The Reflective Educator

Education ∪ Math ∪ Technology

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Month: April 2011 (page 1 of 3)

Donor’s Choose for Global Education

I just sent off this email to someone in the UNESCO office for Global education. What do you think?

Hi there,

I have an idea which I would like to share. There is a website called Donor’s Choose, which lets people choose funding for education projects sponsored by teachers all over the United States. It’s been working well in the US, and you can find out more about it here:

My idea is for a similar website, but focused on education projects all over the world. People could fund particular projects they find appealing directly, and we could help spread the job of keeping the people receiving the fund accountable to everyone who is donating for the projects.

Perhaps with each project, we could send a cheap digital camera, and the people participating could mail back the SD card once they have some photographic evidence of their project being completed. I’m not exactly sure on the accountability model that would be appropriate, but I’d see it as a self-reporting system for project completion tied to the donors themselves being able to report if there is no evidence that a project has been completed.

It would essentially work like a micro-credit system, with lots of small donations being used to fund small projects around the world directly, as opposed large amounts of aid being applied to big projects.

An example of a small project that could be a kick-starter funding is one we are working on through our school, specifically, building a wall for an elementary school in Kipevu. See for some details on our project. We’ve discovered that there are many small schools in the area which also want walls around their grounds, before libraries, computers, electricity, or anything else, they just want their schools to be safe.

The reason why this project would work is that it would add a real human connection to the projects that are being done, one that it is hard for people in the developing world to see. Further, it would focus on projects that people want solved in their local communities, rather than massive aid projects like essentially failing the One Laptop per Child program.

Thank you for your time.

David Wees


I teach kids, not subjects

I listened to a podcast recently where a teacher made the claim that his job is to teach chemistry, not values, and I would argue that if this was really the case, he is failing at his job. If we think of values as being a set of cultural norms, then it is easy to argue that it is impossible to engage in the act of teaching without teaching values.

When we establish classroom rules, we are enforcing our own cultural norms over what is considered appropriate behaviour. For example, if you set the rule that only one person should talk at a time, you are enforcing your cultural norm about respect. If your students come to your classroom without this norm, and you are successful in your indoctrination, when they leave the classroom with the norm, you have taught them a value.

Even if you establish your classroom "rules" democratically, there is still an transfer of values that occurs. First, the value of democracy itself, that it is worthwhile to engage in conversation about things as important as rules, and the rules that are established will likely not reflect the values of an one individual, but rather a blend of the group.

School is filled with hidden values that we pass along to children, as John Taylor Gatto pointed out in his essay, "The Six Lesson School Teacher." Be on time, finish your work, respect each other’s personal space, don’t pick on people, be nice, and many more.

It is impossible to engage in the act of teaching, or even in any communication whatsoever, and not teach values. In every interaction between two or more people, there is an establishment of norms, sometimes explicitly, sometimes implicitly through body language and sometimes through exclusion of people not following your norm.

So when someone says they teach x and not values, I would challenge them and push them to see that this is impossible. We should at least be explicit with each other as educators what our cultural purpose is; the indoctrination of children to our society’s belief system.

A constructivist approach to symbolic logic

First, some background. Symbolic logic is a way of taking ordinary sentences, and turning them into mathematical statements, and then examining the truth value of the sentences by working in the symbolic form. An example of a complex argument which was completed using almost all symbolic logic, see Gödel’s theorem.

Normally when I teach symbolic logic, I stand up at the front of the room and carefully go through each logical connective covered in the course, and the students take notes, then work on some problems to solidify their understanding. Today I decided to try something different.

I went through one example logical connective, specifically the If P then Q connective, normally shown as P → Q. The truth table for this logical connective is shown below.


Update: I’ve fixed the entries in the truth table above (shown in red) as for some reason I put in the wrong values. Thanks to @suburbanlion for pointing out my goof.

We talked about the different possible situations for this one connective, and then I wrote down the other connectives we need to cover for our course, asked the students to break into small groups, and decide in their groups what the truth value should be for these connectives.

