Posts tagged tech toys
Math groups on Flickr
Nov 23rd
This is a guest post for Technology Integration in Education.
Math is beautiful. A tangible proof: there’s a lot of mathematics on the premier social site for sharing beauty. Check out the newest shared images from a few of 700+ Flickr groups that have “math” in their descriptions. Aggregation of similar content is one of the more accessible ways to move from sharing to collaboration (Shirky). Once a large example space is collected and tagged by the community, it becomes a valuable learning object.
Members of Math World, a general math group with about eight hundred members, have collected about three and a half thousand computer and physical models, and photos of found mathematics.
Credits: antarctica246, ~RND Modelshop, dkuropatwa
Seven and a half thousand members of Geometric Beauty are prolific, having shared more than a hundred thousand images. This is an example of collecting pictures by academic subjects.
Credits: mikhailovat, Agnes.L, craig h1
There are many groups devoted to more narrow areas within mathematics that are particularly beautiful. About a thousand groups have the word “fractal” in their descriptions.
For example, the group simply named Fractals shares computer art and fractals from nature.
Credit: 4everMiku
The group Fractal Spirals is more narrow in its focus.
Credit: Thomaniac
Fractals Transformed is devoted to collages and other transformations of fractal images.
Credit: Cal KT
Some groups focus on particular type of spatial transformation. If a picture is worth a thousand words, thousands masterpieces created with each transformation answer the question, “What is this math for?” with an incredible power.
Credits: Duncan C, Lyle58, fotobananas
Credits: Vincent Montibus, helen sotiriadis, Michael LaPalme
Software-centered groups collect images where, to quote the description of Algorithmic Abstracts, “the code is the art.” In image comments, members discuss finer points of programming and arrange to exchange source files for building upon previous work.
Algorithmic Abstracts requires members to write the code for their images themselves. “Obviously the use of frameworks is expressly allowed.”
Credit: Kim Asendorf
Structure Synth is a generative art application, and the group shares images made with it. Focus on a particular tool is a typical principle of collecting pictures.
Credit: wsanter
On the other hand, members of digital flower can use any piece of software, as long as they generate images of flowers with it.
Credit: Marina0195
Math clubs, Olympiads and other events sometimes make Flickr pools for their members. For example, MEMO 2007 is a collection of Middle European Mathematical Olympiad pictures, organized as a group.
Credit: Memo 2007, Eisenstadt
Other collections are organized by tags. For example, I store my math club photos under the tag naturalmath.
Credit: Natural Math
Organizations create Flickr accounts devoted to their work, such as Center for Science and Math Education.
Credit: Center for Science and Math Education
How narrow can a focus of a Flickr group become? You’d be surprised! For example, consider Hyperbolic Crochet. Understandably, it’s not a large group. But isn’t it marvelous that there are 44 people in the world who openly agreed to collect photos of their crocheting projects devoted to hyperbolic surfaces? And that I can not only admire the photos, but comment, ask for tips, and join the project?
Credits: DETEXO, daisymae cs
Multiples of 37 members have collected almost two thousand pictures featuring you-guessed-what. It leaves one sort of speechless. It helps their collecting cause significantly that 666 is a multiple.
Credits: Rodent Badcock, SARK S-W
From Decorative stars to Origami Tesselations – intersections of sets defined by shape, color, technique, software and other qualities make for wonderfully quirky image collections.
Credit: cinderella.girl63, LidyaDiard
This is a sampler, not a comprehensive review. There are very interesting math-rich Flickr communities devoted to 3d modeling, animation, data visualization, networks and so on. If you like math, Flickr is the place to find it by users, groups, galleries and tags.
Dig and fill: The shadow scholar
Nov 22nd
One of the most-discussed articles this month in Chronicles of Higher Education, The Shadow Scholar introduces “Ed Dante” who writes student assignments for hire. Here’s how he describes his daily work…
“In the past year, I’ve written roughly 5,000 pages of scholarly literature, most on very tight deadlines. But you won’t find my name on a single paper.
I’ve written toward a master’s degree in cognitive psychology, a Ph.D. in sociology, and a handful of postgraduate credits in international diplomacy. I’ve worked on bachelor’s degrees in hospitality, business administration, and accounting. I’ve written for courses in history, cinema, labor relations, pharmacology, theology, sports management, maritime security, airline services, sustainability, municipal budgeting, marketing, philosophy, ethics, Eastern religion, postmodern architecture, anthropology, literature, and public administration. I’ve attended three dozen online universities. I’ve completed 12 graduate theses of 50 pages or more. All for someone else.
