"Children learn by having opportunities to explore ideas in these different ways and by making connections or translations between the different representations.
|Image from Page 4 of their report|
Thinking about how we can encourage and foster those connections seems very worthwhile.
I also liked the style of their assessment questions, where they ask the students to show how they would do a problem on the number line or using decimal boards or grids.
I was surprised when they said:
"that of all the manipulatives available for teaching about fractions, fraction circles are the most effective for building mental images for fractions."Because by William Clevland (The Elements of Graphing Data) should that Pie Charts were the worst form of information graphic, because people had a hard time comparing area. Cleveland's research had showed that horizontal lines were best for facilitating comparisons. Of course it may be that children have more experience with Fractions in their Pizza and Cake form, so for them fraction circles make sense. Me I personally prefer the chocolate bar form ;)