Two new Learning Tools available

The Ministry Digital Resources Development team is delighted to announce that two new apps, Money by Mathies and Notepad by Mathies, are now available at the App Store, the Google Play Store and for Desktop.  

Please visit www.mathies.ca/LearningTools.php to access them.  

There is also an email list that you can subscribe to if you would like to receive updates about new resources.  Visit http://oame.on.ca/CLIPS/WhatsNewEmailList.html or click the link at the top of the What’s New dialog inside http://mathclips.ca .

The Money by Mathies app allows students to represent values using realistic coin and bill images provided by the Royal Canadian Mint and the Bank of Canada.

  

The Notepad by Mathies app allows annotations to be made on top of blank, lined, isometric or grid backgrounds.

Supports, including wiki pages with sample screen shots, can be accessed using the i button in each app or from http://mathclips.wikispaces.com/MathCLIPS+Tools . 

We need more patient problem solvers

Dan Meyer says a mouth-full!



Need more? Spend time in his "What can you with this?" series.

It is not everyday that I re-post something I find at the Kitchen Table Math blog which they recommend!

How useful are games in teaching Math?

I have been thinking about this question for a while and the answer depends a lot on the type of games we are talking about. There are cross-number puzzles, ciphers to decode pun-ish riddles, drill and practice games, role-playing games, etc.

It may be that "game" is a organizer for "play" which is really a state of engagement. Students can engage in a game for hours, puzzling out the rules and feeling accomplishment.

I wish that I could be at Maria Andersen's presentation - Playing to Learn Math.

Playing to Learn Math? on Prezi

Does our view of Math education allow us to imagine a time when a robot could do a better job of much of our teaching, as the Koreans and Japanese are working on?

This week my daughter, who is studying Math at UW and is currently in a graph theory course, was reminded of a set of games that she played as a youngster - expressly designed to introduce colouring problems in an engaging way. They are MS-DOS based and I have got them to run enough to recognize the screens, but not really to enjoy.

When I am trying to get Sketchpad or Flash to produce a certain figure or interaction, I can enter an engaged state that social psychologists refer to as "Flow", which I find enjoyable.

Keith Devlin would like a couple of hundred million dollars to develop a MMP game that would allow players to construct math learning. I admit to being a tad skeptical, but what would such an environment be worth?

What role have games and play had in your Mathematical development?

Where are the Math Project sites?

Neil Munro shared a spreadsheet with me of the medal counts by country at the 2008 Olympic Games. You may know that the press in Canada was critical of the performance of the Canadian team, especially prior to a run of medals toward the end of the games. If you adjust the medal count for the population of the country, Canada does better than the United States and much better than China. Others have adjusted for a nation's GDP. Depending on the method used, Jamaica, the Bahamas and Zimbabwe fare very well.

It struck me that the question is a good one for a mathematics exploration - especially since the source data is available in lots of locations, including wikipedia and there are media reports and analysis all over the web. Vancouver 2010 is fast approaching too.

I went looking for a repository of good open-ended questions like this and came up with the square root of 0.

Surely, there is some interested wikiphile who is compiling such things. Isn't there?

If you know of some good resources, please let me know.

A Mathematical Search Engine?

There has been a fair bit of buzz about Wolfram Alpha and even comparisons to Google, but I don't think I really started to get it until I saw Maria H. Andersen's Picasa Web Album via Teaching College Mathematics.

Now the wheels are turning. How is Math education going to change with tools like these available to students? CAS tells students answers, this tells students questions.

Mathematical Music

There have been a surprising number of posts here about poetry.

Here is some Mathematical Music, via Heather. Better to watch at Youtube with the lyrics visible.



The Klein 4 Group.

Math in the Movies

If you are going to subscribe to only one delicious feed, choose dougpete, unless you already subscribe to his blog.

Here is a beauty of a site that Doug tagged: Mathematics in Movies.

Right now it has about 80 clips from movies that involve math, including the explanation of why 7 times 13 is 28 below from Abbott and Costello's In the Navy, which I just love and the clip from Harold and Kumar that I wrote about previously.

