Math Accent
Special Pi Day event at Math 2.0 – “Blockhead”
Mar 14th
Meet author Joseph D’Agnese and discuss ways to use his mathematical picture book, Blockhead: The Life of FIbonacci, to teach not only about the Fibonacci sequence, but a variety of other math concepts.
How to join
- Follow this link at the time of the event: http://tinyurl.com/math20event
- Monday, March 14th (Pi Day!) 2011 we will meet in the LearnCentral online room at 5:00 pm Pacific, 8:00pm Eastern time. WorldClock for your time zone.
- Click “OK” and “Accept” several times as your browser installs the software. When you see Elluminate Session Log-In, enter your name and click the “Login” button
- If this is your first time, come a few minutes earlier to check out the technology. The room opens half an hour before the event.
All events in the Math 2.0 weekly series: http://mathfuture.wikispaces.com/events
About “Blockhead”
In this presentation, author Joseph D’Agnese will discuss writing a mathematical picture books and ways to use his book to teach not only the Fibonacci sequence (fascinating as that is), but also such topics as what is a number, comparing different numeral systems, using an abacus, the value of place values, and more.
You can enter to win a free autographed copy of the book by sharing the title of your favorite math-related picture book in the comments of this web page at the Teaching Your Middle Schooler blog.
To get an idea about the beautiful graphics in this book, please watch the two-minute video trailer for the book:
Event Host
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Joseph D’Agnese is is an author and journalist whose work has been published extensively in Discover magazine, and also in Seed and Wired. His work has twice been named to the renowned annual anthology Best American Science Writing. In addition to his books for adults and children, he has also published in The New York Times, The Wall Street Journal, Child, Parents, Reader’s Digest, Saveur, Money.com, Sports Illustrated and other publications. He is also a regular contributor to This Old House magazine. |
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 Carol Cross, this event’s organizer, is a homeschooling mom with a background in educational policy, philosophy, and social activism. |
Anki: Flashcards 2.0
Mar 8th
“Companies fail and die until their corpses form a bridge to the future”
Tycho, Penny Arcade
This weekend, I researched a genre of social media community platforms: systems for long-term memorization of large groups of facts, based on flashcards. Hundreds of people had the bright idea of making computer-based flashcards. For example, you can see 250+ memorization platform reviews at Quingle.
Most of these tools make sets of virtual cards that have pairs of facts (“sides”), with one shown first and the other shown next. This provides a small convenience compared to paper-based cards, namely, storage and mobility. Most flashcard software stops at this step, where it fails and dies to form a bridge to the future.
Once flashcards are electronic, they can be copied free. So, not hundreds, but dozens of platforms allow users to exchange their card sets, for example, FlashCardExchange. This and a few other platforms, however, take flashcards to the whole new level by helping users track their success.
My top pick for these sophisticated fact learning systems is Anki.This is a powerful open source tool, and a thriving resource exchange community. In addition to making and exchanging sets of cards, Anki automatically schedules cards for review, based on each person’s card-by-card data and psychology of memory. And this is a huge boon for users, compared to paper cards.
Behavior tracking and statistics-based decision making is something humans do incredibly poorly without a computer. This is where software developers should focus their efforts!
I like the interface a lot, as well. I am using the tool for my “Times tables in a week.” In this case, card sets are patterns found in times tables, such as the times nine pattern of digits, or off-diagonal “one less than square” pattern (e.g. 4*6=5*5-1).
Shareable sets of cards can become powerful social objects for peer groups.
Read more
- Anki review from Jeffrey Thomas, a math teacher
- More detailed flashcard software reviews, with the stress on Asian language learning needs, at Fool’s Reviews.
- Articles about spaced repetition – the memory theory behind most flashcard learning systems – at SuperMemo
- Even more articles and links at Wikipedia – Spaced Repetition
My multiplicative, nonlinear kid
Feb 27th
My daughter Katherine is now 12, but she still behaves in ways I trace to her experimental babyhood. Her behavior is opposite to what is described in many articles on mathematical concept developments. When she was little, we did not count, but worked with multiplicative structures such as fractals, iconic units (4=dog feet), splitting and stretching. Some of the materials we used are described in the “SubQuan and Friends” draft.