Logical connective Sample sentence Symbolic sentence
 ∧  I go to the movies and I eat dinner.  P ∧ Q
 ∨  I go to the movies or I eat dinner.  P ∨ Q
 ↔  If and only if I go to the movies, then I eat dinner.  P ↔ Q
   Either I go to the movies or I eat dinner.  P ⊻ Q
 ¬  I do not go to the movies.  ¬P

 (Symbols may not display correctly in all browsers)

What was interesting was that all but one group came up with exactly what mathematicians have agreed upon for the different logical symbols, which is by far a much higher success rate than I’ve had in presenting this topic. The one group that had a disagreement, only had a problem with one line of one of their logical connectives, so even they were mostly correct. Once the groups were done, I asked them to write down an explanation of why they felt like they were correct, and to check with other groups for agreement. There were some great discussions that happened during class, with students arguing about why there particular version was correct.

One of the reasons that I think this approach works is because I am making more use of the prior knowledge of students. Teenagers spend a lot of time arguing semantics and these types of sentences are frequently embedded in the language they use. So rather than ignoring their prior experience, I make critical use of it in this discussion approach. Further, the number of discussions and opportunities for students to draw connections between what they know already, and these new ideas is increased by the fact that they have more than just me to argue with over the logic. I’ve essentially taken an activity which has students talking in series (each of them taking turns to ask me questions, and to bring up their counter-arguments) to one that has them working in parallel (they talk to each other, and at one time, there are multiple students talking and discussing the point).

Here’s a quote from this class that I think sums up the experience nicely for me as well: "This is fun! I like trying to figure this out."

Richard Feynman on Education in Brazil

Richard Feynman writes:


The lecture hall was full. I started out by defining science as an understanding of the behavior of nature. Then I asked, “What is a good reason for teaching science? Of course, no country can consider itself civilized unless… yak, yak, yak.” They were all sitting there nodding, because I know that’s the way they think.

Then I say, “That, of course, is absurd, because why should we feel we have to keep up with another country? We have to do it for a good reason, a sensible reason; not just because other countries do.” Then I talked about the utility of science, and its contribution to the improvement of the human condition, and all that – I really teased them a little bit.

Then I say, “The main purpose of my talk is to demonstrate to you that no science is being taught in Brazil!”

I can see them stir, thinking, “What? No science? This is absolutely crazy! We have all these classes.”

So I tell them that one of the first things to strike me when I came to Brazil was to see elementary school kids in bookstores, buying physics books. There are so many kids learning physics in Brazil, beginning much earlier than kids do in the United States, that it’s amazing you don’t find many physicists in Brazil – why is that? So many kids are working so hard, and nothing comes of it.

The obvious parallel to draw here is that Science and Math education in the United States from K to 12 (and to some degree other places in the world, like Canada) suffers from the same syndrome. Much of science and math is “taught” but not much of it is learned. If you argue with this premise, you need to ask only a few questions to convince yourself that this is true.

Who uses scientific reasoning and experimentation in their day to day life to solve problems? Who uses mathematics as a tool to solve and explore the richer problems of our world? The answer is, unfortunately, an abysmally small number of people. Such a small number of people in fact, that very few of them are in positions of power and authority, and much damage is done by people who do not understand science and math deciding on educational policy.

Only 14% of US citizens (compared to 59% of Canadians) believe that “humans being have developed over millions of years from less advanced forms of life, but God had no part in this process.” Most people you ask believe that the reason we have seasons is because Earth’s distance from the sun varies during the year. Almost no one uses algebra or calculus in their daily lives to solve problems, and even something as simple as the Pythagorean theorem is rarely used. Quite simply, the general population of both the US and Canada is largely ignorant of how science and mathematics is useful in their lives.

(This video is from 1980, but my guess is the results still hold true)

The fact that the US has such an innumerate and scientifically illiterate population is due to nothing else but the poor quality of science and math education over the years. I don’t blame science or math teachers (much) for this problem; in my opinion, it is a problem of a curriculum which attempts to squeeze too much into a few years, and which relies on regurgitation of facts as the primary means of assessment of understanding, rather than any other form of assessment. Further, in many schools experimentation and exploration of ideas is completely gone from the curriculum as the schools attempt to meet requirements of state and federal curriculums.

Everyone I meet falls into two classes of people; those who liked mathematics in school, and those who hated it. From personal experience, the latter group vastly outnumbers the first group, and almost everyone in both groups is pretty feeble at recognizing mathematics in the real world. Neither of these groups has been served by the education they have received.

We rely on a type of pseudo-teaching of ideas in science and math too much. Students can tell you that “the slope of the line is equal to the rise over the run” but couldn’t give you a single practical application of slope if queried. Students can list off the parts of a cell, but given an organism under a microscope they’ve never seen before, they would be hard-pressed to identify those parts of a cell in that organism. We’ve built a generation (or 4) of people who might be able to describe science and math in terms of other simpler mathematical concepts, but who could not identify those concepts in their immediate surroundings, and certainly never apply those concepts to the problems they face in real life.

