What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (21 page)

Activities and Advice for Parents

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iographies of mathematicians who have made great discoveries and inventions are fascinating to read, but I am always struck by the fact that so many were inspired not by school teaching but by interesting problems or puzzles that were given to them by family members in their homes. I was one of the people given the greatest mathematical start in life because my mum brought home puzzles and shapes for me to play with as a young child. It was many years later, at age sixteen, that I was also inspired by a great math teacher, who asked her students to talk about mathematics, which gave me access to a deeper understanding than I had ever met before. It is important not to underestimate the role of simple interactions in the home, and the role of puzzles, games, and patterns, in the mathematical development and inspiration of young people. Such problems and puzzles can be more important than all
of the short questions that children work through in math classes. Sarah Flannery, the young woman who won the European Young Scientist of the Year award when she was sixteen, for inventing a “breathtaking” algorithm, reflects upon the fact that as a child she was given puzzles to work on at home, and how these were more important in her own mathematical development than the years of math that she was taught in classes. Mathematical puzzles and settings are the ideal way for parents—or teachers—to encourage their children into math. This chapter will outline some of the ways that these puzzles and key ways of working in math can be introduced to children with great effect.

Mathematical Settings

All children start life being excited by mathematics, and parents can become a wonderful resource for the encouragement of their thinking. Mathematical ideas that may seem obvious to us—such as the fact that you can count a set of objects, move them around, and then count them again and you get the same number—are fascinating to young children. If you give children of any ages a set of pattern blocks or Cuisenaire rods and just watch them, you will see them do all sorts of mathematical things, such as ordering the rods, putting them into shapes, and making repeating patterns. At these times parents need to be around to marvel with their children, to encourage their thinking, and to give them other challenges. One of the very best things that parents can do to develop their children’s mathe- matical interest is to provide mathematical settings and to explore mathematical patterns and ideas with them.

Colored beads of different shapes, and strings

Nuts, bolts, washers, and colored tape

Cards from the game SET

There are many books filled with great mathematical problems for children to do, but it is my belief that the best sort of encouragement that can be given at home does not involve sit-
ting children down and giving them extra math work, or even
buying them mathematical books to work on. It is about providing settings in which children’s own mathematical ideas and questions can emerge and in which children’s mathematical thinking is validated and encouraged. Fortunately, mathematics is a subject that is ideally suited to the provision of interesting settings that can encourage this. One of my former Stanford doctoral students, Nick Fiori, taught a number of mathematics classes in which he provided students with different mathematical settings—some photographs of the settings are given here—and encouraged students to come up with their own mathematics questions within these settings. Students of different ages and backgrounds, including those who had suffered very negative experiences with math in the past, set about posing important questions. In some cases these questions led to math problems that were completely new and had never been solved before. Fiori documented the various mathematical ways that students worked, and he made a very good case for the encouragement of similar problem posing in school classrooms, for at least some of the time.
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I agree with him, but would
also encourage parents to provide such settings in the home for children of all ages.

Dice of various colors

Snap cubes of various colors

A square lattice grid with colored pegs

Children’s play with building and LEGO blocks in the early years has been identified as one of the key reasons for success in mathematics all through school.
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Indeed, the fact that boys are usually encouraged to play with building blocks more than girls is the reason that differences often occur in spatial achievement among boys and girls, which impacts mathematics performance greatly. Any sorts of play with building blocks, interlocking cubes, or kits for making objects is fantastically helpful in the development of spatial reasoning, which is fundamental to mathematical understanding.

In addition to building blocks, other puzzles that encourage spatial awareness include jigsaw puzzles, tangrams, Rubik’s Cubes, and anything else that involves moving objects around, fitting objects together, or rotating objects. Mathematical settings need not be sets of objects. They can be simple arrangements of patterns and numbers in the world around us. If you take a walk
with your child, you will stumble upon all sorts of items that can be mathematically interesting, from house numbers to gate posts. The creative mind at work will see mathematical questions and discussion points everywhere—there is always something mathematical that can be brought into focus, if we only remember that that is what we should be doing.

Sticks of different unit lengths with eyelets and string

Measuring cups with simple fraction volumes and a bowl of water

Pinecones of various shapes and sizes