In this paper, we address two Roundtable topics: distance education and developing teachers' statistical knowledge. We describe a new professional development program for secondary school mathematics teachers who are preparing to teach statistics. We also discuss what we have learned in our efforts to design a course that has a significant online component and that is relevant and useful from a teacher’s perspective. We describe the ways in which our online environment incorporates group work, self-study, concept exploration, and assessments. We also discuss the challenges associated with delivering the necessary content while simultaneously accommodating the practical time constraints of adult students who are, themselves, teaching full-time.
{"title":"Preparing Secondary Mathematics Educators to Teach Statistics","authors":"R. Gould, R. Peck","doi":"10.52041/srap.04404","DOIUrl":"https://doi.org/10.52041/srap.04404","url":null,"abstract":"In this paper, we address two Roundtable topics: distance education and developing teachers' statistical knowledge. We describe a new professional development program for secondary school mathematics teachers who are preparing to teach statistics. We also discuss what we have learned in our efforts to design a course that has a significant online component and that is relevant and useful from a teacher’s perspective. We describe the ways in which our online environment incorporates group work, self-study, concept exploration, and assessments. We also discuss the challenges associated with delivering the necessary content while simultaneously accommodating the practical time constraints of adult students who are, themselves, teaching full-time.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132648100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mathematics curriculum materials for early secondary school, based on interactive exploration of the huge database of individuals who filled out the “long” form for the US Census back through 1850, illustrate methods for improving statistical literacy and mathematics conceptual understanding while immersing students in social science content.
{"title":"Curriculum Innovations Based on Census Microdata: A Meeting of Statistics, Mathematics, and Social Science","authors":"W. Finzer, Tim Erickson","doi":"10.52041/srap.04304","DOIUrl":"https://doi.org/10.52041/srap.04304","url":null,"abstract":"Mathematics curriculum materials for early secondary school, based on interactive exploration of the huge database of individuals who filled out the “long” form for the US Census back through 1850, illustrate methods for improving statistical literacy and mathematics conceptual understanding while immersing students in social science content.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116698232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this chapter, we explore the challenges of learning about box plots and question the rationale for introducing box plots to middle school students (up to 14 years old). Box plots are very valuable tools for data analysis and for those who know how to interpret them. Research has shown, however, that some of their features make them particularly difficult for young students to use in authentic contexts. These difficulties include: a) box plots generally do not allow perceiving individual cases; b) box plots operate differently than other displays students encounter; c) the median is not as intuitive to students as we once suspected; d) quartiles divide the data into groups in ways that few students (or even teachers) really understand. We recommend that educators consider these features as they determine whether, how, and when to introduce box plots to students.
{"title":"Should Young Students Learn About Box Plots?","authors":"A. Bakker, Clifford E. Konold, Rolf Biehler","doi":"10.52041/srap.04302","DOIUrl":"https://doi.org/10.52041/srap.04302","url":null,"abstract":"In this chapter, we explore the challenges of learning about box plots and question the rationale for introducing box plots to middle school students (up to 14 years old). Box plots are very valuable tools for data analysis and for those who know how to interpret them. Research has shown, however, that some of their features make them particularly difficult for young students to use in authentic contexts. These difficulties include: a) box plots generally do not allow perceiving individual cases; b) box plots operate differently than other displays students encounter; c) the median is not as intuitive to students as we once suspected; d) quartiles divide the data into groups in ways that few students (or even teachers) really understand. We recommend that educators consider these features as they determine whether, how, and when to introduce box plots to students.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125554014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The development of statistical thinking and data sense needs steadily progressive and cohesive building of concepts and learning experiences. Meaningful discussion and analysis of curricular approaches to facilitate such development require a reference context. This paper uses a particularly relevant Australian context to combine a cross-sectional report on interaction with teachers in the development and implementation of school syllabi, with analysis of commonalities in cross-disciplinary tertiary student learning in introductory data analysis. These are used to demonstrate the need and potential for genuine and ongoing collaboration between statisticians, teachers and educationalists to develop strategies in constructing, supporting and implementing curriculum to achieve coherent progression in statistical literacy and thinking across educational levels. Such strategies must also include support for teachers.
{"title":"Coherent and Purposeful Development in Statistics across the Educational Spectrum","authors":"H. MacGillivray","doi":"10.52041/srap.04403","DOIUrl":"https://doi.org/10.52041/srap.04403","url":null,"abstract":"The development of statistical thinking and data sense needs steadily progressive and cohesive building of concepts and learning experiences. Meaningful discussion and analysis of curricular approaches to facilitate such development require a reference context. This paper uses a particularly relevant Australian context to combine a cross-sectional report on interaction with teachers in the development and implementation of school syllabi, with analysis of commonalities in cross-disciplinary tertiary student learning in introductory data analysis. These are used to demonstrate the need and potential for genuine and ongoing collaboration between statisticians, teachers and educationalists to develop strategies in constructing, supporting and implementing curriculum to achieve coherent progression in statistical literacy and thinking across educational levels. Such strategies must also include support for teachers.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126867300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consideration of variation has been identified as one of the fundamental types of statistical thinking, and recent research into the understanding of variation highlights its growing importance. Curriculum needs to reflect this trend. This chapter proposes a model for an integrated approach to curriculum development where consideration of variation is used as the linking thread. The application of this process to a tertiary introductory service statistics course is presented. A hierarchy of levels of consideration of variation is developed from students’ responses to “minute papers” and typical responses in the various levels of the hierarchy are discussed. The hierarchy can be used to evaluate the effectiveness of the integration of variation into the curriculum. This research has implications for teachers of statistics, in the development of curriculum, and for researchers in the growing field of students’ understanding of statistics.
