I haven't posted in over a week, which I think is the longest I've ever gone since I've started this blog without posting. I wish I could say it was due to Screen Free Week and my virtuous decision to eschew all things electronic, but it wasn't. It is because I've been so busy with the Cards, Coral & Kids campaign for my son's environmental awareness group, Healing Oceans Together (H2O).
The idea behind this project, which is to create a Pokemon-like card game that would teach people about coral reef life and ecosystems and actions they can take to help the corals survive, is explained here and here, so I won't go into that again in my blog. What I wanted to talk about here is some of the thinking behind the project.
You know, young teens are interesting creatures. They are old enough to realize some of the problems with the world, and most are hopeful and confident about being part of the solution. They tend to be really into Earth Day and recycling, Save the Planet, Stop Global Warming, Protect the Rain Forests, and the like.
And yet, on a daily basis, we are still telling them "Shut the Refridgerator Door!" "Turn Off the Lights when You Leave the Room!" "Don't Leave the Computer Running All Night!" or the frustrated but perhaps dangerous question of "Why Does it Take You 30 Minutes of Running Water to Take a Shower?"
Maybe it's different at your house. But for many of us, our children's grand rhetoric for saving the planet doesn't match up with their everyday life habits. Of course, that's really true for most of us adults as well...
In H2O, the students have been studying ocean science and math since September. We decided to hone in on coral conservation because coral reefs are really the marine equivalent of rain forests. Although coral reefs only make up about 0.1% of the oceans, they are home to approximately 25% of all marine life! Also, corals take a long time to grow, so our damage to reefs that may be hundreds or thousands of years old can not be replaced within many of our human generations.
But what to do that would make a difference? There are already tons of books and videos and ads and educational resources on this issue, but people continue doing what they've always done. As parents, we've trying nagging, threatening, bribing, begging, and everything short of bloodshed, and yet...we, too, are largely ineffectual. So we needed to come up with something else, something new.
And then we had a brainstorm. Instead of using guilt and threats and dire warnings of environmental catastrophes, what if we made saving the coral reefs fun? What if we made it....into a game?
In approaching it this way, we were influenced by the work of Jane McGonigal, whose work is summarized in a video I included in an earlier post. Her video on that page, a TED talk on how "Gaming Can Make a Better World," is a synopsis of her wonderful book, Reality Is Broken: Why Games Make Us Better and How They Can Change the World. In short, she argues that time people spend on video games actually helps them develop positive characteristics (such as working hard, cooperation, and optomism), and explores how to structure games so that we can channel all the time people spend playing games into social activism games that will help solve Earth's real-world problems. It is a fascinating and inspiring book, and I recommend it highly.
So, in short, that is what we are trying to do with this game. First, the game will teach students (and adults as well) the real science behind food chains and interlocking ecosystems in the coral reefs. We think this is important because we think if people knew more about all these fascinating creatures, they would love them, and we take care of the things we love (for more of our philosophy on that, read the Family Educators Commons article that Maria Droujkova and I co-wrote on the Shareable website). But secondly, we will build into the games a way for them to earn (or lose) points based on their actions in real life. You insist that I drive you to the library? You lose 5 points. You walk or ride your bike there yourself? You gain 5 points. You stand there with the refridgerator open as you drink your water/milk/juice? You lose 3 points. You close the door and drink it at the table? Well, I don't know that we'll give you points for that, since that should be normal behavior, but at least you won't lose points. You keep your showers under 10 minutes? You get 2 points. You keep your showers under 5 minutes? You get 5 points.
You get the idea.
Anyway, we think this game has the potential to give kids incentives for to change those behaviors that we parents have been nagging them about for years, but to no avail. If we all make those small changes, maybe they won't completely solve the problem, but they will make things better. And making things better is something that can make us all feel good.
If you would like to be a part of helping to make this game happen, then please visit our Cards, Coral & Kids campaign. For a small donation, you could get a deck of the cards before they are released to the public, participate in our pilot trials and research project, or even give input into the cards themselves! Also, please spread the word about this idea to all your social media networks, email loops, and friends and family. Getting the funding we need to develop the game requires reaching lots of people, so anything you can do to help is greatly appreciated!
Showing posts with label Maria Droujkova. Show all posts
Showing posts with label Maria Droujkova. Show all posts
Wednesday, May 9, 2012
Thursday, October 27, 2011
Curriculum Resource: Greg Tang Math Puzzles
Yesterday, Maria Droujkova of Natural Math had a web seminar with Greg Tang, the author of math poetry/puzzle books such as The Grapes of Math, Math-terpieces: The Art of Problem Solving, and other similar books. His books are really geared towards elementary students, mostly the 6-10 year old crowd, I believe. So while my son had enjoyed reading his books when he was younger, I hadn't really thought about Greg Tang for several years now.
But I tuned into the webinar, and discovered that Tang now has a website with some resources that I think are appropriate for middle schoolers. It appears that lately Tang has spent less time writing and more time programming some of the games and puzzles into interactive exercises on his website (which is apparently about to be taken over by Scholastic, which is also the publisher of his books).
The games on there, so far, at least, still focus on mastering basic mathematical computational skills. However, I know my son can still use some work on recalling those math facts quickly and accurately. But they are fun games, even though they based on simple mathematics. Some of them are kind of like Sudoku, where you have to figure out the right selections of numbers, but you have to add, subtract, multiply, or divide to choose the right one. I found them kind of fun and interesting to do as an adult, but my son enjoyed doing them as well.
Our favorite was a game called Kakooma, in which you are given a series of hexagons with six numbers in them, and you have to figure out which number can be created by adding, subtracting, or multiplying two of the other numbers in the hexagon. So it doesn't require a math savant, but you are racing against the clock and other players, a bunch of whom have figured out all seven problems in a set in less than 10 SECONDS! Unbelievable!
Anyway, if you buy a subscription, all the games have a bunch of different levels to make the game harder or easier, but there is a free version of each game that has been challenging enough for us so far.
So if your family likes math puzzles, or if you are just looking for a fun way to practice some basic computational skills, check out GregTangMath.com.
If you are interesting in finding out more about how Greg Tang develops the math books, games, and other materials he creates, you can access a recording of the entire webinar at:
http://mathfuture.wikispaces.com/GregTangMath .