You’ve never heard of me, but there’s a good chance that you’ve read some of my work. I’m a hired gun, a doctor of everything, an academic mercenary. My customers are your students. I promise you that. Somebody in your classroom uses a service that you can’t detect, that you can’t defend against, that you may not even know exists.”
One of the most heart-wrenching parts of this story: what took Dante over the moral event horizon was his college experience. He wanted to do some real work that OTHER PEOPLE WOULD FIND USEFUL.
“I was determined to write for a living, and, moreover, to spend these extremely expensive years learning how to do so. When I completed my first novel, in the summer between sophomore and junior years, I contacted the English department about creating an independent study around editing and publishing it. I was received like a mental patient. I was told, “There’s nothing like that here.” I was told that I could go back to my classes, sit in my lectures, and fill out Scantron tests until I graduated.
I didn’t much care for my classes, though. I slept late and spent the afternoons working on my own material. Then a funny thing happened. Here I was, begging anybody in authority to take my work seriously. But my classmates did. They saw my abilities and my abundance of free time. They saw a value that the university did not.”
Some prisons and armies use a form of punishment: first, you dig a trench. Once you are done, you fill it back in. Doing work that nobody will ever appreciate reminds me of this psychological torture.
Different people require different use/practice ratio to find their practice (learning tasks) reasonably meaningful and motivating. Everybody understands that doing work that is useful for others requires some amount of practice tasks. However, many college courses and whole program set this ratio to zero. The prospect of current tasks being useful years into the future is way too distant to motivate most humans.
Have more tasks that have immediate use for some currently living people and communities. Students can write for collaborative open resource projects, review papers for conferences, program and distribute needful software, and otherwise pitch in where work is needed. This way, even if they hire someone to do their work (which will be less likely this way), at least the work will be useful to the society!
A few examples of immediately useful learning tasks that proved successful in my teaching
- Write a Wikipedia article
- Compose music for a clip based on an essay
- Illustrate a book
- Comment on an active popular blog or forum
- Answer questions at a topic help forum
Another big huge motivator is play. In a twisted perverted way, grades provide a game mechanics that supply a sort of motivation. But this is another story.
Traveling with the souls of others
Nov 20th
I have to correct what I said above. Some geeks I know don’t like sci-fi or fantasy, but use math for their otherworldly needs.
The Global Education Conference 2010 is done. Linda Stojanovska compiled the list of links to recordings of math sessions below. When I followed the Twitter stream of Kevin Simpson, the volunteer moderator of my presentation, his first message read: “Silent and Listen are spelled with the same letters.” So I thought it would be nice to animate it. These days, if you can formulate your software requirements as a web search phrase, you will probably find a free tool that does what you want. The search for “anagram animator” brought up this instrument from WordSmith.org which I shared with Kevin.
I will use this for “Magic Lantern Math” guided visualization activities. Long silent pauses are the key component there.
Monday, November 15th
15:00 – 16:00 KEYNOTE: Hall Davidson – Three Classroom Projects that NEED the World
18:00 – 19:00 Dr. J. Gail Armstrong-Hall – A New Spatial Theory.
20:00 – 21:00 Patti Duncan – Developing Essential STEM Skills Through the Use of Digital Media
Tuesday, November 16th
14:00 – 15:00 James Gerry – Web-Based Collaborative Innovation: Beyond Web 2.0
16:00 – 17:00 KEYNOTE: Jim Brazell – The Future is Here: The Role of Science, Technology, Engineering, Arts and Mathematics (TEAMS) in Global Innovation
17:00 – 18:00 Scott Laidlaw – Breaking Through the Emotional Resistance to Math
21:00 – 22:00 Donald Cohen – Calculus By and For Young People-ages 7 and up
Wednesday, November 17th
08:00 – 09:00 Lisa Johnson – The 180 Degree Mathematics Classroom
11:00 – 12:00 Richard Snow – Teaching High School Mathematics Curriculum using TI Nspire CAS
11:00 – 12:00 Linda Fahlberg-Stojanovska – Screencasts, Captions and your Global Audience
12:00 – 13:00 KEYNOTE: Dr. Linda Fahlberg-Stojanovska – GeoGebra in Math Education – Global Community
14:00 – 15:00 Corey Nascenzi – Engage and Motivate Math Students with CYBERCHASE PBS Online Resources
20:00 – 21:00 Maria Droujkova – Math 2.0 Interest Group
21:00 – 22:00 John Sowash – Collaborative Projects for the STEM Classroom
Thursday, November 18th
08:00 – 09:00 Iftikhar Husain – Visual Math with Geometer’s Sketchpad
18:00 – 19:00 Linda Fahlberg-Stojanovska – Classroom Wikis and GeoGebra
Conrad Wolfram, a Progressor
Nov 17th
This is a guest blog post for Technology Integration in Education.
