This paper describes an experiment performed at a Vocational School in Palermo during the school ... more This paper describes an experiment performed at a Vocational School in Palermo during the school year 2010-11. It was designed to teach Statistics at the Secondary level following a multidisciplinary approach. The didactic activity involved the mathematics, Italian, English language and science teachers. We adapted materials and methods from the M@t.abel Elearning program, which is planned for learning basic mathematics in a middle school, in order to use it for experimentation at a professional school. The assessment of the experimentation is based on teachers’ evaluation of each student’s whole learning process. We compare the learning outcomes of students who participated in the program with others who did not.
Statistics Education and the Communication of Statistics International Association for Statistical Education Satellite Conference
In most countries, statistics are included in the mathematics curriculum and taught by mathematic... more In most countries, statistics are included in the mathematics curriculum and taught by mathematics teachers. This leads to students learning the elements of statistical concepts as mathematical and to more emphasis placed on being able to compute different measures (e.g. mean, median, standard deviation) rather than their meaning and use. Moreover, in Quebec, the high school curriculum favours a scattered presentation of statistical concepts: tables and simple graphical representations are seen in the first year; averages, medians and histograms in the third; position measures in the fourth and some aspects of correlation and standard deviation are seen in the fifth. Some elements of probability are seen in the second year. But “statistics requires a different kind of thinking” (Cobb & Moore, 1997). Is it possible by making students compute statistical measures to foster the development of statistical thinking and prepare to draw conclusions from different data sets - all important ...
The objective of this study was to see how students' strategies for solving weighted average ... more The objective of this study was to see how students' strategies for solving weighted average problems change over their high-school years. The questions were: What knowledge of the weighted average do children have before the introduction to the concept? What strategies they use to solve problems through their high-school years? Do they improve after formal instruction? Do they differ across grade levels? Are errors persistent?. A written test with significant situations which covered various contexts and representations was given to high-school students (N= 598) prior to instruction on the average (8 th grade), at the moment of instruction (9 th grade) and a year later (10 th grade). Analysis of the students' papers looked for stable strategies, modifications from one level to another, and the impact of the different variables put in place. Students' low performance in the area of the average is well documented. Over the years many studies have highlighted student diffi...
Les résultats sont tirés d’une étude plus large sur les stratégies de résolution que des élèves d... more Les résultats sont tirés d’une étude plus large sur les stratégies de résolution que des élèves de 2 e, 3 e et 4 e secondaires (14 à 16 ans) utilisent pour résoudre des problèmes de moyenne. Dans ce texte, les résolutions de trois problèmes seront analysées. Ces problèmes ont été composés de telle sorte que nous puissions distinguer entre la capacité des élèves de calculer une moyenne et celle de saisir les liens qu’il y a entre la modification de l’effectif et d’une donnée et celle de la moyenne. Les problèmes visaient aussi à tester l’influence d’une donnée égale à zéro, influence signalée dans les études précédentes. Les résultats de la présente étude font voir que, dans le contexte choisi, le type et le sens des modifications effectuées influencent les comportements des élèves et que des conceptions inadéquates ou des glissements de sens apparaissent dans certaines situations et pas dans d’autres. Note: Un long resume en anglais precede l’article qui est ecrit en francais. Mots-...
The objective of this study was to see how students’ strategies for solving weighted average prob... more The objective of this study was to see how students’ strategies for solving weighted average problems change over their high-school years. The questions were: What knowledge of the weighted average do children have before the introduction to the concept? What strategies they use to solve problems through their high-school years? Do they improve after formal instruction? Do they differ across grade levels? Are errors persistent?. A written test with significant situations which covered various contexts and representations was given to high-school students (N= 598) prior to instruction on the average (8 grade), at the moment of instruction (9 grade) and a year later (10 grade). Analysis of the students’ papers looked for stable strategies, modifications from one level to another, and the impact of the different variables put in place.
