This study investigates how 11- to 12-year-old students construct data-based decision trees using data cards for classification purposes. We examine the students' heuristics and reasoning during this process. The research is based on an eight-week teaching unit during which students labeled data, built decision trees, and assessed them using test data. They learned to manually construct decision trees to classify food items as recommendable or not. They utilized data cards with a heuristic that is a simplified form of a machine learning algorithm. We report on evidence that this topic is teachable to middle school students, along with insights for refining our teaching approach and broader implications for teaching machine learning at the school level.
{"title":"TEACHING AND LEARNING TO CONSTRUCT DATA-BASED DECISION TREES USING DATA CARDS AS THE FIRST INTRODUCTION TO MACHINE LEARNING IN MIDDLE SCHOOL","authors":"Yannik Fleischer, Susanne Podworny, Rolf Biehler","doi":"10.52041/serj.v23i1.450","DOIUrl":"https://doi.org/10.52041/serj.v23i1.450","url":null,"abstract":"This study investigates how 11- to 12-year-old students construct data-based decision trees using data cards for classification purposes. We examine the students' heuristics and reasoning during this process. The research is based on an eight-week teaching unit during which students labeled data, built decision trees, and assessed them using test data. They learned to manually construct decision trees to classify food items as recommendable or not. They utilized data cards with a heuristic that is a simplified form of a machine learning algorithm. We report on evidence that this topic is teachable to middle school students, along with insights for refining our teaching approach and broader implications for teaching machine learning at the school level.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141921022","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 Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report advocates for use of real data with context and purpose. This work contributes to the growing literature on assessing statistical literacy by investigating the influence of context as it relates to assessment performance among post-secondary introductory statistics students. We discuss the development of an isomorphic form of an existing assessment instrument, and report results which concluded that test takers demonstrated lower statistical literacy scores when assessment tasks incorporated real data from published studies as context when compared with functionally similar tasks such as those with a contrived data set and a realistic context.
{"title":"EXAMINING THE ROLE OF CONTEXT IN STATISTICAL LITERACY OUTCOMES USING AN ISOMORPHIC ASSESSMENT INSTRUMENT","authors":"S. Phadke, Matthew Beckman, Kari LOCK MORGAN","doi":"10.52041/serj.v23i1.529","DOIUrl":"https://doi.org/10.52041/serj.v23i1.529","url":null,"abstract":"The Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report advocates for use of real data with context and purpose. This work contributes to the growing literature on assessing statistical literacy by investigating the influence of context as it relates to assessment performance among post-secondary introductory statistics students. We discuss the development of an isomorphic form of an existing assessment instrument, and report results which concluded that test takers demonstrated lower statistical literacy scores when assessment tasks incorporated real data from published studies as context when compared with functionally similar tasks such as those with a contrived data set and a realistic context.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141796978","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}
Lori Viali, Magnus Cesar Ody, Clarissa Coragem Ballejo, Elisabete RAMBO BRAGA
In this article, we first analyze the situation of statistics education in Brazil, within an international context of interest for this discipline. Secondly, we aim to answer the following research question: How has doctoral research in statistics, probability, and combinatorics education evolved in Brazil? For this purpose, we analyzed the Brazilian doctoral research production from 1994 to 2021. We identified 102 completed dissertations in doctoral programs over the last 28 years. Within this research context, we analyzed the graduate programs, advisors, research themes, grade levels and participants studied, theoretical frameworks, and the data analysis methodologies employed. Even though doctoral research has developed slowly and irregularly, there has been an increase in the number of studies, driven by the growth of graduate degrees offered in the last few years.