But I tuned into the webinar, and discovered that Tang now has a website with some resources that I think are appropriate for middle schoolers. It appears that lately Tang has spent less time writing and more time programming some of the games and puzzles into interactive exercises on his website (which is apparently about to be taken over by Scholastic, which is also the publisher of his books).
The games on there, so far, at least, still focus on mastering basic mathematical computational skills. However, I know my son can still use some work on recalling those math facts quickly and accurately. But they are fun games, even though they based on simple mathematics. Some of them are kind of like Sudoku, where you have to figure out the right selections of numbers, but you have to add, subtract, multiply, or divide to choose the right one. I found them kind of fun and interesting to do as an adult, but my son enjoyed doing them as well.
Our favorite was a game called Kakooma, in which you are given a series of hexagons with six numbers in them, and you have to figure out which number can be created by adding, subtracting, or multiplying two of the other numbers in the hexagon. So it doesn't require a math savant, but you are racing against the clock and other players, a bunch of whom have figured out all seven problems in a set in less than 10 SECONDS! Unbelievable!
Anyway, if you buy a subscription, all the games have a bunch of different levels to make the game harder or easier, but there is a free version of each game that has been challenging enough for us so far.
So if your family likes math puzzles, or if you are just looking for a fun way to practice some basic computational skills, check out GregTangMath.com.
If you are interesting in finding out more about how Greg Tang develops the math books, games, and other materials he creates, you can access a recording of the entire webinar at:
http://mathfuture.wikispaces.com/GregTangMath .
Tuesday, October 25, 2011
Steve Jobs as Revolutionary
A couple of weeks ago I wrote a post on Steve Jobs as a great model for our middle schoolers to use to learn about living life with vision and passion. But lately, I have been thinking about Steve Jobs as a model for revolutionary change, prompted by two very different events: reading a blog post by my friend Maria Droujkova of Natural Math, and spending an hour in the Apple Store yesterday.
The post that started me down this road Sunday night was entitled How I imagine change. You should read the entire thing here, because my interpretation doesn't do it justice, but Maria sees radical change as taking two steps:
Step 1: Disengage from the old way/system
Step 2: Build the new way/system
Then yesterday, I ended up in Jobs' living legacy, the Apple Store. My tale of woe: last week, when my son was working on some school work on my big Mac computer, the screen got wonky and the program froze. I advised him to reboot and try again, but the computer wouldn't come up again. So I scheduled an appointment with the Apple Store self-proclaimed "Genius Bar"--the technical experts who help you resolve issues with your Apple technology (computers, iPhones, iPads, etc.). Because it is so big and bulky, so it is hard for me to handle, plus the fact that my son and I had classes all day, my husband took it in and returned with the sad news that the hard drive was gone and had to be replaced. But in only a few hours, the work was done, so I had the computer back that night. Luckily, I did have a back-up drive, and spent the weekend trying to transfer my backup to the new hard drive using Apple's built-in no-brainer backup software, Time Machine.
Unfortunately, it wasn't working. So it was back to the Apple Store for another appointment at the Genius Bar. The guy working on my computer turned out to be Gabriel, which I took to be a good sign--what could be better than having not only a Genius, but an Arch Angel working on your computer? And work on it he did, while I sat there watching him and eves dropping about the other poor souls coming to the Genius Bar for a fix to their technical problems. The bottom line ended up being that my backup hard drive had problems as well. So while Gabriel couldn't do a full restore either, what he could do--that I couldn't--was to transfer my document files off the backup to the new computer hard drive. I would have to reinstall the software at home.....which is a pain, but not nearly as painful as losing all the lesson plans, documents, photographs, music, movies, and other things that I had created and stored on my previous hard drive.
So once again, after having spent an hour trouble shooting and deciding this was the best solution, we left the computer in Gabriel's capable hands, went home, and returned that evening to find a computer with the operating software reinstalled, all my document files transferred, and all of the Apple iLife and iWorks software loaded on (which, frankly, are the packages I use 90% of the time). And the fee for the probably two hours that Gabriel spent working on my computer? Nothing. I got all that service for free, even though the issue was really an external disc drive that failed that was not Apple hardware. I have a problem with my Mac, I take it to the Genius Bar, and it gets fixed, usually that day, for no charge (other than fees for equipment, like buying the replacement hard drive).
So if you look at that transaction from the typical business viewpoint, it makes no sense. Here this highly skilled technician spends two hours of time dealing with a problem that wasn't even Apple hardware for no money. Who can make a business model like that work?
Only a revolutionary....the kind of multi-millionaire corporate CEO who would say, "Why join the Navy ...if you can be a pirate?" (and that was even before Johnny Depp had made pirates cool again).
Because as I understand the man, Steve Jobs (and the company he founded) was never about the money, and was never even about the product. Steve Jobs and Apple Computer were about empowering people to create things they never imagined they could do by using technology (Pixar is also all about that, but the focus was on giving great artists great tools to create great movies). Steve Jobs and Apple Computer were about transformation, not market share. Steve Jobs and Apple Computer were about revolution.
And look how Jobs followed Maria's two steps. When Apple came on the market, the big competition was which operating system--Microsoft's DOS or Intel's CP/M--was going to be chosen by IBM for their personal computers and, by extension, dominate the market. But Jobs and Apple didn't try to get into that game. Instead, they just did their own thing, building a computer that seemed to eschew any pretense of corporate acceptability--what business executive at the time was going to put in an order for a computer that was called an Apple? As Jean Louis Gassee, who replaced Jobs as head of the Macintosh development team when Jobs left the company, said about the famous original Apple logo (an Apple with a bite missing and filled with stripes of different colors):
Lust, knowledge, hope, and anarchy....you almost couldn't pick better words to describe a revolutionary. Or here are some quotes from Jobs in the early years, in which he makes clear that he wasn't going to play the game by IBM or Microsoft or typical business rules--he was making up his own rules as he went along. Plus, his game was so much bigger than just money:
But the revolutionary genius of Jobs and/or Apple was realizing that simply building amazing products also wasn't enough. To transform people's experience with, and willingness to use computer-based products, particularly among the baby boomer generation of which Jobs was a part, you needed to build support structures to help people adapt to an entirely new way of doing things. For example, this was Jobs' explanation about why the iPod basically wiped out all competition from other MP3 music players:
And that is the beauty of the Apple Stores, with their Genius Bar to fix your technical problems, their free classes to educate you about the products' capabilities, and their One to One service, where for $100 a year, someone will sit down with you once a week and work with you individually on whatever project you need help with. The stores and their services are Apple's promise to their clients that when you buy their products, they won't abandon you. You take the leap of faith to go with the non-dominant computer, and they will be your partners in making it work for you. Your hardware isn't working; we'll fix it. You don't know how to use the software; we'll teach you. You can't figure out how to get the music from Garageband to match up with the right pictures in iMovie; we'll work it out with you.
