A design experiment where students in Grade 5 (11–12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space reasoning over idiosyncratic reasoning when the sample space was changed between color runs. In the second and third steps, students used degrees of variation in the distribution of the mode across samples to infer whether an unknown sample space was uniform. Students’ reasoning disclosed the logic: the larger the variation, the greater the reason for rejecting a uniform sample space.
{"title":"HYPOTHETICAL LEARNING TRAJECTORY ON INFORMAL HYPOTHESIS TESTING IN A PROBABILITY CONTEXT","authors":"Per Nilsson","doi":"10.52041/serj.v22i2.425","DOIUrl":"https://doi.org/10.52041/serj.v22i2.425","url":null,"abstract":"A design experiment where students in Grade 5 (11–12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space reasoning over idiosyncratic reasoning when the sample space was changed between color runs. In the second and third steps, students used degrees of variation in the distribution of the mode across samples to infer whether an unknown sample space was uniform. Students’ reasoning disclosed the logic: the larger the variation, the greater the reason for rejecting a uniform sample space.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45507912","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}
Soledad Estrella, Maritza MÉNDEZ-REINA, Pedro Vidal-Szabó
Recent research suggests the benefits of supporting a progressive understanding of concepts of inference prior to the teaching of procedures and formal calculations through the study of informal statistical inference (ISI). To contribute to the growing knowledge about the early learning and teaching of statistics, particularly regarding the development of informal inferential reasoning (IIR), we designed a learning trajectory (LT) that addresses ISI in K–4 students (ages 5 to 9 years). This article describes part of the LT in detail, in which third-grade students (n = 12) were introduced to sampling, frequency distribution, randomness and sampling variation as well as to developing a data sense in online lessons. The results of this type of teaching show that the creation and collection of authentic data in a playful context, together with an exploratory analysis of the data as a precursor to utilizing aspects specific to IIR, promoted the integration progress of IIR components in the oral and written informal inferences of students.
{"title":"EXPLORING INFORMAL STATISTICAL INFERENCE IN EARLY STATISTICS: A LEARNING TRAJECTORY FOR THIRD-GRADE STUDENTS","authors":"Soledad Estrella, Maritza MÉNDEZ-REINA, Pedro Vidal-Szabó","doi":"10.52041/serj.v22i2.426","DOIUrl":"https://doi.org/10.52041/serj.v22i2.426","url":null,"abstract":"Recent research suggests the benefits of supporting a progressive understanding of concepts of inference prior to the teaching of procedures and formal calculations through the study of informal statistical inference (ISI). To contribute to the growing knowledge about the early learning and teaching of statistics, particularly regarding the development of informal inferential reasoning (IIR), we designed a learning trajectory (LT) that addresses ISI in K–4 students (ages 5 to 9 years). This article describes part of the LT in detail, in which third-grade students (n = 12) were introduced to sampling, frequency distribution, randomness and sampling variation as well as to developing a data sense in online lessons. The results of this type of teaching show that the creation and collection of authentic data in a playful context, together with an exploratory analysis of the data as a precursor to utilizing aspects specific to IIR, promoted the integration progress of IIR components in the oral and written informal inferences of students.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46432894","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}
Data modeling is an essential activity in a data-driven society, but such a topic and how the context shapes it has received limited attention. This paper reports on research that investigated the role of context in supporting early statistical reasoning in the data modeling process. The data were collected throughout sessions in which young children (7 year-old) worked out problem activities designed to stimulate data modeling. The problem activities started by reading children’s story books purposefully created as a strategy to provide contexts of interest. The stories were inscribed within culturally relevant contexts in which the characters deal with data in different formats. The data modeling problem activities were closely related to the stories described within the books. Special attention was put into the actions of organizing, structuring, visualizing, and representing data and the role of the context in the data modeling process. The main results suggest that the context of the problem activities for the data modeling process seems to facilitate statistical reasoning in young children. Additionally, the context of the problem activities helped participants to develop strategies to identify attributes of data, assess the model created, make sense of the data, and make informal inferences.