In his TED talk, Conrad Wolfram makes a call to replace traditional math courses with programming. Here are edited quotes from discussions of the talk from two math communities, Natural Math and Math 2.0.
The video:
–
David Weksler started the thread at Math 2.0 and Rachel Lunt started the thread on Natural Math.
Dani Novak:
To me it is all unfolding human consciousness and evolution, but most of
my colleagues do not feel that way, and some students don’t either.
Edward Bujak:
Excellent points are made throughout the Ted Talk by Conrad Wolfram, but I like the one at about the 12 minute mark when he said, “to understand math, program it,” which is certainly true for any topic when you program it, but more so for analytical subjects. The other big take-away is that computers liberate the human from the drudgery of math intensive laborious calculations so that humans can do the more cognitive higher-level thinking that we need to do and that only humans can do.
Bradford Hansen-Smith:
The real incentive that drives math seems to be the money that can be made. How would one expect any different in this money-focused culturally corrupt planet we live on. Money is not how the universe works, nor is mathematics. We have so far shot ourselves in the foot and do not notice our leg turning green because we are looking at the abstractions of our own constructions.
Kirby Urner:
If technology means anything good, it means helping to provide more alternatives. For those who do elect to take the programming route, there are a lot of details to consider, such as “programming what?”, and “programming how?” In my various classes over the years, I’ve put some emphasis on working with pre-written programs, which students are able to read and change. This in contrast to “blank canvas” programming.
A lot of math-with-programming people tend to focus on the very young and go for a lot that’s colorful and glitzy. I’m not against doing this, however my own focus is a more mature audience with an active imagination. A lot of the “picturing” of what’s happening in the code needs to go on in the student’s head, in the mind’s eye. The output may nevertheless be colorful and textured.
Bradford Hansen-Smith:
My question and challenge is to see what can be generated if as much time and effort went into programming of folding with the
circle as is done with the square. That would mean people would have to start seriously folding circles to know the difference and I don’t think that is going to happen very soon.
Kirby Urner:
Your focus on the circle as a starting point is at least well demarcated and easy to comprehend. Sharp distinctions make useful niches in the
ecosystem of ideas, you have that going for you. Likewise this
tetrahedron stuff I’m doing as Martian Math has an easier time gaining traction than just another brand of blah.
Joshua Gay:
I disliked the first 12 minutes of the talk. But, fortunately, he is actually getting into ideas similar to Papert’s constructionism and Montessori’s manipulatives (feeling and playing with math). I like his idea that programming and playful process-oriented investigation can and perhaps, should form a cornerstone of education. However, I think there are a lot of other options such as role-playing games; collaborative activities; new forms of dialectic/brainstorming, etc. that have many things in common with programming that could also be introduced into such a curriculum.
Also, I don’t agree with his call that math should be replaced with a computer focused curriculum. I can see a place in a curriculum where “math class” is an opportunity for students to explore pure math, problem solve, do origami, etc etc. Although, certainly agree that we should demolish what is becoming the traditional mathematics curriculum and course.
Lastly, if we do arrive at an age where we integrate computers into our curriculum, I do hope we consider a purely FLOSS philosophy for our schools and not become entrenched into using Wolfram|Alpha or Mathematica :-)
Rachel Lunt:
I do not necessarily agree with Wolfram on a personal level, but I think more debate and discussions opened about maths and the way it is taught is positive… Here in France, there is no debate and teaching is very stagnant.
Maria Droujkova:
The old Russian sci-fi term “Progressor” means a person from an advanced
civilization who infiltrates a backwards world, trying to promote its progress. Conrad Wolfram is one of the most successful Progressors I know. His projects affect millions of people. That’s one reason I got his TED speech from about a dozen different sources yesterday alone.
Given where humans are now, what math-rich endeavors should a Progressor choose, to make the most impact? Everything
related to computers, such as programming, computer modeling, system analysis, data visualization, and computer science – all these areas are HOT. Millions of people work in computer industries that did not exist a couple of decades ago. Absolutely all areas of life are affected.