In short, Apple has built not only the computers and other devices they sell, but the infrastructure necessary to help the non-computer generation get control over the computer's more creative capabilities than simply using it as a fancy typewriter. And that is how you create a technological revolution.
So, once again, Jobs has a lot to teach us about how to make fundamental changes in society. I'm keeping my fingers crossed that Apple will continue to keep its revolutionary outlook going now that its pirate captain has sailed on to other waters.
The post that started me down this road Sunday night was entitled How I imagine change. You should read the entire thing here, because my interpretation doesn't do it justice, but Maria sees radical change as taking two steps:
Step 1: Disengage from the old way/system
Step 2: Build the new way/system
Then yesterday, I ended up in Jobs' living legacy, the Apple Store. My tale of woe: last week, when my son was working on some school work on my big Mac computer, the screen got wonky and the program froze. I advised him to reboot and try again, but the computer wouldn't come up again. So I scheduled an appointment with the Apple Store self-proclaimed "Genius Bar"--the technical experts who help you resolve issues with your Apple technology (computers, iPhones, iPads, etc.). Because it is so big and bulky, so it is hard for me to handle, plus the fact that my son and I had classes all day, my husband took it in and returned with the sad news that the hard drive was gone and had to be replaced. But in only a few hours, the work was done, so I had the computer back that night. Luckily, I did have a back-up drive, and spent the weekend trying to transfer my backup to the new hard drive using Apple's built-in no-brainer backup software, Time Machine.
Unfortunately, it wasn't working. So it was back to the Apple Store for another appointment at the Genius Bar. The guy working on my computer turned out to be Gabriel, which I took to be a good sign--what could be better than having not only a Genius, but an Arch Angel working on your computer? And work on it he did, while I sat there watching him and eves dropping about the other poor souls coming to the Genius Bar for a fix to their technical problems. The bottom line ended up being that my backup hard drive had problems as well. So while Gabriel couldn't do a full restore either, what he could do--that I couldn't--was to transfer my document files off the backup to the new computer hard drive. I would have to reinstall the software at home.....which is a pain, but not nearly as painful as losing all the lesson plans, documents, photographs, music, movies, and other things that I had created and stored on my previous hard drive.
So once again, after having spent an hour trouble shooting and deciding this was the best solution, we left the computer in Gabriel's capable hands, went home, and returned that evening to find a computer with the operating software reinstalled, all my document files transferred, and all of the Apple iLife and iWorks software loaded on (which, frankly, are the packages I use 90% of the time). And the fee for the probably two hours that Gabriel spent working on my computer? Nothing. I got all that service for free, even though the issue was really an external disc drive that failed that was not Apple hardware. I have a problem with my Mac, I take it to the Genius Bar, and it gets fixed, usually that day, for no charge (other than fees for equipment, like buying the replacement hard drive).
So if you look at that transaction from the typical business viewpoint, it makes no sense. Here this highly skilled technician spends two hours of time dealing with a problem that wasn't even Apple hardware for no money. Who can make a business model like that work?
Only a revolutionary....the kind of multi-millionaire corporate CEO who would say, "Why join the Navy ...if you can be a pirate?" (and that was even before Johnny Depp had made pirates cool again).
Because as I understand the man, Steve Jobs (and the company he founded) was never about the money, and was never even about the product. Steve Jobs and Apple Computer were about empowering people to create things they never imagined they could do by using technology (Pixar is also all about that, but the focus was on giving great artists great tools to create great movies). Steve Jobs and Apple Computer were about transformation, not market share. Steve Jobs and Apple Computer were about revolution.
And look how Jobs followed Maria's two steps. When Apple came on the market, the big competition was which operating system--Microsoft's DOS or Intel's CP/M--was going to be chosen by IBM for their personal computers and, by extension, dominate the market. But Jobs and Apple didn't try to get into that game. Instead, they just did their own thing, building a computer that seemed to eschew any pretense of corporate acceptability--what business executive at the time was going to put in an order for a computer that was called an Apple? As Jean Louis Gassee, who replaced Jobs as head of the Macintosh development team when Jobs left the company, said about the famous original Apple logo (an Apple with a bite missing and filled with stripes of different colors):
One of the deep mysteries to me is our logo, the symbol of lust and knowledge, bitten into, all crossed with the colors of the rainbow in the wrong order. You couldn't dream of a more appropriate logo: lust, knowledge, hope, and anarchy.
Lust, knowledge, hope, and anarchy....you almost couldn't pick better words to describe a revolutionary. Or here are some quotes from Jobs in the early years, in which he makes clear that he wasn't going to play the game by IBM or Microsoft or typical business rules--he was making up his own rules as he went along. Plus, his game was so much bigger than just money:
We're gambling on our vision, and we would rather do that than make "me too" products. Let some other companies do that. For us, it's always the next dream. (1984)
Being the richest man in the cemetery doesn't matter to me ... Going to bed at night saying we've done something wonderful... that's what matters to me. (1993)
I was worth about over a million dollars when I was twenty-three and over ten million dollars when I was twenty-four, and over a hundred million dollars when I was twenty-five and it wasn't that important because I never did it for the money. (1996)
What a computer is to me is the most remarkable tool that we have ever come up with. It's the equivalent of a bicycle for our minds. (1991)So after turning his back on what the rest of the computer industry was doing, Jobs had to come through with Step 2: he had to deliver the goods. There was a long-time saying at Apple Computer that was attributed to Jobs (although I haven't been able to find an official citation), which was "Real artists ship." And there is no doubt that Apple Computer has shipped some of the finest consumer technology products of the 20th and 21st Century.
