In preparing for a test on a set of material, is it better to study one topic at a time or to study topics mixed together? In one study,¹ a sample of fourth graders were taught four equations. Half of the children learned by studying repeated examples of one equation at a time, while the other half studied mixed problem sets that included examples of all four types of calculations grouped together. A day later, all the students were given a test on the material. The students in the mixed practice group had an average grade of 7777, while the students in the one-at-a-time group had an average grade of 3838. What is the best estimate for the difference in the average grade between fourth-grade students who study mixed problems and those who study each equation independently?

a) Give the notation (as a difference with a minus sign) for the quantity we are trying to estimate. Let group 11be the fourth-grade students who study mixed problems and let group 22be the fourth-grade students who study each equation independently.

b) Give the notation for the quantity that gives the best estimate. Let group 11be the fourth-grade students who study mixed problems and let group 22be the fourth-grade students who study each equation independently.