Here are two recent examples. I asked Katherine, in the style of the visualization game we call “Magic Math Lantern” – imagine y=x and now imagine y=x+3. However, she imagined y=3x. This is not random, but a constant in her behavior: if she forgets to pay attention to the operation, the default is multiplication or exponentiation, not addition. Multiplication is just easier for her to imagine.
Working further on families of functions, to my chagrin, it turned out Katya does not remember how they are called. Poking fun and chatting and laughing about our private “baby names” for entities brought up something that consistently prevents her from remembering, however: “How do you call those non-curvey thingies?”
The traditional names are:
- linear functions (default)
- nonlinear functions (anything else)
What Katherine wants:
- curvey functions (default)
- non-curvey functions (this one rare and special case of straight lines)
The linear/nonlinear terms do not match Katherine’s nonlinear default and is hard for her to remember. In the world, linear functions are very rare, but in secondary math, linear is king. There are a lot of articles about “linear misconceptions” – that is, students thinking that every operation or function is linear. Well, we have the opposite problem on our hands. Which shows that misconceptions as such are not inherent properties of the human brain development, but social constructs, and can be addressed by different practices in early childhood. My “Math-rich baby” course at P2PU is all about it.
Where in the world is math?
Feb 27th
So, the world sends two million emails every minute. This counter is mesmerizing! It’s also fake, in that it does not REALLY count emails as they are sent.
For MathSeeker, we not only need to count, but analyze, categorize, tag, aggregate and display the flows of mathematical interactions online. Web searches do it very poorly. Just try to use Google to answer some of questions I get:
- Where can pre-service teachers from my program start building their personal networks?
- How can I approach good guest math bloggers for our new math and science project?
- What is an appropriate forum for my eight-year-old who loves to talk about calculus?
- Who can help visitors of my open courseware depository with a question about a particular topic?
- How can I invite readers to collaborate on making my book draft?
90-9-1
Feb 21st
When people first organize online experiences, they are frequently alarmed by phenomena that veterans expect. For example, you start a short open course online and you send the word out through your networks. A hundred people finish the sign-up task and become members. How many do you expect will respond to an assignment three weeks down the road?
Most people who buy books never read past the first few pages. Most people online lurk rather than participate actively. In the majority of situations, only about ten percent of people who sign up for online participation will contribute anything whatsoever at all, and about one percent contribute actively. If you have different distribution, your situation is special and you need to be sharing what it is you are doing!
The power law describes the distribution of contributions by members of most communities. Most recently, I encountered it in P2PU (peer-to-peer university), where School of the Mathematical Future offers its courses. Here is the discussion about School of Webcraft data, and a typical graph from it:
A newbie, looking at this graph, may think it unbalanced and problematic. But this is actually a course that is doing better than is normal! About a third of people are actively contributing, versus the typical ten percent. And that one person who does more talking than anyone else? It is a role someone has to play!
Google Books for publishers: O’Reilly online event review
Feb 15th
I am exploring the book component of math content aggregation, since several of us are working on community book projects, including Sue’s anthology of informal mathematics, Dani’s GeoGebra, and my math clubs. Content aggregation is what we are doing at the moment; the next steps are packaging, distribution, and co-production of open content around the books, which is a part of their overall “campaign.” This letter is about the distribution step.
Last week, O’Reilly, a good book-centric community role model by the way, organized an interview with people from Google Books, which you can view here: http://post.oreilly.com/rd/9z1z1rfsahrh14rvf71o4blhp13pqkkl88cb5194s8o
I took notes for our book projects:
- These days, people find the majority of books they eventually buy through internet searches. Therefore, the key component of any book venture is supporting online content discovery.
- Google Books indexes 100% of the text, which is searchable, without necessarily making it available for preview beyond the phrase found. Some of us will want 100% preview or Creative Commons license and others will want smaller previews.
