Education ∪ Math ∪ Technology

Month: March 2011 (page 1 of 2)

What should be on a high school exit exam in mathematics?

Personally, I think an exit exam for school (an exam a student needs to graduate from secondary school) is not necessarily the best way to determine if a student has been prepared by their school. That aside, some of sort of assessment of what a student has learned from their school, whatever form that would take, should satisfy an important criterion; that the student is somewhat prepared for the challenges that life will throw at them.

A typical high school exit exam is testing a student’s preparation for one component of life, specifically college academics. It seems obvious to me that this narrow definition of "preparation" doesn’t actually prepare students for the challenges of life. A student could quite easily pass the NY Regent’s exam in mathematics, any of the IB mathematics exams, their SAT, and any number of other standardized exams, and not know a lick about how to apply the mathematics they are learning in school to solving problems they will encounter in life.

While this shouldn’t be the only goal for mathematics education from K to 12, it seems to me to be a minimal goal, and one which at which we are failing quite dramaticly. Some evidence of this failure is seen by our mostly innumerate public who; lack basic literacy of graphs & statistics, are largely mathphobic, do not understand probability (casinos are good evidence for this), and generally only use relatively simplistic mathematics in their day to day life for problem solving. 

There is nothing inherently wrong with teaching how to do a calculation for it’s own sake, or for sharing some of the beauty and power of mathematics, but it should be framed by the notion that our education of mathematics is intended for a greater purpose. If we only focus on the 4 years people spend in college, we do a disservice to the decades of life they have after college.

It’s Spring!

My mom, my son and I went outside today and looked for signs of Spring together.

Signs of spring Signs of spring Signs of spring
Signs of spring Signs of spring Signs of spring
Signs of spring Signs of spring Signs of spring
Signs of spring Signs of spring Signs of spring
Signs of spring Signs of spring Signs of spring

(click on the photos to view them in a larger size)

We found flowers blooming, buds and leaves on trees, new plants rising out of the soil, and a nest of baby spiders. My son was very interested in all these signs of spring and followed us all over my mother’s property while we searched for more signs of Spring.

My son has the advantage that he has a grandmother with a house on a small island nestled in a forest and with a nice garden. As I walked around the garden, I felt very fortunate to have the ability to explore nature with my son. In our home in Vancouver, there are signs that Spring is here, but they are harder to find amid the concrete jungle. I can’t imagine what it would be like if your home was less "green" than Vancouver. I rememembered, for example, that in New York City that there were a lot fewer green spaces than in Vancouver.

What do we do for children who do not live in places where the coming of Spring (or even the change of seasons in nature) is obvious? How can we ensure that all children get to experience nature?

More importantly, what do we do for children who live in places like this?

Child in slum in Kampala (Uganda) next to open sewage

image credit: gtzecosan on Flickr

I know that our world is not fair, but it worries me that it is becoming less fair in many ways rather than more fair. I worry that the vision I would like to see for our future, where we all live in a sustainable world, is much different than what some of our leaders envision. When I see our own social services eroding, and less concern for the living conditions of people abroad from our local governments, it makes me worry, and wonder what I can do to work toward a brighter future.



Reposted with permission from my school’s monthly magazine, the Imprint.

Stratford Hall is not a school that uses carrots and sticks to get students to perform. Instead, we generally rely on building on students’ intrinsic motivation to learn. Daniel Pink, a researcher in the area of what motivates us all, says (in his book Drive) that when people are working on work “which requires even rudimentary cognitive ability,” they are actually demotivated by reward systems. Instead, Pink suggests, people are motivated strongly by the ability to demonstrate autonomy, mastery, and purpose. You can watch a summary video of his ideas here:


For me, autonomy means that students need to have some choice in what they do. I’ve noticed that my students tend to put more effort into assignments for which they have some opportunity for choice, and the ability to demonstrate their creativity.

