Education ∪ Math ∪ Technology
In the video below (which was a flash mob performance from our school Stratford Hall, in support of glocal issues around water), the young man who starts the dance off also choreographed the dance, organized the student practices, helped organize the actual event itself (with a fair bit of teacher input) and then took a huge risk and started the dance himself. That’s leadership.
How do you think this video will look on his future resume?
Some highlights from the video above (thanks to @smartinez for sharing it):
Here are ten fairly good points from his talk:
These are some pretty serious problems. What could you do to modify your practice? Should you lecture for an hour? I don’t think so. Instead, I recommend that you cut your lecture to only 10 minutes, on a small amount of material, and then give your students time to practice and engage with the material immediately.
I’ve created a simulation, which vastly over-simplifes classroom dynamics and information flow, in an attempt to look at some of the differences between a lecture style classroom and a cooperative learning classroom.
View this simulation here if you are having trouble seeing it above.
Other than the obvious "you can’t simplify learning that much" comments, please give me some feedback on this system, and what other potential variables should be included. Please also play around with this simulation and explore the differences between the different classroom styles that you see.
In his commencement speech ( story shared by @monsoon0 ) to a Memphis graduating class, President Obama said:
Through education, you can also better yourselves in other ways. You learn how to learn – how to think critically and find solutions to unexpected challenges. I remember we used to ask our teachers, “When am I going to need algebra?” Well, you may not have to solve for x to get a good job or be a good parent. That’s true. But you will need to think through tough problems. You will need to think on your feet. So, math teachers, you can tell your students that the President says they need algebra.
I really don’t get how solving for x in 3x + 17 = 5x + 2 will "help students think through tough problems [in life]" and "think on their feet." I see algebra skills as useful, but not out of context of the types of problems they help us solve. Instead of students learning an algorithm for which almost none of our students will ever get to see a real application; what if we taught students areas of mathematics which had direct application in their lives, and which actually helped them think?
I think that we do need some people who learn algebra in a really deep way, but the type of algebra that people use in their day to day lives is fairly simple, and doesn’t take very long to teach, especially if students see the value in what they are learning. Too long people have learned math because someone said they should.
Well Mr. President, I don’t think that telling my students that just because you think it is useful will mean they will want to learn it. I’m going to keep focusing on presenting the mathematics I teach in the context of the lives of my students instead, thank you.
When I was watching Eli Pariser’s Beware Online Filter Bubbles TED talk, I wondered initially how one could work against this problem of the customization of the web. I thought to myself, wouldn’t be handy if there was a way to find an assortment of almost randomly aggregated content from a wide variety of interests.
I then remembered that newspapers are an aggregate of content from a wide variety of areas. Maybe they serve a purpose after all? Perhaps newspapers, at least some of them, should continue to focus on providing stories without bias that come from all over the world, from all walks of life. Not sure what the business model is, as most people seem to be content in their bubbles, but perhaps as Eli’s message is shared, they will be able to monetize their random access nature.
I read this article today about philosophy for children, which was shared in last night’s discussion about math in the real world. I thought it was pretty appropriate because my own son has started asking some difficult questions, and I’d like to find some more resources for exploring them with him. Obviously, I can give him my perspective on the issues, but I think it would be better to find resources which are more familiar to him.
Here are some of the questions he has asked me in the past few months, which are in my mind a sign he has entered a period of philosophical reflection.
My son is 4. I don’t want to stop his questioning of the world, because I see his curiousity as something to nurture and help thrive. I’m worried that if I give him none of the answers to these questions, he’ll stop asking. Similarly, if I give him all of the answers, will he see me as the primary source of information? Will he stop asking other people?
I can give explanations for all of these. It’s sometimes hard not to answer in terms of other things he doesn’t know yet, but I suppose that can lead to more questions. Still with effort I could help my son find all of the answers to these questions. I’m wondering if it is better to leave some of them unanswered though, to leave space for him to continue to question, and to grow.
One way I’m going to encourage this kind of thinking is by reading books which ask some of the same kinds of questions, and encouraging thinking about "big ideas."
Here is a suggestion of books you can read with your kid (or give them to read) with a philosophical perspective:
Thanks to all who shared these suggestions on Twitter earlier. For more information on teaching philosophy to children, you can also check out this useful wiki.
Today I talked on the radio with Bill Good on CKNW, announced that George Abbott, British Columbia’s Minister of Education will chat with us on Twitter, and chatted with Alan Papert and a bunch of other amazing math educators about ways to make mathematics more engaging and rooted in the "real world."
