Fake-World Math, Real-World Engagement

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Dan Meyer is currently leading a very engaging #MTBoS discussion regarding “Real World Math
” and it’s effects on student engagement with respect to completing (with quality) mathematical tasks. In general, “real world” is a term describing a task that attempts to emulate a task that might actually happen to someone in a non-school setting. The prevailing thought in many circles is that as a mathematical task becomes more “real world” it will become more engaging to students.

Many of us have plenty of anecdotal evidence to challenge that generalization.

Enter the “fake world” math tasks.

“Fake World” is a term used by Meyer to describe mathematical tasks that are engaging to students and encourage/require authentic mathematical problem-solving, but doesn’t attempt to emulate any actual action or task that one might use in a non-school setting. The Magic Octagon is an excellent example of a “fake-world” task. This is not a task that would EVER be asked of you in your family, work, or spiritual lives outside of school, but it is worth 20 good minutes of almost 100% engagement in a geometry classroom. These types of experiences cast doubt on the presupposed direct relationship between “real world” and student engagement.

As part of this, Mr. Meyer is attempting to do a bit of data collection to get a sense of what fake-world math activities we find engaging in our free time.

For me, it’s Flow Free on my iPad. I’ve seen this wonderful little logic game draw in 31-year-olds (my wife and I), high school kids (in my classes), and my 4-year-old daughter can get lost on it for an hour straight if I’d let her.

The task of a game is fairly simple. There are exactly two dots of each color on a grid. The goal is to connect each dot to its corresponding dot with a path that doesn’t intersect any other path. Also, each square on the grid needs to have a path going through it. No empty boxes.

So one solution to the above board would look like this:

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At this point, you can either try again to complete the same puzzle in fewer moves or move on to the next puzzle. As you might expect, the puzzles get progressively more difficult with additional colors added and the grids increasing from 5 X 5 to 6 x 6 and 7 x 7.

But what is it about this game that is so engaging?

The simplicity of the goal is a start. It takes very little explanation to begin playing. Also, the first couple of puzzles are quite easy to allow you to get the hang of the game.

The progressively more difficult puzzles is helpful as well. As you play, you start to develop some strategies and thought processes that you want to take for a spin on some harder puzzles. This game makes sure you get that chance.

Also, I like that the game has unlimited do-overs. If I had to do some guessing-and-checking to complete a puzzle and I want to start it over again, I can do that an unlimited number of times until I am happy enough to move on. Or I can move on right away.

It seems like those qualities could be integrated into math class. Consider an activity with a low entry point, a simple goal, some do-overs offered, and additional pieces that make the problem more difficult once the easier “levels” are solved. That would require us who design activities to take a more inductive approach to building engagement models. Look at what is engaging and see what elements they have in common.

I would absolutely encourage everyone to get involved in Mr. Meyer’s conversation. Do you have a “fake-world” math activity that you find engaging? Head over and tell the MTBoS about it in the comments.

Thegeometryteacher hits 2000

thegeometryteacher has passed 2000 views

thegeometryteacher has passed 2000 views

Thanks everyone!

Thegeometryteacher blog has passed 2000 views. Now, I know that there are blogs whose posts get 2000 views every day, but none of them are written by me. This isn’t me looking for any Webby awards or anything. My blog is clearly not the most popular, nor is it going to impart the most wisdom, but my goal has been to contribute to the global conversation about education.

This has been an fascinating experiment for me. An experiment that has taught me how the social web works. I am feeling energized and excited by recent interactions. I feel like I am beginning to find my voice and I feel like you are all helping me do that. There is a fantastic conversation happening that I want to be a part of. Not because I feel like I have anything important to say, but because I want to be able to sit and listen.

Now, some stats.

This will be my 62nd post. My post on Armor Logic 2 is my most popular post followed by my post on Dr. James Tanton’s video about the Two Pancake Theorem. The Gas Pump Problem is the next most popular (significant because it was one of the first videos that I ever made for a math problem).

My first post was May 26th, 2011. It has taken a shade over 18 months to pass that milestone.