For example, we did an assignment at the beginning of Science 8 last year where students had to “use a creative method to help remember the parts and functions of a cell.” Some students wrote haikus, some students did raps, and some students created videos. As the assignment was formative in nature, I never graded the submissions, except to give students descriptive feedback about their work. We shared the work in class. That unit we did a summative assessment on the parts of a cell, and most students achieved a 6 or 7 (note: 7 is the maximum score for an assessment in the International Baccalaureate). What was even more interesting to me was that, about seven months later, one of the students discovered the video of her rap. On her own time, and completely without any push from me, she decided to redo her rap video. She spent another several hours working on her video and then re-shared the new video with the class. Before this exercise, I couldn’t have imagined a student taking a prescriptive assignment and ever giving it another thought.


Mastery means that we want to get better at doing things. It’s fun to become an expert at something, which is why so many of our students practice playing music on their own time. They have complete control over their learning, and they can see themselves improving. I think we do this really well. We have lots of opportunities at Stratford Hall for students to find things that interest them and to follow those interests. We have the PYP exhibition in 5th grade, the MYP personal project in the 10th grade, and the extended essay in the IB Diploma, for example. We also have a rich variety of elective subjects, especially considering the size of our school. These elective subjects are crucial for allowing students to follow their passions and develop mastery.


Purpose is a key element of motivation as well. In schools, for me, this means that the learning students do has relevance, and that there is an obvious result and effect students can see from what they do. For example, Harry Armstrong in grade 11 is working to help run the MUN club. He gets nothing for this (except possibly a small bonus to his likelihood of being accepted to college because of his extra-curricular activities) and it takes a huge amount of time. We were exchanging emails over the weekend about what we were going to do on Tuesday, and it was clear by the discussions that happened during the day that a lot more emails had been exchanged amongst the students that I hadn’t been included on. Harry does this work for the MUN because he sees that he has an important role to play, and that the activity has purpose. He wants the younger students to get better at debating and to understand how the MUN functions.

More generally, we see purpose in our global outreach. Many of our students work extra hard to help make that program function, and, although I know the excitement of going to a far-away place is the draw for some of them, when they come back from their trips it is interesting to see how many of them continue to work hard for the program. The learning doesn’t stop at the end of the trip; it continues, hopefully, for the rest of their lives.

So if we want students to become more self-directed in their learning, and more motivated to work hard to succeed, we need to find ways to give them autonomy, mastery, and purpose.

(Created by a Stratford Hall student in 6th grade)

One way that we do this is through the use of technology. Students are able to practice using technology skills over a number of years, and will master various forms of technology. They are given the opportunity for autonomy through the enormous amount of choice and opportunity to be creative through different technologies. Further, they can see purpose in what they do, given that learning the uses of technology is helping to prepare them for a future outside of our school.

For example, during Arts Week, we had a session on using Google Sketchup to create artwork for video games. Once they had some of the basic skills in place, they were given the instructions, “play with this and see what you can get.” Afterwards, they attended a workshop wherein the CEO of a small special effects company provided some background on what goes into creating special effects for movies, and students could see from the style of artwork he presented that a tool like Google Sketchup could be useful in sketching out ideas for use in movies.

(Created by a Stratford Hall student, 12th grade)

Corner store
(Created by a Stratford Hall student, 12th grade)

There are also some interesting examples of using technology in Photography class, for example, where Mr. Wheeler’s students have no limits to their imagination.

(Created by a Stratford Hall student, 9th grade)

I’d also recommend checking out this excellent video by some of our grade 9 Global Challenges students.

Our words are not enough: It’s time for action

I’m fortunate to work in a school which gets it. We do a lot of the stuff that people on #edchat are describing as innovative, particularly in the area of student leadership and assessment policy. I feel respected every day, and my opinions and thoughts have a real impact on the direction our school goes. I know this is not true for many teachers though, and I hear it through the discussions we have on Twitter. It seems most teachers work in places where they have very little influence on school policy.

We discuss a lot of stuff on Twitter, but given the number of people meeting, and our individual influence, I have often wondered how powerful we could be as an organizing force. I’ve often found #edchat to be a great starter of ideas, but the ideas seem to go nowhere and we often talk in circles without seeing any change. Sometimes #edchat feels like a gigantic echo chamber where we all pretty agree with each other, and find the best ways to share our agreement in 140 characters. 