But the revolutionary genius of Jobs and/or Apple was realizing that simply building amazing products also wasn't enough. To transform people's experience with, and willingness to use computer-based products, particularly among the baby boomer generation of which Jobs was a part, you needed to build support structures to help people adapt to an entirely new way of doing things. For example, this was Jobs' explanation about why the iPod basically wiped out all competition from other MP3 music players:
We had the hardware expertise, the industrial design expertise and the software expertise, including iTunes. One of the biggest insights we have was that we decided not to try to manage your music library on the iPod, but to manage it in iTunes. Other companies tried to do everything on the device itself and made it so complicated that it was useless. (2006)In short, the iPod took over the market not just because it was a beautiful and functional machine, but because Apple created the entire iTunes music delivery system that simplified the process to the point that even grandparents could find and download the music they wanted.
And that is the beauty of the Apple Stores, with their Genius Bar to fix your technical problems, their free classes to educate you about the products' capabilities, and their One to One service, where for $100 a year, someone will sit down with you once a week and work with you individually on whatever project you need help with. The stores and their services are Apple's promise to their clients that when you buy their products, they won't abandon you. You take the leap of faith to go with the non-dominant computer, and they will be your partners in making it work for you. Your hardware isn't working; we'll fix it. You don't know how to use the software; we'll teach you. You can't figure out how to get the music from Garageband to match up with the right pictures in iMovie; we'll work it out with you.
In short, Apple has built not only the computers and other devices they sell, but the infrastructure necessary to help the non-computer generation get control over the computer's more creative capabilities than simply using it as a fancy typewriter. And that is how you create a technological revolution.
So, once again, Jobs has a lot to teach us about how to make fundamental changes in society. I'm keeping my fingers crossed that Apple will continue to keep its revolutionary outlook going now that its pirate captain has sailed on to other waters.
Monday, October 3, 2011
Math Trek at the North Carolina Museum of Art
Our Math Trek series has started up again for the new year. This is one of the creative math activities organized by Maria Droujkova of Natural Math. It is a multi-aged program where students of all levels take quests to find and photograph different math concepts. We then share them with each other, whether by discussion, acting them out, or posting them on the web.
This week's Trek took place at the North Carolina Museum of Art, which has so many wonderful things to look at, whether mathematical or not. Maria's colleague, Brad Herring, was there to capture the action on film, so that we could share it with other similar groups around the world so they could have their own Math Treks:
Maria have the students various "quests" to find and photographs, including recording examples of fractions, proportions, and fractals. Then we came together to discuss and recreate some of our favorite mathematical concepts/photographs:
As always, it was a fun and educational outing. Plus, the weather was beautiful this weekend. But to see students discovering math in settings all around them--that was even more beautiful!
This week's Trek took place at the North Carolina Museum of Art, which has so many wonderful things to look at, whether mathematical or not. Maria's colleague, Brad Herring, was there to capture the action on film, so that we could share it with other similar groups around the world so they could have their own Math Treks:
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| Our intrepid leader, Maria Droujkova |
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| Our videographer, Brad Herring |
Maria have the students various "quests" to find and photographs, including recording examples of fractions, proportions, and fractals. Then we came together to discuss and recreate some of our favorite mathematical concepts/photographs:
 |
| Recurring Circles |
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| Acting out the proportions of seats in a circular amphitheater |
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| Making a human fractal |
As always, it was a fun and educational outing. Plus, the weather was beautiful this weekend. But to see students discovering math in settings all around them--that was even more beautiful!
Sunday, September 25, 2011
Math and MBTI Psychological Type
Happy Math Storytelling Day! This is an event in honor of my dear friend, Maria Droujkova of Natural Math, whose birthday is it today. The idea is that we share our stories about math with each other.
So my story involves math education and psychological type as measured by the Myers-Briggs Type Indicator (MBTI). This past winter, I taught an online class through P2PU on the Psychology of Math Learning. The idea of the class was to look at various psychological theories, including MBTI personality type theory, to see if it would give us insight on why math can be such a struggle to so many learners. (For more details on the class, you can read my original blog post about it).
The structure of the class was that each week, we would take an online test about one of these theories, then post our "score," such as our MBTI type, which in my case is ENFP (Extravert, iNtuitive, Feeling, Perceiving). Then we would reflect on our experience learning math, and see if we noticed any ways that our test results might have helped or hindered our math education.
The class didn't work out quite like I planned, because even though this approach was explained in all the class descriptions, and had a couple dozen people sign up, the only students who ever posted their scores or their reflections on the theory and their math experience were the Extraverts! So, we ended up with a skewed sample of respondents. But we Extraverts had a great time talking about things between ourselves.
However, it was an eye-opening revelation for me. Math had always been my worst subject at school; worst NOT in the sense of grades, since I was the kind of student who would do whatever I needed to do to get an A, but in the sense that I knew I didn't really understand the answers I was regurgitating back on my graded work. And that wasn't usually the case for me--generally, I understood the concepts behind all my other subjects. So I never liked math, thought I wasn't good at math, and never took any academic math classes past my required Algebra II/Trig in my junior year of high school.
But by looking at MBTI, I could see at least part of the reason why. Because the way I was taught math was EXACTLY opposite to my personality style.
So my story has a happy ending. Maria and others have helped me to "grow new math eyes" so I can appreciate math in a way that works for my personality. But I think my story also has a moral, which is that math instruction (and all instruction, really) needs to meet the individual's personality and style, at least to some extent. If you are a teacher or a parent or a homeschooler (some of my readers are all three), and your math teaching isn't working, consider the personality of the student who is having problems. It is easy for us to get so caught up in our own MBTI preferences that we don't even notice that we are only giving open-ended exploratory problems to students who do better with more structure, or refuse to even consider a response from our creative thinkers that is different than the one in the answer key, which we find so reassuring.
So my story involves math education and psychological type as measured by the Myers-Briggs Type Indicator (MBTI). This past winter, I taught an online class through P2PU on the Psychology of Math Learning. The idea of the class was to look at various psychological theories, including MBTI personality type theory, to see if it would give us insight on why math can be such a struggle to so many learners. (For more details on the class, you can read my original blog post about it).
The structure of the class was that each week, we would take an online test about one of these theories, then post our "score," such as our MBTI type, which in my case is ENFP (Extravert, iNtuitive, Feeling, Perceiving). Then we would reflect on our experience learning math, and see if we noticed any ways that our test results might have helped or hindered our math education.
The class didn't work out quite like I planned, because even though this approach was explained in all the class descriptions, and had a couple dozen people sign up, the only students who ever posted their scores or their reflections on the theory and their math experience were the Extraverts! So, we ended up with a skewed sample of respondents. But we Extraverts had a great time talking about things between ourselves.