{"title":"THE ROLE OF CONTEXTS IN SUPPORTING EARLY STATISTICAL REASONING IN DATA MODELING","authors":"Lucía Zapata-Cardona","doi":"10.52041/serj.v22i2.448","DOIUrl":"https://doi.org/10.52041/serj.v22i2.448","url":null,"abstract":"Data modeling is an essential activity in a data-driven society, but such a topic and how the context shapes it has received limited attention. This paper reports on research that investigated the role of context in supporting early statistical reasoning in the data modeling process. The data were collected throughout sessions in which young children (7 year-old) worked out problem activities designed to stimulate data modeling. The problem activities started by reading children’s story books purposefully created as a strategy to provide contexts of interest. The stories were inscribed within culturally relevant contexts in which the characters deal with data in different formats. The data modeling problem activities were closely related to the stories described within the books. Special attention was put into the actions of organizing, structuring, visualizing, and representing data and the role of the context in the data modeling process. The main results suggest that the context of the problem activities for the data modeling process seems to facilitate statistical reasoning in young children. Additionally, the context of the problem activities helped participants to develop strategies to identify attributes of data, assess the model created, make sense of the data, and make informal inferences.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42555957","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}
This paper focuses on two third-grade students’ work on the same statistical question whereby one acts with analogue material and the other with TinkerPlotsTM. The aim of the research was to find out whether different material influences the actions and, thus, possibly the mathematical interpretations of the learners. To investigate this research interest, a semiotic perspective on mathematical learning according to Peirce was adopted. Based on this perspective, a modification of Mayring’s context analysis was made, which allowed the analysis of actions to reconstruct the learners’ diagram interpretations. From the analyses, there is evidence that some materials can shorten actions and can automatically establish mathematical relationships and, thus, affect the mathematical interpretations of the learners. At times, however, other actions on different materials can also lead to the reconstruction of the same diagram interpretations. Using these insights, implications for mathematics teaching practice were formulated to assist teachers in selecting materials for designing learning environments to support early statistical thinking.
{"title":"A SEMIOTIC PERSPECTIVE ON LEARNING MATHEMATICS WITH DIGITAL AND ANALOGUE MATERIAL: PRIMARY SCHOOL CHILDREN ACTING ON STATISTICAL DIAGRAMS","authors":"L. Billion","doi":"10.52041/serj.v22i2.420","DOIUrl":"https://doi.org/10.52041/serj.v22i2.420","url":null,"abstract":"This paper focuses on two third-grade students’ work on the same statistical question whereby one acts with analogue material and the other with TinkerPlotsTM. The aim of the research was to find out whether different material influences the actions and, thus, possibly the mathematical interpretations of the learners. To investigate this research interest, a semiotic perspective on mathematical learning according to Peirce was adopted. Based on this perspective, a modification of Mayring’s context analysis was made, which allowed the analysis of actions to reconstruct the learners’ diagram interpretations. From the analyses, there is evidence that some materials can shorten actions and can automatically establish mathematical relationships and, thus, affect the mathematical interpretations of the learners. At times, however, other actions on different materials can also lead to the reconstruction of the same diagram interpretations. Using these insights, implications for mathematics teaching practice were formulated to assist teachers in selecting materials for designing learning environments to support early statistical thinking.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49265977","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}
Developing statistical thinking is vital to fostering students’ critical thinking; however, it requires suitable curricula, appropriate textbooks, and well-prepared teachers. For many decades, statistics education was almost absent in the K–12 education in the Arab world. During the past few years, noticeable education reform efforts at all educational levels have introduced advanced curricula that aim to equip students with the skills that would enable them to compete internationally. This study aims to analyze the new statistics curricula in the United Arab Emirates (UAE), as a leading educational model, and assess their alignment with the best international practices in developing statistical thinking at the primary school levels. Content analysis of the statistics component in mathematics textbooks from Grades 1–4 in UAE is presented in this paper, benchmarking the statistics content with the best international practices. Finally, recommendations on efficient and practical approaches to ensure appropriate development of statistical thinking at early educational stages are showcased.
