are three factors at play – first that his perspective is different while walking than while crawling and that he is not able to adjust his internal model of "looking for an avoiding obstacles" because of this. Another is that he does think that he should worry about obstacles while walking because it does not occur to him that the obstacles he successfully avoided while crawling could be obstacles while walking. Finally, walking probably takes my son quite a bit of cognitive effort. He has to spend his time thinking about balancing, and he is unable to think about all of the other things that could happen while he is doing this. Walking is not something for which he has automaticity. All of these reasons are results of a change in context between crawling and walking.

The space is the same, the obstacles are the same, but the context is different, and this makes the tasks different enough that even what seem like simple obstacles to us are currently challenging for my son.

We need to consider this issue for our students as well. How often do we see them unable to solve problems in an even slightly different context that they seemed completely capable of solving before?

It’s not just music

Listen to the two songs linked below, and ask yourself, is this the message we should be sending our children?

After the horrible rape case in the now infamous town of Steubenville, I have been thinking about what could possibly have made this act seem justified by the boys who committed it, and although I do not think we can lay all of the blame on popular media, as it is a reflection of our culture, some of the blame must lie there.

I listened to this song, at the request of my son, and I was quickly horrified. It reminded me of a song I knew growing up, and how my uncritical mind had been deceived into liking this song, until a friend quietly pointed out (while I was singing the song) what the lyrics to the song meant.

I remember the moment that opened my mind, and started me thinking about music more critically.

My friend and I were walking from Koerner Library to the Student Union building on UBC campus, as part of our weekly Safewalk shift, and I started to hum, and then sing. As I got to "how easy it would be to show me how you feel", my friend interrupted me and asked, "Do you know what those lyrics mean?" I stopped singing, and said, "Uh…" I was slightly embarrassed. "That song is about pressuring girls to have sex with their boyfriend," she continued, "Are you sure you want to be singing it?" I paused, and ran through the lyrics in my head, and realized just how right she was.

I will admit that at the time I had more than my fair share of naïveté, but I believe that this is a common experience for many to not think very critically about the music to which they listen (or any media which they consume, for that matter).

I certainly know that young children, like my son, are especially unlikely to think critically about music. I wonder where my son learned of this song, and who introduced it to him and I wonder if they talked about the meaning of the song. I am especially worried that songs like this will influence his developing perspective on women, and his later relationship to them.

I would like my son, and all other boys, to grow up to be men of which we can be proud. Please, if you are exposing children to music or any other media, please, please think about what music to which you expose them, and ask yourself, if this child accepted the message of this music whole-heartedly, would this make them a better person?

Ten commandments for teachers

  1. Do not feel absolutely certain of anything.
  2. Do not think it worth while to proceed by concealing evidence, for the evidence is sure to come to light.
  3. Never try to discourage thinking for you are sure to succeed.
  4. When you meet with opposition, even if it should be from your husband or your children, endeavour to overcome it by argument and not by authority, for a victory dependent upon authority is unreal and illusory.
  5. Have no respect for the authority of others, for there are always contrary authorities to be found.
  6. Do not use power to suppress opinions you think pernicious, for if you do the opinions will suppress you.
  7. Do not fear to be eccentric in opinion, for every opinion now accepted was once eccentric.
  8. Find more pleasure in intelligent dissent that in passive agreement, for, if you value intelligence as you should, the former implies a deeper agreement than the latter.
  9. Be scrupulously truthful, even if the truth is inconvenient, for it is more inconvenient when you try to conceal it.
  10. Do not feel envious of the happiness of those who live in a fool’s paradise, for only a fool will think that it is happiness.

From Bertrand Russell’s "A Liberal Decalogue" via the Brain Pickings blog.



Migrating away from Google Reader

A few weeks ago I read someone (whom I cannot remember…) predict that Google Reader would soon disappear, and this person was right. Fortunately, I took the advice at the time and started looking into alternatives as Google just announced that Google Reader will be shut down in July.

First, I exported all of my RSS feeds from Google Reader. To do this, I needed to find the export option, which is hidden in the settings page.

Find the settings page



Next, I had to find the export link. I noticed right away that this exporting process used to be a LOT easier. Sigh.

Export link


Clicking on this link took me to a sign-in page for Google’s Takeout service (which seems to be a utility for exporting any of your data out of Google). After a couple of failures, I finally managed to download an archive of my Google Reader information.

Actual export page


Clicking on Create Archive generated an archive of my RSS subscriptions, which I then had to download and extract (I recommend 7Zip for this). Inside this archive was the one file I wanted, the OPML file for my subscriptions. I knew I would need this file so I could import my subscriptions into another service.

Subscriptions file


Once I had a copy of my subscriptions in place, I looked into desktop alternatives, and found Thunderbird, Outlook, RSS Bandit, and RSS Owl. After installing RSS Bandit and successfully importing all of RSS feeds into it, I realized I did not want a desktop application because I would end up only ever being able to read my RSS feeds from that specific computer. I really appreciated the portability of Google Reader, and this was one feature I didn’t want to lose.