- Meta-data further adds to convent discovery. It includes information on where to buy ebooks and paper books, and Google Books can sell ebooks and paper books then and there as people find them through the browser. In this, they are competing with other programs like Kindle.
- They answered my question about co-production with readers with, “we are planning for reader content in the next major update” which tells me we need to plan for it separately for now.
- They support partnerships with local paper booksellers and can guide people to them. This was important for Sue.
- The cloud model means that ebooks are accessed from anywhere online (like your Google Docs) and on smartphones. People can also download ebooks with or without DRM – the ability to disable it is important for me).
- If the book is “high design” (non-standard page layout, fancy backgrounds) there is a choice for this original view or “reflowed” view for smartphones and such.
- The starting page for publishers is here http://books.google.com/support/partner/
Lowering prices or making wealth? Games and math
Feb 14th
This is my answer to a discussion Colin Chambers started at his game developer group Symbiotic Learning. Colin’s prompt was:
Please read the passage below, and then read it again, swapping GAME for SCIENCE, and decide whether you believe it applies to either games, science or both. I strongly believe gaming, as outlined by Jane, has a strong relation to science. What about you?
A GOOD GAME HAS: (Jane McGonigal)
1. A goal
2. Rules
3. Feedback
4. Voluntary participation“Playing a game is the voluntary attempt to overcome unnecessary obstacles” ~ Bernard Suits
Let us talk about the concept that’s important for “voluntary participation” – PRICE OF ENTRY. The price is in several currencies, including time, money, and reputation.
For example, the proverbial rocket science or brain surgery science have very high price of entry in all three currencies. You need to study for years, it costs a lot of money (yours or the society’s) and you need to gain a lot of reputation as you go along to be supported in any serious experiments and publications.
Environmental science or nutrition science have lower price of entry, and in fact, there are many citizen science projects in both.
Let us look at games. Eve Online has a monthly fee, requires about 30 hours before you understand what’s going on, and in-game connections to corporations to have any sort of fun with it. As games go, it has one of the highest price of entry. Not coincidentally, it involves rocket science.
World of Warcraft has the same monthly fee, but it is fun to play from the first five minutes, can be played solo, and supports casual gaming. It has much lower overall price of entry. Both are excellent games, but the difference in price of entry correlates with the number of players, which is about fifty times higher in WoW.
Now take Farmville, with five times more players still than WoW… You see where this is going!
Right now, mathematics is like “Eve Online” – the price of entry is such that, for example, only about 5% of adult Americans are algebraically literate.
Should we lower the price of entry for education? Should we aim, instead, of making people wealthier in all currencies so they can pay high entry prices?
An outsider takes on “subitizing and unitizing”
Feb 6th
I am yet to find a good way to package discussions that happen in email-based forums. What follows is an attempt in that direction. First, I pasted some discussions into SubQuan and Friends page, and invited participants to edit it. This works reasonably well – here’s the page “SubQuan and Friends” that resulted.
Then I invited Maria, one of the people who ask to be guest bloggers for this blog up in exchange for SEO links, to write something about that draft. I thought to myself: here are all these people offering me their time and effort in exchange for one of the brave new currencies. Can I use it for something good? The idea was to give people who participated in the draft feedback from someone who is not math educator and isn’t directly related to math ed, but took time to investigate what we did. I have tried doing something similar with others who offered before, but it never produced relevant content until now. So here is the result of this, if you will, social experiment. I think some key ideas came through, if not always in ways I would expressed them. I think it’s curious. What do you think?
~*~*~*~*~*
How Subitizing Systems Support Creativity
It would be nearly impossible to eliminate unitizing from early mathematical education, and we’d probably regret it even if we did succeed in the reestablishment of subitizing as the primary sense of quantity. But if we could supplement unitizing instruction with subitizing, innumerable creative opportunities would surface for both teachers and students. Why? Think of the ramifications: elementary math is taught only as a “stepping stone” to the active solving of real-world problems with mathematical tools. What if the functional applications of math could be taught and realized earlier? Subitizing might be able to help math teachers accomplish that goal.