Yeah, I agree, social media is useless. You don’t need to use it. #sarcasm
When George Abbott first became education minister, I sent out an email to him inviting him to join us on Twitter, and find out how educators are using it to communicate with each other across vast geographic distances. Unfortunately, the email got lost during his leadership attempt in BC, and I forgot about it. However, a few weeks ago, his aide, Chris Sandve contacted me through my website and indicated they were interested in getting back to my email. George Abbott sent me back an email recently, suggesting that he would like to participate in a discussion through Twitter on the topics of "technology and personalized education and how we can work together to build a great education system in British Columbia."
We’ve planned the discussion for June 13th, at 4pm. Chris Wejr and myself will be the moderators for the event, so direct any technical questions our way.
Anyone who wants to follow along in the conversation can read the threads on the #BCed hashtag on Twitter by following this link. If you have a Twitter account, and are interested in participating in the conversation, just make sure to read the #BCed hashtag at the right time, and include the hashtag #BCed in your tweets. If you want to try out Twitter for this conversation, but are unsure of how to get started, you can see my series of videos on using Twitter for some help.
We are considering this an open dialogue so that anyone with an interest in education in British Columbia is welcome to participate. This includes, but is not limited to, teachers, administrators, school support staff, parents, school trustees, media personel, and students. We welcome both participants from the private and public sectors of education, since George Abbott is the minister of all education in BC. We are even happy to have participants from outside of British Columbia participate.
Please be aware that the chat will be very fast, and George Abbott will not be able to respond to every reply sent his way. However, it will still be an opportunity to express our opinion, and potentially shape the vision of education in British Columbia. We should feel free to respond to each other in this chat, as well as to Mr. Abbott. Further, let’s try and make this a productive dialog about the future of education in British Columbia. I would like this not to end up being a political discussion about the lack of funding for BC schools, and focus more on what we think the role of technology and personalized learning means for our students.
Update:
If you are planning on participating in this discussion at your school (or workplace) you could project the conversation on #BCed using an LCD projector, and invite your colleagues (or friends) to participate in the conversation as well. This way we can include people in the conversation without requiring them to create a Twitter account.
I had an idea for a proposal which I put in the TED-ED forums for a TED talk on Math in the Real World. Here’s my presentation, notes are below the presentation.
Presentation notes:
Slide 1:
Hi all. My name is David Wees, and I’m a learning specialist for technology and mathematics teacher for Stratford Hall, in Vancouver, BC.
Slide 2:
I want to first state that I don’t believe that doing mathematics is the same as doing computations or following algorithms.
Many math teachers seem to be stuck on the notion that teaching kids how to do computations out of context is the same as learning how to do mathematics.
Slide 3:
So what exactly is a mathematician, and what is mathematical thinking?
Mathematicians think. A lot. They spend much more time thinking about problems than doing computations to solve those problems.
Slide 4:
A mathematician is someone who problem solves using mathematics as their tool.
Slide 5:
As proof that change in how we teach mathematics is necessary, we can look at the overall numeracy of our society. Numeracy levels in Canada are pretty abysmal, despite years and years of formal mathematics instruction occurring in schools.
It is a badge of honor in our society to admit that you are bad at mathematics. Almost no one would admit that they are illiterate, why do so many people celebrate their lack of numeracy?
Perhaps it’s time to try something new?
Slide 6:
The problem, I see, with most mathematics instruction, is that we start by choosing the mathematics curriculum we want covered, and then find problems to suit this curriculum.
The flaw with this plan is that choosing a compelling problem to fit a particular area of mathematics is really difficult, and many math teachers don’t even try.
As a result, much of mathematics instruction lacks motivation in the eyes of the learner.
Slide 7:
Here’s the crux of my argument. We’ve had curriculum which is mostly unrelated to experiences in kid’s lives for multiple generations which has only compounded the problem.
Slide 8:
What I suggest instead is that we look at the world, and we find problems kids find compelling, and then we tease out the mathematics which is relevant to those problems. This is more difficult for math teachers to do, but will result in kids never asking the question, "Why do we need to know this."
Note that we can teach most of what we teach now to a motivated kid in a few years, rather than spreading it over all 12 years, so this way of exploring mathematics shouldn’t stop kids who are really interested in mathematics from exploring it further.
Slide 9:
It is clear that our world has some deep mathematical structures. Which of those structures do we share with our students? Why isn’t more of the world we live in shared throught the lens of mathematics? If mathematics truly is the language of the universe, our current approach has kids learn some of the vocabulary, but never construct any sentences.
Slide 10:
Trees for example have a fractal structure which is worth investigating. It is not hard to see that there is a mathematical formula of some kind which helps determine tree growth, but we can also see the idea of replication errors, and environmental factors that play a role as well. It also means that kids get a better connection between nature and the mathematics they learn.