For example, as I was walking on the street, I heard a man say to another, “That’s why I play blackjack. Cause if you play it right, the dealer busts every time.” This kind of misconception accurately represents the typical person’s understanding of probability, which is to say, not much. Casinos and lotteries get rich because of the ignorance of the people who play.

Why do we insist on teaching using methods which do not produce what we should want as a society; a public which sees the value in the “universal language” of the universe, and uses it on a regular basis to solve problems?


Electronic Textbook reader

I’m in contact with a company called Active Textbook which aims to produce an electronic reader and a platform for sharing pre-existing content in web ready format. Currently their technology uses Microsoft Silverlight (use Moonlight beta on a Mac) but I asked about moving to HTML 5 and the company spokesperson said that this is in the works.

Here is an example (it will take a while to load, and you may need to install Silverlight first):

What does math in the real world actually look like?

This is a great video from the Alberta Ministry of Education. I definitely see it as explaining the purpose of mathematics in a way that kids can understand. I also think it gives mathematics educators something to think about when they watch it. Have they done enough to embed what they are teaching in contexts which are recognizable and important to their students?

TED application – Math in the real world

I saw on the TED blog that they were accepting applications to do a TED talk in May in Long Beach, so I thought that it was worth trying to create a video application. This isn’t the most amount outstanding video I’ve created, but give me a break, I had limited time. 🙂


Here’s an idea: How about each of your students creates their own TED-style 1 minute video to talk about their big idea?

Transformation of education through communication

If you look at every major change in our society, you will find that communication between individuals was instrumental to the change, and that in many cases, a change in how communication occurred between individuals precipitated the change itself. For example, the revolutions in Egypt and Tunisia, and the current revolution in Libya are all the result of the masses who believe in change being able to communicate that belief through social media.

What is strange about education is that by and large we know an awful lot as a profession, but the rate of change is glacial. We actually know a tremendous about how kids learn best, but schools keep re-inventing the wheel every time they encounter a new problem. Why is this? My thought is that while there are lots of great ideas out there in education, they are not generally communicated well.

So if we want to institigate change in education (and I think we do need a change) then we need to change how communication happens in schools. As much as the people reading this blog believe that change is around the corner in education, the vast majority of people involved in education are not on Twitter, they don’t read blogs, and we are lucky if they are even on an email list of any kind related to education.

We need to bring down the barriers to using these types of communication tools if we want to deepen and enrich the conversation about education. Some of the barriers include:

  • Knowledge:

    Most educators don’t even know that educators are using Twitter and other social media tools to connect about education. We can counteract this by being proactive and talking about these tools with other teachers. Be brave and introduce teachers you meet to productive uses of social media.

  • Access:

    Many educators work in areas where they don’t have access to the tools themselves because they are blocked at their workplace. It is ironic that in places that are supposed to foster learning, that some of the best tools available for learning are blocked. Here the problem is administrative, and if your school district is one in which social media is blocked, it is worth having a conversation with your administrators about its potential value to their district.

  • Time:

    It is hard to convince someone who is already overworked that social media isn’t just going to be "another thing" to add to their pile. Take the time to show how to use Twitter as a search engine, and as a time-saver. Show them how they can engage with other educators to brainstorm lesson plan ideas, and just generally save themselves time re-inventing the wheel. Savvy school administrators could even build time into schedules expressly for the purpose of communicating & sharing with other educators.

  • Permission:

    In many school districts, there is an explicit policy against using social media professionally. In others, there is a fear of using it incorrectly and having it destroy your career. This problem can be best mitigated by sharing the stories of the thousands of educators who are using it effectively (while keeping their jobs). Point out that the people who have lost their careers as a result of social media were actually involved in some pretty stupid activities already. Make the recommendation that if you wouldn’t say it to your boss, you probably shouldn’t put it in print. We also need to develop policies around social media which recognize that teachers are learners too, and that people who are learning make mistakes.

  • Fear:

    Educators are afraid someone will steal their ideas. They are afraid that someone will reject their thoughts and dismiss them out of hand. When you visit stories on major news websites about education, and read the comments, you can see that a lot of their fear is justified. How can we combat this? I think we need to build a sphere of trust wherein educators feel comfortable sharing and know that at least within this sphere, they will at worst receive constructive criticism.

