The Reflective Educator

Education ∪ Math ∪ Technology

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Month: May 2011 (page 2 of 3)

Philosophy for Children

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.

  • Why don’t we fly away from the Earth, if it is spinning so fast?
  • Does the Earth spin this fast (starts to spin himself very slowly)?
  • Are people on the other side of the Earth sleeping when we are awake?
  • How did monkeys become people?
  • Where does the universe end? Does it go on forever? How did it start?
  • Is Earth in outer space?
  • Why does gravity happen?
  • Were you alive before I was born?

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.

 

Nah, social media is useless

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

A discussion with our Education Minister George Abbott

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.

TED talk proposal: Math in the real world

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.

Interview on the Bill Good show on CKNW

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:

  • The Internet is not private, it is mostly public space.
  • Children need positive role-models in online social spaces, in many cases this is lacking in their lives.
  • We should adopt a scaffold approach to social media, recognizing that when students graduate from school, they will be entering an unfiltered world.
  • The Internet is not as dangerous as make it out to be, in many ways our physical spaces are more dangerous.
  • 67% of children report being bullied offline more than online.
  • Someone who knows your child is still much more likely to abuse them than a stranger.
  • The Internet is permanent, and most children do not understand this. They are unlikely to look ahead and see the consequences of their actions. When we grew up, this was less of a problem because "society" forgot our mistakes. For today’s children, we somehow expect them to be perfect while they are growing up.
  • Social media hasn’t changed our behaviour much, it merely amplifies both the good and the bad.
  • Children are learners, and we should treat them as people who make some mistakes. They need guidance and feedback in order to learn from their mistakes.

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:

The Biobook – a nonlinear textbook

I just read an interesting article from Mashable about mobile technology in education, and it included a section on the Biobook which is a textbook arranged in a non-linear fashion. This allows someone reading the book to peruse the information in the book in the fashion which suits them, rather than the order predetermined by the textbook company. 

Traditional textbook vs Biobook

Image credit: Wake Forest

The idea is interesting. I’ve certainly been annoyed myself when accessing traditional textbooks because of the difficulty finding the piece of information I want to access. In all fairness, a traditional textbook does have a table of contents would you can access the material in a non-linear fashion if you desire.

One question though, does the order of the information matter? Organizing information is one way of curating it, and helping ensure students have the sometimes necessary background information to understand content they access. Is this a critical part of our containers of information (we’ll call them textbooks in lieu of a better word)? How important is the traditional structure to accessing information?

I wonder if you could go further and use content recommendation systems to suggest possible orders of content for students? Ie, you can access this content in anyway you like, but your friends accessed it this way, you might like that particular path.

I like how it challenges one of the assumptions about texts we have, which is that page numbers are necessary. A non-linear book would need none, they wouldn’t even make sense.

Interesting stuff. 

Gamification of education

Here’s an interesting video which was shared with me by @misterlamb today.

While I’m not thrilled about the use of experience points as group awards (external motivator), I do like the idea of incremental improvement rather than requiring students to make large changes in order to improve. I also get the point that the traditional grading system is poorly designed, and that if we must use some sort of grading system, one that expects improvement through "trying again" is a huge improvement over our "you failed, oh well" system. Further, in a system of levelling up, it would be easier to get away from the notion that how old a student is determines what path they should be taking.

There are some questions I do have about implementation of this kind of system.

  • Would students tend to become specialists in this system rather than generalists? Would they think that because they are doing well in x subject that they can forget about y subject? I’m level 55 in math, but only level 3 in writing, but it’s okay because level 55 is really good! Is this something we should worry about, or just part of the further personalization of education?
     
  • A huge part of any game I’ve played is the competition between the players. Most games are zero sum, in which one player has to do poorly in order for another to do well. Our comparison system of grades is such an example. In order to feel good about your A, there can’t be too many people who get one, hence your gain, is someone else’s loss. In a leveling system, being level 50 feels better when you realize you’ve beaten other people in the race to that stage of the game. I worry that this type of system might foster more competition than it would encourage cooperation. There are some suggestions in the video on how to counteract this, but none of them seems sufficient to me to overcome this effect. How can we encourage greater cooperation in a gamified classroom?
     
  • What do we do with a child who refuses to play the game? We have this problem already in education, where there are lots of kids who don’t participate in the classroom because they can see they will "lose" at the game, or the rules of the school game aren’t interesting to them.
     
  • Should we give points for mastery, or for good learning behaviours? Who hands out the points? How do we ensure that kids don’t find ways to get lots of points without really learning (gaming the gamification system)?

 

How to solve a song by Karen Cheng

Karen Cheng demonstrates fairly convincingly that music and mathematics are linked. This video is definitely worth watching.

How could this be incorporated into the classroom? Any ideas?

TEDxKIDS@BC – Call for speakers

Screen-shot

As some of you may know, I’m on the TEDxKIDS@BC organizing team, in the community section of the organization. We are looking for speakers for our event, which will be happening on the 17th of September, at the Roundhouse in Vancouver. The speakers can be of any age, adult or kids, but they should ideally have a story which appeals to kids. We’d be happy with a 5 year old with an interesting story about an experience they’ve had, or a 75 year old who can give an engaging experience about either their work with kids, or their own childhood.

Think of people like Adora Svitak, who are highly engaging speakers who have stories that need to be heard.

We also need exposure for our event, so that we can find sponsors for the event, and promote the event in Vancouver, particularly outside of the digital community. 

You can add suggestions for either speakers or entertainers here in our open nomination page. You can also add any press or media contacts you have here.

Eli Pariser: Beware online “filter bubbles”

Eli Pariser makes a great point about the dangers inherent in online "filter bubbles."

I have a thought. Perhaps there should be someone in our student’s lives whose job it is to make sure that students are aware of divergent points of view, and the danger inherent in not seeking alternative explanations of reality to what is easily handed to us. Students should know that they are forming these search bubbles around themselves, and be given options for circumventing them to find other perspectives.

I wonder who could do ensure this happens for our students? Any ideas on who should help students avoid living entirely inside these Internet filter bubbles?