I had heard about other online RSS readers, but after Google Reader announced that they were shutting down, I decided that I would prefer to try hosting my own online RSS reader. I had a suspicion that some open source projects would exist, and with some minimal searching, I found three options: Tiny Tiny RSS, Selfoss, and RSS Lounge.

I tried to install Tiny Tiny RSS, but for some reason it failed, and so I quickly gave up on it (given I had other options). I then looked at some screen-shots of Selfoss and RSS Lounge, and decided I liked the look and feel of RSS Lounge better, so I installed it instead.

Installing RSS Lounge was relatively easy as web applications go. I had to extract the files from the archive I downloaded, and uploaded them to my site using Filezilla into a subfolder on this website. Next, I created a database for RSS Lounge using Cpanel, set the file permissions as per the installation instructions, and then navigated to the online installation page.

Installation page


I entered in the information required for the database, and chose a username and password for the site. I also chose to keep the public access option unchecked, not because I am particularly concerned about other people knowing what I am reading, but because I want to keep extra traffic to my site to a minimum. Next, I logged into my new RSS reader, and found the OPML import option. I selected my subscriptions file and uploaded it to the site.

OPML import


At first, I thought nothing had happened, until eventually the page refreshed and I saw a progress bar filling up. It took a very long time for all of the subscriptions to be updated, as each of the 729 blogs I am currently subscribed to had to have it’s RSS feed fetched, parsed, and "new" entries added to the site.

Once all of the RSS feeds were updated, I had over 4000 "unread" posts. Of course, I had actually already at least scanned all of these posts in Google Reader and marked them as read, so I started to mark them manually as read, 50 posts at a time. After 3 or 4 minutes of clicking, I gave up, and ran the following command in my database which updated all of my unread items as read. Whew!

MYSQL command


I’ve now completely migrated away from Google Reader, and have access to my RSS feeds in an online program that I can control myself. The only reason I’ve used Google Reader since is to verify that my online reader is in fact fetching all of my feeds, which it apparently is.

RSS Lounge working

Learning to walk

My young son just started walking a few days ago. You can see from this video that he is still somewhat unstable but that he is able to do the essential mechanics of walking.



The thing is, he did not learn how to do this in a vaccuum. He had significant support from us, both in creating a safe environment for him to practice in (we added a rug to our living room and removed any sharp edges from his reach) and even helping him walk around by holding his hands. Most importantly, we modelled what walking looks like every day of his life so that he has a clear sense of the goal.

Walking is more efficient than crawling around, once you are proficient at it, but there is this awkward stage of learning how to walk when babies fall down a lot, cannot move very quickly, and when walking is actually not a very efficient mode of locomotion. If their parents did not walk, babies would not spontaneously learn how to do it on their own. They require models of what walking proficiently looks like so that they have a reason to continue to practice through the very inefficient early stages of learning how to walk.

Why then do we expect children to learn anything else when it is not modelled? Let us be clear here – telling children how something works is not modelling it. If we want children to learn how to think like mathematicians, for example, then we need to model how mathematicians think and act as mathematicians do.

Become a mathematician

I posted this on Twitter a few weeks ago:

In response, someone asked a very sensible question; how do I do this?


Here are some ideas.

  • Find an area of mathematics with which you are not currently very familiar, and start exploring it. This might look like a combination of reading what other people have written about this topic, and experimenting with it yourself (mix and match according to your preference). One excellent starting place here I recommend is Paul Lockhart’s Measurement book. Another area of mathematics (or that uses mathematics) that I recommand all math educators learn at least a little bit about is programming.

    Alternative: take an area of interest and see if you can develop your own mathematical framework around it. After all, no mathematical framework existed until someone started exploring patterns and the relationships between objects and then creating a language to describe these relationships.

  • Solve the challenging problems from whatever textbook you are using. Don’t rely on the answer key! Ask for help from colleagues if necessary. Getting stuck will help you develop empathy for your students when they get stuck. Try and reflect on how you got "unstuck" and help students learn this process. Another source of challenging problems: past mathematics contests.
  • Explicitly look for mathematics. Keep a journal of the mathematical ideas you find. Share what you find with others. Incorporate whatever you can into your classroom. See if you can apply mathematics you know to solving some of the problems you encounter in your daily life.

Social media

Tweet distribution
(Image source: Twtrland)


The image above is a pie chart of the distribution of the types of tweets I have. Notice that the bulk of my tweets are replies. If you aren’t having discussions via the media, or not very many discussions, then it’s not really social media.

Preparing Students for an Uncertain Technological Future

I wrote this article for our parents in our school’s monthly magazine a few months ago, and realized I had not yet shared it here.


(Image credit: Will Lion)

No one knows exactly what form the technology of the future will take, although there are those attempting to make predictions. Ray Kurzweil, a futurist, has this to say on the accelerating rate of change of technology:

Now back to the future: it’s widely misunderstood. Our forebears expected the future to be pretty much like their present, which had been pretty much like their past. Although exponential trends did exist a thousand years ago, they were at that very early stage where an exponential trend is so flat that it looks like no trend at all. So their lack of expectations was largely fulfilled. Today, in accordance with the common wisdom, everyone expects continuous technological progress and the social repercussions that follow. But the future will be far more surprising than most observers realize: few have truly internalized the implications of the fact that the rate of change itself is accelerating.