Mathematical Applications
Developing a sense of proportion and a glimpse of the “big picture” early on could help young math students grasp both the basics and the potential for creative mathematics. By making the “basics” more intuitive and accessible with subitizing, teachers could even get more creative with their assignments and projects. When I was a freshman in college, I remember an assignment from one of my favorite math professors that involved constructing a specific three-dimensional image out of three-sided modules. I knew how to construct it using four-sided modules, but this was a new challenge and required a deeper study of proportion. After considering the problem, I knew how many modules to use – not by counting, but by subitizing. At the time, I didn’t know how I was able to get started on the project so quickly, but now that I understand the concept of subitizing, I realize that it’s truly necessary for creative mathematical endeavors. Everything from trigonometry to origami is immediately more accessible when approached from a subitizing perspective, as I have experienced. Counting can only get you so far, but the spatial perceptions and real-world connections made by subitizing can provide more creative potential for young students.
Subitizing in Music
Still not convinced? Most people would consider music to be a more “creative” discipline than math, but subitizing is used to a great extent in both. If you’re a musician, you know that sight-reading isn’t much more than training your mind to subitize as quickly as possible and building muscle memory in your body. The physical movements of a musician who’s sight-reading (or even performing) are in response to immediate subitization of the notes on the page. And, as they say, practice makes perfect – by working to improve sight-reading, musicians can improve their subitization abilities (or at least the ability to process subitization). A professional musician knows exactly how many notes are in a measure after the briefest glance and plays them mere milliseconds later. That’s taking subitization to new creative heights.
Instructional Implications
So, if the ability to subitize can be honed and “practiced”, what are the classroom applications? Drilling students with subitization exercises rather than counting or operation-based activities could improve their abilities to sense quantity and proportion. And being able to recognize and apply those abilities is the first step toward getting creative with math.
Bio: Maria Rainier is a freelance writer and blog junkie. She is currently a resident blogger at First in Education and performs research surrounding online degrees. In her spare time, she enjoys square-foot gardening, swimming, and avoiding her laptop.
CO11: Connecting Online conference, February 4-6, math presentations
Jan 24th
The theme of the conference is connecting online for instruction and learning that goes beyond the classroom. Presenters from around the globe will discuss the following topics:
- Connecting online to improve instruction and learning: Online learning and instructional experiences
- Experiences with the use of technology in face-to-face and online classes. What worked and what didn’t work for you?
- How do you use technology to promote your online workshops, consultation, and communities?
- Research conducted on e-learning
- Books written on e-learning
The conference takes place in WiZiQ. There are 41 sessions and 3 of them are on mathematics education. At the time of the event, click the “join” button at the event’s page to enter the webinar room.
Here are details about the three math sessions, in the chronological order.
CO11: Intellectual consumerism in mathematical learning Dr. Maria Droujkova
Friday, February 04 2011 | 8:00 AM (EST)
February 4th, 8am Eastern Time
Focusing on mathematics, I invite participants to discuss how pure learning promotes intellectual consumerism. Multiple social forces, such as child labor laws, formal schooling, institution and extension of adolescence, and more recently degree inflation, are preventing students from meaningfully participating in productive endeavors until relatively late in life. Online communities hold the hope of change, supporting healthier balances of consumption and creation, as I show using examples of online mathematical communities.
CO11: SubQuan: A cross-reality solution to understand mathematics by Dream Realizations with Daniel Cooper Patterson, Rebecca Reiniger, and Anna-Marie Robertson
February 4th, 11am Eastern Time
We will demonstrate the necessity of connecting online to improve instruction and learning. We will be using the new field of visual mathematics as our case study which will show the need for a cross-reality solution.