{"title":"BRAZILIAN RESEARCH IN STATISTICS, PROBABILITY AND COMBINATORICS EDUCATION: A LOOK AT THESES","authors":"Lori Viali, Magnus Cesar Ody, Clarissa Coragem Ballejo, Elisabete RAMBO BRAGA","doi":"10.52041/serj.v22i3.583","DOIUrl":"https://doi.org/10.52041/serj.v22i3.583","url":null,"abstract":"In this article, we first analyze the situation of statistics education in Brazil, within an international context of interest for this discipline. Secondly, we aim to answer the following research question: How has doctoral research in statistics, probability, and combinatorics education evolved in Brazil? For this purpose, we analyzed the Brazilian doctoral research production from 1994 to 2021. We identified 102 completed dissertations in doctoral programs over the last 28 years. Within this research context, we analyzed the graduate programs, advisors, research themes, grade levels and participants studied, theoretical frameworks, and the data analysis methodologies employed. Even though doctoral research has developed slowly and irregularly, there has been an increase in the number of studies, driven by the growth of graduate degrees offered in the last few years.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138961437","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}
Reform efforts in statistics education emphasize the need for students to develop statistical thinking. Critical to this goal is a solid understanding of design in the process of collecting data, evaluating evidence, and drawing conclusions. We collected survey responses from over 700 college students at the start of an introductory statistics course to determine how they evaluated the validity of different designs. Despite preferring different designs, students offered a variety of productive arguments supporting their choices. For example, some students viewed intervention as a weakness that disrupted the ability to generalize results, whereas others viewed intervention as critical for identifying causality. Our results highlight that instruction should frame design as the balancing of different priorities: namely causality, generalizability, and power.
{"title":"RESOURCES AND TENSIONS IN STUDENT THINKING ABOUT STATISTICAL DESIGN","authors":"Kelly Findley, Brein Mosely, Aaron Ludkowski","doi":"10.52041/serj.v22i3.662","DOIUrl":"https://doi.org/10.52041/serj.v22i3.662","url":null,"abstract":"Reform efforts in statistics education emphasize the need for students to develop statistical thinking. Critical to this goal is a solid understanding of design in the process of collecting data, evaluating evidence, and drawing conclusions. We collected survey responses from over 700 college students at the start of an introductory statistics course to determine how they evaluated the validity of different designs. Despite preferring different designs, students offered a variety of productive arguments supporting their choices. For example, some students viewed intervention as a weakness that disrupted the ability to generalize results, whereas others viewed intervention as critical for identifying causality. Our results highlight that instruction should frame design as the balancing of different priorities: namely causality, generalizability, and power.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001852","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 research paper examines tasks related to mean, median, and mode in seven Swedish textbook series for students aged between 10–13 years. The tasks were analysed based on context, mathematical properties, input and output objects, and transformations. These categories allowed for a thorough analysis of the opportunities afforded to students to understand these measures. The analysis revealed that most tasks focus on the mean and on procedural transformations with quantitative values. The findings suggested that the textbooks do not afford enough explicit context for students to develop a deep understanding of the mathematical properties of different measures of central tendency. By analysing various textbooks, a broader understanding of the learning opportunities afforded to students was gained. The discussion includes the implications of these results for task design.
{"title":"OPPORTUNITIES TO LEARN MEAN, MEDIAN, AND MODE AFFORDED BY TEXTBOOK TASKS","authors":"Karin Landtblom","doi":"10.52041/serj.v22i3.655","DOIUrl":"https://doi.org/10.52041/serj.v22i3.655","url":null,"abstract":"This research paper examines tasks related to mean, median, and mode in seven Swedish textbook series for students aged between 10–13 years. The tasks were analysed based on context, mathematical properties, input and output objects, and transformations. These categories allowed for a thorough analysis of the opportunities afforded to students to understand these measures. The analysis revealed that most tasks focus on the mean and on procedural transformations with quantitative values. The findings suggested that the textbooks do not afford enough explicit context for students to develop a deep understanding of the mathematical properties of different measures of central tendency. By analysing various textbooks, a broader understanding of the learning opportunities afforded to students was gained. The discussion includes the implications of these results for task design.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138603816","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 study builds on previous studies that have examined guided project-based learning in undergraduate statistics courses to examine students’ attitudes toward statistics after participating in a graduate-level statistics course that used guided project-based learning as an andragogical technique. This phenomenological qualitative case study utilized multiple student interviews and reflections over a semester-long statistics course in a doctoral education degree program. The results showed that guided project-based learning immersed students in the quantitative inquiry process and emboldened them to read and use statistics in their academic and professional lives. It also revealed several elements of guided project-based learning that are important for instructors looking to implement this approach in their own courses.