However, it was an eye-opening revelation for me. Math had always been my worst subject at school; worst NOT in the sense of grades, since I was the kind of student who would do whatever I needed to do to get an A, but in the sense that I knew I didn't really understand the answers I was regurgitating back on my graded work. And that wasn't usually the case for me--generally, I understood the concepts behind all my other subjects. So I never liked math, thought I wasn't good at math, and never took any academic math classes past my required Algebra II/Trig in my junior year of high school.
But by looking at MBTI, I could see at least part of the reason why. Because the way I was taught math was EXACTLY opposite to my personality style.
- Math was taught as a completely I (Introvert) subject. You stayed in your own seat, stuck to your own paper, came up with your own answers. Any working together on a problem wasn't collaboration, it was cheating. Even in Science, we at least had lab partners when we worked on experiments, and did lots of group projects in the Arts and Humanities (my favorite subjects). But in math, I don't ever remember working with another student.
- Math was taught as a million different discrete problems that built up, bit by bit, to larger concepts--which is a very S (Sensing) approach. Everything had an order and a sequence that eventually led to a comprehensive explanation of the subject. But N (iNtuition) people like to see the big picture first, so that they understand why they are doing all the individual problems. N people also usually don't fare very well in the high-sequenced, "show all steps of your work" approach that was used in my academic math classes.
- Why subject could possible be more T (Thinking) than math? What does F (Feeling) have to do with whether 2 plus 2 adds up to 4, or that the area of the circle is Pi times the radius squared? I was presented math as a completely abstract, logical, impersonal subject, which isn't something that we emotional, subjective, relationship-oriented F people particularly like.
- Finally, I was taught math as a very black/white, right/wrong, only one right answer kind of way, which is what MBTI calls J (Judging). P (Perceiving) people like open-ended answers, multiple possibilities, and options. But I was never given any of those shades of gray in my math classes.
Let me make two things clear. First, I'm not saying that any of those approaches are "bad" or "wrong." The whole basis of MBTI is these different preferences, which we are born with, are not better or worse than each other. They are just different. I doubt I had bad math classes, because I went to good schools and I'm sure I had good math teachers. That was just how math was taught in those days. And I'm sure that approach works brilliantly for some people--just not for me and my personality style.
Secondly, I now know that math doesn't have to be that way. Math education has come a long way since then, and there are many more ways that math is presented these days in schools. I am also so thankful that I met Maria, and through her, all the people on the Natural Math loop who have shown me math as a rainbow, not just a black and white subject. For example, Math Mama Sue Van Hatten just recently had a blog post about how her students work together in groups. The wonderful math-rich puzzles presented by Math Pickle encourage students to find many answers to the same problem. Maria is constantly presenting math as fun, and as beautiful, and as creative, and as a vehicle for individual expression. And I could go on and on about the wonderful new math educators who are diversifying the experience of this important field.
So my story has a happy ending. Maria and others have helped me to "grow new math eyes" so I can appreciate math in a way that works for my personality. But I think my story also has a moral, which is that math instruction (and all instruction, really) needs to meet the individual's personality and style, at least to some extent. If you are a teacher or a parent or a homeschooler (some of my readers are all three), and your math teaching isn't working, consider the personality of the student who is having problems. It is easy for us to get so caught up in our own MBTI preferences that we don't even notice that we are only giving open-ended exploratory problems to students who do better with more structure, or refuse to even consider a response from our creative thinkers that is different than the one in the answer key, which we find so reassuring.
Friday, September 23, 2011
Post Updates, AKA Good News
I wanted to let everyone know the good news about a couple of my recent blog posts.
Most recently, I wrote a couple of posts--the original Eliminate Math Anxiety post and then the popular Mobius Marinara post--about my friend Maria Droujkova of Natural Math and her attempt to raise $6,200 through Tipping Bucket to extend her work on teaching significant math topics to children from 0-5 years into a book and online community that could reach many more people. The deal with Tipping Bucket is that people pledge money to projects they want to support, but if the organizers don't attract all the money they need to make the project work by a set deadline, the pledges are returned to the donors.
However, I'm happy to report that Maria's Moebius Noodles received its full funding! So the project is now a go, thanks to many generous donors (including, I'm proud to say, my son, who gave a full week's allowance to support this effort). If you want to find out about developments on this project, follow Maria's blog, Math Accent (which is a font of wonderful information about all sorts of different math topics, not just those related to our youngest learners).
And speaking of our youngest...at the end of last month, I also posted about one of our local homeschooling families who, unfortunately, had lost both of their twin babies. On top of the terrible loss of their infant girls, they had a lot of bills to deal with, so we were having an online fundraising effort to support them financially.
In this case, it is still a sad story. However, I am happy to report that this Internet effort between friends, and friends of friends, and friends of friends of friends of...., well, it resulted in raising $8,372.32 for the family. I know that the family really appreciates every gift, not only for helping them deal with their financial issues, but as a vote of confidence in their ability to survive through the worse circumstances that a family ever needs to confront--a loss of one (or, in this case, two) of their beloved children.
Both of these remind me of one of my favorite quotes from Mother Teresa, who once said:
I also heard from several readers of this blog who said they had supported these efforts. So I want to thank you personally for your support. I know many will reap benefits from your gift, and I'm glad that you were part of our ocean.
Most recently, I wrote a couple of posts--the original Eliminate Math Anxiety post and then the popular Mobius Marinara post--about my friend Maria Droujkova of Natural Math and her attempt to raise $6,200 through Tipping Bucket to extend her work on teaching significant math topics to children from 0-5 years into a book and online community that could reach many more people. The deal with Tipping Bucket is that people pledge money to projects they want to support, but if the organizers don't attract all the money they need to make the project work by a set deadline, the pledges are returned to the donors.
However, I'm happy to report that Maria's Moebius Noodles received its full funding! So the project is now a go, thanks to many generous donors (including, I'm proud to say, my son, who gave a full week's allowance to support this effort). If you want to find out about developments on this project, follow Maria's blog, Math Accent (which is a font of wonderful information about all sorts of different math topics, not just those related to our youngest learners).
And speaking of our youngest...at the end of last month, I also posted about one of our local homeschooling families who, unfortunately, had lost both of their twin babies. On top of the terrible loss of their infant girls, they had a lot of bills to deal with, so we were having an online fundraising effort to support them financially.
