The Power of Math Games

Today's generation is born plugged in.  They seem to inherently know how to use an ipad or smartphone.  The ramifications of this are awesome and I have no doubt they will go on to do some amazing things throughout their lives.  However, for every creative application we discover, for every innovative way it helps us learn, there are at least as many ways technology is harming us.  Recently I read about an older women in Europe who used her new navigator to find the local grocery store and wound up driving half way across the continent.  I also see practically everyone texting while driving and rear ending one another.  So as we progress toward a more tech savy generation and lifestyle we need to not lose sight of other experiences that keep us grounded socially and keep us sharp mentally. 

My grandmother hated computers but she was sharp as a knife for 93 of her 94 years.  What kept her mind going were puzzles and games.  Cribbage, dice games, 1,000 piece puzzles were her repertoire.  Recently I asked teachers in my building if they could lend a cribbage board for our "Math Games Night" they looked at me like I was crazy.  Only a few people knew what one was.  This led to me taking a closer look at the SMP and Common Core Math Standards and seeing how many of them could actually be taught with some age old timeless games.  It turns out a whole lot of them can be!

Cribbage is a great game for teaching basic number sense and probability.  It helps students learn to make choices based on basic math and critically think.  There is also a concrete component where opponents compete by racing their pegs on what is basically a number-line from 0-120.  The game was invented several hundred years ago and it survived this long because of how dynamic it is. 

Mancala is another game that promotes number sense, estimation skills, and cardinality.  Students as young as 4 or 5 can master this simple game, which again is a very concrete game.  It is often played on a wooden board with stones, which as Maria Montessori pointed out, are materials found in nature that children are instinctively drawn to.  Often the child sees a pile of stones and makes a quick guess as to how many are in the pile.  Students then place one stone in each bucket or mancala until they have used them all.  What better way to teach counting skills!  As the game progresses they hone their estimation skills, ability to perform one to one correspondence, greater than and less than comparisons, and counting skills.

Legos are perhaps the foundation for mathematical thinking for many young people.  This is often where children really start to encounter large numbers and need to mentally and concretely manipulate them.  Recently I watched my son play with legos and was astounded at the mathematical reasoning I witnessed.  He had a large block that was 2 by 12.  He began counting by 2s but then stopped, started over and counted by fours, "Four, eight, twelve...".  Then he was unable to go on so he switched back to counting by 2's (fourteen, sixteen, eighteen, twenty, twenty-two, twenty-four").  Later we were searching desperately for a block that was 1 x 8.  After some time he finally said, "Lets just use a 2 and a 6 or maybe even two 4s".  Essentially my 6 year old was decomposing numbers.  Now if only the lego company would build blocks that are 1 x 5, 1 x 10 and 10 x 10!

Pips are the fancy little word for the dots found on dice and dominoes, and subitizing refers to our ability to immediately count a small set of object such as pips.  Humans can typically subitize a set between 7 and 10.  Dice and dominoes develop this skill and provide opportunities for us to improve those skills.  In particular, Yahtzee and dominoes are great subitizing games that promote lots of mathematical thinking.  Yahtzee is a great game for young and old.  Children particularly love games of chance.  It requires students to multiply numbers up to 6 x 6 and at the conclusion of the game students typically wind up with a score that is a sum in the hundreds place value.

There are various versions of  dominoes but my favorite is called muggins.  In muggins, players have to match the pips and sum the ends.  So a 5 has to match with another 5 and a 4 has to match with another 4.  However, that is really only the beginning.  In order to score points the pips at the end of each domino have to add up to a multiple of 5!  This little twist makes the game incredibly powerful and essentially leads to some of the same thinking that legos and other activities support, namely; decomposing.  So for example if you play a domino and the end is 4 but on the board there is already a 6, 2, and 3, then you will score 15 points.  Most stores also sell "double 9" dominoes which offers a wider array of sums and patterns.  Unlike dice, dominoes include zero, which is a funny thing to include and arguably is always around, but mathematically speaking zero plays a huge role in dominoes.  So a set of dominoes does not begin with the 1 and 1 domino and work up to the 9 and 9 domino with all other combinations present.  They start with the 0 and 0 domino, then the 0 and 1, 0 and 2 and so on.  As students get more proficient at the game they will begin to consider what dominoes are played and make predictions about what ones are still in their opponents possession as well, which builds on algebraic thinking and solving for unknowns using some deductive reasoning.

In addition to this there is a deeper meaning for teaching math through games, it promote more psychologically sound children.  They learn to lose, preserve, socialize with family and friends.  They learn that in life there really never is a "Game Over" and you can improve and compete at a higher and higher level.  But their are even stronger lessons at hand here.  Families spend time together, something we all can do a better job of.  It is quality time, were siblings can compete and push one another.  Last but not least, you learn a healthy respect for your elders, especially when you can only count on one hand the number of times you were able to beat your grandmother in cribbage!

Growing exponentially as an educator.

Leaving the classroom and becoming an instruction math coach was a difficult decision and one that took me years to finally accept.  One experience in particular convinced me to take this plunge and brought me to where I sit today.  A few years ago I was an intervention specialist and was allowed to go into classrooms and work with struggling students.  One teacher in particular was as hungry as I am for new ideas and approaches to teaching math.  What we discovered and developed was a wonderfully symbiotic relationship.  I would often take advantage of her enthusiasm and present an idea, her calm presence as a 2nd grade teacher and her delivery of the concept would improve upon it more than either of us could have predicted.  Last, but certainly not least, the children would take this idea, beautifully molded by the teacher, and put it into practice that would surpass everyone's expectations.  Here is an example, we once had a student named Maddie, who like most 2nd graders had a lot of difficulty subtracting.  We spent some time trying to use base ten blocks to show how we could regroup and solve subtraction problems, we tried writing numbers in expanded form and we tried subtracting on a number line, all with limited success.  On the day we attempted the number line she asked for the base ten blocks but she used them in an unexpected way.  She made a line of tens and ones with the larger number and then did the same with the smaller number below it.  Pointing enthusiastically, she smiled and said, "if I fill in this space I will have my answer!"

Whether or not this scenario mathematically makes sense is less important than the lesson learned. The point is all three of us, two teachers and a student, grew that day.  I realized the potential of being a lead teacher.  We provide ideas, teachers improve upon them, and students are allowed to take it to a whole other level.  At that point the teacher student relationship is broken down and we are all learning from one another!  Little Maddie instantly transformed us into what Paulo Freire called "teacher-student"  He wrote: 

“through dialogue, the teacher of the students and the students of the teacher cease to exist and a new term emerges: teacher-student with students-teachers. The teacher is no longer merely the one who teachers, but one who is himself taught in dialogue with the students, who in their turn while being taught also teach”

When the traditional student relationship is dismantled an entirely different culture begins to take root in the classroom.  Anyone who enters the classroom can feel it, there is something to be learned there, it is in the air we breath.  Math is a perfect vehicle for transforming classrooms and creating this climate because it is a subject that can be self taught through discovery.  There are infinite ways to go about this discovery, which is both exciting and terrifying to many educators.  Nonetheless, if teachers can empower their students through mathematical exploration and facilitate reasoning and dialogue, then soon we are learning just as much from the students as they are from us.  The classroom is non-compulsory, highly motivated and autonomous.  Its a mathematical equality on a whole other level.