|August 11-17 2007
|University of Warwick, UK
|Reasoning about Statistical Inference: Innovative Ways of Connecting Chance and Data
|Reasoning about statistical inference
Presentations from SRTL5
THINKING-IN-CHANGE ABOUT INFORMAL INFERENCE
PETER JOHNSTON-WILDER, JANET AINLEY, & DAVE PRATT
A small modification to Pratt’s ChanceMaker enabled us to explore young students’ (age 10-11) informal inference. The students were challenged to guess the configuration of a hidden dice by generating as much or as little data as they wanted. After the first iteration, we found it necessary to give the students experience of mending dice, as in Pratt’s original study, before they engaged in inferential activity. Nevertheless, the students’ confidence in their inferences was not stronger for larger samples of data. Recent evidence has shown that the connections that students make between sample and population are based on naive understandings of complexity theory (emergent phenomena). We use this theory to explain why students focussed on local rather than global aspects, and to postulate the future direction of our work.
INFORMAL INFERENTIAL REASONING IN STATISTICS EDUCATION: SOME ASSESSMENT AND RESEARCH ISSUES
MAKING NON-FORMAL STATISTICAL INFERENCES TO MONITOR PRODUCTION PROCESSES
ARTHUR BAKKER, PHILLIP KENT, JAN DERRY, CELIA HOYLES & RICHARD NOSS
This paper studies non-formal statistical inference in industrial settings. The focus is on statistical process control, which is used to monitor and improve production processes. After a comparison of formal statistical inference and non-formal statistical process control, we give examples of how employees make statistical inferences from data at work. One key observation is that the right decision cannot be left to a formal procedure, but that contextual knowledge plays a crucial role in drawing conclusions in what we call a “space of reasons”. The results will hopefully contribute to our understanding of informal statistical inference and fuel the discussion about which types of statistical inference students will need to apply in their future jobs.
TO UNDERSTAND A DISTRIBUTION, TRY BUILDING IT FROM SCRATCH
CLIFF KONOLD, SIBEL KAZAK, RICHARD LEHRER, & MIN JOUNG KIM
We describe two recent teaching experiments in which students build and run models that produce distributions similar to ones they have observed in the real world. These modeling capabilities are being incorporated into a new version of the data-analysis software TinkerPlots with the intention of providing a single tool that students can use to explore fundamental connections between data and chance. In a fifth grade classroom, students used these capabilities to build and evaluate “factories” that created distributions of measurement errors intended to reproduce characteristics of actual measurements they had made. In the second study, grade 6-8 students evaluated similar factories built to model group difference.
A Statistician’s View on the Concept of Inferential Reasoning
Allan’s opening talk.
ENHANCING REASONING ABOUT STATISTICAL INFERENCE IN 8 YEAR-OLD STUDENTS
EFI PAPARISTODEMOU & MARIA MELETIOU-MAVROTHERIS
This paper focuses on developing students’ informal ideas of inference skills. We study third grade students’ development of informal understanding of statistical inference in real data, using the dynamic statistics learning environment Tinkerplots® (Konold and Miller, 2005), a software specifically designed to meet the learning needs of students in early grades. The data presented in the paper, come from a scenario where students conducted a survey about health, nutrition and safety habits of students in their school. Children analyzed their data collected using Tinkerplots® as an investigation tool, and made a presentation of their findings to the whole school. Findings from the study support the view that statistics instruction can promote the development of learners’ inferential reasoning at an early age, through an informal, data-based approach. They suggest that use of dynamic statistics software does indeed have the potential to enhance statistics instruction by making inferential reasoning accessible to young learners.
SOUP OR STEW: METAPHORS FOR THE RELATIONSHIP BETWEEN SAMPLES AND POPULATIONS
ANDEE RUBIN & JIM HAMMERMAN
Much research has been devoted to people’s attempts to relate samples and populations, most of it demonstrating how difficult the process is. Rubin et al (1990) characterized the process of making inferences from samples to populations as one that requires simultaneously understanding the representativeness of samples and the variability of samples, two characteristics that inherently provide a tension for the analyst. This paper provides another perspective on this complex issue, one in which a series of metaphors sheds light on a group of teachers’ developing ideas about the relationship between samples and populations.
FACILITATING BEGINNING INFERENCE WITH TINKERPLOTS FOR NOVICE GRADE 7 STUDENTS
JANE M. WATSON
This study sought to explore the use of TinkerPlots software to facilitate ideas associated with beginning inference in a group of novice grade 7 students in a rural school. An action research design was intended to modify teaching and learning opportunities in the light of observation of components of a model developed by Pfannkuch for the teaching of informal inference with box plots. Seven episodes of the study are described with data in the form of TinkerPlots files collected and analyzed on four occasions. The outcomes provide evidence of change on the part of students’ appreciation of decision making with data, as well as the potential for TinkerPlots to assist in the process.
STUDYING THE DEVELOPMENT OF COLLEGE STUDENTS’ INFORMAL REASONING ABOUT STATISTICAL INFERENCE
ANDREW S. ZIEFFLER, JOAN GARFIELD, ROBERT DELMAS, & ROBERT GOULD
This paper describes one part of a longitudinal study that explored the question of how students’ informal inferential reasoning develops in a research and standards-based introductory college statistics course that is designed to promote this type of reasoning. A teaching experiment was conducted in a 15-week course that embedded numerous interactive simulation activities and discussions to help students develop informal knowledge and reasoning about statistical inference. This paper focuses primarily on a set of three interviews with the same student, one at the beginning of the course, one midway through the course, and one at the end of the course. A framework to analyze the nature and development of this students’ informal inferential reasoning was developed and refined. This framework provides a model of four different dimensions that contribute to informal inferential reasoning. Implications for teaching, assessment, and further research are suggested.
DANI BEN-ZVI, EINAT GIL, & NAOMI APEL
CHALLENGING STUDENTS’ INFORMAL INFERENTIAL REASONING BY MEANS OF SMOOTHLY INTRODUCING P-VALUE BASED HYPOTHESIS TESTING
BEYOND THE BAR GRAPH: TEACHING INFORMAL STATISTICAL INFERENCE IN PRIMARY SCHOOL
KATIE MAKAR & ANDEE RUBIN
- Please contact authors directly to request a copy of their paper.
Participants SRTL 5