In this case, it is still a sad story. However, I am happy to report that this Internet effort between friends, and friends of friends, and friends of friends of friends of...., well, it resulted in raising $8,372.32 for the family. I know that the family really appreciates every gift, not only for helping them deal with their financial issues, but as a vote of confidence in their ability to survive through the worse circumstances that a family ever needs to confront--a loss of one (or, in this case, two) of their beloved children.
Both of these remind me of one of my favorite quotes from Mother Teresa, who once said:
"What we are doing is just a drop in the ocean. But if that drop was not in the ocean, I think the ocean would be less because of that missing drop."Both of these projects show what is possible when a lot of ordinary people give just a little to a good cause. It is easy to think that what you can afford--$1, $5, $10--can't make a difference. But you put all those drops together, and it creates an ocean.
I also heard from several readers of this blog who said they had supported these efforts. So I want to thank you personally for your support. I know many will reap benefits from your gift, and I'm glad that you were part of our ocean.
Monday, September 19, 2011
Curriculum Resource: Edible Mobius Strips
There is only one day left in the fundraiser for my friend Maria of Natural Math, who is trying to raise $6,200 for a community-based initiative to help parents, caretakers, and preschool teachers to introduce deep math concepts to children from infants to age 5. Since the deadline is so near, we kind of have mobius strips on the brain (because the name of the project is Moebius Noodles). We are thinking, breathing, and eating mobius strips...
And I mean that literally:
Yes, tonight's dinner consisted of edible mobius strips, made out of handmade pasta, courtesy of my brilliant son. He is the one who had the idea of showing our support for the Moebius Noodle projects by making mobius strips out of actual noodles!
So we made some dough and pulled out the old pasta rolling machine:
Then we rolled out the dough, cut them into strips, and joined the ends of each strip together in that paradoxical inside/outside form that is the mobius strip:
It took quite a while, and it seemed like we had made 6,200 pieces of pasta, although I imagine it wasn't quite that many:
I had also made a homemade tomato sauce out of the fresh tomatoes and peppers from our local farmers market, combined them with some turkey meatballs, and VOILA!
Mobius Marinara!
And I share all this, not only because it is fun, but because it demonstrates the potential of the Moebius Noodles project. First, I doubt my son would ever have had this idea without his exposure to Maria, because let's face it--cool things like Mobius strips aren't covered that much in traditional math curricula. Secondly, it illustrates the way that Maria makes math fun and concrete and real life in a way that works for children of all ages. Sure, my son is a middle schooler, but toddlers could enjoy making a meal of mobius strips just as much. Finally, Maria's concept for Moebius Noodles is to make it a community project, not just her personal product. She wants to publish the ideas under a Creative Commons license, which means it would be free for others to use and adapt. She also wants to make it a open web-based program where everyone can contribute ideas and resources. So my son came up with this project, which was fun and worked out really well and which we are glad to share with others. But what might you or your children come up that would not only work for your family, but might really benefit others--if you had a way to get it to them. THAT is the idea behind Moebius Noodles--not simply a book or a commercial product, but a vehicle by which we can all access and add to the community of ideas about teaching even our youngest how to use and enjoy math.
So as of the time I'm writing this (10:00 PM on Monday, September 19), we only have 24 hours to raise the remaining $2,500 for this project (remember, with Tipping Bucket, if the entire sum isn't raised, all the money goes back to the donors). So if you have been meaning to donate, but haven't gotten around to it, now is the time. And whether you donate or not, stay tuned to developments with the Moebius Noodles project. Maria wants your educational ideas and experience as much, if not more, as she would like your money.
And I mean that literally:
Yes, tonight's dinner consisted of edible mobius strips, made out of handmade pasta, courtesy of my brilliant son. He is the one who had the idea of showing our support for the Moebius Noodle projects by making mobius strips out of actual noodles!
So we made some dough and pulled out the old pasta rolling machine:
Then we rolled out the dough, cut them into strips, and joined the ends of each strip together in that paradoxical inside/outside form that is the mobius strip:
It took quite a while, and it seemed like we had made 6,200 pieces of pasta, although I imagine it wasn't quite that many:
I had also made a homemade tomato sauce out of the fresh tomatoes and peppers from our local farmers market, combined them with some turkey meatballs, and VOILA!
Mobius Marinara!
And I share all this, not only because it is fun, but because it demonstrates the potential of the Moebius Noodles project. First, I doubt my son would ever have had this idea without his exposure to Maria, because let's face it--cool things like Mobius strips aren't covered that much in traditional math curricula. Secondly, it illustrates the way that Maria makes math fun and concrete and real life in a way that works for children of all ages. Sure, my son is a middle schooler, but toddlers could enjoy making a meal of mobius strips just as much. Finally, Maria's concept for Moebius Noodles is to make it a community project, not just her personal product. She wants to publish the ideas under a Creative Commons license, which means it would be free for others to use and adapt. She also wants to make it a open web-based program where everyone can contribute ideas and resources. So my son came up with this project, which was fun and worked out really well and which we are glad to share with others. But what might you or your children come up that would not only work for your family, but might really benefit others--if you had a way to get it to them. THAT is the idea behind Moebius Noodles--not simply a book or a commercial product, but a vehicle by which we can all access and add to the community of ideas about teaching even our youngest how to use and enjoy math.
So as of the time I'm writing this (10:00 PM on Monday, September 19), we only have 24 hours to raise the remaining $2,500 for this project (remember, with Tipping Bucket, if the entire sum isn't raised, all the money goes back to the donors). So if you have been meaning to donate, but haven't gotten around to it, now is the time. And whether you donate or not, stay tuned to developments with the Moebius Noodles project. Maria wants your educational ideas and experience as much, if not more, as she would like your money.
Sunday, September 4, 2011
The Great Potato Cookoff
As we look back on summer, my son has learned a lot of things. His greatest accomplishments have come in his swimming--he went from refusing to put his head underwater in May to being able to dive in and swim the length of the pool with free style or backstroke, and is working on breast stroke and butterfly. Granted, his form could still use some work, but still, he has really come so far this summer that it is really impressive.
He's also created his own book of poetry, completed several small books on dividing a fraction by a fraction, tried some calligraphy, and learned the difference between the three major periods of classical music and whose music exemplifies the trend in each.
But then there is one think he learned that may be more useful than all of those. For this summer, we learned to make....gnocchi.