I don’t want to change #edchat, but I would like to see space for organizing group action we can take, and it seems to me that Twitter would be a valuable tool for doing this. I’ve proposed the #edaction hashtag, where educators can post ideas for action we can take, and then we can meet to decide on actions (and brainstorm future actions) we will take for the week. 

Here are some suggestions of relatively easy actions we can all take:

  1. Talk to a neighbour education and your vision for what it should look like. Listen to their opinion. If you disagree, discuss core beliefs and find out what you agree on.
  2. Write a letter to a traditional print newspaper. We might be firm adopters of the digital world, but many people with influence do not read blogs & follow Twitter. We need to spread our message to a different audience.
  3. Share ideas about education we have in #edchat with your colleagues at school. You don’t have to become an evangelist for #edchat, but we need to see what our non-Twitter educator colleagues think and ensure that when innovative ideas come out of #edchat that a larger community hears them. We need critical evaluation of our ideas as well, and our colleagues are a great source of criticism, and improvement of our thoughts.

Please post other ideas you have for #edaction in Twitter using the #edaction hashtag. Our objective? Take action to transform education.

ISTE 2011 Board Elections

I’m running for the International Society for Technology in Education General Board elections. Their objective is to promote and support the use of technology in education which is one I support largely because I personally support the appropriate use of technology in schools.

When I saw the board elections coming up, I decided to submit an application and nominate myself to the board. My application was accepted, and I’m now on the ballot for the upcoming elections for the position of the International Representative of ISTE. I’m running because I’d like to see some Canadian representation on the board, and because I want to get more involved in the educational technology community.

People who have strong opinions about educational technology should get involved with advocacy groups like ISTE. It is important that we get involved or we risk letting these organizations disappear, which means that educational policy on the use of technology will end up being shaped solely by business interests.

The opposition for my position is Julie Lindsay, who I think would also make an excellent representative for the International Representative of ISTE. Just make sure you log into the ISTE website (if you are an ISTE member) and vote for either of us before April 11th.


If high jumps were run like standardized tests

Howard Kellogg suggested over on the Edutopia assessment forum that "While the "test" may represent the "bar" we have to clear, it is not the "bar" that must occupy our total attention." I think the analogy of clearing the bar is a good one for a number of reasons.

High Jump Meeting 2008

(image credit:Jeanine Besemer)

Imagine you are back in school at a track meet (which by the way don’t happen anymore in a lot of schools because of budget cuts, safety issues, and a narrow focus on math and reading skills) and you have a high jump set up. The bar for the high jump is initially set so that every student has an opportunity to jump over the bar. Students who cannot jump, for whatever reason, do not participate. Over time, the bar is raised until only a few top students manage to make it over, and eventually a tie occurs, or there is a winner of the competition declared. Every child gets to experience some level of success, although for many children this success will still be a relative success as they will naturally compare their ability. In many cases, students actually choose which events they will compete in, and so not every student will even try the high jump event, prefering to focus on events in which they feel more capable, or have more interest in.

If the high jump was like how we run standardized tests, every child would be expected to be able to jump over the same bar and labelled a failure if they don’t succeed. For some children the bar would be set too low, and they would set lower expectations for themselves in the future. For other children the bar is set too high, and they will label themselves a failure. Many of them would not participate in future competitions simply by dropping out of the track and field event. For some children, the entire exercise would be ridiculous because they couldn’t possibly jump over the bar, no matter where we set it. Further, we would judge schools and teachers based on their ability to make kids jump over the bar, without concern about who they are working with. As an aside, some school districts (like NYC for example) would be using a special rubber bar that they can bend and flex to ensure that the "right" number of kids are able to pass it.

Misleading graphs

This graph, taken from Coca Cola’s Water stewardship page, presents a very misleading picture on how effectively Coca Cola has improved their water efficiency.

