Stochastic and Deterministic Views of Statistics: A Pedagogical Perspective (original) (raw)
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Necessary Knowledge for Teaching Statistics: Example of the Concept of Variability
ICME-13 Monographs, 2018
This chapter explores teachers' statistical knowledge in relation to the concept of variability. Twelve high school mathematics teachers were asked to respond to scenarios describing students' strategies, solutions, and misconceptions when presented with a task based on the concept of variability. The teachers' responses primarily helped us analyze their comprehension and practices associated with the concept of variability and gain insight into how to teach this concept. Secondly, the study shows that students and high school teachers share the same conceptions on this subject. Keywords Professional knowledge • Statistics • Teacher's knowledge Teaching practices • Variability 10.1 Context The importance of statistics in our lives is such that data management has become a major key in the education of responsible citizens (Baillargeon 2005; Konold and Higgins 2003). The abundance of statistical data available on the internet, the studies reported on television news, or the studies and survey results published in newspapers and magazines all show that nowadays, citizens must have analytical skills to develop critical judgment and a personal assessment of the data they are confronted with daily. This role of statistics in our current society makes it necessary to consider teaching this discipline to train our students to be citizens of tomorrow. If the goal is to encourage statistical thinking in students as future citizens, then not only do we need to teach basic statistical data interpretation skills, but it is also essential to teach the
International Journal of Computers for Mathematical Learning, 2007
New capabilities in TinkerPlots 2.0 supported the conceptual development of fifth-and sixth-grade students as they pursued several weeks of instruction that emphasized data modeling. The instruction highlighted links between data analysis, chance, and modeling in the context of describing and explaining the distributions of measures that result from repeatedly measuring multiple objects (i.e., the height of the school's flagpole, a teacher's head circumference, the arm-span of a peer). We describe the variety of data representations, statistics, and models that students invented and how these inscriptions were grounded both in their personal experience as measurers and in the affordances of TinkerPlots, which assisted them in quantifying what they could readily display with the computer tool. By inventing statistics, students explored the relation between qualities of distribution and methods for expressing these qualities as a quantity. Attention to different aspects of distribution resulted in the invention of different statistics. Variable invention invited attention to the qualities of ''good'' measures (statistics), thus meshing conceptual and procedural knowledge. Students used chance simulations, built into TinkerPlots, to generate models that explained variability in a sample of measurements as a composition of true value and chance error. Error was, in turn, decomposed into a variety of sources and associated magnitudes-a form of analysis of variance for children. The dynamic notations of TinkerPlots altered the conceptual landscape of modeling, placing simulation and world on more equal footing, as first suggested by Kaput (Journal of Mathematical Behavior, 17(2), 265-281, 1998). Keywords Statistics education Á Modeling Á Learning The discipline of statistics originated in problems of modeling variability (Stigler, 1986). History has not changed all that much: Professional practices of statisticians invariably include efforts to model variability (Wild and Pfannkuch 1999). It is through the contest among alternative models that statistical concepts become more widespread and stable
A way of teaching statistics: An approach to flexible learning
International Journal of Innovation in Science and Mathematics Education, 2012
Over the past few decades there has been a debate about the reform of statistics education. In particular, many educators are interested in finding a better answer to the question, 'How can students' learning be improved in statistics education?'. Although modern statistics has many visible applications as well as a high demand in employment, students are still moving away from learning statistics. Since the reason for this is not very clear, we must tell the students (and potential students) that statistics forms a strong basis or foundation for many fundamental and experimental studies apart from standing on its own as a discipline. Since most of the theories in statistics are based on mathematics, teaching statistics becomes more difficult than other subjects. Teachers need to find better ways to resolve these difficulties in teaching and answer the common question, 'Why do students need to learn theoretical statistics via mathematics if statistics is supposed to ...
Development of the concept of statistical variation: An exploratory study
Mathematics Education Research Journal, 2000
An appreciation of variation is central to statistical thinking, but very little research has focused directly on students' understanding of variation. In this exploratory study, four students from each of grades 4, 6, 8, and 10 were interviewed individually on aspects of variation present in three settings. The first setting was an isolated random sampling situation, whereas the other two settings were real world sampling situations. Four levels of responding were identified and described in relation to developing concepts of variation. hnplicatioris for teaching and future research on variation are considered.
A FRAMEWORK FOR TEACHING AND ASSESSING REASONING ABOUT VARIABILITY
SERJ EDITORIAL BOARD, 2005
SERJ is a peer-reviewed electronic journal of the International Association for Statistical Education (IASE) and the International Statistical Institute (ISI). SERJ is published twice a year and is free. SERJ aims to advance research-based knowledge that can help to improve the teaching, learning, and understanding of statistics or probability at all educational levels and in both formal (classroombased) and informal (out-of-classroom) contexts. Such research may examine, for example, cognitive, motivational, attitudinal, curricular, teaching-related, technology-related, organizational, or societal factors and processes that are related to the development and understanding of stochastic knowledge. In addition, research may focus on how people use or apply statistical and probabilistic information and ideas, broadly viewed.
This chapter presents a literature review of theories used to frame and underpin Statistics Education Research. The aim is to describe, characterize and arrange the nature and use of theories in SER and hint at some potential trends and required directions for further theorizing the SER discipline. The review includes empirical research papers, published from 2004 to 2015, and focuses on students’ learning of statistics or probability at the primary and secondary school level. The number of papers that fulfilled our inclusion criteria was 35.
Teaching and Learning of Statistics
The Proceedings of the 12th International Congress on Mathematical Education, 2015
Being able to provide sound evidence-based arguments and critically evaluate data-based claims are important skills that all citizens should have. It is not surprising therefore that the study of statistics at all educational levels is gaining more students and drawing more attention than it has in the past. The study of statistics provides students with tools, ideas and dispositions to use in order to react intelligently to information in the world around them. Reflecting this need to improve students' ability to think statistically, statistical literacy and reasoning are becoming part of the mainstream school and university curriculum in many countries. As a consequence, statistics education is a growing and becoming an exciting field of research and development. Statistics at school level is usually taught in the mathematics classroom in connection with learning probability. Topic Study Group 12 (TSG-12) included probabilistic aspects in learning statistics, whereas research with a specific focus on learning probability was discussed in TSG-11 of ICME-12.
On middle-school students' comprehension of randomness and chance variability in data 1
Understanding variability in empirical data is at the core of statistical reasoning and thinking. Of particular interest is how students' comprehension of chance and variability develops over time. This article reports the results of a crosssectional study that examined how students' statistical literacy evolves with increasing age. Our results are discussed and related to earlier studies with children by Fischbein and Green and with adults by Sedlmeier. Our study replicates in a modified form earlier investigations in other countries and confirms for German students conclusions from earlier studies. In particular, there are no indications of an improvement with increasing age. Our findings are consistent with findings in judgment research.
Where do students get lost? The concept of variation
Many college students have difficulties in understanding and making connections among the main concepts of statistics. Compounding the difficulties is the misconception of a variety of statistical concepts that students hold even before taking any statistics course. It is, thus, crucial to investigate how the understanding of statistical concepts is constructed and at which stage students start to lose making connections among various concepts. This article reports some findings from our study of investigating the path of learning statistical concepts, specifically on how students learn the concept of variation. We focus on investigating the missing connections about their understanding of variation. The framework of statistical thinking, PPDAC investigative cycle, is used as our guideline for analyzing our interview data.