{"title":"STATISTICS ATTITUDES AFTER USING GUIDED PROJECT-BASED LEARNING AS AN ANDRAGOGICAL STRATEGY IN A GRADUATE STATISTICS COURSE","authors":"Adam Elder","doi":"10.52041/serj.v22i3.436","DOIUrl":"https://doi.org/10.52041/serj.v22i3.436","url":null,"abstract":"This study builds on previous studies that have examined guided project-based learning in undergraduate statistics courses to examine students’ attitudes toward statistics after participating in a graduate-level statistics course that used guided project-based learning as an andragogical technique. This phenomenological qualitative case study utilized multiple student interviews and reflections over a semester-long statistics course in a doctoral education degree program. The results showed that guided project-based learning immersed students in the quantitative inquiry process and emboldened them to read and use statistics in their academic and professional lives. It also revealed several elements of guided project-based learning that are important for instructors looking to implement this approach in their own courses.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138618156","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}
We present an exploratory study of Costa Rican and Spanish students’ (11–16-year-olds) competence to compare probabilities in urns and compare ratios in mixture problems. A sample of 704 students in Grades 6 through to Grade 10, 292 from Costa Rica and 412 from Spain, were given one of two forms of a questionnaire with three probability comparison and three ratio comparison problems each. The full questionnaire consisting of both forms covers six different proportional reasoning levels for each type of problem. We analysed the percentages of correct responses to the items and the strategies used by students in each grade and in each country. The results suggest students had the highest difficulty in comparing probabilities for items at the same proportional reasoning level. The results also point to the probabilistic biases in students’ responses, although these biases were less frequent than in previous research.
{"title":"ANALYSING COSTA RICAN AND SPANISH STUDENTS’ COMPARISONS OF PROBABILITIES AND RATIOS","authors":"C. Batanero, L. A. Hernández-Solís, M. Gea","doi":"10.52041/serj.v22i3.659","DOIUrl":"https://doi.org/10.52041/serj.v22i3.659","url":null,"abstract":"We present an exploratory study of Costa Rican and Spanish students’ (11–16-year-olds) competence to compare probabilities in urns and compare ratios in mixture problems. A sample of 704 students in Grades 6 through to Grade 10, 292 from Costa Rica and 412 from Spain, were given one of two forms of a questionnaire with three probability comparison and three ratio comparison problems each. The full questionnaire consisting of both forms covers six different proportional reasoning levels for each type of problem. We analysed the percentages of correct responses to the items and the strategies used by students in each grade and in each country. The results suggest students had the highest difficulty in comparing probabilities for items at the same proportional reasoning level. The results also point to the probabilistic biases in students’ responses, although these biases were less frequent than in previous research.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139200710","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}
Martha Elena AGUIAR BARRERA, Humberto Gutiérrez Pulido, Verónica Vargas Alejo
This research presents the results of the implementation of a model-electing activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the Bachelor Civil Engineering Program at the University of Guadalajara, Mexico. The activity was refined during three semesters, and here we report the models generated by the students in the fourth implementation. In the first stage of the activity of this implementation, students proposed wrong solutions, which were based on ideas of proportionality and linear thinking. The activity was designed to inhibit these types of solutions and to encourage students to realize when they are dealing with a random phenomenon, and that they need a probability distribution to solve the activity. The students used RStudio software to calculate probabilities.
{"title":"MODEL-ELECTING ACTIVITY WITH CIVIL ENGINEERING STUDENTS TO SOLVE A PROBLEM INVOLVING BINOMIAL DISTRIBUTION","authors":"Martha Elena AGUIAR BARRERA, Humberto Gutiérrez Pulido, Verónica Vargas Alejo","doi":"10.52041/serj.v22i3.431","DOIUrl":"https://doi.org/10.52041/serj.v22i3.431","url":null,"abstract":"This research presents the results of the implementation of a model-electing activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the Bachelor Civil Engineering Program at the University of Guadalajara, Mexico. The activity was refined during three semesters, and here we report the models generated by the students in the fourth implementation. In the first stage of the activity of this implementation, students proposed wrong solutions, which were based on ideas of proportionality and linear thinking. The activity was designed to inhibit these types of solutions and to encourage students to realize when they are dealing with a random phenomenon, and that they need a probability distribution to solve the activity. The students used RStudio software to calculate probabilities.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139208951","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}
N. Rotondi, David Rudoler, William Hunter, Olayinka Sanusi, Chris Collier, Michael Rotondi
This article reports on an evaluation the effectiveness of e-mailed grade “nudges” on students’ performance and engagement in an introductory statistics course for undergraduate health science students. In 2020–2021, 358 students were randomized to an e-mail (n = 178) or no e-mail (n = 180) group. The intervention e-mail contained information on each student’s predicted final grade (grade nudge). Using two-sample t-tests, the statistical analysis of final grades in the course showed a higher compatibility with a model of no mean difference for students in the e-mail (73.5%) vs. no e-mail (72.1%) group. Comparison of the distributions of final grades between the two groups, however, suggested the e-mailed nudges may be related to slight improvements in final grades. Specifically, the median final grade was higher in the e-mail group (74.6 vs. 72.4); the Q1 value in the e-mail group was also higher, and the interquartile range was similar: no e-mail group (15.8) vs. e-mail group (14.2). Students also completed the Scale of Student Engagement in Statistics (SSE-S). Total engagement, affective and cognitive subscale scores of the SSE-S were higher in the e-mail group, resulting in low compatibility with a model of no difference in engagement scores. Overall, the results showed there is potential for our midterm warning system to be used to improve outcomes, particularly given that it is simple to implement, cost-effective, and easily scalable.
