Posts tagged Math 2.0
There are forty-five fine presentations at this weekend’s web conference, CO12: http://www.wiziq.com/events/co12.htm
In particular, check out these four presentations from Math Future people:
Friday, February 3
1pm ET Math game development, by Maria Droujkova http://www.wiziq.com/online-class/701943-math-game-development-communities-and-networks
Mathematics educators need to create excellent learning games, which is a hard enough task. But even more challenging is the task of helping everybody – millions of kids, parents, teachers – design or remix their own games. Communities, peer groups and cognitive tools such as taxonomies of games can make these two tasks possible and sustainable.
2pm ET Mathematical art: Learning mathematics by doing mathematics, by Dani Novak http://www.wiziq.com/online-class/701953-mathematical-art-learning-mathematics-by-doing-mathematics
We will present the MuMart “Music Math and Art” wiki and the computer language APGS and give examples of how to learn and teach math in an intuitive way using computers.
9pm ET Place shape vs. place value: A visual foundation for math, by the Dream Realizations team http://www.wiziq.com/online-class/707754-place-shape-vs-place-value-a-visual-foundation-for-math
What do decimal place values actually mean: thousands, hundreds, tens, ones? Let us show you their shape and you can determine the value. Four- and five-year-olds can do it, how ‘bout you? Get a glimpse into the fantabulous payoff of learning to subQuan. Come enjoy a math topic that doesn’t involve much thinking because your eyes do most of the work.
Saturday, February 4
1pm ET Numbered notes music notation, CO12 presentation by Jason MacCoy http://www.wiziq.com/online-class/701971-numbered-notes-music-notation
We will be introducing a revolutionary new form of music notation called Numbered Notes. It uses numbers instead of letters and is so easy to learn that people can play in just minutes. We will be explaining a brief summary of the history of music notation, how numbered notes is the next step forward from what we currently do and how Numbered Notes is an ideal tool to show the connections between music and math. Free sheet music will be available and participants will be able to try it out for themselves on our free website keyboard.
See you there!
I am leading a MOOC (massive open online course) this Spring. The sign-up is open January 17-22 at P2PU School of Math Future:
The course is offered for credit to Arcadia University students, and for School of Math Future completion certificate to everybody. It has the following overarching themes:
- Personally meaningful and relevant mathematics achieved through projects, games, problem-posing and problem-solving.
- Computer-based mathematics, including interactive simulations, modeling tools, solvers, and children programming platforms.
- Lifelong learning for teachers, with the focus of online communities and networks for teacher support, and building your personal learning networks
You can learn more about MOOCs here: http://en.wikipedia.org/wiki/
Join the adventure, and spread the word!
Can you explain how using this virtual zome tool will give students a better understanding of polyhedra than actually building it from scratch for themselves? I have the same question about any virtual experience when compared to actual experience of doing something. I assume you have done a lot of model construction and it is easy for you to understand having the experience, but what understanding do students get with only virtual experience?
Here was my reply:
It is better to have both experiences. The reason is that they are different. In particular, and to answer your question, there are three major features of virtual tools that physical tools don’t have.
1. EASY SHARING
Virtual constructions can be uploaded to the web and emailed around. I can’t directly email you the construction of the lopsided origami dragon I made yesterday, though I am attaching a photo of the end product (and I could take a video, for sure). But it’s not as easy as with virtual objects, and you don’t get the perfect copy of the real thing, but a representation of it. I remember our exchange of many emails about me trying to replicate one of your constructions. It took quite a lot of work to share.
2. EASY STEP REVIEW & UNDO
Speaking of the dragon, I would love to rewind the construction step-by-step and find where I made the extra fold: the wings look different. It’s somewhere around step 9 of 21. I don’t feel like finding the mistake in my paper version: it will ruin the dragon completely, and I am not sure I will trace the mistake anyway. Repeatable step-by-step review, analysis and changes are hard to do by hand, especially for young students whose memory works differently and has fewer registers than adults have.
Step review works wonders with sharing. A student can send the whole construction (often animated, or a screencast – easily made!) and ask peers or mentors to analyze steps, or post questions like, “What would you do differently in Step 5?” With some environments, they can then all share their fully interactive constructions that are answers to that question.
3. EASY DYNAMIC LINKS AMONG REPRESENTATIONS
You can dynamically link formulas, graphs and constructions, which support depth of mathematics. It provides a certain holographic view on the essence of math, metaphorically speaking. GeoGebra is probably a better-known example of this, with algebraic representations linked with geometric constructions. Check out DGS (dynamic geometry software) systems in Paul Libbrecht’s i2geo series (more coming up, stay tuned) at Math Future for beautiful examples:
The word “easy” here is the difference between thousands and millions doing the three activities I described above.