Misleading Coca Cola graph

This graph for me highlights an important reason that we need to teach critical analysis of graphs and statistics. Do you see the problem with the graph? (Hint: check the scale of the graph).

TIMMS and Universal health care

Here are the top 10 TIMMS rankings for 2010 according to Wikipedia for math, science, and reading.

Programme for International Student Assessment (2009)[1]
(Top 10; OECD members as of the time of the study in boldface)
Maths Sciences Reading
1. People's Republic of China Shanghai, China 600
2.  Singapore 562
3.  Hong Kong, China 555
4.  South Korea 546
5.  Taiwan 543
6.  Finland 541
7.  Liechtenstein 536
8.  Switzerland 534
9.  Japan 529
10.  Canada 527
1. People's Republic of ChinaShanghai, China 575
2.  Finland 554
3.  Hong Kong, China 549
4.  Singapore 542
5.  Japan 539
6.  South Korea 538
7.  New Zealand 532
8.  Canada 529
9.  Estonia 528
10.  Australia 527
1. People's Republic of ChinaShanghai, China 556
2.  South Korea 539
3.  Finland 536
4.  Hong Kong, China 533
5.  Singapore 526
6.  Canada 524
7.  New Zealand 521
8.  Japan 520
9.  Australia 515
10.  Netherlands 508

The countries highlighted in green have some sort of public health care system, either with or with-out a co-pay. Not all of the health care systems are of equal quality, and in New Zealand only hospitals are free (hence the light green shading), not necessarily all of the medical services.

Draw whatever conclusions you like, but at some stage analyzing the data just gets a bit ridiculous.

Race to Nowhere

We had our mock exams today for math. There are a pair of exams students take so that they get a feel for what their real exams will be like in May. At the end of the first exam, we had a break, and during this break, one of the students came up to me as I set up the room for the next set of exams.

“Mr. Wees, I left a note on the test paper I want my teacher to read,” she said tears in her eyes.

I looked at her and could see how upset she was so I asked her how she felt.

More tears came to her eyes as she said, “Not so good. I’m sure I totally failed that exam.”

“Well, it is a mock exam,” I started, but she cut me off.

“But the universities will look at my results from this exam!” she complained.

And there it was, the concern that her lack of preparation for this one exam was going to ruin her life.

I wanted to give her a hug and reassure her, which is what I would have done had she’d been my child. However, I decided a hug would be imprudent and chose to reassure her with my words instead.

“It is going to be okay. You will get into university,” I started. I consoled her and tried to make her feel better about her future. “Remember,” I continued, “universities don’t just look at grades, they look at the whole person. You helped plan a conference! I’m sure that has to count for something.”

“But everyone plans a conference!” she nearly yelled. In her eyes I could see her thinking, Everyone I know is doing such amazing things. How do I stand out?

I challenged her on this statement, “How many people really?” remembering that people often believe their own hyperbole. “How many kids your age have planned a conference?”

“40 or 50,” she said quietly, realizing the ridiculousness of her earlier assertion.

“Out of thousands of students.” I responded, “What you have done is amazing, don’t sell yourself short.”

She seemed a little bit better. “Yah okay, you are right.”

I talked about my own history of being accepted to university late. It wasn’t until June that I received my original UBC acceptance, and not until August 9th that I received acceptance to my teaching degree. I remember the day exactly because it was the same day I went into work and quit my warehouse job.

What I wanted to say was that it doesn’t matter, that she should judge her personal success by her ability to get into university. That there are other ways to be successful, and that many people survive happily in life having never stepped foot in a university. 

Our students today put so much of their focus on being successful, and on standing out from the crowd. Students compete to try and outdo each other, always feeling like it is never enough. Just today one of my students complained that his parents had it easy. “They only had a C average and got into university!” he said.

I watched the movie Race to Nowhere recently. It was a very powerful experience, and it spoke to me on many levels. Here’s a trailer which describes the movie.

The movie shows lots of examples of how US students are over-worked, and most of those examples speak to the Canadian experience of school as well. Kids are developing symptoms of stress very early in life. They lack the time to actually do everything they are expected to do because they are being over-scheduled, and over-burdened with work early in life.

