Transfer and Learning • Teaching Statistics

We have found that students often do not transfer statistical ideas from school to the playground or vice versa, and we assume this is in part due to initial learning that did not prepare children to learn in new settings. Multiple classroom studies have examined the prospect of preparing high-school and college students for future learning in statistics and assessing that preparedness. Preparing students for future learning is important, because no training in problem solving can prepare students for every situation they will encounter, and they will need to learn.  Additionally, the creation of test instruments that assess student preparedness for future learning would make teaching to the test a desirable activity. Students invented graphic and symbolic procedures to discriminate the “spreads” of contrasting data sets. For example, in the figure, students had to invent a reliability index to determine which pitching machine was more reliable. Each of the circles represent the location of a pitch and an X represents the target. The goal was not to guide students to invent conventional solutions, but rather to help students develop an appreciation of the quantitative properties of distributions that formal representations need to characterize. The contrasting pitching machines helped students notice important features of distributions including density, outliers, the distinction between variability and accuracy, and sample size. In turn, this would ideally prepare students to deeply understand conventional solutions when given resources for learning them.

Here are some solutions that students generate:

Our experiments have found that preparation for learning (PFL) activities like these prepared 9th-grade students to learn from a brief lecture on variance. Even after a year’s delay the 9th-grade students had learned to compute and explain variance better than college students who had taken a semester of statistics. Students were also prepared to learn in transfer situations. In one assessment, for example, students completed a double transfer. They transferred prior instruction to learn from a worked-example embedded as a test problem, and they transferred this example to solve a target problem later in the test. Students who did not receive the worked-example problem or who completed another form of instruction did not solve the target problem as frequently. The studies demonstrate that instruction that prepares students to learn may not reveal its value on standard tests of sequestered problem solving but can show superior effects when students have an opportunity to learn at test.