Informal Inferential Reasoning: Interval Estimates of Parameters

Theodosia Prodromou

doi:10.5539/ijsp.v2n2p136

Abstract

This research examined the informal inferential reasoning of senior secondary school students (age 17) when engaged in a computer-simulated sampling activity calling for the estimation of population parameters. The students undertook a task involving interval estimation of parameters within a computer-simulated environment. The research observed the students while they made and then explained their parameter estimates in order to better understand how the students formed the interval estimates, with particular attention to different strategies they adopted in forming these estimates. Activities involved sampling and estimating across three different sample size situations followed by a reflection stage to compare the estimates. Results of the analysis of the discussion between the students and the researcher during the students' activities are presented. A number of strategies for forming an interval estimate emerged. The students experimented with choosing different strategies for forming the interval estimate when a new sample (observed values) was drawn. The research findings are useful for informing the teaching of interval estimation to school-aged students.

Highlights

Informal Inferential Reasoning is the process of drawing generalised conclusions from data
This research examined the informal inferential reasoning of senior secondary school students when engaged in a computer-simulated sampling activity calling for the estimation of population parameters
This paper reports exploratory research into how students reason when estimating population parameters, in particular when making interval estimates of the parameters

Summary

Introduction

Informal Inferential Reasoning is the process of drawing generalised conclusions from data. Four key principles have been identified as important to making informal inferences from data: “(1) Generalization, including predictions, parameter estimates, and conclusions, that extend beyond describing the given data; (2) the use of data as evidence for those generalizations; (3) employment of probabilistic language in describing the generalization, including informal reference to levels of certainty about the conclusions drawn.” For the first critical principle of making informal inferences, generalising beyond data, much of the research into students’ reasoning has focused on drawing conclusions (e.g., Bakker & Derry, 2011; Pfannkuch, 2005; Watson & Moritz, 2000a) and making predictions (e.g., Makar & Rubin, 2009; Prodromou, 2011). The strategies used by students to create interval estimates and the developing conceptions of the process of sampling were of interest to the researcher

Methods

Results

Conclusion