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IntMath Newsletter: Subitizing, Jacob, Fractals and Donald Duck

By Murray Bourne, 12 Feb 2013

12 Feb 2013

In this Newsletter:

1. Gong Xi Fa Cai
2. Counting game and Subitizing
3. Jacob's Staff
4. Creating a Google-like classroom climate
5. Math puzzles
6. Friday math movie
7. Final thought - Perfect days

1. Gong Xi Fa Cai!


Happy Year of the Snake to all those enjoying Chinese New Year festivities this week!

Chinese calendars are quite interesting. A "standard" year has around 354 days, and there are leap years containing a leap month, with around 384 days. The calendar is always adjusted so the winter solstice (the shortest day of the year) falls in the 11th month. Months always start on the new Moon (when it is completely in shadow).

Chinese New Year falls on the second new Moon after the December solstice (unless a leap month messes things up). The earliest possible date is Jan 21st, and the latest is Feb 21st (but that won't happen until 2319).

2. Counting game and subitizing


Can you count faster than a chimp? Our "number sense" is important for understanding math, and it begins with our ability to count.

First, try the counting game. All you have to do is count the dots as quickly as you can.

Counting Challenge

Next up is a short article on why I created the game, and some early observations:

Counting Game and Subitizing

Then, for some interesting background, see this article:

Number Sense

3. Jacob's Staff

Jacob's Staff

Scientists used Jacob's Staff during the Renaissance to find heights and distances, using trigonometry. It was a forerunner to the sextant.

Math teachers could design some interesting activities using this, so students would learn some math, and some math history.

See: Jacob's Staff

Here's a similar activity based on historic math: Noon Day Project. This activity re-creates Eratosthenes' famous experiment 2000 years ago where he produced a good approximation of the size of the Earth based on measuring shadow lengths at noon in different parts of Egypt.

4. Creating a Google-like classroom climate

Google is well-known for being one of the best companies in the world to work for. Around 7,000 people per day apply to work there. The company offers excellent benefits and a relaxed, almost playful atmosphere that keeps creative juices flowing.

They put a lot of effort into finding the right people, and because Google doesn't want to lose anyone, they create conditions that encourage success and fulfillment.

The article, Inside Google’s Culture of Success and Employee Happiness, got me thinking about why so many students drop out of school (often because of acute math anxiety, or because they don't have a feeling of belonging, or a host of other reasons).

Good classroom "climate" is very important for effective learning, especially in math!

Here are some of the things Google does that could apply in class:

Hire (and reward) good teachers! I enjoy living in Asia where education is generally held in high esteem, and teachers are, for the most part, regarded as valuable members of society. Good teachers almost always leads to better learning outcomes. Keep the good ones by giving them purpose, recognition, and reward.

Collect data on (and share) what works: I don't mean what works for standardized tests, here. I mean quality class activities, different approaches to explaining things, or different resources. What works? What needs changing? Teachers aren't given enough time to think about what they're doing, nor enough opportunities to learn from each other. (Google collects huge amounts of data to improve its processes, and creates many situations where workers mingle and share ideas.)

Warm greetings make a huge difference: Google found their best managers were warm and accepting of input from their team, leading to a "15% increase in productivity". Sadly, I see a lot of classrooms where there are no greetings at the beginning of the day, and no friendly talk with students about mutual interests. It's often no more than "OK, today we're going to do the quadratic equation...". A sense of belonging is important for learning and for sticking around.

Too much bureaucracy: Google has a "flat" structure where middle managers have quite a bit of responsibility, compared to many other companies. That's not always the situaion with teachers.

Too many distractions: Many classrooms have too many interruptions. Are those announcements about sport buses - or uniforms - really that crucial? There are already too many things trying to grab everyone's attention. Focus is good.

In summary, we need to create the best working & learning environment we can, whether it's in school, or in a company.

5. Math puzzles

The puzzle in the last IntMath Newsletter involved finding the time taken to fill a bath.

Correct answers with reasoning were given by Christopher Buchanan, Christian Mills, Nicos Mavrommatis, S. Nickerson, Thomas A Buckley, Bonnie, Hamid Zandi, Lachezar Borisov, Dineth, Ramesh Babu and Mawanda Ismail.

It was interesting to see the variety of thought processes used to solve the puzzle. Some of you went straight for the algebra, and that's fine. My approach with this kind of puzzle is to assume a reasonable amount of water for the bath (say 100 liters) and then work the rest of it from there. It makes it easier (for me) to check if my "rate in" and "rate out" values make sense.

Please note: As usual in math, the best answers are those that include reasons!

New puzzle: Peter is an enthusiastic student and runs to school each day, but usually gets tired and walks the rest of the way. His running speed is twice his walking speed. He notices on Monday that he walks twice the time he runs and it took 20 minutes to get to school. On Tuesday, he runs twice the time he walks. How long does it take to get to school on Tuesday?

You can leave your responses, with reasoning, here.

6. Friday math movies


(a) Fractals - Hunting the Hidden Dimension

See this PBS documentary about the development of fractals and how they are used in computer graphics. (It's 55 minutes, but good value.)

Friday math movie: Fractals - Hunting the Hidden Dimension

Donald in Mathmagic Land

(b) Donald in Mathmagic Land

This is a classic late-1950s cartoon where Donald learns where math comes from.

Friday math movie: Donald in Mathmagic Land

7. Final thought: A perfect day

I enjoy helping people, and I hope you do, too. I think this sums things up nicely:

You have not lived a perfect day, unless you've done something for someone who will never be able to repay you. [Ruth Smeltzer]

Until next time, enjoy whatever you learn.

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