Slide 11:
Dan Meyer suggests finding "real" examples, rather than pseudo-context is key to developing student understanding of the world. The questions about the world have to be real, and from the students. The textbooks we use today include lots of "word" problems but for what purpose? Most of the textbook word problems are too poorly constructed to be obvious representations of the world, so why bother? What purpose does exposing kids to a bunch of pretend problems serve?
Slide 12:
Outside of our own world, the whole universe has a strong mathematical structure on a large scale.
How often is this mathematical structure shared with students?
Slide 13:
Or the relationship between this fractal and the previous picture of the galaxy?
Fractals and chaos theory are an important part of our world, mathematically speaking, yet neither one sees much "playing time" in our curriculum.
Slide 14:
This is a complex project I’m working on where I am attempting to model mathematically the transfer of information in a classroom, and hence compare a didactic classroom to a cooperative learning classroom.
It’s not near done yet, so I can’t share any results, but if I do manage to complete it, the project will involve percentages, probability, graph theory, statistical distributions, geometry, Cartesian coordinates, and algorithms.
Slide 15:
Flash card apps and other ways to memorize computations and algorithms aren’t going to improve our problems with numeracy. In fact, I don’t think these are really examples of technology at all, since they do nothing new. If you are going to use technology in your teaching, you should at least be using it effectively. Graphing programs, computer assisted algebra and calculus, multimedia to emphasize patterns, all of these are much more effective uses of technology than the current generation of apps for education.
Slide 16:
To summarize my argument so far. Most people lack sufficient numeracy skills for our complex world. Our mathematics instruction really hasn’t changed in most schools for decades. Perhaps it’s time for a change? I’d recommend a focus on relevance to the real world, rather than a hierarchy of algorithms.
Slide 17:
First, put aside that useless textbook with all of the prepackaged problems.
Start by finding an interesting problem that your students find compelling and look at the mathematics involved in that problem.
Better yet, turn your kids into investigators and have them find the problems and bring them to class. Finding interesting mathematics problems isn’t hard.
Don’t worry about that test so much. If your kids can solve real problems, and those problems are in some way related to your curriculum, they will do fine on the tests.
It would be nice if we could dump our current curriculum and replace it with something more aligned to the world views of our students, but that’s not really possible, so in the transistionary stage, we should find ways to include more of what kids experience in your teaching. Don’t be so afraid to experiment, if even a few of your kids recognize math outside of your classroom, you’ve done the world a huge service.
Slides 18 through 21:
So what does this look like? I did a project with my students last year where we explored the cost of owning a cell phone, based on the number of minutes used.
First we graphed the initial cost to join a cell phone plan, and then we graphed the cost of the cell phone plan. This got us talking about graphs, equations of lines, horizontal lines, and slope. As we went through the unit, I introduced the mathematics in pieces as the students needed more to explain the problem. For example, when students asked how we could find out exactly where the two lines met, we did a couple of lessons on algebra.
Then we recognized the optimal solution was actually the green line. We ignored the negative numbers, since they didn’t represent real values, and we focused on the part of the graph which was actually our solution to the problem. We discussed domain and range, within the context of a problem the kids understand. Notice also that our solution wasn’t a single number.
Finally, we needed to tidy up our solution so that we only represented what was actually the solution the problem. Clearly, without labels on the axis, the graph of our solution to the "what is the cheapest cell phone plan" didn’t make a lot of sense. I had the kids keep the first steps, so they can talk about their solution and communicate the reasoning they went to solve the problem.
Slide 22:
There are lots of other examples like this one of real things kids want to know that involve challenging mathematics. We don’t need to dumb down the curriculum for students, we need to reenvision it. If we had a curriculum which emphasized the purpose of mathematics much more, I think we’d see a change in a single generation of students.
Slide 23:
Here’s my contact information and the license for this presentation.
Tomorrow at 11am (PST), I’m going to be on the Bill Good show on CKNW. They have asked me to talk because I recently presented at my school on social media for parents.
They sent me the following two articles as some background on the issue of young children using social media.
Five million Facebook users are 10 or younger
That Facebook friend might be 10 or younger, and other troubling news
If you want to listen to the interview, you can visit the CKNW website, and click on "Listen Now" on the left hand side of the page.
I’m thinking of these basic talking points:
Are there any other important points you think I should bring up?
Update: This happened and went fine. I didn’t get as much time I would have liked to talk about this issue, but I didn’t make a fool of myself either. 🙂 You can download and listen to the interview here:
