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Last week, I wrote about how our math education differs from how we learned math as children in response to a changing world. I want to get into more detail about the specifics of how we do this at EAB. Teachers at EAB teach the content standards through the math practice standards, which guide the methods we use for teaching strong conceptual understanding.

The math practice standards are embedded in the curriculum at all grade levels. These practices are reinforced in each unit, and the level of sophistication increases each year.

For example, math practice 4 is "model with mathematics." In early grades, students translate between numbers, pictures, and written or spoken words. If a teacher talks about six daisies, for example, these can be represented in a picture of six daisies, abstracted to six dots, or abstracted even more to the number 6.  As children get older and their thinking develops, these models become more abstract and are represented as arrays, bar models, and eventually variables and mathematical symbols.

There are eight Standards for Mathematical Practice listed here:

1. Make sense of problems & persevere in solving them
2. Reason abstractly & quantitatively
3. Construct viable arguments & critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for & make use of structure
8. Look for & express regularity in repeated reasoning

Each is hyperlinked; you can read about them in more detail by clicking on the links.  

If you want to help your children develop the skills outlined in these practice standards, math games are a great way to do it. Below, I've described two math games that help develop these skills, and I have several dozen more - feel free to email me if you want me to send them to you (tcalcagni@eabdf.br).  

Nim is a simple game involving math strategies that you can play without extra resources.  With two players, make a pile of counters and alternate taking 1, 2, or 3 counters. The winner takes the last counter. In all versions of Nim, the winner is predetermined by the number of counters you start with and who goes first. When your kids have figured out how to win going first with 19 counters, for example, you can change the rules: can they find a winning strategy starting with 22 counters, where the last person to take a counter loses instead of wins. What if all the counters are divided into three piles, and you can only take from one pile each turn? There are lots of versions, and changing the rules strategically helps develop strong tools of perseverance (practice 1), reasoning abstractly (practice 2), making use of strategy and structure (practices 5 and 7), and looking for regularity in repeated reasoning (practice 8).  

The card game Set is one of my favorites for developing pattern recognition and repeated reasoning skills. It requires the purchase (or creation) of a specific set of 81 cards, each containing a different configuration of these four traits: color (red, purple, or green), shape (diamond, oval, or squiggle), number (one, two or three) and filling (solid, striped or empty). The goal is to collect as many "sets" of three cards as possible from a 12-card array. Three cards are a "set" when they are either all the same or all different in each attribute separately.  

You can adapt the game for younger players by eliminating one of the traits and playing with 27 cards. For example, you could play with only the red cards. Another way to make the game more accessible is to lay out an array of 15 cards instead of 12. This increases the probability of more sets being present. 

The goal, as always, is to have fun with math. So if your children aren't into it, there is no need to push - you can try again at a different time. If you decide to play either of these games with your kids, I would love to hear how it goes!