I posed the same question to Katherine, my daughter, who added two items to the list:
In virtual constructions, you can see infinity. (In particular, I am thinking of fractals – MD).
It really helps to change a variable and see what happens to the construction as a result. It is very hard to do in physical space.
I am adding another key item that came to mind: modularity. Once you build a module in a virtual space, you can copy and paste it whole. In physical space, you have to repeat all constructions step-by-step at all times.
- Pre-event discussions can help interested people find one another and form preliminary topics and questions to be discussed live during the event. This means…
- …advance schedule: announcing events at least 2-3 weeks ahead of time. Together with the list of following events coming up, and possibly past events on related topics.
- Open multi-community discussion points. That is, event announcements are prompts to discuss the event topic, right there. I suggest this group plus the LinkedIn group “Math, Math Education, Math Culture” plus Twitter hashtag #mathchat plus any groups associated with the event (for example, the blog of the host, or their community forum). We can also frame this as a one-week seminar at P2PU’s School of Math Future.
- Curation and aggregation. We will aggregate contents from all these platforms before the event starts, and summarize threads – in a place with a “reply” button for post-event discussion. We will also have a taxonomy of events by topics and other qualities, such as math game design, computer-based math, family math and so on (the same event can have all these tags and more).
- Announcements by topic. We need an email-based list, separate from discussion groups, that allows people to monitor upcoming events by specific topics, based on event taxonomy, and without any other email traffic whatsoever.
- Research paper. We ask every event host, “How can people collaborate with you and help you?” The answers are excellent data for a study. Seeking co-authors.
- Conference. This January, we can have a Math Future strand at the Learning 2.0 conference, with the goal of organizing a blended (face-to-face plus online) conference soon, as well.
Yesterday, David Chandler and Allison Krasnow hosted an event at the Math Future series, called “Pi in July.” You can see the full recording here: http://mathfuture.wikispaces.com/PiInJuly
Here are answers to the two questions, one we always asked before, and one we are starting.
David Chandler: Pi is the Greek letter for P. It actually stood for the perimeter. It was just a symbol that some mathematician dreamed up to stand for this famous ratio – that’s the origin of Pi, as P. If you read a sign on a billboard in Greece, you are going to see Pi’s and Sigmas and all sorts of letters we use in mathematics as extra symbols. Let me tell you a little story. I went to Harvey Mudd, which is a science and math school, and across the street was a girls’ school – excuse me, a women’s college as we say now. One of the students was sitting outside, and she had this book – she was studying Classical Greek. She said, “Boy, is this weird – I can’t read a word of this!” She showed it to me, and I started reading. I did not know the meaning of the words, but I could phoneticize it! Basically, just by doing physics and math, you end up encountering virtually every single Greek letter. You see a Pi – that’s P sound, you see a Sigma – that’s S, and you can figure out the way words are pronounced.
MariaD: This leads to a question we are going to ask everybody from now on. Can you tell us a little story about math from your childhood?
Allison Krasnow: Oh, I can tell you one thing I did not like, but then it led to a teacher, for many years, who I adored. When I was in second grade, I could do all the math that they were doing. I would get kicked out of class every day because I explained I could do everything and I wanted harder work. My teacher had nothing for me to do, and she made me memorize my times tables all the way through 25s. And every day, I would have to come in and tell her the 13s, and the next day the 14s… It was an example of the worst thing you can do to a bright young girl interested in math. Consequently, I finally ended up in a right place for math classes, with a teacher I fell in love is, whom I had for four years. I was really inspired by a teacher who was so excited about math that he taught, and that led me to where I am today.
MariaD: What would you tell your teacher now, if you met – the one who made you memorize times tables to 25s?
Allison Krasnow (laughs): I think I would invite her to one of my classes!
MariaD: Here is the second question we always ask. How can people help you in what you do and collaborate with you?
Allison Krasnow: I met David originally online, and later in person. For me, it’s being a part of professional networks. I am currently at a three-week math institute, where I am meeting the most inspiring teachers from all over the country, and learning so much. It’s staying connected to like-minded people who can really inspire you, help you learn more math, and also become better at your own teaching. I met David through a common interest – “Escape from the Textbook” network – and then we met at this conference in person. (Math Future event with Henri Picciotto, the founder of “Escape from the Textbook” – MD.) He is eager to share his ideas with me, and I sort of took them and ran with them in my own direction, integrating them with GeoGebra which is my own personal interest. So, for me, it’s about staying connected with people who inspire you.