CO11: Integrating Math Art and Music in a computer language by Dani Novak
February 6th, 4pm Eastern Time
This session will introduce a new piece of software called MuMart (Music Math Art), programmed and developed by David Rosenthal with help of Dani Novak and support form Ithaca College. It can be used to create Dynamic Mathematical Art and to teach kids Mathematics in a meaningful way.
January 2011 Math 2.0 events
Jan 8th
Math 2.0 Interest Group’s January Online Events: Open to the Public
If you’ve never experienced the thrill of having a conversation with a math celebrity, you’ll want to clear out a few spots on your calendar for this month’s Math 2.0 online events. The four meetings will be held in an Elluminate virtual room, which opens half an hour before the start of each event – so you can “arrive” early and take a look around if you’ve never used this service. Simply make sure you have a microphone, navigate to the Elluminate room’s URL, click “OK” and “Accept” until you’ve reached the login page, and enter your name. It’s simple and easy, and you’ll be amazed at the enjoyment you’ll get out of communicating directly with each event’s prestigious guest. The following descriptions of Math 2.0’s events will help you decide which ones you’d like to attend.
MoMath: Museum of Mathematics, 1.12.11
North America’s first museum devoted entirely to math will be opening soon in Manhattan. The goal of this exciting new institution is to enhance the public understanding of mathematics with engaging activities that range from riding a square-wheeled tricycle to studying colorful geometric exhibits. The event will be hosted by Cindy Lawrence, Chief of Operations at the Museum of Mathematics, starting at 6:30 PM Pacific (9:30 PM Eastern). Feel free to ask her about the Math Midway traveling exhibition, her organization’s fundraising efforts, when the museum is scheduled to open, and any other topics you might want to address. This is a great opportunity to learn from the success of this organization’s efforts to bring math into the public eye.
Sliceforms, D-Forms, Anamorphic Art and “Bridges” Conference: Art and Mathematics, 1.15.11
This event is hosted by John Sharp of the London Knowledge Lab, who is well-known for his work in art and mathematics. He will be discussing his work in sliceforms, which are mathematical models made from paper sections. You can view his YouTube channel and Flikr page on sliceforms as you prepare to engage this honored guest in conversation. Sharp will also be talking about D-Forms, which are made by connecting simple shapes with equal perimeters or connecting different parts of a shape to itself. His work in anamorphic art is also interesting, using intentional image distortion to help explain coordinate systems and spatial awareness. Finally, you can ask Sharp about his role in the 2006 Bridges Conference in London, an annual event that continues to showcase both mathematics and art. Join the Elluminate room by 11 AM Pacific (2 PM Eastern) to enjoy this event.
Bootstrap World Programming Environment, 1.22.11
If you’ve never heard of the Bootstrap curriculum, you’ll be amazed to learn about its impact on at-risk middle school students around the country. It’s a free algebra-focused curriculum that introduces students to functional programming by encouraging them to design their own videogames online. There are nine 90-minute lessons available, designed for use in after-school programs that can be run by volunteers. The curriculum makes it easy to teach algebra while making the experience fun and accessible. Math 2.0 has invited creator and program director Emmanuel Schanzer to host this special event, so don’t miss it – log in by 11 AM Pacific (2 PM Eastern) to participate.
HowToSMILE.org: Science and Math Informal Learning Educators, 1.26.11
This intriguing online resource is a comprehensive collection of math and science activities that are available to anyone free of charge. Although they were designed to be used by educators who teach school-age children outside of the classroom (in museums, after-school programs, zoos, and similar venues), they can also be used by others to teach math and science concepts in a fun way. Dr. Sherry Hsi, Co-Leader of the SMILE Pathway, hosts this session on informal education with the high-quality resources available on the SMILE project’s website. Join her at 6:30 PM Pacific (9:30 PM Eastern) for an interesting conversation and a great opportunity to learn more.
This is a guest blog post, written by Maria Rainier. Thank you, Maria!
Maria Rainier is a freelance writer and blog junkie. She is currently a resident blogger at First in Education, researching various online degree programs and blogging about student life. In her spare time, she enjoys square-foot gardening, swimming, and avoiding her laptop.
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