It all began when we got some potatoes from our friend, Maria Droujkova of Natural Math, and my son decided we should use them in "The Great Potato Cookoff." The idea of this grand event was to invite some people over and have everyone cook a different potato dish. The purity of his vision was muddied by his mother, who insisted we include at least a couple of other things, like maybe VEGETABLES and PROTEIN, but the mainstays of the meal was potato, potato, and potato.
We were so lucky, however, because one of our friends had an Italian grandmother who had shown her how to make gnocchi, the Italian potato dumpling. So she came over and showed us. The secret, at least according to the Italian grandmother, is that the gnocchi must be formed with a SILVER fork--not stainless steel. So I pulled out the silver, and we went to town.
It was really fun, and the gnocchi turned out so well!
Meanwhile, my son, who is a soup lover, made some creamy potato soup, not, alas, from an ancient relative's recipe, but from some site he found on the Internet. However, he did a good job with it, and it tasted really good, even if it it didn't have that personal family connection.
We preceded the meal with an outside fire (a frequent occurrence at our house) made by my husband, over which we brewed some tea:
Here is our final assortment of dishes. The bowl by the silver water bottle has potatoes from the grill (and we also grilled some vegetables and chicken and pork sausages), plus gnocchi with tomato sauce, gnocchi with pesto sauce, and the potato soup.
Just one of the many happy memories we have of the Summer of 2011!
He's also created his own book of poetry, completed several small books on dividing a fraction by a fraction, tried some calligraphy, and learned the difference between the three major periods of classical music and whose music exemplifies the trend in each.
But then there is one think he learned that may be more useful than all of those. For this summer, we learned to make....gnocchi.
It all began when we got some potatoes from our friend, Maria Droujkova of Natural Math, and my son decided we should use them in "The Great Potato Cookoff." The idea of this grand event was to invite some people over and have everyone cook a different potato dish. The purity of his vision was muddied by his mother, who insisted we include at least a couple of other things, like maybe VEGETABLES and PROTEIN, but the mainstays of the meal was potato, potato, and potato.
We were so lucky, however, because one of our friends had an Italian grandmother who had shown her how to make gnocchi, the Italian potato dumpling. So she came over and showed us. The secret, at least according to the Italian grandmother, is that the gnocchi must be formed with a SILVER fork--not stainless steel. So I pulled out the silver, and we went to town.
It was really fun, and the gnocchi turned out so well!
Meanwhile, my son, who is a soup lover, made some creamy potato soup, not, alas, from an ancient relative's recipe, but from some site he found on the Internet. However, he did a good job with it, and it tasted really good, even if it it didn't have that personal family connection.
We preceded the meal with an outside fire (a frequent occurrence at our house) made by my husband, over which we brewed some tea:
Here is our final assortment of dishes. The bowl by the silver water bottle has potatoes from the grill (and we also grilled some vegetables and chicken and pork sausages), plus gnocchi with tomato sauce, gnocchi with pesto sauce, and the potato soup.
Just one of the many happy memories we have of the Summer of 2011!
Friday, June 24, 2011
Does Khan Academy Represent the Future of Education, Part 2
Last month, I wrote a blog post about the free, online Khan Academy and whether or not that represents the future of education. My friend Maria of Natural Math has just written an interesting post on her blog on Metaphors explaining Khan Academy that encouraged me to think a bit more about this matter. So this is the metaphor I would offer about Khan Academy:
Forrest Gump taught us that life is like a box of chocolates. I would say that Khan Academy is like a can of soup. Education, however, is like a family dinner.
To explain this metaphor, I have to go back, wow, like 20 years ago, when I visited the National Air Force Academy in Colorado Springs (which does the same sort of thing for the Air Force that its more famous cousins in West Point and Annapolis does for the Army and the Navy). Our guide, who was one of the instructors at the Academy, told me something that really stuck with me. He claimed that only about 25% of his job as an instructor was to teach the content in his classes. The vast majority of his job--75%--was to be a role model who exemplified by his character and his behavior what it is to be an exemplary Air Force officer.
And while that ratio may be off compared to traditional schools, given the special nature of those military academies, I think that there are some similar roles for all teachers. So much of education is all about the kind of person that student is becoming, not the academic subjects at all. We send children to classes to learn math, indeed, but also to learn to be responsible, to be punctual, to get work done by deadlines, to get along with other people, to continue to struggle with something you don't understand until you do, to work collaboratively, to be creative, to be a problem-solver....tons of things besides math (or science or English or whatever).
So, for example, if it were just about the content, you would think homeschoolers would be all over Khan Academy. We could set our children up on the computer and tell them to work their way through the videos until they are all done.
But nobody I know homeschools like that. When people uninformed about homeschooling talk to us, their first question is always, "But what about socialization?" And it is all we can do not to gaffaw in their face, because at least in an area like the Triangle NC, our kids are the most socialized kids on the planet. My son had some kind of group learning situation almost every day last year. He went to Math Clubs and Math Treks, did group nature explorations, participated in an history coop and a large, multi-age and multi-disciplinary coop, had art classes, wrote group stories for the homeschool newspaper, read and discussed over 100 books in several different book clubs, played on a homeschool baseball team, and studied world religions in Sunday School.
If it were just about the content, why would I do that to myself? The answer is, of course, that what I want for my son's education is so much more than just the academic content of his classes.
So, to return to my can of soup....Khan may be a master teacher (maybe...there are certainly lots of master teachers), and the Internet is a vehicle by which he can can himself (or other master teachers) and make it easily available. And canned soup is certainly handy to have. You can get canned soup from Master Chefs--for example, Wolfgang Puck sells canned soup--that probably tastes pretty good and that is pretty healthy (although I don't think it can match the homemade chicken, barley, and vegetable soup that I make weekly for my son's lunch and that takes a minimum of about 30 hours, since I use my friend Laura's recipe for making super-healthy 24 hour bone broth as the base for the soup).
But canned soup does not a family dinner make. The family dinner is about the other people, and the relationships, and tablecloths and silverware and candlesticks, and the conversations, and all of that, even if the family is eating canned soup for dinner.
So, Maria, there is my analogy. Khan Academy is like a can of soup. I might occasionally give my son a can opener and tell him to go heat one up, but I would never confuse it with a meal.
Forrest Gump taught us that life is like a box of chocolates. I would say that Khan Academy is like a can of soup. Education, however, is like a family dinner.