The results are taken from a much larger study on the strategies that pupils in the 2nd, 3rd and ... more The results are taken from a much larger study on the strategies that pupils in the 2nd, 3rd and 4th stages at secondary school (ages 14-16) use for solving problems concerning the mean. In this paper the solutions of three problems are analysed. These problems have been formulated to be of such a kind that we can distinguish between the ability of pupils to calculate a mean, and that of realising the effect of a change in the number of observations or in the value of an observation, on the mean. The problems were also seen to test the influence of a value equal to zero on the
The term “average” is a common expression often used wrongly. The purpose of this paper is to loo... more The term “average” is a common expression often used wrongly. The purpose of this paper is to look at the average or its equivalent through history and to examine how it is translated in schools today. First we will investigate the word itself, its origins, and its different meanings. We will see how the concept of average evolved. Average can be seen as a philosophical concept of “general” but its earlier uses probably developed within science. This concept also has some sociological significance in developing industrial societies where standardisation was essential. The concept of average played a role in politics: the idea of confidence intervals supports the statistical tools underlying opinion polls. The concept of average has become important enough to be taught in schools but little is said about the various senses of the concept and its difficulties are not really addressed.
Statistics is generally taught in schools as part of the mathematical curriculum and, as a result... more Statistics is generally taught in schools as part of the mathematical curriculum and, as a result, statistics is perceived as a mathematical concept. Moreover, the teaching emphasis is often placed on the computation of statistical information instead of the development of an “ authentic data analysis point of view” (Cobb, 1999). In this paper we consider whether a constructive relationship between statistics and mathematics is possible? We examine examples of statistical teaching situations and analyze them both from a mathematical content point of view and from a statistical perspective, to point out that the interaction between mathematics and statistics is in fact feasible/(practicable). To achieve this, it is necessary to complete a mathematical conceptual analysis of statistical concepts. It is essential to highlight the mathematical concepts beneath the statistical concepts in order to link both of them in creating classroom activities.
Le probleme de la mathopobie fait partie de la vie des professeurs de mathematiques et, de facon ... more Le probleme de la mathopobie fait partie de la vie des professeurs de mathematiques et, de facon plus genante, de la vie de certains etudiants. Notre pratique comme enseignants en mathematiques, a laquelle s’ajoutent les temoignages, commentaires et remarques formules par d’autres intervenants, nous permettent de constater que de tres nombreux etudiants refusent de s’inscrire a certains programmes d’etudes parce que ceux-ci comportent quelques cours de mathematiques.
This research sought to explore teachers’ pedagogical content knowledge of the concept of variabi... more This research sought to explore teachers’ pedagogical content knowledge of the concept of variability. Twelve mathematics high school teachers were tested on their knowledge of the concept of variability. Subjects were then asked to react when presented with scenarios describing students’ strategies, solutions and misconceptions when faced with a task based on the concept of variability. Outcomes of this study uncovered interesting teaching interventions that could prove useful to teachers faced with such scenarios. Results of both teachers’ tests and interviews revealed that teachers had difficulties and misconceptions related to the concept of variability. Furthermore, teachers’ reactions to some scenarios highlighted the influence of content knowledge of the concept of variability on the pedagogical content knowledge related to this concept.
A large experiment, investigating to what extent the use of real data and/or technology and/or pe... more A large experiment, investigating to what extent the use of real data and/or technology and/or pedagogical methods favour student’s learning of statistics concepts, was carried out in Italy. The experiment has been monitored both from the side of pupils and teachers. This paper shows the findings from the teachers’ point of view, through the analysis of their professional profile, attitudes towards statistics and opinions on its teaching before and after the experiment. The study reveals that, as teachers’ training was in mathematics, they taught statistics with a mathematical approach, instead of “teaching statistics as a respectable subject” (Moore, 1992, p.14). The experiment produced a further more significant result, as it produced a substantial modification of teachers’ perception of the approach to adopt for teaching statistics.
L’importance de la statistique est largement admise et son utilisation est repandue. Pour eviter ... more L’importance de la statistique est largement admise et son utilisation est repandue. Pour eviter son emploi inadequat sinon errone, il serait necessaire d’inclure son enseignement dans la formation, mais ou, quand et comment ? Toutes ces questions sont interreliees. Ou : dans un contexte de transfert des competences, il n’est pas exclu que la statistique soit presente en geographie, en economie ou encore en physique par exemple, la ou l’on trouve des donnees. Toutefois, le plus souvent, s’il se trouve a l’ecole, l’enseignement de la statistique s’insere dans le cours de mathematiques. Quels sont les avantages et inconvenients de cette situation ? Quand : a quel moment peut-on le faire, a l’ecole ou vaudrait-il mieux attendre l’universite ? Quand les eleves sont-ils prets a comprendre les concepts de la statistique ? Quel que soit l’endroit ou le moment, il reste qu’il faut se demander comment cet enseignement doit etre fait. Un enseignement de la statistique favorisant le developpem...
