Teacher narratives in making sense of the statistical mean algorithm

Abstract

Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to mathematical concepts and enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements and comparison of varying measurements to a central anchoring value. Teachers who understand the concepts and tools of statistics in an isolated and processual way cannot teach in such a connected way. Teachers’ discourses about the mean tend to be particularly processual and lead to limited understanding of the statistical mean as measure of centre in order to compare variation within data sets. In this article I report on findings from an analysis of discussions about the statistical mean by a group of teachers. The findings suggest that discourses for instruction in statistics should explicitly differentiate between the everyday ‘average’ and the statistical mean, and explain the meaning of the arithmetic algorithm for the mean. I propose a narrative that logically explains the mean algorithm in order to establish the mean as an origin in a measurement of variation discourse.

Statistical Reasoning Process of Students in Decision Making Using Commognitive Framework

“…In this connection, commognitive as a lens in reasoning research has been carried out by previous researchers, such as research on mathematical reasoning (Jeannotte & Kieran, 2017;Rabin et al, 2013), geometric reasoning (Toscano et al, 2019;Wang, 2016;Wang & Kinzel, 2014), and statistical reasoning (Lampen, 2015;Park & Lee, 2014;Rahmatina et al,2020). This shows that commognitive reasoning has become a trend in reasoning research.…”

“…However, not many researchers have studied how the commognitive framework has been used as a tool in the statistical reasoning process. Lampen (2015) and Park & Lee (2014) investigate the use of commognitive framework in statistical reasoning. Lampen's research (2015) focused on analysing Sfard's commognitive theory (2008) on teachers' narrative in making sense of the average algorithm as a discourse basis of variability measure.…”

“…Meanwhile, the research focus of Rahmatina et al (2020) was to examine students' statistical reasoning from a narrative perspective regarding variability in the process of analysing and interpreting data. Thus, research conducted by Lampen (2015) and Park & Lee (2014) investigated how to analyse data to get a conclusion, but they did not examine in more detail how the statistical reasoning process was before reaching the conclusions. Unlike the research case of Rahmatina et al (2020), they studied the process of statistical reasoning from a commognitive perspective, but the use of the commognitive framework they studied was limited to the use of narrative in data analysis and interpretation.…”

Language and multilingualism in the teaching and learning of mathematics in South Africa: A review of literature in Pythagoras from 1994 to 2021

“…The authors develop analytical language to examine how coherently a teacher moves from a stated mathematical problem towards a solution. Lampen (2015) uses the concept of MDI to explore required teacher knowledge and skill to meaningfully conduct classroom discussions on the statistical mean algorithm in a connected manner. Contrastingly, Berger (2013) examines student discourse from the perspective of Sfard's theory of commognition.…”

Statistical Reasoning of Variability in the Narrative Perspective of Students

“…The form of the narrative was indicated when the students explained the theorem of a rectangular area using the concepts of addition and subtraction. Similarly, Lampen (2015) studied the narrative of the concept of statistics in a teacher. He found that initially, the teacher could not create narratives about the mean as a statistical object.…”