To explain this metaphor, I have to go back, wow, like 20 years ago, when I visited the National Air Force Academy in Colorado Springs (which does the same sort of thing for the Air Force that its more famous cousins in West Point and Annapolis does for the Army and the Navy). Our guide, who was one of the instructors at the Academy, told me something that really stuck with me. He claimed that only about 25% of his job as an instructor was to teach the content in his classes. The vast majority of his job--75%--was to be a role model who exemplified by his character and his behavior what it is to be an exemplary Air Force officer.
And while that ratio may be off compared to traditional schools, given the special nature of those military academies, I think that there are some similar roles for all teachers. So much of education is all about the kind of person that student is becoming, not the academic subjects at all. We send children to classes to learn math, indeed, but also to learn to be responsible, to be punctual, to get work done by deadlines, to get along with other people, to continue to struggle with something you don't understand until you do, to work collaboratively, to be creative, to be a problem-solver....tons of things besides math (or science or English or whatever).
So, for example, if it were just about the content, you would think homeschoolers would be all over Khan Academy. We could set our children up on the computer and tell them to work their way through the videos until they are all done.
But nobody I know homeschools like that. When people uninformed about homeschooling talk to us, their first question is always, "But what about socialization?" And it is all we can do not to gaffaw in their face, because at least in an area like the Triangle NC, our kids are the most socialized kids on the planet. My son had some kind of group learning situation almost every day last year. He went to Math Clubs and Math Treks, did group nature explorations, participated in an history coop and a large, multi-age and multi-disciplinary coop, had art classes, wrote group stories for the homeschool newspaper, read and discussed over 100 books in several different book clubs, played on a homeschool baseball team, and studied world religions in Sunday School.
If it were just about the content, why would I do that to myself? The answer is, of course, that what I want for my son's education is so much more than just the academic content of his classes.
So, to return to my can of soup....Khan may be a master teacher (maybe...there are certainly lots of master teachers), and the Internet is a vehicle by which he can can himself (or other master teachers) and make it easily available. And canned soup is certainly handy to have. You can get canned soup from Master Chefs--for example, Wolfgang Puck sells canned soup--that probably tastes pretty good and that is pretty healthy (although I don't think it can match the homemade chicken, barley, and vegetable soup that I make weekly for my son's lunch and that takes a minimum of about 30 hours, since I use my friend Laura's recipe for making super-healthy 24 hour bone broth as the base for the soup).
But canned soup does not a family dinner make. The family dinner is about the other people, and the relationships, and tablecloths and silverware and candlesticks, and the conversations, and all of that, even if the family is eating canned soup for dinner.
So, Maria, there is my analogy. Khan Academy is like a can of soup. I might occasionally give my son a can opener and tell him to go heat one up, but I would never confuse it with a meal.
Thursday, October 21, 2010
Happy Birthday Martin Gardner
Tonight I went to a different type of party--it was a celebration of the life of American mathematician Martin Gardner, who died earlier this year at the age of 95. Martin Gardner is considered to be the father of recreational math, because he focused on exposing people to fun mathematics through games, puzzles, toys, and such. He wrote math columns in popular magazines, such as Jack and Jill and Scientific America, that first brought broad exposure to such math topics as fractals, tangrams, M. C. Escher, and other math-related games and puzzles.
The evening was called "Gathering for Gardner: Celebration of Mind," and there were over 60 parties of this type taking place around the world on this date. All the parties had a common theme: to honor the life's work of this extraordinary man by having people come together to play with math.
Our particular gathering was focused on the intersection of math and art. It was organized and run by two women who are very important to our family: Maria Droujkova of Natural Math, who is a great friend and works with my son to find his passion for mathematics, and Jenny Eggleston of Egg in Nest studio, who is a wonderful artist and an intuitive and effective art coach/teacher for my son. Both women have a great talent for understanding each student with his or her unique talents and challenges, and individualizing their instruction to provide each one with just the assistance s/he needs. So spending an evening with them, and some other friends who are homeschooling parents and teen, is going to be valuable, regardless of what we do.
We began by making 3-D sculptures out of drinking straws and/or pipe cleaners. Then we admired some fantastic origami, art, and artistic videos related to numbers in nature. But the bulk of the evening was spent playing "The Glass Bead Game," which was inspired by Herman Hesse's book of the same name. We covered a long table with a roll of white paper and drew around small plates to form our first set of glass beads. We were given a question to answer visually, and we drew our answers inside our own beads. Then we found someone else's bead that inspired us, drew a new bead close to it, and drew a picture that "rhymed" visually with the first bead (as well as drawing a line of connection between the two). We did this for a couple of rounds, and soon the paper was filled with all sorts of visualizations related to math, life, death, the universe, and Jackie Chan (that last one was my fault...I kind of got off track a bit).
Anyway, it was a fun and thought-provoking night and a great way to recognize a great mathematician.
The evening was called "Gathering for Gardner: Celebration of Mind," and there were over 60 parties of this type taking place around the world on this date. All the parties had a common theme: to honor the life's work of this extraordinary man by having people come together to play with math.
Our particular gathering was focused on the intersection of math and art. It was organized and run by two women who are very important to our family: Maria Droujkova of Natural Math, who is a great friend and works with my son to find his passion for mathematics, and Jenny Eggleston of Egg in Nest studio, who is a wonderful artist and an intuitive and effective art coach/teacher for my son. Both women have a great talent for understanding each student with his or her unique talents and challenges, and individualizing their instruction to provide each one with just the assistance s/he needs. So spending an evening with them, and some other friends who are homeschooling parents and teen, is going to be valuable, regardless of what we do.
We began by making 3-D sculptures out of drinking straws and/or pipe cleaners. Then we admired some fantastic origami, art, and artistic videos related to numbers in nature. But the bulk of the evening was spent playing "The Glass Bead Game," which was inspired by Herman Hesse's book of the same name. We covered a long table with a roll of white paper and drew around small plates to form our first set of glass beads. We were given a question to answer visually, and we drew our answers inside our own beads. Then we found someone else's bead that inspired us, drew a new bead close to it, and drew a picture that "rhymed" visually with the first bead (as well as drawing a line of connection between the two). We did this for a couple of rounds, and soon the paper was filled with all sorts of visualizations related to math, life, death, the universe, and Jackie Chan (that last one was my fault...I kind of got off track a bit).
Anyway, it was a fun and thought-provoking night and a great way to recognize a great mathematician.
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