We present the results of an in-depth qualitative study that examined ninth graders' conceptual and procedural knowledge of fractions as well as their approach to mathematics learning, in particular fraction learning. We traced individual differences, even extreme, in the way that students combine the two kinds of knowledge. We also provide…

We studied developmental trends in 5 important reasoning tasks that are critical components of the operational definition of rational thinking. The tasks measured denominator neglect, belief bias, base rate sensitivity, resistance to framing, and the tendency toward otherside thinking. In addition to age, we examined 2 other individual difference…