Students’ Informal Hypothesis Testing in a Probability Context With Concrete Random Generators

Abstract

This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning environment, and what role processes of data production play in their investigations. The study outlines aspects of students’ informal understanding of hypothesis testing. It shows how students with no formal education can follow the logic that a small difference in samples can be the effect of randomness, while a large difference implies a real difference in the underlying process. The students distinguish the mode and the size of differences in frequencies as signals in data and used these signals to give data-based reasons in processes of informal hypothesis testing. The study also highlights the role of data production and points to a need for further research on the role of data production in an informal approach to the teaching and learning of statistical inference. First published December 2020 at Statistics Education Research Journal: Archives

Hypothetical Learning Trajectory on Informal Hypothesis Testing in a Probability Context

“…Some students argued it matters how the bottle was shaken and turned around and other students argued that the order of how the different colors were put into the bottle would play a role. In Nilsson (2020b), however, students did not fall as much into contextual reasoning as in Nilsson et al (2018), despite a similar bottle being used and students being at the same age. How can we understand this difference?…”

“…Only a few students used the relative frequency table provided, to confirm or refute an imagined theoretical distribution. Instead, and like students in Nilsson (2020b), students attended to and compared absolute frequencies within samples. For instance, that one outcome appeared only a few times, compared to other outcomes in the sample, was used as a reason to refute that a computersimulated die was fair.…”

“…For instance, that one outcome appeared only a few times, compared to other outcomes in the sample, was used as a reason to refute that a computersimulated die was fair. In Nilsson (2020b) focus was on the mode; if an outcome was observed significantly more times than other outcomes in a sample, students inferred that the underlying, theoretical distribution was not uniform.…”

“…It is suggested that the learning of inferential statistics should start in the early years of schooling (Meletiou-Mavrotheris & Paparistodemou, 2015), with instructional support that allows students to engage in inferential statistics informally. In other words, there is a need to understand more of how to elicit and develop students' informal methods on inferential statistics to facilitate the learning of the formal methods (Makar & Rubin, 2009;Nilsson, 2020b).…”

“…However, studies usually take a relatively general perspective on informal statistical inference. There is less of detailed knowledge about the teaching and learning of informal statistical inference specific to hypothesis testing, that is, about informal hypothesis testing (Lee et al, 2010;Nilsson, 2020b).…”