If you are a Bostonian by address, birth, or just a connection, you can’t help but be full of pride this morning for your baseball team. The Red Sox were amazing, keeping us up late at night and giving us so much to cheer about in a time otherwise to often dreary. And if you are a math teacher you cannot but wonder why so many of our kids find math irrelevant, uninteresting, and difficult when so much of what they heard and saw as we watched those World Series Games was math, math that helped us understand the game, math that we found fascinating, math that we understood. It is truly amazing how much math there is in our national pastime.

There are numbers and shapes everywhere from the backs of player uniforms to counting of balls, strikes, and outs, numbers for the innings and even numbers for the game, the series, the postseason, and the regular season. There are addition totals shown on the scoreboard for hits and runs along with the count for each inning. There is the shape of the diamond, measurements to the bases, the mound, and the various walls, the square bases and pentagonal plate. This is only the beginning because baseball is all about statistics. Batting averages and earn run averages, hits off right handers and hits off left handlers, even stats about which team will win the series after being down by 2 games. Pitchers throw balls that curve in left or right, go straight and rise or go straight and fall. The speed of the ball is posted for each pitch along with its position in the rectangular strike zone..

The game is full of algebra and not just arithmetic, geometry, or simple statistics. The amazing TV graphics shows the parabolic path of the ball when a player hits a homerun where we think quadratically as we wonder about height vs. distance, or time to land. It is about how long it takes for a ball to be thrown across the infield compared to how fast a runner can get to first base. It is about where on the bat the ball hit and the shape of the swing for maximum momentum transfer. It is today about building models for managing teams, salaries, salary caps, offence vs. defence, the number of starting pitchers you must acquire vs. the number of relievers and even the specialized relievers, the closers. And it is about the wealth of statistics and statistical analysis rivaling the stock market in richness and complexity.

I have only begun to scratch the surface of math and our national pastime. For as I watch and listen to the games, I hear and see math everywhere. How could it then be that our school math is so out of sync with this sport math we learn and enjoy so much? That is the question I leave you with today as I cheer Go Sox as loud as I can and think about how much mathematics helped me enjoy the game.

Here is a sophisticated baseball What if Math Lab you may want to try: Hit Streak.

When MOOCs were the rage in higher education, I asked my friend David Kaiser, a physicist and professor of the history of science at MIT, when he was going to do a MOOC. Dave has won teaching awards at MIT and writes brilliant books on the history of physics. Who better to do a MOOC or two bringing his wonderful style of teaching and presentation of important physical ideas to more people. But he was not at all interested, and as far as I can tell several years later has not done any.

“Why” I asked. “Because you can’t change them.” he replied. As he explained, one of the most wonderful aspects of teaching a course year after year for a great teacher is the opportunity, indeed the necessity, to change and adapt the courses in general and the presentations in particular. His reaction brought back a vivid memory of my first couple of years of teaching high school physics. I usually carefully prepared my lectures which were the standard fare for most of my classes. Occasionally too busy, too tired, or too lazy to develop a new one, I would grab my lecture notes from the previous year which I thought pretty good. The class usually started all right, but I soon got into trouble. The coherence was gone, the presentation no longer seemed to make sense to me. I don’t know if my students realized that I was stumbling, they were too busy taking notes, but I did. So, I would stop lecturing, told my class what I had done, apologized, would come back the next day with a fresh lecture and gave them time to work on their assignments. One of the things that makes teaching such a great job is the year-to-year, day-to-day, and even student to student opportunity for improvement, for growth, for learning. This has not been true of curriculum.

MOOCs like textbooks are expensive to produce. They are linear, moving from topic to topic in a standard form, a continuous line of lesson following lesson. They are thus difficult, often impossible, to update or change. Once created, except for minor revisions they are for all practical purposes, fixed. Yet, the world is constantly changing, and even more importantly students are constantly changing. A fixed curriculum or presentation cannot work. It will no longer work to expect textbooks to have a 7 year lifespan. Nor will MOOCs, made once and used again and again, work either. The analog continuous linear sequence of lessons that represent a course is no longer functional in the digital world.

The digital world is a discrete world. It needs education to be flexible, easy to change, constantly renewing, and growing. The metaphor for the analog age and the MOOC is the book, done once and then published. The metaphor for digital age educational content is the newspaper, renewed and reimagined everyday. One is fixed, unchanging, the other constantly refreshed. One is designed to be the same for all students, the other can be different to suite the needs and interests of every individual student. One is the education of the past, the other is the education of the future.

Envisioning technology that reinvents our schools not automates them should, I believe, be our goal and our dream for personalizing learning.

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The words curious and curiosity do not appear in the Mathematics Common Core Standards document, yet they are arguably the most important words in mathematics education. If there is any single habit of mind or critical skill I want our students to learn, don’t you agree, it is to be curious, to question, to experiment, to wonder, to imagine what we will do or become. Isn’t this what it means to reason quantitatively?

Curiosity is certainly the most human of traits. It is the reason we explore, the reason we invent, the reason we question, the reason we love mysteries and games. We are naturally curious. And curiosity is at the heart of mathematics as well. We wonder if particular numbers form a pattern, we want to know whether all triangles that fit in a semi-circle are right, whether all right triangles have two sides that when squared are equal to the square of the longest side. We wonder if our business will make money or our budget will enable us to buy that new computer. We are curious big and small, is the universe infinite or finite, is the chance of winning the lottery worth the price of the ticket, is global warming really that bad.

At What if Math we are all about curiosity. How many of the products in a 12 by 12 times table are odd numbers? If we choose any whole number and divide it by 2 if it is even and multiply it by 3 and add 1 of it is odd will repeating that pattern always make a sequence, 4, 2, 1…? What if we make a table using 1 simple rule, add the two cells in the row directly above it? What does the graph of a quadratic equation do if I change the b term? Was Ted Williams or Joe DiMaggio a greater hitter in the 1941 season? Was Napoleon right about using the Great Pyramid to build a wall around France or Moore right about the exponential rate of growth of microprocessors? What does absolute value do to the graphs of polynomials? Is the rate of change of C02 increasing or decreasing? Should I lease or buy that new car?

If curiosity is so central to our lives, then I am curious to know why it doesn’t appear in our math standards or in all too many of our math classrooms. I am curious to know whether students can care about what they are learning in their math classes if they are not curious about the problems we give them or the concepts they are supposed to learn. I am curious to know whether learning math can be fun for kids if they are not curious about it. I am curious to know…

Art