Archive for the ‘Mathematics: The Science of Patterns’ Category

Keith Devlin’s lecture — — –math for real reasons?

Sunday, November 15th, 2009
Keith Devlin

Keith Devlin



Keith Devlin, the Math Guy on NPR  spoke at Harvey Mudd College in Claremont.  Keith is the author of  20+ fascinating books on mathematics including:

 The Math Gene:  How Mathematical Thinking Evolved and Why Numbers Are Like Gossip

  •  The Language of Mathematics:  Making the Invisible Visible
  • Mathematics:  The Science of Patterns.

Having heard Keith on NPR and been entertained by his droll humor and abilityto explain complex mathematics, I marked this event on the calendar.  So Thursday evening after being interviewed about my TeaCHildMath start-up company on On the Money, a business talk radio show, a friend and I drove to the Claremont Colleges.  Before the lecture, we strolled through the Scripps campus,   With its  beautiful Mediterranean architecture (beauty and symmetry dependent on  mathematical proportions and patterns?) illuminated at night, the evening seemed magical.   My daughter is a Scripps grad and this no doubt added to the magic.

In a crisp British accent, Professor Devlin spoke of how math is about doing rather than knowing.  His message was:  “Let me experience it and I will know how to do it forever.”  He recounted an experiment in Recife, Brazil in which mathematicians ran an experiment in a bustling marketplace.  There boys tended fruit stalls for parents.  Each boy was able to do complicated computations in their heads when the mathematicians asked to puchase “17 of those mangoes plus 23 of those guavas.”  To arrive at the correct sum, they boys would do sophisticated math in their heads such as figuring out for the 17 mangoes that they could compute the answer for 5 and triple it and then add the price of two mangoes.  The boys were 98% accurate in their computations.  However, when these same  boys were given these exact problems to solve at home on paper,  they were able to solve them with 37% accuracy.  Why would this be?

Professor Devlin explained that not only was math more difficult when the boys were doing it symbolically but that stripped of its real marketplace context, their interest declined.  Learning should be fun, engaging and enjoyable,  Devlin said.  To teach students, we should simulate the real world as much as possible.  We have textbooks because we can’t take thirty students to the marketplace and have them sell produce all day.  But teachers and parents should do their best to simulate the real world.  Devlin mentioned how pilots learn to fly and land planes using simulators.  This provided the closest “real world” context.  The professor explained that children will be improving math skills through simulated “real world” contexts through computer games.   Some of these games are being developed now.  The games have the added advantage that losing has consequences just as making an error in the marketplace has consequences.

What can parents and teachers take from this lecture?  Just as students learn and retain a second language when immersed in another culture because there are consequences to not understanding, students will learn and retain math concepts better when immersed in a real situation.  I have suggested parents involve their children in purchases.  Let them compute how much the popcorn and Coke at the movies will cost and figure out the change if  paying with a $20 bill.  Have them help you bake brownies and do the measuring.  They will be learning fractions.  Double the recipe and have them do the math.  What happens when all the ingredients are doubled except the flour?  Any real consequences there?  Perhaps this is one of the reasons homeschooling works so well.  The parent/teacher can work one on one with the child and illustrate math problems in a real context. Not everyone homeschools. However, EVERY parent is a teacher (your child’s first and primary teacher) and has the opportunity to do the same for his/her child.

My workbook, Teach Your Child the Multiplication Tables, attempts to create the “real world” of the circus for your child.  Not only will your child learn the tables but the impetus to do so is to help Rudy the Ringmaster out.  I wanted to engage your child’s feelings.  I wanted him to want to do the math.  All word problems have a “real life” context whether the Circus Snack menu or tickets to the circus.   I would like to develop my book into a computer game.  If you have experience in this, let me know.

After the lecture, I spoke with Professor Devlin.  In my hand, I had a copy of his Mathematics:  The Science of Patterns.  I came across this after writing my book and was intrigued.  It is a history of mathematics, accessible to all, beautifully written and illustrated.   I approached him at the book signing table and said, “A wise man said, ‘mathematics is the science of patterns.'”  He smiled and we exchanged a few words as he signed my book.  For a history of math, I highly recommend this book.  If you are intrigued by math, you will convey this to your child.  Your child learns from you.  What are your interests and your passions?

Mathematics: the Science of Patterns?

Friday, July 17th, 2009

I came across this quote in Lockhart’s Lament: (                                                                                                                                          “In

In fact, if I had to design a mechanism for the express purpose of
destroying a child’s natural curiosity and love of pattern-making, I
couldn’t possibly do as good a job as is currently being done I simply wouldn’t have the imagination to come up with the kind of senseless, soulcrushing ideas that constitute contemporary mathematics education.” [Paul Lockhart published in 2002]

This quote resonated with me because my intent in my workbook is precisely to engage a “child’s natural curiosity” and “love of pattern-making.” 

Mathematics is the Science of Patterns.  For more on patterns in mathematics, I recommend Keith Devlin’s  Mathematics, the Science of Patterns.  The book’s subtitle is:  the Search for Order in Life, Mind, and the Universe.