{"title":"USING A MIDTERM WARNING SYSTEM TO IMPROVE STUDENT PERFORMANCE AND ENGAGEMENT IN AN INTRODUCTORY STATISTICS COURSE: A RANDOMIZED CONTROLLED TRIAL","authors":"N. Rotondi, David Rudoler, William Hunter, Olayinka Sanusi, Chris Collier, Michael Rotondi","doi":"10.52041/serj.v22i3.406","DOIUrl":"https://doi.org/10.52041/serj.v22i3.406","url":null,"abstract":"This article reports on an evaluation the effectiveness of e-mailed grade “nudges” on students’ performance and engagement in an introductory statistics course for undergraduate health science students. In 2020–2021, 358 students were randomized to an e-mail (n = 178) or no e-mail (n = 180) group. The intervention e-mail contained information on each student’s predicted final grade (grade nudge). Using two-sample t-tests, the statistical analysis of final grades in the course showed a higher compatibility with a model of no mean difference for students in the e-mail (73.5%) vs. no e-mail (72.1%) group. Comparison of the distributions of final grades between the two groups, however, suggested the e-mailed nudges may be related to slight improvements in final grades. Specifically, the median final grade was higher in the e-mail group (74.6 vs. 72.4); the Q1 value in the e-mail group was also higher, and the interquartile range was similar: no e-mail group (15.8) vs. e-mail group (14.2). Students also completed the Scale of Student Engagement in Statistics (SSE-S). Total engagement, affective and cognitive subscale scores of the SSE-S were higher in the e-mail group, resulting in low compatibility with a model of no difference in engagement scores. Overall, the results showed there is potential for our midterm warning system to be used to improve outcomes, particularly given that it is simple to implement, cost-effective, and easily scalable.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139209042","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}
Statistical reasoning about a population through samples can be achieved by modeling the relationship between population and sample. One way to do this is to model real data situations in a technology-integrated environment. With this view, we aimed to investigate how middle school students formed distributions and examined their statistical modeling processes through the informal reasoning process within the Reasoning with Informal Statistical Models and Modeling (RISM) framework. The case study reported in this paper focuses on how the conjecture and data models students designed throughout three activities evolved and how their inclusion of a fundamentally probabilistic mechanism matured. Findings show the students approached the distribution probabilistically with their inferences during the modeling process and grasped the statistical concepts they would encounter at a more advanced level. Therefore, we claim that students shifted from understanding empirical distributions to understanding theoretical distributions.
{"title":"MIDDLE SCHOOL STUDENTS’ STATISTICAL REASONING ABOUT DISTRIBUTION IN THEIR STATISTICAL MODELING PROCESSES","authors":"TUĞÇE BALKAYA, GAMZE KURT","doi":"10.52041/serj.v22i1.312","DOIUrl":"https://doi.org/10.52041/serj.v22i1.312","url":null,"abstract":"Statistical reasoning about a population through samples can be achieved by modeling the relationship between population and sample. One way to do this is to model real data situations in a technology-integrated environment. With this view, we aimed to investigate how middle school students formed distributions and examined their statistical modeling processes through the informal reasoning process within the Reasoning with Informal Statistical Models and Modeling (RISM) framework. The case study reported in this paper focuses on how the conjecture and data models students designed throughout three activities evolved and how their inclusion of a fundamentally probabilistic mechanism matured. Findings show the students approached the distribution probabilistically with their inferences during the modeling process and grasped the statistical concepts they would encounter at a more advanced level. Therefore, we claim that students shifted from understanding empirical distributions to understanding theoretical distributions.","PeriodicalId":38581,"journal":{"name":"Statistics Education Research Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135926244","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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