My blog has been viewed in 54 countries. After my home country (USA), the next five most numerous hits have come from India (perhaps due to my posts about Kolams here and here), The United Kingdom, The Philippines, Canada, and Brazil. This is the part that is the most fascinating for me, quite frankly.

Thanks to all my followers. Thanks for commenting, liking, and sharing what you thought was interesting. This is about me getting a chance to learn from you all. I feel like I’ve done that. I would like to keep doing it.

Thank you and I’ll see you in 18 months when I cross 4000 hits.

There’s always a reason…

Photo Credit: Flikr user “Jan Tik” – some rights reserved

A many years to Michael Benson, author of “Mystery Master,” for making my job as the teacher of reasoning a heck of a lot easier.

Math and logic can be daunting (or at the very least, boring), but in the last week, my use of the Benson’s logic puzzles (found at http://www.mysterymaster.com/puzzles.html) has allowed for a lot of good conversation about how deductive reasoning (following factual guidelines to build logical conclusions) differs from inductive reasoning (basing conjectures on perceived patterns of specific examples, events or cases).

The puzzle that we solved as a class was “A Day at the Zoo“. Check it out and give it a try. There are lots of much more challenging ones on Benson’s website.

Put your experiences in the comments and if you find one that thegeometryteacher absolutely MUST try, then post it.

Good Game, Vol. 5: Sudoku

Photo Credit: Flickr User "Random McRandomhead" - some rights reserved


In the spirit of Minesweeper, Sudoku is another game where the game play and rules are take about 30 seconds to explain. Then you begin trying to solve the puzzle.

The game goes like this: You are given a 9X9 square with 81 boxes. You win when you fill in each box with a single one-digit number (1, 2, 3, 4, 5, 6, 7, 8, or 9)  such that each row and column contains no repeats. Also, the 81 squares are divided into 9- 3×3 squares that can’t contain any repeats, either.

That’s it. That’s the whole game. Click here to play a free online version. There are tons of variations as well.

In my opinion, this game flexes the same logic muscles as Minesweeper (see Good Game, Vol. 4) and Armor Logic 2 (see Good Game, Vol. 3). The idea of making-decisions while staying within a small set of parameters is an important step in developing mathematical thinking.

Good Game, Vol. 4: Minesweeper

Photo Credit: Jim Loy

With the world becoming increasingly Apple based, this wonderful game, which came free on every Windows-bearing computer for the last 20 years could be fading out of style, but allow me to set the record straight: As far as simple logical training goes, this game knows no parallel.

If you have never played before, it goes like this. Each box will be hiding a blank spot, a number or a mine. The object is to identify all of the mines without clicking one, which, of course, blows you up.

If you click a box with a blank spot under it, that means that there aren’t any mines touching that box. If you click a box to reveal a number, that number represents the number of mines in contact with that box. For example, if you click a box and you see a “2”, then of the 8 boxes touching that “2”, 2 of them have mines and 6 do not. The more numbers you reveal, the more clues you get.

If you don’t have a Windows computer, this seems like a pretty good link to play a Java version of the game. Also, I know that the Apple App Store has a very good free download (because I use it) to install on your iDevice.

Good Game, Vol 3.: Armor Logic 2

In the spirit of Minesweeper, Armor Games brings Armor Logic 2, which is a logic game that uses number clues to give away the location of white boxes hidden within the playing area. This games starts easy and quickly becomes more and more difficult.

The reason that I love this game is that it plays off the basic if-then thought process. If there is a “2” above this column, then there can only be two white boxes hidden in that column. It gives you a set of givens and you need to use a deductive thought process to discover the pattern… which is exactly what we do in geometry. If you can master this game, you can master proof! Guaranteed!

Good Game, Vol. 2: Interlocked

Interlocked, by Armor Games, could be the game that most strongly speaks to my undeveloped spatial reasoning skills (an odd skill set for a geometry teacher, I know.)

However, for developing a stronger ability to visualize three-dimensional objects, I have seen no match. This game consists of figures put together in such a way that you can only move one at a time. Your job is to analyze each figure from the different views and then get the pieces apart. Sounds simple, but wait until you try it.