Education ∪ Math ∪ Technology

Month: January 2011 (page 2 of 4)

Clark Kent or Superman? Why you should blog

Blogging is like becoming a super-hero. It is a costume you wear and while you are in this costume you can say almost anything and speak your thoughts in ways you would never do while at work. You can choose a pseudonym, design the appearance of your costume, and feel like you have a kind of imperviousness if you choose anonymity. Even normally mild-mannered people can have their ferocious opinions shared and scrutinized.

You are a superhero while you blog because you give a voice to ideas that would otherwise remain trapped in your head, and through the proliferation of ideas will eventually come about the change our society so desperately seeks. In some areas of the world, just having a blog is considered a an act of heroism as the state seeks to control the minds of its citizens. When you blog, you become larger than yourself. You become a symbol of a movement, and a leader. You become a risk-taker and an adventurer.

When you go to work, of course, you shed this costume and become like Clark Kent. While secreting recognizing the inadequacies of the system, you follow orders and act meek to preserve your job and your public identity. You might have some small acts of rebellion, but by and large, you follow orders and lay low. Inside you might be a super-hero, but to everyone else you are merely ordinary. No one blames you for being Clark Kent at work.

There are many of us who have yet to done our costumes and join in sharing our thoughts. We could use more super-heroes! We need a stronger voice in the blogging community. Become a super-hero today, and start a blog. We need your voice.

School Teaches Obedience

Our current school system teaches students how to be obedient instead of independent. Almost every time our students show even the slightest deviation from the path schools set, we beat them back into line using our bludgeons made of consequences, grades, and self-esteem. I’ve been thinking about this a lot since reading John Taylor Gatto’s essay, The Six-Lesson School teacher so I’m sure that many of the thoughts below are reflected in his essay. What follows are some sarcastic comments about how we strip children of their independence.

Want to go to the bathroom? Oh, you’ll need a hall-pass for that, and don’t try to go more than three times in a semester because We are keeping track.

Want to speak and share your thoughts? We have a roadblock for that too. First you have to raise your hands and We will let you know when you can speak. You can always tell who learned this lesson especially well by those people who raise their hands when chatting with their friends. We choose where you sit too.

Want to display your individuality in your clothing? Be careful! We’ve got rules about what you can wear. We would hate to let give you some freedom of expression.

Maybe you’d like to use your precious time outside of school for other pursuits instead of school? Oh, no! We have that time locked up with homework and school sanctioned sports. If you do not do what we tell you outside of school, we will be sure to put the pressure on through your parents and through our mechanical grading system.

Want to think outside the box? Perhaps come up with a unique solution to a boring problem? You’ll find your grades suffer for that. Write about what interests you and we may have to suspend you from school, and prevent you from seeing your friends. You must write about what interests us, after all we are the gatekeepers of literature.

Get bored easily in class? They’ve got drugs for that. If what Sir Ken Robinson says about the rise of ADHD as you travel East from Ohio is true, then we are literally drugging our kids into obedience. Take the blue pill and slip back into our Matrix.

Got some self-esteem? We’ve got ways to take that away from you too. We will assign grades to your thoughts, give your peers awards for their obedience, and train you to loathe your independence.

If you have dreams for your future, they will in fact be our dreams and we will shatter them with our standardized tests and our common curriculum. We will take away the parts of school you love and drill you until the other part of school becomes repulsive.

Want to diss your school in your graduation speech? Be careful or they’ll threaten to take away your diploma.

Perhaps you’d like to bring your partner to your prom? That’s only okay if each of you has different pairs of chromosomes, otherwise it is immoral and wrong and we will be sure to remind you of this fact over and over again.

Once you enter post-secondary, we will force you into enormous loans, and then servitude to pay off these loans in some job you didn’t want anyway. You believed us when we said college was the only answer and look where that got you! If you choose a different route than this, we will deride you and embarrass you for your choice in front of your peers in our final secondary school assembly.