{"title":"STATISTICAL THINKING AT EARLY PRIMARY SCHOOL LEVELS: CURRICULUM PERSPECTIVES IN UAE TEXTBOOKS","authors":"Rafiq Hijazi, Ali S. Shaqlaih","doi":"10.52041/serj.v22i2.447","DOIUrl":"https://doi.org/10.52041/serj.v22i2.447","url":null,"abstract":"Developing statistical thinking is vital to fostering students’ critical thinking; however, it requires suitable curricula, appropriate textbooks, and well-prepared teachers. For many decades, statistics education was almost absent in the K–12 education in the Arab world. During the past few years, noticeable education reform efforts at all educational levels have introduced advanced curricula that aim to equip students with the skills that would enable them to compete internationally. This study aims to analyze the new statistics curricula in the United Arab Emirates (UAE), as a leading educational model, and assess their alignment with the best international practices in developing statistical thinking at the primary school levels. Content analysis of the statistics component in mathematics textbooks from Grades 1–4 in UAE is presented in this paper, benchmarking the statistics content with the best international practices. Finally, recommendations on efficient and practical approaches to ensure appropriate development of statistical thinking at early educational stages are showcased.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48339681","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}
Young children encounter uncertainty and challenges on a daily basis; through their intuitions, experiences and experimentation they construct knowledge, skills and dispositions towards probabilistic concepts. The aim of this exploratory ethnographic study is to identify how young children engage with probabilistic thinking and reasoning while playing outdoors. Twelve 3–4-year-old children and two practitioners were observed during free and structured activities outdoors. Critical events, that reflect contexts of probability, chance and uncertainty, were identified for further analysis based on participants’ linguistic interactions. Children’s probabilistic thinking was mainly expressed in three instances: while solving problems, in creative play, and while considering risk and safety issues. These authentic understandings can become the basis for more instructional pedagogical sequences on probability in early years.
{"title":"PRESCHOOLERS’ INTUITIVE PROBABILISTIC THINKING DURING OUTDOOR PLAY","authors":"Z. Nikiforidou, Jennie L. Jones","doi":"10.52041/serj.v22i2.444","DOIUrl":"https://doi.org/10.52041/serj.v22i2.444","url":null,"abstract":"Young children encounter uncertainty and challenges on a daily basis; through their intuitions, experiences and experimentation they construct knowledge, skills and dispositions towards probabilistic concepts. The aim of this exploratory ethnographic study is to identify how young children engage with probabilistic thinking and reasoning while playing outdoors. Twelve 3–4-year-old children and two practitioners were observed during free and structured activities outdoors. Critical events, that reflect contexts of probability, chance and uncertainty, were identified for further analysis based on participants’ linguistic interactions. Children’s probabilistic thinking was mainly expressed in three instances: while solving problems, in creative play, and while considering risk and safety issues. These authentic understandings can become the basis for more instructional pedagogical sequences on probability in early years.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41744052","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}
Arjen de Vetten, R. Keijzer, J. Schoonenboom, B. van Oers
The study reported in this article investigated the appropriateness of Mathematical Knowledge in Teaching of three pre-service primary school teachers (PSTs), teaching an informal statistical inference (ISI) lesson to primary school students. Using an ISI framework and the Knowledge Quartet framework., the presence and appropriateness of the PSTs’ teaching actions were coded and categorized. The results showed that PSTs were consciously engaged in making inferences based on sample data. The PSTs struggled to correctly interpret students’ conceptual input and to explain ISI, in particular, how generalizing from a sample is possible. Teacher education should focus on how PSTs can foster students’ understanding of the logic of drawing conclusions about a population based on a sample.
{"title":"PRE-SERVICE PRIMARY SCHOOL TEACHERS' KNOWLEDGE DURING TEACHING INFORMAL STATISTICAL INFERENCE","authors":"Arjen de Vetten, R. Keijzer, J. Schoonenboom, B. van Oers","doi":"10.52041/serj.v22i2.424","DOIUrl":"https://doi.org/10.52041/serj.v22i2.424","url":null,"abstract":"The study reported in this article investigated the appropriateness of Mathematical Knowledge in Teaching of three pre-service primary school teachers (PSTs), teaching an informal statistical inference (ISI) lesson to primary school students. Using an ISI framework and the Knowledge Quartet framework., the presence and appropriateness of the PSTs’ teaching actions were coded and categorized. The results showed that PSTs were consciously engaged in making inferences based on sample data. The PSTs struggled to correctly interpret students’ conceptual input and to explain ISI, in particular, how generalizing from a sample is possible. Teacher education should focus on how PSTs can foster students’ understanding of the logic of drawing conclusions about a population based on a sample.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47928792","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}
A. Leavy, Maria Meletiou-Mavrotheris, Efi Paparistodemou, Daniel Frischemeier
Welcome to a special issue of SERJ.
