Mix It Up for Better Learning

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,¹a 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 77, while the students in the one-at-a-time group had an average grade of 38. 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?

¹Rohrer, D. and Taylor, K., "The Effects of Interleaved Practice,"Applied Cognitive Psychology, 2010;24(6): #837-848.

(a) Give the notation (as a difference with a minus sign) for the quantity we are trying to estimate.

Let group 1be the fourth-grade students who study mixed problems and let group 2be the fourth-grade students who study each equation independently.

p

1

-

p

2

p

^

1

-

p

^

2

1

-

2

x

-

1

-

x

-

2

1

-

2

r

1

-

r

2

(b) Give the notation for the quantity that gives the best estimate.

Let group 1be the fourth-grade students who study mixed problems and let group 2be the fourth-grade students who study each equation independently.

p

1

-

p

2

p

^

1

-

p

^

2

1

-

2

x

-

1

-

x

-

2

1

-

2

r

1

-

r

2

(c) Give the value of the best estimate.

Enter the exact answer.

The value of the best estimate is ________________

Enter your answer in accordance to the question statement