David Chandler: I am doing a lot of things on my own, but I learn by interacting. I only discovered GeoGebra a few months ago. I became pretty fluent at it, but there is lots more… I should not even say “fluent” because I know there is a lot of depth to it I have not even touched yet. I am really interested in various kinds of tools. I have done Algebra I and Algebra II – some people here are aware of that. I have actually recorded an entire school year and I have it out on DVDs. (David’s home study sets are at Math Without Borders – MD.) I am working on Pre-Calculus and one of the things I am doing is integrating various kinds of technology in the process. I am using GeoGebra, Geometer’s Sketchpad, spreadsheets and probably several others – Open Source Physics I really like, and use for math, too. You can take a video and put a number on any frame, so you can toss a ball and study the projectile motion and so forth. All these wonderful tools give you access to the real world at much more depth than you can have with a handheld calculator and pencil and paper. So, if anybody has things like that to share, I am really keen on learning them!
I am happy to announce Math Future received a corporate sponsorship offer from DZone, a technology publishing company. We will now have an instance of their new, enterprise-class platform for knowledge sharing, called Qato. This answers to the needs of Math Future as a network of communities.
Consider the network structure of Math Future, which I won’t attempt to diagram because of multiple dimensions. It consists of groups with dense connections (everybody talking with everybody), but also more loose and distributed conversations among the groups, as well as some communities with distributed conversations within.
Image credit: AliceWebb.com
Between groups formed by projects, communities and topics of interest, there is much overlap, as people participate in multiple threads. Groups may be long-term, such as the math game group, or short-term, such as School of the Math Future courses that run for a few weeks. The are also “flash mobs” that get together around a one-time topic. It is frustrating trying to have that sort of communication through a forum structure, such as email groups, as many of you noted.
When people communicate, they need to subscribe to multiple groups and topics, but not all of them: following a book making or a book review group, a seminar, a presentation discussion, a brainstorm about a math game, and so on. Larger topics and groups need to form sub-topics and sub-groups, which in turn may not involve everybody.
Image credit: Tom James, futurismic.com
Some of the groups involved with Math Future use our webinar room for their one-time or regular meetings, which any project organizer is welcome to do as long as meetings are open. This is supported by Web 2.0 Labs and LearnCentral (Steve Hargadon) sponsorship. During the events, as we ask project leaders The Question, “What does your project need and how can people help?” their answers involve spreading the word and aggregating communication. Some of the projects don’t have any social platforms, or only have email lists, though leaders usually participate in other projects’ communities. Currently, Math Future members help with such needs by hand, so to speak, through email or their blogs and microblogs. This is better than nothing, but it does not scale well.
Qato supports Quora-like interface, but also groups and subgroups within the community. People can follow particular groups for ongoing collaborations, and tags for inter-group communication, and individual topics for one-time discussions. This architecture will allow us to support the book projects, conferences, and mathematics education communities much better, because it matches the way Math Future rolls.
Image credit: cameronius.com
Yelena McManaman and I are two homeschooling moms who love math and science. We would like to invite you to a four-week free online adventure for the youngest mathematicians, starting April 25th.
Young children are naturally drawn to harmony, balance and order. They are naturally drawn to math, the math that goes beyond counting and simple arithmetic. Math is beautiful and fun and it all starts early on with a few simple games.
This is what Moebius Noodles, our online parent math club, is about – quick, simple and fun games that parents can play with kids to explore math.
Every weekday for four weeks you will see
- a new math activity to try with your child that takes virtually no time to prepare
- a math concept behind it
- how to adapt it for children of different ages, from infants to elementary school students
- variations to keep it interesting for children with various learning styles – and for parents!
Once a week you will have an opportunity to join us and other parents in live webinars to learn more about teaching math to your child naturally, and to share your stories.
You can also share your ideas, photos, and stories by e-mailing the group, uploading pictures to Flickr, or joining the Moebius Noodles Facebook group – whichever is more convenient for you!
To sign up, think of one question about doing mathematics with your child, and email the question to email@example.com We will use the questions in the second week of the club. Please send this to your friends who may be interested.
Carol is organizing an open online event today, April 21st 2011, at 7:30pm ET, about the science of energy, with a writer Kathleen Reilly. You can also add your name to win Kathleen’s book. Check it out!
Here is my favorite puzzle about the Earth. Imagine you put a string all around the Earth. Now imagine you want to enlarge your string so it can hang one meter from the surface. How much longer will your string need to be? Here are some data about the size of the Earth and here is the awesome Noon Day project for measuring it for yourself with kids and grown-ups from all over the world.
What is the answer if you use an orange instead of the Earth?
PBS Teachers has a collection of three series of group activities for Earth Day Mathematics. The recursive equation activities (population growth and decay) are rather fun.
The trash inventory activity consists of carefully tracking your trash for a day, a week or a month. We have done it with Girls on Track camp at NCSU, and it was a whole lot of fun. The shocking part comes when you start to multiply your trash by the number of days in a year or a decade, or by the number of people in your neighborhood. This is one of better examples of contextual mathematics activities I know.
In the last five years or so, calculating offset costs for this or that activity became popular. Here is an example of a lesson about it – how many trees do you need to plant to offset your car use. I would suggest finding and using online calculators, such as this one for carbon footprint, to see what online communities are engaged with them and in what ways – like Go Zero.
Here is a quote (pre-editing) from the Green Mathematics article I wrote this January for an encyclopedia of mathematics. I am really looking forward to the encyclopedia of 500+ articles on subjects from Accident Reconstruction to Zero. Meanwhile…
Different areas of mathematics allow different approaches to environmental problems. Algebraic reasoning, for example, assumes functional dependencies among variables and known operations. It is most appropriate in cases where algebraic relationships among variables are stable over time and can be established with empirical measurements. For example, producing one megajoule of energy by burning coal emits 92g of CO2. One can compute the carbon footprint of heating a house by coal algebraically, by measuring the energy consumption and multiplying it by 92g.
Calculus is the study of rates of change in variables, and limits of change. In green mathematics, calculus methods are most appropriate when algebraic relationships between variables and their changes over time are measurable. For example, rocket propulsion consumes fuel stored within the vehicle, making the vehicle lighter with time. The efficiency of rocket engines can be computed applying integrals over time to equation connecting changes in mass and the momentum resulting from the engine.
Differential equations is the study of unknown functions by known values and their rates of change, that is, derivatives – the situation frequent in ecology. Differential equations are extensively used in green mathematics to model interactions within systems, such as predator-prey dynamics, fluid dynamics in natural and human-made water and gas systems, radioactive decay, or economic growth.
Statistical methods deal with organization and interpretation of data that includes random elements. Descriptive statistics summarizes patterns in data collected from some group of objects or events, called population. It may include data calculations such as mean or frequency. Descriptive statistics is useful for comparing systems that include randomness, such as per capita consumption of energy in different countries, or recycling behaviors in neighborhoods of a city.
Inferential statistics predicts patterns in the whole population based on data observed in a sample of the population. It is extensively used in biology, ecology, and economics, because collecting data about everything or everybody in the population is rarely possible. One of the most powerful methods of inferential statistics is the analysis of correlations within data. For example, the levels of air pollution in cities correlate with the incidence of asthma among the population. Notably, even strong correlations between two variables do not necessarily mean particular cause-effect relationships. The first variable may depend on the second, or the second on the third, or both may depend on another factor. For example, in children under six problem-solving abilities strongly correlate with foot size. The reason is that both foot size and problem-solving abilities increase with age.
Data visualization is an interdisciplinary area spanning descriptive statistics, grid and graph use from algebra and calculus, specific representation methods from more narrow areas of mathematics such as tree diagrams from combinatorics, psychology of perception and learning, and design. Visual literacy combines the ability to understand and critically analyze visualizations produced by others, and to create quality visualizations for the purposes of analysis and sharing of messages. Because green mathematics frequently deals with controversial issues, individuals and groups promoting different agendas use and often abuse data visualization to make their point. Visual literacy is one of the “twenty-first century skills” whose importance is growing with heavier use of mathematics in ecology, and more emphasis on ecological approaches in all areas of life.
Join Henri Picciotto, involved in mathematics education since 1971, in building a safe haven for math teachers who Escape from the Textbook!
- Follow this link at the time of the event: http://tinyurl.com/math20event
- Wednesday, March 23rd 2011 we meet in the LearnCentral online room at 6:30pm Pacific, 9:30pm 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.
Math 2.0 weekly series: http://mathfuture.wikispaces.com/events
“Escape from the Textbook” is a sharing and collaboration network for middle and high school math teachers who want to escape from the textbook for a lesson, a unit, or an entire course. Hopefully some of the 400+ members will attend this event!
While our schools are very different from each other (large and small, middle and high school, public and private), the challenges facing us are similar. The Escape from the Textbook! network can help us take up those challenges through:
- networking with like-minded teachers
- sharing of successful approaches
- multischool collaboration groups that focus on specific courses or topics
- strategies on how to complement or replace textbook material
- assessment ideas
- different lenses to analyze curricular and pedagogical ideas
The first Escape from the Textbook! conference was held on February 12th, 2011 at the Urban School of San Francisco. You can watch the conference video recordings. The speakers were:
- Jo Boaler (author of What’s Math Got to Do with It?) on pedagogy
- Paul Zeitz (author of The Art and Craft of Problem Solving) on problem-solving
|Henri Picciotto writes:
Please visit my Math Education Page, where I share much curriculum and philosophy, particularly about tool-based learning, and my Math Education Blog, where alas I post rather irregularly.
I have been involved in mathematics education since 1971, at every level from counting to calculus.
I am also involved in word puzzles, particularly cryptic crosswords.