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Working prototypes: MathLexicon, Multiplication Models, Special Snowflake
Oct 24th
Working prototypes are games and interactives that are programmed enough to play, but are still being developed rather actively. In other words, these are public alpha versions.
MathLexicon creates silly new math words out of prefixes and suffixes from its database, and nouns of your choice. Main interactions:
- Enter a noun, receive generated silly math words, with definitions
- Add a prefix or a suffix to the collection
- Add a definition (in the MathLexicon format) of a prefix or a suffix
- Add artwork depicting the new silly word
Multiplication Models is a collection of illustrations for the twelve main models. Main interactions:
- Browse past models
- Submit a model
- Submit a description of a model
Special Snowflake makes word snowflakes. Main interactions:
- Select a word, letter colors, the number of sides and the background for a snowflake
- Select an animation effect
- Save embeddable snowflakes
- Browse past snowflakes
Multiplying polynomials: Quilts from Judy Chaffee
Jun 9th
I met Judy Chaffee at Escape from the Textbook community. She mentioned a polynomial quilt activity that was a hit with her students. This are materials for the activity, posted with Judy’s permission here since she does not have a blog yet – maybe one day!
Judy writes:
I start with showing them how regular multiplication looks (shape wise) using an array. We discuss that when you multiply one digit by another, you get a rectangle and when you multiply one digit by itself you get a square. We then look at how a variable looks when multiplied by itself a number. Next they draw it on paper and then cut their scrapbook paper to match the sizes used in their drawing.
I just started quilting myself and I think this summer I will actually make a quilt using this idea. Oh yeah, I start the lesson with talking about quilting and how some mathematicians are using quilting and math. I’ve included my powerpoint for this part.
Here are a few of the quilts students made:
This is the summary Judy made for the students:
On fractals and corporate sponsors
May 12th
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
Book review: “What’s unnatural?” by Jeremiah Dyke
May 8th
Making abstract entities into characters with their own looks and personalities is a great idea related to many traditions. “Flatland” featured creatures embodying shapes in different dimensions. More recently, moe anthropomorphisms embody entities such as Wikipedia.
The book “What’s unnatural” by Jeremiah Dyke of Hands on Math has a cute anthropomorphic numeral 1 as its main character. The images overall have peaceful, slow and steady feel to them, which I like a lot.
The character goes through different number lands, largely corresponding to the extension of numbers from natural to real. It’s a useful topic, and representing it spatially makes a lot of sense, given the traditional Venn diagrams showing relationships among numbers.
Here are things I would change in the next version of the book.
Show number properties rather than telling about them. It’s done beautifully for negatives, but not for other number types.
I was concerned about negatives presented as “positive numbers that carry a bar.” A negative number is a single entity, even though it takes two symbols to represent it. The same goes for fractions represented as “numbers chopped into pieces” – a fraction is a number in its own right, a single number at that. This seems like a minor point, but kids get confused around this issue.
I would continue to the land of reals rather than irrationals, because it breaks the previous pattern. Natural-whole-rational-… is the previous adventure, and the next in line seems real, not irrational.
I would use the book with kids for its roleplaying potential, and the strength of its overall travel metaphor. Thank you for making it!
Moebius Noodles online math club for parents of the youngest mathematicians
Apr 22nd
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 droujkova@gmail.com We will use the questions in the second week of the club. Please send this to your friends who may be interested.
Earth Day Math
Apr 21st
I am aggregating information on mathematical holidays, but now I want to think of another angle – mathematics IN holidays. Carol Cross from Teaching Your Middleschooler blog inspired this.
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.
Guest post: Why math really does matter to your child – and you
Mar 24th
Edward Khoo is a teacher who enjoys teaching math at his local high school and spends most of his time apart from teaching with his cute 5 year old kid. Edward writes about technology news and updates on his blog. He asked to post this essay to the Natural Math blogs to reach its readers. I really like the multiple solutions example. What do you think?
Math is a subject that many struggle with at school. In fact, I’m sure a big proportion of us would admit to saying “I hate math!” at some point in a frustrated homework session. But there are basic skills that you can draw from math that do matter. And they’re not necessarily the same as those that teachers may give to their struggling students. Whatever they say, being less than fully familiar with Pythagorean theory is not going to condemn you to stacking shelves at the mall. And having trouble with multiplication tables isn’t going to prevent you from shopping at those very same malls.
Neither does having a shaky grasp on the intricacies of computer logic stop you from surfing the internet. When teachers wield such threats over their charges, they’re just using them as blunt tools for bludgeoning students – to get them moving on with the nitty-gritty in their math class. But put those false concerns aside. Then dig a little deeper and you’ll see that math can give your child, and you, the means to ease your way through some real-life problems – both expected and surprising.
The most obvious things that math does for your child is to make them familiar with numbers. But what good math teaching should also do is to go that step further, and make your kid confident with numbers. That doesn’t mean turning them into miniature calculators, able to do long division in their head. It means helping kids to understand that numbers are not scary.
It is the fear of numbers, often created by bad teaching experiences at an early age, which stick through to adulthood – and can make many everyday situations awkward and difficult. If you’re scared of numbers, you might not want to tip after a meal, in case you get the amount wrong. You might end up on the wrong side of a bank loan, because you never did understand how to use percentages. So losing that fear is important, to navigate through life with confidence.
An example of that ‘number confidence’ is dealing with, say, a sales tax at 20% – so that you know how to work out the dollar and cent amount, without freezing. A big problem with math as it’s often taught is that most math problems are presented as only having one solution. If you don’t get that solution, after some gentle hammering to get it into your brain, the bad teachers move on. The good teachers won’t bow out that easily – they’ll try and place a number of tools into your hand, and spend time funding the one that fits you comfortably.
So 20% of $125 isn’t some complex equation – maybe it’s shifting the decimal place along twice, to give $1.25, and then times-sing by 20. Or maybe it’s looking at a fifth of $125; or how many times does 5 go into $125; or twice a tenth of $125. Eventually one of these will click with a pupil– and with a little practice, they’ll have cracked that fear of percentages.
That approach, of trying a method out, failing, and then changing tack until it slips into place – is a really valuable life skill. It’s something a child can take with them, and apply to lots of problems in their life, both as a child and later as an adult: don’t give up, be patient, and find what works for you. So math also teaches kids to problem-solve: learning to step back from an issue, break it down into its component pieces, and then trying out solutions.
Then there’s another side to math which goes beyond those basic questions of numeracy, and onto the issue of understanding the numbers pumped out by the media and politicians. This is a huge life skill, one that underpins our ability to take part in the debates about where our world is going. And as has often been pointed out, in relation to such numbers, there are lies, damned lies and statistics. It is the skill of knowing what politicians and the media are trying to say, through the numbers they quote, that makes you a properly engaged citizen.
So when you are told that the risks of skin cancer, from overuse of tanning salons, has gone up 50%, a strong math skill would tell you what this means. You’d be asking – “well if it’s gone up by half, what was it before, and what is it now?” Compare that to, “holy, molely, half of sun-bed users are going to die of cancer!” That is why math matters to you and your child – without it, you can make bad decisions that can seriously affect your life.
Circle on the Road 2011
Mar 22nd
The community of math circles and clubs just had its annual gathering, called Circle on the Road, at the University of Houston. We had panel discussions, conducted math circles for the local community, and attended topic presentations. I made a short presentation about alternate reality games and the Math Trek game I designed. Here are a few highlights of the event.
The hub for the community is this wiki: http://www.mathcircles.org/ It includes an interactive map of the US math circles and clubs and other tools for finding local groups, programs and summer opportunities. It also features a collection of math problems, the book “Circle in a Box” and other resources.
The Yahoo group for the community is called Circle of Circles.
During the conference, everybody was welcome to play in the large room full of math games such as Set, toys and puzzles.
A couple of hundred people from the local communities were treated to a day of math circles organized by the conference participants in small groups. This gave the participants an opportunity to observe one another conducting activities, and to collaborate more directly. Most of us communicate online, but working together live is a significantly different experience. Also, local parents observed activities, asked questions, and formed groups that started to talk about organized their own math clubs.
The two panels talked about comparing different types of math circles, and relating circles to curricula.
There were two presentations by students: one on experiences of a female circle participant, and another on student-organized, student-run Orange County Circle.
Here is Vi Hart, who gave a presentation about her favorite workshops, drawing an elephant from her popular short movie “Doodling in math class: Infinity elephants”
And here is the movie itself:
Escape from the Textbook! March 23rd at 9:30pm
Mar 22nd
Join Henri Picciotto, involved in mathematics education since 1971, in building a safe haven for math teachers who Escape from the Textbook!
How to attend the event
- 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
About the “Escape from the Textbook!” community
“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
Event Host
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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. For more information about me, check out my résumé and my personal home page. |
Knight Sortalot
Sep 6th
I am sorting and tagging thousands of comments and emails to package them by topics – as essays and/or books. I can’t do repetitious tasks for longer than about 20 minutes at a time. My solution is to “two-time” with some other task, or two. When I was working on the dissertation, I wrote a Flash program called “two-timer” with two timers for task switching, a black hole, blue and red pills for slider handles and probably some other 5yo playfulness I can’t remember. Today, side effects of my two-timing with other things while doing the Big Sort of Texts is a shiny kitchen and a new dragon mount.
That GeoGebra clock divisibility tool is so awesome. It does not seem to work right for high numbers, but the concept!!! Such richness of topics. Now to make one for our “alien clocks”…
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