Web 2.0 for Ontario Math Leaders (reprise)

In a previous post, I asked for help in creating a one day workshop on Web 2.0 for Math Education leaders. My Personal Learning Network provided some excellent ideas in the comments.

The workshop was delivered yesterday to an eager and experienced group. Many indicated that they had seen Will Richardson at one of his appearances in Ontario, like the EDUGAINS symposium, and were ready to do more with Web 2.0.

In preparation for the session, I worked on a wiki to capture some of our ideas about

* What is Web 2.0 and why should Math Educators Care
* What are some Web 2.0 Tools (with a page for each)

I have updated the wiki with some of the ideas of the participants as well. It is a little light in the sections that I was not responsible for. Perhaps some of you will edit it to beef it up.

If you were at the session yesterday, please feel free to comment and describe a interesting discovery that you made or pose a question that is still bothering you.

Math Coaching in Ontario

The provincial government has announced a large investment in Math Coaches (Grades 7-12).

I have created a wiki page with some support links (please feel free to add to it).

Does anyone have any experience with coaching at this level that they are willing to share?

Web 2.0 for Grade 7-12 Mathematics Leaders and Teachers

Jeff, Greg, Frank and I are presenting Web 2.0 to a group of Mathematics Leaders for a full day in February. We have been thinking about how to introduce them to the Web 2.0 world and make connections to their personal learning (easy) and their classroom practice (harder).

Here is a test of the strength of my professional network:

What topics, concepts, exercises, or messages would you see as vital for such a day? What pitfalls should be avoided? What is the elevator pitch for Web 2.0 to Math teachers?

What is Mathematics? What is Multiplication?

The Text Savvy blog has an interview with Keith Devlin that is worth reading.

Two quotes stood out for me. The first is about the nature of "doing" mathematics:

I think many students give up on mathematics because they don’t see how they could possibly come up with the solutions to problems they see in their textbook, or which the teacher gives on the board, or which some of their classmates produce. What they don’t understand is that the clever argument they have just been presented with was not arrived at by deliberate, rational thought. It was constructed after-the-fact. And so the student misses the crucial lesson that the secret to doing mathematics is not an unusual brain but sheer persistence, trying one thing after another and failing each time until eventually the light comes on.

and the second about the "multiplication as repeated addition" furor:

Using a brittle metaphor (multiplication is repeated addition, for example) inevitably leads to problems later, when the metaphor no longer holds but gets in the way of a better understanding of the concept. It’s hard enough grasping the abstractions of mathematics without compounding the issue with brittle metaphors. One problem is that metaphors inevitably lead to natural inferences. For instance, thinking of multiplication as repeated addition leads to the belief that multiplication makes things bigger. This false belief often persists throughout people’s lives. It’s particularly hard to eradicate since it is often something the child observes him or herself, and as we all know, knowledge we generate ourselves tends to stick like glue. When it comes to mathematics, I think it is probably always unwise to use metaphors as “interim definitions”, which is what often seems to be done, since they all break sooner or later. Rather we should present the student the same instances, but as motivational and illustrative examples of, not metaphors for. Mathematics is abstract. It does students no good in the long term to present it as something concrete. Moreover, there is no need to do so. There is plenty of evidence that children can handle abstraction, particularly when the learning is scaffolded by a range of concrete examples.

Do you think that we make math too tidy for students? Do you have a favourite example of a "brittle metaphor"?

Squashing the Bugs in Education

vlorbik sent me to LeftoverPi where it is argued that the Number 1 bug in Education is that it is done by force.

What do you think the biggest bug in K-12 education is?

BTW, there are some interesting posts on LeftoverPi about topics that I have touched on, like the Math Wars and Lockhart's Lament. I love the description of the Number 1 bug in Ubuntu!


On his main page he asks:

If March 14th is Pi Day, what's the 15th?

Math Manipulatives

In April of 2005, a group of teachers from North East Ontario got together for a regional Leading Math Success working session and created introductory videos and powerpoints for six Math manipulatives. These were then used in local training events. When I let the participants know that they had been posted to a popular video sharing site, I got lots of replies and recollections about how worthwhile a professional development experience people thought it was - fodder for Judy's resume! The full collection of files has been posted for a while.