{"title":"Consideration of Variation: A Model for Curriculum Development","authors":"C. Reading, J. Reid","doi":"10.52041/srap.04103","DOIUrl":"https://doi.org/10.52041/srap.04103","url":null,"abstract":"Consideration of variation has been identified as one of the fundamental types of statistical thinking, and recent research into the understanding of variation highlights its growing importance. Curriculum needs to reflect this trend. This chapter proposes a model for an integrated approach to curriculum development where consideration of variation is used as the linking thread. The application of this process to a tertiary introductory service statistics course is presented. A hierarchy of levels of consideration of variation is developed from students’ responses to “minute papers” and typical responses in the various levels of the hierarchy are discussed. The hierarchy can be used to evaluate the effectiveness of the integration of variation into the curriculum. This research has implications for teachers of statistics, in the development of curriculum, and for researchers in the growing field of students’ understanding of statistics.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125199773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Roundtable theme selected by the International Association for Statistical Education (IASE) organizing committee (2004) focuses on the ability to make “reasoned decisions based on sound statistical thinking.” This string of words rolls easily off one’s tongue; as an outcome, however, it remains elusive. This paper examines the journey taken by one school, from 1997 to 2004, in an effort to empower its students to make reasoned decisions based on sound statistical thinking. It outlines the background reasons for the journey, and presents a general description and some critical commentary on some of the learning experiences used. The last twelve months of the journey are addressed in some detail. Six phases of teaching and learning that may assist in realizing the goal of reasoned decision- making based on sound statistical thinking are discussed. Complementing these phases is a preliminary approach to data analysis called "distribution division". The effects of this approach on the middle school curriculum are also discussed.
{"title":"Distribution Division: Making It Possible For More Students to Make Reasoned Decisions Using Data","authors":"A. Harradine, Noel Baker","doi":"10.52041/srap.04303","DOIUrl":"https://doi.org/10.52041/srap.04303","url":null,"abstract":"The Roundtable theme selected by the International Association for Statistical Education (IASE) organizing committee (2004) focuses on the ability to make “reasoned decisions based on sound statistical thinking.” This string of words rolls easily off one’s tongue; as an outcome, however, it remains elusive. This paper examines the journey taken by one school, from 1997 to 2004, in an effort to empower its students to make reasoned decisions based on sound statistical thinking. It outlines the background reasons for the journey, and presents a general description and some critical commentary on some of the learning experiences used. The last twelve months of the journey are addressed in some detail. Six phases of teaching and learning that may assist in realizing the goal of reasoned decision- making based on sound statistical thinking are discussed. Complementing these phases is a preliminary approach to data analysis called \"distribution division\". The effects of this approach on the middle school curriculum are also discussed.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133204292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Curriculum is often developed without due consideration of what curriculum means or how it is developed. In part one of this paper I explore some meanings of curriculum and development and critique the present curriculum development model. In part two an alternative model is presented and its inter-related activities considered. In the third part other influences on development are discussed, and in part four some implications for curriculum in the future are listed.
{"title":"Statistics Curriculum and Development: New Ways of Working","authors":"A. Begg","doi":"10.52041/srap.04101","DOIUrl":"https://doi.org/10.52041/srap.04101","url":null,"abstract":"Curriculum is often developed without due consideration of what curriculum means or how it is developed. In part one of this paper I explore some meanings of curriculum and development and critique the present curriculum development model. In part two an alternative model is presented and its inter-related activities considered. In the third part other influences on development are discussed, and in part four some implications for curriculum in the future are listed.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129516698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Constructivist learning theory has suggested that students can only obtain conceptual understanding of a knowledge domain by actively trying to integrate new concepts and ideas into their existing knowledge framework. In practice, this means that students will have to explain novel ideas, concepts, and principles to themselves. Various methods have been developed that aim to stimulate the student to self-explain. In this study, two such methods were contrasted in a randomized experiment. In one condition students were stimulated to self-explain in an undirected way. In the other the stimulus to self-explain was directed. We examined whether the directive method leads to a greater level of conceptual understanding. To assess conceptual understanding we asked students to construct a concept map and to take a 10-item multiple-choice test. The results are somewhat contradictory but do suggest that the directive method may be of value. We discuss the possibility of integrating that method in the statistics curriculum.