It is my opinion that if a school district adopted a social media policy which was intended to promote open dialog between the educators in their district, and then encouraged educators to use social media responsibly to communicate with each other, that this would be far more effective in terms of changing their school system than any professional development day could ever be.

The effect of communication tools on education

It should be clear to anyone reading this that the type of tools we have for communication strongly affect how education occurs. If we examine communication tools over time, we can see two trends in our communication tools.

History of communication tools

The first is that our communication tools have evolved from more personal and intimate, to greater mass distribution of information and less personal engagement. When we communicate via body language only, you have to be fairly close to the person, and you need some understanding of who they are for the communication to be successful. At the other end of the extreme, the Internet requires almost no intimacy, no personal connection, and only a modicum of cultural understanding.

Evolution of communication tools

(Graph not to scale)

The purpose of the graph above is to illustrate that the communication tools we have invented tend to allow for both a greater communication speed, and for a greater reach. I can  talk to a few hundred people from on a top of a hill, but I can potentially reach millions of people through a single tweet. The effect of this trend on education is that the flow of information, once painfully slow, is now more like a fire hydrant.

Another interesting trend is the evolution of communication tools in such a way as to promote the more personal, more intimate communication but at a greater distance. For example, tools like Skype allow for a greater degree of interpersonal communication than is possible through sending text messages back and forth. If this trend continues, we will soon be able to communicate in 3d holographic projection to people across the planet, allowing for the subtlety of body language to be included as part of our communication. We will be able to have truly intimate and personal conversations with people who we have never met in person.


A flaw with the current system of mass communication is that most of the "communication" that is occurring is just noise. There is vastly more information than one can ever possibly digest available through the web, and a huge amount of that information is just garbage. There may be 35 hours of video footage uploaded to Youtube every minute, but how much of it is worth watching? How much of it is family vacation videos?

If the flow of information through the interactive web is like a fire hydrant, then it should be the role of schools to help our students develop tools for filtering that flow.

We must also recognize that if the intimacy of the classroom can be replicated through the Web, that it will be, and that educators will need to adapt to this change. Already schools have seen their traditional classroom students start the migration toward online learning. While I still think that services like the Khan Academy and MIT’s Open Courseware are poor substitutes for the intimate classroom experience, I do not think we are far away from the kind of technological changes which will place a huge strain on the typical didactic classroom model.

I think we need to ensure that the importance of personal and intimate communication, which has always been important to us as a species, is not lost during this transition. While our communication tools may change how and where we connect with our students, we must remember that our value as educators lies not in what we know, but in the relationships we form with our students.

Here is my presentation from the Digital Learning conference in April.

Have you been cyber-bullied?

I sent out a request for responses to a cyber-bullying survey a number of weeks ago, and I’ve finally gotten around to analyzing the results. I asked two questions: "Have you been cyber-bullied?" and "What is your age?"

Pie chart - Have you been cyber-bullied?

From this chart we can see that half of the people who responded indicated that they have never been cyber-bullied, and that about one third indicated that they had been cyber-bullied, and a final sixth of the participants were not sure. This seems to match the results of the 2010 Pew survey of 800 teens.

Cyberbullied - bar chart with age and results

From this chart we can see that the peak age of the people who responded was 13 or 14 and that there aren’t any obvious trends. I’m sure that we have a strong selection bias that skews our results, as only 124 people responded, and those people who responded are just people who I was able to reach with the survey via Twitter and my school’s email. I was hoping for a much larger pool of data with which to work. If you are interested in further research, see this Wikipedia article for summaries of larger research studies.

There were a few interesting comments added to the survey. At least one person (over the age of 18) said "Boo hoo, block and move on" which really has a complete lack of understanding of the seriousness of bullying. Obviously not every young teenager is going to be able to just block the offending person and move on, as they may also be cutting out a significant portion of their social circle.

These results do suggest that cyber-bullying is a problem, but that it is not a significantly bigger problem than face to face bullying ever has been. However, since we have historically had problems combating face to face bullying, the significance of these results is that the online social spheres have similar risks as the traditional social spheres. From this you can conclude that if your school has a bullying problem in the playground, they have a similar bullying problem online. My suspicion is that the best way to spot cyber-bullying is through the same channels we spot more traditional playground bullying, by watching the social interactions of the teenagers involved.

How do these results fit in with what you know is happening at your school?