A variety of math niches is very important for ecological health, and intrinsically valuable. Modeling activities such as Sliceforms, Differential Analyzer, and SubQuan have to keep finding followers, grow, develop and spread. That’s what our Math 2.0 Interest Group is all about!
I just can’t blame Conrad for riding the computer wave. As a Progressor, he’s maximizing his impact. People may find the rest of our
work easier to comprehend, once they accept SOME change. Programming communities spearheaded the incredible recent growth of modeling, math art, amateur physics, maker and other
math-rich communities.
Dani Novak:
Things are changing now so fast in the Physical dimension that what we will do in education 10 years from now is beyond imagination. Just
like what we are using now was hardly imagined ten years ago. What is important is to remember the holistic nature of human beings: what it is like playing on the beach, building sand castles and just having fun: integrating physical activities, mental activities, spiritual activities, working in communities, etc.
Murray Bourne:
I was in a meeting yesterday demonstrating Wolfram|Alpha to some lecturers. For the math people, I showed some integrals and graph drawing, for the chemistry lecturers, I showed some chemical compounds, and for the non-scientists, I searched on one of their birthdays.
The non-scientists were very impressed, wanted more and could see the immense potential, but the math/science people felt threatened and said things like “I would never show my students this tool. They wouldn’t know what to do with it or understand what it is telling them.”
I don’t totally agree with all of Conrad Wolfram’s talk, but I am very concerned about the lecturers who refuse to use powerful mathematical tools that have been around for a quarter century.
Live online math ed events: A review
Sep 20th
This is a guest post for Technology Integration in Education.
This summer I taught an online graduate course, “Teaching and Assessment in Secondary Mathematics.” One goal of the course was to help future teachers to join the global educator networks. Toward this goal, one of the assignments was to participate in a live online event every week. I would like to share my list of event sources I started then. I only list free and open events, and communities that hold events somewhat regularly.
Math events:
- Math 2.0 Interest Group holds weekly events, where different math community leaders present and answer questions about their work.
- #mathchat is a weekly mathematics educator Twitter chat, meaning it’s text-only and limited to 140 characters per message. It’s an unexpectedly lovely medium, accessible from mobile devices. The events are egalitarian and highly interactive.
- GeoGebra NA Network has a calendar of GeoGebra-related events in North America, including online events
- Wolfram Education provides Elluminate events for users of Mathematica, Wolfram Demonstrations and Wolfram Alpha.
General education events that may include math topics:
- Technology Integration in Education has online seminars, surveys, meetings, and a Twitter chat with #lrnchat tag.
- LearnCentral‘s Host Your Own Webinars invites educators to post their own events. There are usually 5-10 every week, with several weekly series.
- CauseWeb has monthly online seminars about teaching college-level statistics. Participants can’t interact with one another, but can submit text questions for the leaders.
- Educator’s Guide to Innovation has 5-7 events per week, on a variety of topics including mathematics.
- Classroom 2.0 holds interviews with book authors and community leaders, virtual conferences, and a variety of other online events, usually a dozen or two per week. This is currently the most active event-centered community
- TappedIn is a text-based community with multiple weekly chats for teachers. It is one of the oldest educator communities online.
- #edchat is a weekly Twitter chat with general ed topics. It is very active, with hundreds of people following and participating, and a thriving blogger community involved.
Please add event sources I missed!
3 Large Math Applet Communities
Sep 13th
This is a guest post for Technology Integration in Education. I review three large active online communities centered on sharing applets, widgets, interactive models, and other pieces of “executable mathematics.” What other applet-making communities are currently alive, active and promising? Please add to the list!
- Scratch from MIT, the most popular descendant of Logo, currently has about 130 million applets. There are two very good reasons for this popularity. First, the programming environment itself is visual, intuitive, and so simple I used it with kids under three and they got it. It looks and feels like building with Legos.
Second, Scratch has excellent tools satisfying all principles of community building. Applets are shareable with one click of the “share” button, as you make them. Each applet gets its own linkable and taggable page with comments, information about the author, ratings, tags and other community feature. Applets are remixable, with automatic tracking of previous authors. I use Scratch to show kids what is open source software, as you can open any applet’s code in your editor with a click of a button on its web page. Also, applets are easily embeddable. Here is one of my students’ favorites:
Because Scratch community does not have any top-down taxonomies, categories, or quality controls, it may be hard to find applets that satisfy a particular set of topic, level and quality requirements – what teachers need for lesson planning. On the other hand, kids can usually find what they need, such as games with particular game mechanics.