We do know that new technologies impact our society in profound ways. Of this issue, Neil Postman, a media theorist, said this of technology change:

Technological change is not additive; it is ecological. I can explain this best by an analogy. What happens if we place a drop of red dye into a beaker of clear water? Do we have clear water plus a spot of red dye? Obviously not. We have a new coloration to every molecule of water. That is what I mean by ecological change. A new medium does not add something; it changes everything. In the year 1500, after the printing press was invented, you did not have old Europe plus the printing press. You had a different Europe. After television, America was not America plus television. Television gave a new coloration to every political campaign, to every home, to every school, to every church, to every industry, and so on.

The introduction of the car influenced both how and where we live, and the environments we live in. The television radically transformed how information and culture are transmitted in our society. Airplanes changed where we travel, and how far away from our extended families we are willing to live. The Internet is in the midst of transforming every aspect of our society, from how we shop, to how we learn new things, to how we work. These disruptive technologies could not have been predicted 120 years ago, and we are still feeling the ripples of the changes these technologies have wrought on our society.

If we know that an unknown change is going to greatly influence our students’ lives, how do we prepare them for it?

The first key to preparing for an uncertain future is adaptability. One has to be willing to explore new technologies and see how those technologies influence us. This is one of the strengths of our ‘bring your own computer’ program. Students see that we accept a wide variety of different computers, and can often be seen exploring and sharing each others’ technology. In this way, they learn that computers are not about one model, or one brand, but instead about the functionality of the computer.

The second key to preparing is critical thinking. This is part of the purpose of the IB education our students experience. They learn to question everything. They learn not to accept ‘facts’ at face value, and to recognize that people use facts to represent their perspective on an issue. The same thing is true of technology change. Most people see technology as this magical thing that influences and improves our lives; our students will hopefully see technology as a thing to be examined and critiqued. The critiques students learn how to do in their IB History class will help them critique their own use of technology. They will hopefully be able to ask two important questions of each new technology they encounter: what abilities does this technology give us, and what does it take away?

A third key to preparing for the future is balance. We are not a technology school, we are a school that uses technology. Our students learn a wide variety of different tools, but they also learn, through our Outdoor Experiential Education and our Creativity, Action, Service programs, about the balance necessary to have a successful life. Our hope is that students will be able to apply this understanding of balance to all aspects of their lives, including their use of technology.

Our students face an uncertain future as our society adapts to as yet unknown technologies. They may see the introduction of flying cars, microscopic computers, artificial intelligence, and other technologies that we cannot even imagine. They will likely experience more radical changes in our society than all of the most disruptive technologies from the past century have managed to do. Our hope is that the education they experience at Stratford Hall helps prepare them for these changes.

Assessment for learning

The director of our senior school, Brad Smith, is doing a workshop today in our staff meeting on assessment for learning. He’s found the following quotes, which he wants to use in his presentation. I’m helping him edit his presentation (since I have time, and he does not), and I’m hoping to find some photos or other prompts which describe these statements to include in his presentation.


Many argue that “Formative Assessment” is a misleading term and is open to a variety of interpretations. “Assessment for learning” may be preferable and requires 5 elements to be in place:

  1. The provision of effective feedback to students
  2. The active involvement of students in their own learning
  3. The adjustment of teaching to take into account the results of assessment
  4. The recognition of the profound influence assessment has on the motivation and self-esteem of students, both of which are crucial influences on learning
  5. The need for students to be able to assess themselves and understand how to improve

Dylan Wiliam


When a teacher teaches, no matter how well he or she might design a lesson, what a child learns is unpredictable. Children do not always learn what we teach. That is why the most important assessment does not happen at the end of learning – it happens during the learning, when there is still time to do something with the information.

Dylan Wiliam, 2011


The worst scenario is one in which some pupils
who get low marks this time
also got low marks last time
and come to expect to get low marks next time.

This cycle of repeated failure
becomes part of a shared belief
between such students and their teacher.

Black and Wiliam, 1998


The more you teach without finding out who understands the concepts and who doesn’t, the greater the likelihood that only already-proficient students will succeed.

Grant Wiggins, 2006


The initiate-respond-evaluate cycle:

I’ll ask the question,
a few of you will answer
for the entire class,
and we’ll all pretend
this is the same thing as learning.

Fisher and Frey, 2007


If students left the classroom before teachers have made adjustments to their teaching on the basis of what they have learned about the students’ achievement, then they are already playing catch-up. If teachers do not make adjustments before students come back the next day, it is probably too late.

Dylan Wiliam, 2007


For teachers, getting annual test scores several months after taking the test and in most cases long after the students have departed for the summer sends a message: “Here’s the data that would have helped you improve your teaching based on the needs of these students if you would have had it in time, but since it’s late and there’s nothing you can do about it, we’ll just release it to the newspapers so they can editorialize again about how bad our schools are."

Doug Reeves, 1998


If you know of any photos or visual prompts/diagrams which you think may be useful, please let me know. His workshop is this afternoon, but I’m sure the resources will be useful another time as well. If I find resources which are useful, I’ll share them here.