Many schools unwittingly play a kind of psychological warfare against students. We work hard to ensure adhere to strict guidelines of conformity and use ladders of consequences to chip away at the self-esteem and independence of our children. We make too many choices for our students because of an economic need with our current factory model of schooling to teach each child for the least amount of money possible. We cannot afford to teach each child individually, or to provide them too many choices. Such models of education are not scalable!

The primary way you can help your students turn into independent and capable thinkers is to give them lots and lots of opportunities to make choices. You do not need to specify exactly what they write about. You can let them choose when to use the bathroom, and what to wear to school. You can give them choices about what they learn and when they learn it. You can turn your school into a democracy.


How many hours do teachers work?

I just conducted a very unscientific poll. I sent out a link on Twitter only and asked people who happened to be around how many hours they worked. It’s not rigorous. However, in the limited sample group I have of 85 (update actually 132) educators on Twitter, here are the results as a CSV file. If you haven’t responded to the survey, and want to add yourself, please feel free to do so, but please be as honest as you can.

First, I had to discard some outliers. While I do believe that there are educators who work 100+ hours in a week, there are too few of you, and you are skewing my results. One lonely soul even indicated that they work 168 hours per work, or 24/7.

Number of hours educators work. Elementary: 60.5 Secondary: 58.7 Post-Secondary: 48.4 Other: 61

First, we can see that elementary school teachers work about the same as secondary school teachers. Some people responded other, and they worked 57.1 hours per week (One of the people in the "other" category contacted me to let me know he was an administrator so maybe this is true of everyone in the other category?).

Post-secondary school teachers apparently have it easy at only 47.8 hours a week, but only 8 of them responded so obviously this a pretty tiny sample size. I don’t think we can conclude much from their responses without more data.

Here’s another chart where I’ve grouped the data.

Grouped data, hours educators work

The most important message I think we can get from these graphs is that teachers work damn hard. Look at how many educators work more than 40 hours a week! Over 90% of the educators who responded to the survey indicated that they work over 40 hours a week. I still think the 3 people at 100+ hours of work a week are a bit extreme and might be exagerating slightly…

The next time someone complains to you about how long teacher vacations are, ask them to count total hours worked in a year, not weeks. You’ll come out ahead in that argument for sure.

All I have are questions

I might post on this blog like I know what I’m talking about but each of these posts is a question really, an internal discussion that I share. I’m finding I have more questions than answers now.

The current model of education doesn’t work in my opinion, but I can’t see what should replace it.

The best models don’t look like they are very scalable, and would be difficult for the general public to even understand. The recent uproar in the Canadian media over the simple idea that we should value every child has certainly taught me that we need to do a lot of work educating the public about what we do.

I like using technology in my teaching. It lets me do things and have my students construct meaning in ways that I never could have managed even a few years ago. I am worried however that generalizing what a few teachers do really well can be really damaging when diluted to the general teaching population. Introducing computers in most teachers classrooms leads to mass distraction in my opinion, especially given the lack of training that teachers have with them.

Formative assessment is good for example, and the best educators recognize that we should be assessing our students understanding informally all the time. Some schools have turned this into "thou shalt test and grade thy kids insessantly until their fingers bleed where they grasp their #2 HB pencils," and really damaging students. Using technology ineffectively can similarly turn into a gong show.

Worse, applying this use of technology to every school is incredibly expensive. There are 76.6 million people in some sort of school in the United States alone, if each of these people had a $500 laptop, that would cost the US about $40,000,000,000 to outfit each student, not including the cost of distribution, maintenance, and software which could potentially triple those costs. By comparison this article suggests that to end world hunger, it would cost $195 billion. Given a choice between using my fancy tools with my students, which I LOVE to do, and ending world hunger, even for a year, I’m going to choose the latter. Obviously it’s not that simple, but it gets you thinking, is it worth it?