Algebra Tiles



Colour Tiles



Connecting Cubes



Fraction Circles

My contribution was a Geometer's Sketchpad sketch - a Fraction Circle tool and virtual manipulative.



Geoboards



Pattern Blocks

Tickling my odd sense of humour

In a Pair-a-dimes post, David Truss embedded this cartoon:



I thought it was sly, so I looked for some more. I laughed out loud at this one:

Math on a SMART, I mean Interactive White, Board

In a shout out to someone he calls the Northern Mathman, Geoff Day drew my attention to this incredible Java application for doing mathematics that is particularly well-suited to an IWB or tablet. Although it doesn't work quite as well for me as it does in this introductory video, with a little practice it could change the way I think about equations and mathematical calculations.

You can download it or use it directly on the web.

Prove that you are human

From the Top 10 Worst Captchas via Jane's E-Learning Pick of the Day:



It reminds me of the aerobics in hell cartoon.

What is number sense?

I have been participating in an interesting discussion about number sense, the nature of Mathematics, the role of rote learning as a result of a post at the Kitchen Table Math blog.

Perhaps you would like to add your two cents worth? There seems to me to be a remarkably large chasm created by the so-called 'Math wars'. I have been taking Will Richardson's advice and subscribing to some blogs that I don't necessarily agree with.

Math Wars, The Pre-eminence of Algebra and the Presidential Math Panel

The blogosphere has been abuzz with opinions about the Presidential Math Panel report. Five good ones are found at the Pulse blog. Gary Stager's opinion includes the following:

Not only is the progression from arithmetic manipulation of fractions to Algebra tenuous, but neither of the assumptions underlying the value of teaching fractions or Algebra are ever questioned. The President’s Math Panel, like most of the math education community maintains a Kabbalah-like belief in an antiquated scope and sequence. Such curricular superstition fuels a multigenerational feud in which educators fight over who has the best trick for forcing kids to learn something useless, irrelevant or unpleasant.

and

The Report of the National Mathematics Advisory Panel
does not dispute that teachers spend lots of time teaching fractions. The report merely urges that teachers do even more of the same while hoping for a different result. A definition of insanity comes to mind.

I wonder if Math teachers are so unwilling to question the supremacy of algebra because they are worried that they will lose market share in the high school curriculum and lose sections at summer school.

Large Numbers

I have come across three resources on this topic lately:

The first is a swf from an Australian e-card company. I believe this was the song sung to convince a woman to give up her liver in Monty Python's Meaning of Life.

The second is a fascinating set of images meant to give perspective to numbers like
one million plastic cups; the number used on airline flights in the US every six hours.



The third is the Power of 10 video, which many of us remember watching in Science class. The field of view expands out to the universe and then back in to the atomic level.



Do you have any favorite resources to give students a sense of scale?

Wanted Mathematical Words

CBC Radio ran a highly entertaining radio spot called Wanted Words, in which listeners submitted suggestioned new words to describe things:

• What do you call the long, cold, dark Canadian period between New Year's and Good Friday? Forevuary.
• What do you call someone whose plants always die prematurely? Hortikillturist.
• What do you call @? Atpersand, ampersend, Circle-A (from a rancher in B.C.)
• What do you call the warmth left behind when you sit in a recently occupied seat? Bumcano.

In working on CLIPS, we have come up with a few surprising wanted Mathematical words:

• What do you call the superclass of transformations that take (x,y) and map it to (x,ay)? For some values of a we call it a stretch, for others a compression, for still others the composition of a reflection and a stretch/compression. Some sites seem to allow for a vertical stretch of factor 1/2, but would you allow one of factor -3?
• What do you call the line in the middle of a sinusoidal? Medial axis, median line, mid-range, mean level (like mean sea level)...

Don't you think it is wild that there doesn't seem to be a least one word around for these things? I would be happy to hear any suggestions that you might have - maybe CLIPS will use your suggestion. How about the Isenegger-Clarke line? A compstretchion?