This paper describes an experiment performed at a Vocational School in Palermo during the school ... more This paper describes an experiment performed at a Vocational School in Palermo during the school year 2010-11. It was designed to teach Statistics at the Secondary level following a multidisciplinary approach. The didactic activity involved the mathematics, Italian, English language and science teachers. We adapted materials and methods from the M@t.abel Elearning program, which is planned for learning basic mathematics in a middle school, in order to use it for experimentation at a professional school. The assessment of the experimentation is based on teachers’ evaluation of each student’s whole learning process. We compare the learning outcomes of students who participated in the program with others who did not.
Statistics Education and the Communication of Statistics International Association for Statistical Education Satellite Conference
In most countries, statistics are included in the mathematics curriculum and taught by mathematic... more In most countries, statistics are included in the mathematics curriculum and taught by mathematics teachers. This leads to students learning the elements of statistical concepts as mathematical and to more emphasis placed on being able to compute different measures (e.g. mean, median, standard deviation) rather than their meaning and use. Moreover, in Quebec, the high school curriculum favours a scattered presentation of statistical concepts: tables and simple graphical representations are seen in the first year; averages, medians and histograms in the third; position measures in the fourth and some aspects of correlation and standard deviation are seen in the fifth. Some elements of probability are seen in the second year. But “statistics requires a different kind of thinking” (Cobb & Moore, 1997). Is it possible by making students compute statistical measures to foster the development of statistical thinking and prepare to draw conclusions from different data sets - all important ...
The objective of this study was to see how students' strategies for solving weighted average ... more The objective of this study was to see how students' strategies for solving weighted average problems change over their high-school years. The questions were: What knowledge of the weighted average do children have before the introduction to the concept? What strategies they use to solve problems through their high-school years? Do they improve after formal instruction? Do they differ across grade levels? Are errors persistent?. A written test with significant situations which covered various contexts and representations was given to high-school students (N= 598) prior to instruction on the average (8 th grade), at the moment of instruction (9 th grade) and a year later (10 th grade). Analysis of the students' papers looked for stable strategies, modifications from one level to another, and the impact of the different variables put in place. Students' low performance in the area of the average is well documented. Over the years many studies have highlighted student diffi...
Les résultats sont tirés d’une étude plus large sur les stratégies de résolution que des élèves d... more Les résultats sont tirés d’une étude plus large sur les stratégies de résolution que des élèves de 2 e, 3 e et 4 e secondaires (14 à 16 ans) utilisent pour résoudre des problèmes de moyenne. Dans ce texte, les résolutions de trois problèmes seront analysées. Ces problèmes ont été composés de telle sorte que nous puissions distinguer entre la capacité des élèves de calculer une moyenne et celle de saisir les liens qu’il y a entre la modification de l’effectif et d’une donnée et celle de la moyenne. Les problèmes visaient aussi à tester l’influence d’une donnée égale à zéro, influence signalée dans les études précédentes. Les résultats de la présente étude font voir que, dans le contexte choisi, le type et le sens des modifications effectuées influencent les comportements des élèves et que des conceptions inadéquates ou des glissements de sens apparaissent dans certaines situations et pas dans d’autres. Note: Un long resume en anglais precede l’article qui est ecrit en francais. Mots-...
The objective of this study was to see how students’ strategies for solving weighted average prob... more The objective of this study was to see how students’ strategies for solving weighted average problems change over their high-school years. The questions were: What knowledge of the weighted average do children have before the introduction to the concept? What strategies they use to solve problems through their high-school years? Do they improve after formal instruction? Do they differ across grade levels? Are errors persistent?. A written test with significant situations which covered various contexts and representations was given to high-school students (N= 598) prior to instruction on the average (8 grade), at the moment of instruction (9 grade) and a year later (10 grade). Analysis of the students’ papers looked for stable strategies, modifications from one level to another, and the impact of the different variables put in place.
