Book contents
- Frontmatter
- Preface
- Contents
- 1 Teaching with Primary Historical Sources: Should it Go Mainstream? Can it?
- 2 Dialogismin Mathematical Writing: Historical, Philosophical and Pedagogical Issues
- 3 The Process of Mathematical Agreement: Examples from Mathematics History and an Experimental Sequence of Activities
- 4 Researching the History of Algebraic Ideas from an Educational Point of View
- 5 Equations and Imaginary Numbers: A Contribution from Renaissance Algebra
- 6 The Multiplicity of Viewpoints in Elementary Function Theory: Historical and Didactical Perspectives
- 7 From History to Research in Mathematics Education: Socio-Epistemological Elements for Trigonometric Functions
- 8 Harmonies in Nature: A Dialogue Between Mathematics and Physics
- 9 Exposure to Mathematics in the Making: Interweaving Math News Snapshots in the Teaching of High-School Mathematics
- 10 History, Figures and Narratives in Mathematics Teaching
- 11 Pedagogy, History, and Mathematics: Measure as a Theme
- 12 Students' Beliefs About the Evolution and Development of Mathematics
- 13 Changes in Student Understanding of Function Resulting from Studying Its History
- 14 Integrating the History of Mathematics into Activities Introducing Undergraduates to Concepts of Calculus
- 15 History in a Competence Based Mathematics Education: A Means for the Learning of Differential Equations
- 16 History of Statistics and Students' Difficulties in Comprehending Variance
- 17 Designing Student Projects for Teaching and Learning Discrete Mathematics and Computer Science via Primary Historical Sources
- 18 History of Mathematics for Primary School Teacher Education Or: Can You Do Something Even if You Can't Do Much?
- 19 Reflections and Revision: Evolving Conceptions of a Using History Course
- 20 Mapping Our Heritage to the Curriculum: Historical and Pedagogical Strategies for the Professional Development of Teachers
- 21 Teachers' Conceptions of History of Mathematics
- 22 The Evolution of a Community of Mathematical Researchers in North America: 1636–1950
- 23 The Transmission and Acquisition of Mathematics in Latin America, from Independence to the First Half of the Twentieth Century
- 24 In Search of Vanishing Subjects: The Astronomical Origins of Trigonometry
- About the Editors
16 - History of Statistics and Students' Difficulties in Comprehending Variance
- Frontmatter
- Preface
- Contents
- 1 Teaching with Primary Historical Sources: Should it Go Mainstream? Can it?
- 2 Dialogismin Mathematical Writing: Historical, Philosophical and Pedagogical Issues
- 3 The Process of Mathematical Agreement: Examples from Mathematics History and an Experimental Sequence of Activities
- 4 Researching the History of Algebraic Ideas from an Educational Point of View
- 5 Equations and Imaginary Numbers: A Contribution from Renaissance Algebra
- 6 The Multiplicity of Viewpoints in Elementary Function Theory: Historical and Didactical Perspectives
- 7 From History to Research in Mathematics Education: Socio-Epistemological Elements for Trigonometric Functions
- 8 Harmonies in Nature: A Dialogue Between Mathematics and Physics
- 9 Exposure to Mathematics in the Making: Interweaving Math News Snapshots in the Teaching of High-School Mathematics
- 10 History, Figures and Narratives in Mathematics Teaching
- 11 Pedagogy, History, and Mathematics: Measure as a Theme
- 12 Students' Beliefs About the Evolution and Development of Mathematics
- 13 Changes in Student Understanding of Function Resulting from Studying Its History
- 14 Integrating the History of Mathematics into Activities Introducing Undergraduates to Concepts of Calculus
- 15 History in a Competence Based Mathematics Education: A Means for the Learning of Differential Equations
- 16 History of Statistics and Students' Difficulties in Comprehending Variance
- 17 Designing Student Projects for Teaching and Learning Discrete Mathematics and Computer Science via Primary Historical Sources
- 18 History of Mathematics for Primary School Teacher Education Or: Can You Do Something Even if You Can't Do Much?
- 19 Reflections and Revision: Evolving Conceptions of a Using History Course
- 20 Mapping Our Heritage to the Curriculum: Historical and Pedagogical Strategies for the Professional Development of Teachers
- 21 Teachers' Conceptions of History of Mathematics
- 22 The Evolution of a Community of Mathematical Researchers in North America: 1636–1950
- 23 The Transmission and Acquisition of Mathematics in Latin America, from Independence to the First Half of the Twentieth Century
- 24 In Search of Vanishing Subjects: The Astronomical Origins of Trigonometry
- About the Editors
Summary
Introduction
Although variation is central to statistics (e.g., [28, 29]), before the end of the 90's not much attention was given to it in didactical research, as Bakker [1, p. 16], Reading [33] and others have remarked. Only recently have there been some systematic studies on the development of students' conception of variation (e.g., [43, 33, 34, 3, 14, especially pp. 382–386]). However, although didactical research on variance and standard deviation (s.d.) is very limited, it still points out that students face important difficulties in understanding these concepts. Mathews, Clark and their colleagues [25, 5, 14, pp. 383, 385–386, 388] examined students in four tertiary USA institutions, shortly after they had completed their introductory statistics course with an A. The majority of the students had not understood even the basic characteristics of the s.d.: (i) one third of them considered the s.d. simply as the outcome of an algorithm to be given and performed, did not understand its meaning and were unable to calculate it if the formula was not given; (ii) some confounded the s.d. with the Z-values; (iii) others believed that the s.d. of an ordered set of numbers depends on the distance between the successive values of this set and expresses a kind of mean value of these distances. Although these students got an A, they had not even formed the simplified idea that the s.d. is a kind of an average distance from the mean.
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- Publisher: Mathematical Association of AmericaPrint publication year: 2011