When will it be enough? When will we decide that our emphasis on competition for limited college seats is unacceptable? When we allow our children to just be, and not have to worry about competing for their future?

We need to tell our students that the notion that there are limited pathways to their future success is a myth. We need to show them that success comes in many forms. We need to give them the opportunity to live their lives, rather than our failed dreams.

There are some things we can do we can do as educators and as parents.

  • We can give less homework or end the practice completely. Homework at the elementary and middle school levels is fairly pointless anyway, and at the high school level only shows a modest correlation with success (at least how we measure success in schools currently). Parents can talk to other parents about the harmful effects of homework and take back their family time.
  • Governments can scale back our bloated curriculums. Rushing through content a “mile wide and an inch deep” does no one any good. You cannot learn deeply about that which you are rushed through. Our children are being force-fed content, but are often intellectually malnourished.
  • We can recognize our kids for who they are, rather than for who we would like them to be. Instead of asking your child about school, ask them to join you in doing something, ask them to talk to you about the world. Find out how they feel, and really listen to them.
  • It is crucial that we end the competition. Educators can do this by abandoning failed metrics like traditional grading systems, and parents can do this by advocating for their students. Grades don’t measure what we think they measure in most cases anyway.
  • We need to stop over-scheduling our children. Find a couple of things they really like to do, and give them more free time to just play. Play outside with your children, and learn how to be a kid again. Go camping, ride a bicycle, have some fun. We should not abdicate our responsibility to raise our children to a worksheet or a computer.
  • We should fight for more arts and experiential learning opportunities in schools. It is unreasonable to expect every child to become a scientist or engineer when they grow up. Artistic and creative people are exceptionally important to our well-being as a society. Without the arts, life would be very bland and not really worth living. Imagine if the next generation had no music, no theatre, no movies, no art of any kind? Can you imagine living in a world without art? We need to recognize that for many children, this is very nearly their reality.

What other specific suggestions do you have?

You want feedback on your public education policy? Here’s some feedback.

The Whitehouse has posted a form to gather feedback from parents, teachers, and students. I recommend adding your opinion about education in the United States here. Here is the letter I sent in through the form.

Dear President Obama,

The first suggestion I have is to abandon the notion that every child is going to succeed at college until we solve the problem of poverty at home. If you really want to increase the number of college graduates, and give everyone equal opportunities, your nation’s children need to enter kindergarten at the same stage of development. Some children enter school with absolutely no academic readiness skills.

The second suggestion I have is to find a way to funnel funds from the penal system into education. A high school drop-out costs the US $260,000 over the course of their life-time in additional services, and for this cost, you could send every child in danger of dropping out to private schools from k to 12, or even better, fund public schools at the same levels as private schools.

You need to stop focusing on a bipartisan approach to education. Your Republican libertarian counterparts want nothing less than a complete dismantling of public education, and you cannot compromise on this point. If you lose public education, you lose the ability to transmit American culture from one generation to the next, except through the consumption of media. Given the track record of the media in the US especially, I would not trust them to do anything but control the minds of the youth for corporate interests. Public education is therefore essential, everyone must have an opportunity to absorb culture, and to think and discuss it critically.

College readiness is not going to be done by making kids study on math and reading. NCLB, RTTT are both forcing schools to reduce the amount of time kids spend learning real things, and focus on rote learning. Please don’t try to claim otherwise, this particular message is easy to find in nearly every school in the US. College readiness requires critical thinking skills, which can be found in any subject area, but especially science, humanities, and the arts.

In a nation whose people are the most overweight on the planet, cutting back on physical fitness and other activity programs in schools will lead to greater health-care costs in the long run, as your population’s health degenerates.

Finally, socialism is not a four letter word. The countries with the strongest education systems in the world are all socialist.

Thank you for your time,

David Wees

(A reminder: If you aren’t sure why a Canadian is at all interested in public school education in the United States, remember that my son and wife have US citizenship, and that our local politicians have a habit of watching US education reforms too closely for my comfort.)