The results are taken from a much larger study on the strategies that pupils in the 2nd, 3rd and ... more The results are taken from a much larger study on the strategies that pupils in the 2nd, 3rd and 4th stages at secondary school (ages 14-16) use for solving problems concerning the mean. In this paper the solutions of three problems are analysed. These problems have been formulated to be of such a kind that we can distinguish between the ability of pupils to calculate a mean, and that of realising the effect of a change in the number of observations or in the value of an observation, on the mean. The problems were also seen to test the influence of a value equal to zero on the
The term “average” is a common expression often used wrongly. The purpose of this paper is to loo... more The term “average” is a common expression often used wrongly. The purpose of this paper is to look at the average or its equivalent through history and to examine how it is translated in schools today. First we will investigate the word itself, its origins, and its different meanings. We will see how the concept of average evolved. Average can be seen as a philosophical concept of “general” but its earlier uses probably developed within science. This concept also has some sociological significance in developing industrial societies where standardisation was essential. The concept of average played a role in politics: the idea of confidence intervals supports the statistical tools underlying opinion polls. The concept of average has become important enough to be taught in schools but little is said about the various senses of the concept and its difficulties are not really addressed.
Statistics is generally taught in schools as part of the mathematical curriculum and, as a result... more Statistics is generally taught in schools as part of the mathematical curriculum and, as a result, statistics is perceived as a mathematical concept. Moreover, the teaching emphasis is often placed on the computation of statistical information instead of the development of an “ authentic data analysis point of view” (Cobb, 1999). In this paper we consider whether a constructive relationship between statistics and mathematics is possible? We examine examples of statistical teaching situations and analyze them both from a mathematical content point of view and from a statistical perspective, to point out that the interaction between mathematics and statistics is in fact feasible/(practicable). To achieve this, it is necessary to complete a mathematical conceptual analysis of statistical concepts. It is essential to highlight the mathematical concepts beneath the statistical concepts in order to link both of them in creating classroom activities.
Le probleme de la mathopobie fait partie de la vie des professeurs de mathematiques et, de facon ... more Le probleme de la mathopobie fait partie de la vie des professeurs de mathematiques et, de facon plus genante, de la vie de certains etudiants. Notre pratique comme enseignants en mathematiques, a laquelle s’ajoutent les temoignages, commentaires et remarques formules par d’autres intervenants, nous permettent de constater que de tres nombreux etudiants refusent de s’inscrire a certains programmes d’etudes parce que ceux-ci comportent quelques cours de mathematiques.
This research sought to explore teachers’ pedagogical content knowledge of the concept of variabi... more This research sought to explore teachers’ pedagogical content knowledge of the concept of variability. Twelve mathematics high school teachers were tested on their knowledge of the concept of variability. Subjects were then asked to react when presented with scenarios describing students’ strategies, solutions and misconceptions when faced with a task based on the concept of variability. Outcomes of this study uncovered interesting teaching interventions that could prove useful to teachers faced with such scenarios. Results of both teachers’ tests and interviews revealed that teachers had difficulties and misconceptions related to the concept of variability. Furthermore, teachers’ reactions to some scenarios highlighted the influence of content knowledge of the concept of variability on the pedagogical content knowledge related to this concept.
A large experiment, investigating to what extent the use of real data and/or technology and/or pe... more A large experiment, investigating to what extent the use of real data and/or technology and/or pedagogical methods favour student’s learning of statistics concepts, was carried out in Italy. The experiment has been monitored both from the side of pupils and teachers. This paper shows the findings from the teachers’ point of view, through the analysis of their professional profile, attitudes towards statistics and opinions on its teaching before and after the experiment. The study reveals that, as teachers’ training was in mathematics, they taught statistics with a mathematical approach, instead of “teaching statistics as a respectable subject” (Moore, 1992, p.14). The experiment produced a further more significant result, as it produced a substantial modification of teachers’ perception of the approach to adopt for teaching statistics.
L’importance de la statistique est largement admise et son utilisation est repandue. Pour eviter ... more L’importance de la statistique est largement admise et son utilisation est repandue. Pour eviter son emploi inadequat sinon errone, il serait necessaire d’inclure son enseignement dans la formation, mais ou, quand et comment ? Toutes ces questions sont interreliees. Ou : dans un contexte de transfert des competences, il n’est pas exclu que la statistique soit presente en geographie, en economie ou encore en physique par exemple, la ou l’on trouve des donnees. Toutefois, le plus souvent, s’il se trouve a l’ecole, l’enseignement de la statistique s’insere dans le cours de mathematiques. Quels sont les avantages et inconvenients de cette situation ? Quand : a quel moment peut-on le faire, a l’ecole ou vaudrait-il mieux attendre l’universite ? Quand les eleves sont-ils prets a comprendre les concepts de la statistique ? Quel que soit l’endroit ou le moment, il reste qu’il faut se demander comment cet enseignement doit etre fait. Un enseignement de la statistique favorisant le developpem...
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