Triss just started the Transitions textbooks by Scott Foresman, and I read through the sidenotes in the teacher's guide as I was correcting. They have some neat features, such as Error Alerts for specific questions in the book that might give a child trouble-- they even tell *why* the child might be having trouble and how to remediate the concept. (I just love it when a book considers me intelligent enough to be "let in on the joke," so to speak. Especially if it is a math book. Makes me feel like thumbing my nose at the math books I had in school. Neener, neener, neener, I can understand math. But I digress. Ahem.)
I had been working with Mariel (not Triss) on converting fractions to decimals, and had run out of ways to explain it. Triss happened to be dealing with converting fractions to decimals in her book too, and the lesson overview from Triss' math program really helped me understand where my explanations might be falling short with Mariel:
Often a fraction is introduced via shading equal sectors of a circle, so that a/b means that a of b sectors are shaded. If this is the only way that fractions are presented, students associate the numerator and the denominator of a fraction with counting and they have no meaning for the fraction bar. [The fraction bar is the line between the numerator and the denominator for those of you who-- like me-- might have forgotten.] Thus, many students never think of the fraction as being a single number and it becomes more difficult for them to order fractions or rename a fraction as a decimal. Some students spend years of work with fractions before they are taught that a/b means dividing a by b. The changing of fractions to decimals and the graphing of fractions on the number line help develop the concept of the fraction as representing a single number.
Ohhhhhh. All of a sudden I was really excited about cornering Mariel for some more math. I knew we had to stop with the pizza math and work with.... chocolate bars.
Why is that? Why didn't I just do the number line and converting fractions to decimals thing? Well, that was a very good suggestion from Triss' math book, and Mariel's math book actually had her working like that, but it wasn't clicking for her. She kept forgetting that a/b is a divided by b, kept thinking that 1/10 was one out of ten *wholes*. And I realized that every time we have ever talked about fractions we have been dividing things in which each person gets a portion that is considered a fair amount, or a *whole* piece. Do you know what I mean? When you order a pizza, you don't expect to eat the whole thing yourself. You think each person will have a piece-- a *whole* piece. So, even though we call them pieces, they are wholes. Whole servings, you see? Same with pie. Each piece is a whole serving for one person.
Chocolate bars are different. When you have a chocolate bar, you expect to eat the whole thing yourself. So the bar is the whole. But if you have only one chocolate bar and nine chocolate-loving friends, the nice thing to do is break the bar into even pieces. And the pieces are little. It is easy to see that they are fractions of the whole, because after you eat your little piece you know it wasn't a whole serving. You could easily have eaten the whole chocolate bar yourself. The reality of dividing is thus brought into sharp relief. (Especially if you are very fond of chocolate.)
By the way, I curbed my urge to grab Mariel right that minute, and instead waited for the next day's math lesson. And chocolate bars really did help.
(And I still want to post about Elvis math. Maybe this week.)