I’ve read that people think that students should be taking online courses, or moving at their own pace through videos, but this model worries me. I’m worried because I’m beginning to feel more and more that the important parts of education happen between the lines of the curriculum. If students spend more of their time learning in physical isolation from each other, these moments will begin to disappear.

I’m also worried that this will become another way to fleece the public pocket as educational publishing companies move toward a rental model of content and that educators as a whole are not yet ready to embrace the open source movement. We might get locked into a proprietary model before the open content model has gained enough of a foothold. Why is this important? Given the deep philosophical divisions in our society, do you want someone else having even more control over what your children learn? It is a lot easier to delete an "inconvenient" moment in history when all of your information is in digital form. I’m not being paranoid, revisions to history happen all the time in public school textbooks.

Some have suggested that we need to refine the accountability model for education. If we just test the students more carefully, and then use this data to change how we hold teachers accountability, that this will drive educational improvement. Of course this model conveniently forgets the narrative that we’ve been testing our students more and more for the past 20 years and seeing a steady decrease in school quality at the same time. It also forgets that there is an extremely strong relationship between student test scores and their poverty level. Poverty is a result of poor education, is their claim, rather than an effect of a decrease in real earnings, or a widening gap between the rich and the disappearing middle class. The only benefit I can see, as these so called reformers spout their nonsense, is that they have helped crystalize my opposition to the use of standardized tests for high stakes purposes. How did these educators, and many of them are educators although some are not, get so far off track from student learning?

I also wonder about alternative education. I’ve been reading about homeschooling, unschooling, Montessori schools, Waldorf schools, and all sorts of interesting ways to educate people. I’ve read some of John Gatto’s work recently and beginning to wonder if I haven’t done a great deal of evil over the course of my career unwittingly. "Think like I do" I say, and help erode my student’s ability to think independently. How do I balance an obvious need of society for some structure with my belief that everyone needs to be capable of independent reasoning? Gatto has some strong arguments exposing some serious flaws with public schooling and reading them makes me feel uncomfortable.

A year from now I may look at what I’ve written here and think I’m being pretty foolish. Right now though I feel like I have a million questions and not enough time to answer all of them. 


You need to give them the tools

Container of coins

Every elementary school classroom should have about $20 in change. Not fake money printed on a piece of paper, but real money. Yes, some of it will go missing over time, and you might need to lock it up depending on your community, but honestly it’s worth the risk. It’s only $20.

Like it or hate it, money is an integral part of our lives. If you want your students to understand the world, you have to provide them with the tools they need. Your students aren’t going to learn about how to add up change without holding it in their hands.

What is the International Baccalaureate?

I read an article on the Principal’s blog by Mel Riddile talking about the changes the AP is implementing and how these changes will make it more like the International Baccalaureate (IB) program. He asks a teacher who has been fortunate enough to teach both programs for a long time. Her response kind of irked me because she focused almost entirely on what I consider to be the logistical set-up of the IB as compared to the AP, rather than the major philosophical differences, which at least Mel touched upon.

She said:

"The IB requires laboratory work but the instructor can choose which labs will be performed and they must be at least partially developed by the student."

I left a comment on his blog that the IB was about so much more than just a few labs.

There is more of a philosophical difference between the IB and AP as well which Sherry seems to miss. The IB is not about the courses or the content, it is primarily about their mission statement.

"The International Baccalaureate aims to develop inquiring, knowledgeable and caring young people who help to create a better and more peaceful world through intercultural understanding and respect.

To this end the organization works with schools, governments and international organizations to develop challenging programmes of international education and rigorous assessment.

These programmes encourage students across the world to become active, compassionate and lifelong learners who understand that other people, with their differences, can also be right." (from their website:

The IB is about developing a whole student. You can’t just take an individual course and consider yourself an IB student, it doesn’t work like that. Teachers have to frame the curriculum from the perspective of the 10 learner profile traits of the IB (see and watch the video).

Students also do a self-directed course as part of the IB where they all write an academic essay of about 4000 words on almost any topic they choose. They have to show a commitment to learning outside of school in the form of the CAS program.

