Estimating Parameters from Samples: Shuttling between Spheres

Abstract

In order to better understand the thinking of students' learning to make informal statistical inferences, this research examined the thinking of senior secondary school students (age 17) engaged in the task of using observed data to make point estimates of a population parameter within a computer-based simulation. Following the "Growing Samples" instructional model, the point estimation activity involved sampling and estimating across three tasks with different sample sizes. This research study aimed to trace the evolution of the students' thinking, with particular attention to use of the statistical concepts in making informal inferences from sampling. The students in this study were observed to rely primarily on mathematical thinking, which, perhaps, inhibited their ability to construct meanings about the basic statistical concepts underpinning sampling when performing point estimates. At times in the process students were seen to shift between mathematical thinking, statistical thinking, and thinking about the context, but the mathematical thinking seemed to dominate their attempts to create estimates. These research findings are useful for informing the teaching of point estimation of a population parameter to school-aged students. The research findings also stress the need for teachers to rethink the relationship between statistical thinking and mathematical thinking in order to promote statistical thinking in relevant learning situations for their students.