欢迎收看SERJ特刊。
{"title":"EDITORIAL: RESEARCH ON EARLY STATISTICAL AND PROBABILISTIC THINKING","authors":"A. Leavy, Maria Meletiou-Mavrotheris, Efi Paparistodemou, Daniel Frischemeier","doi":"10.52041/serj.v22i2.706","DOIUrl":"https://doi.org/10.52041/serj.v22i2.706","url":null,"abstract":"Welcome to a special issue of SERJ.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47249459","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}
This article reports on a study in which third-grade students (8–9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained the outcomes, quantified their chances of colour selections, and created two representations displaying the probabilities. Children displayed awareness of randomness and variation, together with proportional reasoning, as evident in their identification of one or more colours as having a greater chance of being selected, or equal chances when proportions of colours were equal. Evidence of children’s metarepresentational competence appeared in their creation of two representations to display their probabilistic outcomes, with bar and circle graphs, as well as stacked bars, created. The inclusion of their own forms of inscription revealed a range of probability and statistics understandings. In selecting and justifying their preferred representations for conveying their outcomes, students favoured both bar and circle graphs, with a focus on how accurately, effectively, and efficiently their representation displayed the data, with the importance of the inscriptions highlighted.
{"title":"LINKING PROBABILITY AND STATISTICS IN YOUNG STUDENTS’ REASONING WITH CHANCE","authors":"Lyn D. English","doi":"10.52041/serj.v22i2.418","DOIUrl":"https://doi.org/10.52041/serj.v22i2.418","url":null,"abstract":"This article reports on a study in which third-grade students (8–9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained the outcomes, quantified their chances of colour selections, and created two representations displaying the probabilities. Children displayed awareness of randomness and variation, together with proportional reasoning, as evident in their identification of one or more colours as having a greater chance of being selected, or equal chances when proportions of colours were equal. Evidence of children’s metarepresentational competence appeared in their creation of two representations to display their probabilistic outcomes, with bar and circle graphs, as well as stacked bars, created. The inclusion of their own forms of inscription revealed a range of probability and statistics understandings. In selecting and justifying their preferred representations for conveying their outcomes, students favoured both bar and circle graphs, with a focus on how accurately, effectively, and efficiently their representation displayed the data, with the importance of the inscriptions highlighted.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42414754","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}
Various sources suggest preparing teachers of early- or primary-age students to teach probability and statistics involves various challenges. Some of the approaches researchers take for resolving these challenges include developing preservice teacher content knowledge, pedagogical knowledge, as well as providing other opportunities to learn. Various sources also suggest that research in this area is missing or underemphasizing some components. The systematic review undertaken here considers this question by comparing extant literature to teacher preparation standards. Results show that studies emphasize development of probability and statistics concepts and procedures, and an underrepresentation of development of pedagogical knowledge, learning from school experiences, such as student teaching, and reflection on practice.
{"title":"PREPARING PRESERVICE TEACHERS TO TEACH PROBABILITY AND STATISTICS TO EARLY LEARNERS: A SYSTEMATIC REVIEW","authors":"D. Denton","doi":"10.52041/serj.v22i2.437","DOIUrl":"https://doi.org/10.52041/serj.v22i2.437","url":null,"abstract":"Various sources suggest preparing teachers of early- or primary-age students to teach probability and statistics involves various challenges. Some of the approaches researchers take for resolving these challenges include developing preservice teacher content knowledge, pedagogical knowledge, as well as providing other opportunities to learn. Various sources also suggest that research in this area is missing or underemphasizing some components. The systematic review undertaken here considers this question by comparing extant literature to teacher preparation standards. Results show that studies emphasize development of probability and statistics concepts and procedures, and an underrepresentation of development of pedagogical knowledge, learning from school experiences, such as student teaching, and reflection on practice.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44565497","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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