Learning Fractions in a Country Where Mathematics is a Foreign Language
Source: Rick Ackerly
When Judy Stone was teaching 5th grade, she did an experiment with her fractions unit. First, she gave her class the test at the back of the textbook section covering adding, subtracting, multiplying and dividing fractions to find out how much they already knew. One student got 100% and only third of the class passed.
However, rather than getting right down to teaching fractions in the traditional way, the class cooked. Every student had to pick a recipe they liked (usually cookies) and halve it and double it. Their homework was to cook them at home. They had to write out the recipes in half and double using the appropriate fractions. They also had to make a poster showing their process for one of the iterations and bring the finished product to share with the class. Judy divided the class into groups and the cooking group for the day first had to make something using the actual recipe. The next time they met, some doubled the recipe; some cut it in half.
At the end of the cooking unit, still not having "taught" fractions, she gave the test again. One third of the class got 100%, and all but one student passed the test. Then she taught fractions directly and after a week of that gave a fresh version of the test. All of her fifth graders got 100% except for one who got 75%. Judy's class of 22 ten-year-olds mastered fractions in record time.
One of the main reasons so many American children decide "I am no good at math," is that mathematics is like a foreign language to them. Math is not spoken at home--in fact it is only spoken in math class. So, by the time a child is in fifth grade the calisthenics of numbers is not tied to anything real in their brains. Only the best teachers make fractions real to students.
Earlier this summer I wrote three articles pointing to what parents can do at home so that mathematics won't be a foreign language for kids in school. But all is not lost if by age ten mathematics is still not spoken at home. Judy Stone's experiment shows that using fractions in the real world was the key factor in mastering the arithmetic of fractions, and this can happen at home and be fun, too.
Working with your children in the kitchen and using the language of mathematics as you do it can be a big help in supporting them to learn what they are being taught in school. If you get playful, you can start doing experiments together--experiments for which you don't even know the outcomes, like "what if we cut the sugar by a third?" (Which is the same as using two-thirds as much sugar, right?) What if you double an ingredient, or add one that is not in the recipe book? What happened? Record the results.
You could start a little journal to record your research so that you can keep track of your findings. In the family or at parties you could do surveys of the yumminess of two different recipes and record the results. Soon you might decide you need a formula. What is the optimal ratio of sugar to flour? You could invent an equation S + F+ B = Y (where Y=yumminess as measured on a scale of 1-10.) What does 2S get us? Should we make Baking Soda a constant or a variable? Why?
Can our subjects taste the difference between two cookies that each uses a different kind of sugar? Is Yumminess a function of only the two "variables" sugar and flour? What other variables could we try? And so on. The possibilities are endless once you start playing researcher and keeping data.
Kids are never too young to be taught big words. You should use the word "function" as soon as you want to raise awareness that a certain outcome is the result of one or more inputs. (Yumminess is a function of what combination of which variables?)
But cooking is only one of the many ways that parents can bring math and science into the home. Notice how many everyday questions can only be rigorously answered by gathering, organizing and processing data. Start using numbers to record how long it takes us to get ready for school in the morning. Break it up into the time for each activity (eating, brushing teeth, getting dressed, etc.)
Statistics need not be an esoteric subject. For fun, watch Tim Harford on how important trial and error research is in learning. Historically, so many breakthroughs occurred only when people started using numbers.
See how many breakthroughs you can cause in your home by simply quantifying things and keeping track.
Rick speaks to parent and school groups and presents at numerous education conferences around the country. His articles about education and diversity have appeared in The Independent School, Multicultural Education, Education Week, the New York Times. Rick publishes a new essay each week on his blog www.rickackerly.com. His first book, The Genius in Children: Bringing out the Best in Your Child is available at Amazon.com and Books Inc in San Francisco.