There is also an educator community ScratchEd, and International Scratch Day celebrated in May by hundreds of local communities, and online. - GeoGebra is a powerful platform for making sketches and animations, solving problems, and supporting rapid development of math interactives. Its particular strength is the dynamic connection between a computer algebra system and geometric constructions. Drawing with Euclidian tools is automatically or easily linked with graphs, functions, formulas and tables of values. A lovable feature is the ability to remember any multi-step geometric construction as a custom tool. For example, once you build a star using Euclid’s construction axioms, your next star can be created with a click of a button.
GeoGebra community has a strong support for local groups through GeoGebra institutes and regional conferences, and has applet-sharing wikis in 27 languages. Applets are shareable, embeddable, and remixable, but community tools, such as an active forum, are not applet-specific. This promotes creation of many different communities for aggregation and discussion of GeoGebra content in groups, such as the wiki where I first met the above animation. - Wolfram Demonstrations requires software with a somewhat steep learning curve. This means every Demonstration is made by a math geek, with the obvious implications for quality. Mathematica software is not free (the viewer is), but volunteers for Wolfram used to get a free copy. Volunteer tasks are accessible to novices.
Demonstrations are linkable, and their code is available for remixing. There are no other social features, such as discussions of applets, tags or ratings. The site uses top-down categories for browsing applets. The sense of community is sustained largely through academic connections of authors, and isn’t apparent from the site.
Aggregation
Sep 4th
One of the best ways to engage kids is to provide collections of many similar objects. Games and activities happen. “Playing webs” – while not a game – can occupy a couple of four-year-olds for an hour or so, if you provide enough yarn. The emerging complexity is fascinating for them. Please send your pictures and I will write it up with illustrations.
Bullying (1, 2) can be many people doing something slightly unpleasant – to the same person, at once. Aggregation, too.
On the happier note – blog carnivals, like Math and Multimedia. Significant amounts of fun aggregated!
Tech toy of the day: Mekanimo. Check out animations!
Dimensions
Sep 1st
Instead of “brick and mortar” for LearnSpace we plan to open, I’d like to have something like Luminarium! What learning won’t happen in a cool space like this? One can dream, right?!
15 million people in Britain are “innumerate” – hence too many could not play the lottery that required them to compare numbers like negative eight and negative six. I wonder if the humanity will grow out of lottery any time soon, by the way.
Neil Stephenson announced his “post-book” project just a couple of days after Seth Godin announced he’s not going to make traditional books anymore. Hmmm!
I really like how WIRIS graphs. I want to teach it to talk to Makerbots.
Actually, it would be nice if more of my things, real and virtual, talked to one another. Even announcing webinars to all the places isn’t automatic at all, because of format differences. I hesitate to give mundane tasks of this sort to interns, too.
Mobius metaphor
Aug 29th
Jos Leys makes great math movies, including this gem of a metaphor:
I can’t wait to use his Mobius Bloom’s footage to strengthen the point I’ve been trying to make – that the Creating tasks are not for advanced students, gifted people, or graduate school only! Actually, struggling students, young kids and noobs need Creating tasks much more.
There are always jobs for kid, teen and grown-up interns at Natural Math. You help the world, develop valuable skills, and enhance your portfolio. What’s not to love?
Yesterday Karen Mellendorf of MonarchBooks alerted me to a math t-shirt from Woot, with this design:
I was too slow to buy the limited edition, but I really admired the thoughtfulness and deep knowledge of “who’s who in math entities” that went into designing it. It’s a list of topics for two-three years of a good math club meetings, right there! Including the Mobius strip, of course.
Speaking of support
Aug 27th
Ironically, some of the more developed, well-supported and widely used community meta-currencies happen in massively multiplayer online games. Also, the name for these currencies has the word “dragon” in it, of which I highly approve. Everything is better with dragons!
I hope we can learn from Carrboro Creative Coworking. They helped a lot of lovable local projects.
I would dearly love for my webinar software to do what my laptop+projector does so well: stream whatever is on my screen and sync it with the sound. As it is, you can tell people to view a video in their browser, but you can’t view in-sync and thus point out a frame to everybody. Nibipedia-like software may provide a solution, if this “bookmarking of a moment in the video” can be done in real time. Right now any “live” media does not do well at all with “live” event software I know! Yet people like Steve Hargadon can do amazing things with tools we do have, and help others.
Off I go to the Cary Homeschoolers party. The local family educator networks have been incredibly kind and supportive toward our family.
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