The IB program is about so much more than just some instructor choice in what labs students do.

Almost all of Sherry’s explanation of the differences between the AP and the IB is about the ways courses are structured and what information was given to instructors in order to prepare them for teaching the course. Only one sentence in mind spoke out to the really big difference between the two programs.

"Obviously, the benefits to the students working in this kind of laboratory situation where problem solving was critical transformed lab days for me and my students."

So the IB is about critical thinking but also about a host other important skills. It is a complete program, not a small part of a larger high school curriculum. A much wider range of students will be successful in the IB program than a full complement of AP courses. The IB is not just the AP dressed in different clothing or wearing a different skin.

It’s The Skills

So a student of mine just mentioned me in this tweet.

Teaching ppl how to use google docs. Never thot Id be using it after high school. Thankyou mr. davidwees

So the background to this story is that this is a student of mine, and that I taught her IB Mathematical Studies and Calculus in school a couple of years ago. The calculus class was taught using much lecture (unfortunately) but had this huge project we worked on about trying to figure out if a mission to Mars would be possible, using some calculus to help answer the question. One of the tools that I taught them how to use as part of this project was Google Docs.

Apparently she is working in a children’s television and thought that they might find using Google Docs useful for writing scripts.

davidwees I'm working at a kids TV company and their writing scripts so I told them that google docs will be very useful and they love it!

So she’s actually using something she learned in my class and applying it to her work. Very cool. Notice though that it’s not the calculus that she’s applying, or the ability to sit in a lecture and listen quietly. Nope. It’s one of the technology skills that I taught her that she is finding useful.

So I decided to ask her if she had used any of the mathematics I taught her. I actually had this student for two courses and one of those courses was an applied mathematics course so you’d think that there might be some chance she’d used some of it. Here’s her response.

davidwees um no, sorry :(

This is just more anecdotal evidence for me that the most important things we teach in our classes don’t lie between the pages of the textbooks we use. It’s the skills, not the content.

Reward Innovators with Responsibility

A problem with education is that we have too many "best practices" and not enough innovation. Once you establish a procedure as a best practice there’s no room for argument about whether or not it works. We should call it a "current practice" instead. Now we have the freedom to explore this practice and confirm whether or not it is actually working, and find new innovations in education.

We need to encourage more innovation in education and explore a wider range of what is possible. People need to be rewarded for their innovation by being given the responsibility to implement it, provided that they can show solid evidence that it works for other educators too. We need more peer review of what we do as educators.

Imagine a teacher has an idea for improvement in their teaching. They try it in their classroom, bounce the idea off of a friend and collect evidence that it works. They convince a colleague to do the same, and show that whatever it they are doing differently works for both teachers. They submit their idea to a peer review panel, which then would make recommendations on what ideas have wider merit. The teacher who had the original idea would then be given the responsibility and the authority to try out their idea with a wider group of students or teachers. Teachers would be rewarded for innovation with the responsibility to see their idea through, and spreading it to other schools where it could also work.

We would end up with a lot of benefits from this system. First, the amount of collaboration between educators would increase. Next, school improvement ideas would spread out of the school in which they are initially implemented. There would be encouragement to share one’s ideas rather than jealously guard them. Furthermore, educators would be encouraged to innovate. It would lead to improvements in education by greatly increasing the pool of talent to produce possible innovations. So many educators come up with awesome ideas that never make it past the door of their classroom.

Let’s turn our system which just uses "best practices" as determined into researchers into one which includes innovations from educators in the field.

Computers should transform mathematics education

Stephen Shankland posted an interesting article on CNET today. Here is an exerpt from his article, which you should read in full. He says:

Clearly, children need some understanding on their own of math, and reliance on a computer has a lot of drawbacks. But computers can also aid those who otherwise would fall by the mathematical wayside, or let people with more advanced abilities bypass drudgery and move on to the challenging material. Graphing calculators can let many students explore curves and functions that realistically they’d more likely ignore if they had to plot them by hand.