{"title":"Directed Self-Explanation in the Study of Statistics","authors":"N. Broers, Marieke Mur, L. Budé","doi":"10.52041/srap.04102","DOIUrl":"https://doi.org/10.52041/srap.04102","url":null,"abstract":"Constructivist learning theory has suggested that students can only obtain conceptual understanding of a knowledge domain by actively trying to integrate new concepts and ideas into their existing knowledge framework. In practice, this means that students will have to explain novel ideas, concepts, and principles to themselves. Various methods have been developed that aim to stimulate the student to self-explain. In this study, two such methods were contrasted in a randomized experiment. In one condition students were stimulated to self-explain in an undirected way. In the other the stimulus to self-explain was directed. We examined whether the directive method leads to a greater level of conceptual understanding. To assess conceptual understanding we asked students to construct a concept map and to take a 10-item multiple-choice test. The results are somewhat contradictory but do suggest that the directive method may be of value. We discuss the possibility of integrating that method in the statistics curriculum.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125292542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
College-level students pursuing majors that don’t require a quantitative course still need a statistical literacy course that helps them develop the skills to evaluate arguments that use statistics as evidence. Such a course should entail utility in everyday use such that statistical literacy results in a lasting appreciation of the value of statistics as needed in everyday life, civic life, and professional life as a data consumer. A course designed to promote statistical literasy should help students understand and analyze various influences on the size and direction of a statistical association and should include key topics in conditional probability, confounding, and the vulnerability of statistical significance to confounding. This paper describes some new ways of presenting these ideas that are based on the results of field trials conducted in connection with the W. M. Keck Statistical Literacy project at Augsburg College. After studying statistical literacy, 43 percent of Augsburg students strongly agreed that the course helped them develop critical thinking skills and 18 percent strongly agreed that successful completion of the course should become requirement for graduation.
攻读不需要定量课程的大学专业的学生仍然需要统计素养课程，这有助于他们培养评估使用统计作为证据的论点的技能。这样的课程应该包括日常使用的实用性，这样统计素养就会导致对日常生活、公民生活和作为数据消费者的职业生活所需的统计价值的持久欣赏。旨在提高统计素养的课程应帮助学生理解和分析对统计关联的大小和方向的各种影响，并应包括条件概率、混淆和统计显著性对混淆的脆弱性等关键主题。本文描述了一些基于与奥格斯堡学院的W. M. Keck统计素养项目相关的实地试验结果来呈现这些想法的新方法。在学习了统计素养之后，43%的奥格斯堡学生强烈同意这门课程帮助他们培养批判性思维能力，18%的学生强烈同意成功完成这门课程应该成为毕业的必要条件。
{"title":"Statistical Literacy Curriculum Design","authors":"M. Schield","doi":"10.52041/srap.04104","DOIUrl":"https://doi.org/10.52041/srap.04104","url":null,"abstract":"College-level students pursuing majors that don’t require a quantitative course still need a statistical literacy course that helps them develop the skills to evaluate arguments that use statistics as evidence. Such a course should entail utility in everyday use such that statistical literacy results in a lasting appreciation of the value of statistics as needed in everyday life, civic life, and professional life as a data consumer. A course designed to promote statistical literasy should help students understand and analyze various influences on the size and direction of a statistical association and should include key topics in conditional probability, confounding, and the vulnerability of statistical significance to confounding. This paper describes some new ways of presenting these ideas that are based on the results of field trials conducted in connection with the W. M. Keck Statistical Literacy project at Augsburg College. After studying statistical literacy, 43 percent of Augsburg students strongly agreed that the course helped them develop critical thinking skills and 18 percent strongly agreed that successful completion of the course should become requirement for graduation.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123790236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the reform of the Italian school system, a new pedagogical point of view has shifted attention away from content and skills and toward competencies. Also contributing to the proposal of a new mathematical curriculum is a new way of looking at mathematics that takes globalised societal needs into consideration. This paper describes the role of the Italian Statistical Society (SIS) in proposing knowledge and skills of the “Data and predictions” nucleus, which has emerged as one of the basic themes in the new mathematics curriculum. We present the guidelines which have been implemented to enhance the visibility of statistics and probability in the mathematical curriculum, taking into account the results of some recent research on statistics education carried out in Italy.
{"title":"“Data and Predictions” Emerging as One of the Basic Themes in the Mathematical Curriculum of the First Cycle School Level in Italy","authors":"M. Ottaviani, S. R. Luchini","doi":"10.52041/srap.04501","DOIUrl":"https://doi.org/10.52041/srap.04501","url":null,"abstract":"In the reform of the Italian school system, a new pedagogical point of view has shifted attention away from content and skills and toward competencies. Also contributing to the proposal of a new mathematical curriculum is a new way of looking at mathematics that takes globalised societal needs into consideration. This paper describes the role of the Italian Statistical Society (SIS) in proposing knowledge and skills of the “Data and predictions” nucleus, which has emerged as one of the basic themes in the new mathematics curriculum. We present the guidelines which have been implemented to enhance the visibility of statistics and probability in the mathematical curriculum, taking into account the results of some recent research on statistics education carried out in Italy.","PeriodicalId":447331,"journal":{"name":"Curricular Development in Statistics Education IASE Roundtable Conference","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126341526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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