My response to some of the negative comments about his article is:

Some of you have decided that using technology to handle calculations in mathematics is going to weaken student’s understanding of mathematics. I have to tell you, our student’s understanding of mathematics, and even the vast majority of people’s understanding of what mathematics is pretty bad. Awful. Horrible. I mean, really, really bad.

Mathematics is not about calculations. Mathematics is about understanding how our world works through the lens of logical reasoning and pattern forming, and then communicating our understanding of that process to other people.

Calculations are a tool in mathematics to understand a process. In my opinion, I want students to understand the processes and ideas that mathematics represents, not the calculations which short-cut that understanding.

Here’s an example that Gary Stager suggested to highlight this problem. Ask a typical math teacher to explain to you why "you invert the 2nd fraction and multiply instead" when dividing two fractions works. Ask them to explain the concept behind "inverting and multiplying" two fractions, and you know what, they can’t. They’ve learned a recipe for doing a calculation but have no conceptual understanding of why that rule works, and these are people who are teaching our children about mathematics!

We need to move away from the mindset that the most important part of the mathematics curriculum we teach is the rote calculations which can generally be done much faster on a computer, and towards the mindset that students need to be able to formulate problems, decide on appropriate mathematics to use to solve these problems, and then do the calculations on an appropriate device, and finally check that these solutions make sense. These are the steps that Conrad Wolfram and Dan Meyer (in their TED talks) outline as crucial to mathematical understanding, and I completely agree.

Mathematics education needs to change. Those people who want a "back to basics" approach and get rid of the calculators seem to think that this will improve the mathematics education in our schools. This is flatly not true.

If you ask a random sample of people, they either "weren’t very good at mathematics" and generally hated it, or a very small minority loved it. This opinion spans all age groups and goes back many years, far before the introduction of calculators in schools. If we judge the success of an educational approach by the number of people who enjoy working in a subject, why are so many people who were exposed to that approach before the introduction of calculators hate mathematics so much?

Maybe we need to rethink our approach?

What works in education

Let’s suppose the picture below represents the possible states schools can be in, with the peaks being "good" places to be and the valleys being bad places to be. We don’t really know yet what variables we are even representing with this picture, in fact it is likely that the picture itself would be better represented in 20 or 30 dimensions, as there a huge number of factors which affect how successful schools are.

Peaks and valleys

(For those of you who are interested, the equation of this curve is z(x, y) = sin(3x) + cos(2y) + 1.5sin(x) – 3sin(0.5y) and it was created using GraphCalc)

The first thing which is clear from this picture is that there are a lot of ways to be a good school. No one formula works, no single arrangement of the variables corresponds to the best solution. Similarly there are a unfortunately lot of ways to be a bad school. 

The next thing I notice about this picture is that it’s not easy to be at the top of one of these peaks. Make a small nudge in policy, lose a key teacher or administrator at your school, and you can quickly move from a peak to a valley, and your students suffer. The valleys are hard to move out of because of the inertia of a bad school and the energy required to overcome that inertia. Educators can literally feel like Sisyphus, pushing their school out of a valley only to see it collapse back down again with a change in district support, funding, or policy.

Worse, this picture changes over time and the peaks and valleys don’t remain in the same places as external pressures push on schools. Outside pressures from society can have huge influences on school. Think about what schools would look like if the Internet had never been invented. Would they need to change that much? What about if the civil rights movement hadn’t happened?

It is also equally possible that two people from different schools could be standing on different peaks and not recognize that each person works in a wholely different but equally successful school. Or that two people could be in different valleys, and what works to improve one school is completely unsuccessful at another school.

The key message here is that there is no one single formula to improve a school. All standardizing curriculum and increasing accountability in schools will do is shift schools in the same direction on this graph. This will work for some schools, and fair at others, and can potentially push successful schools out of a peak.