Statistical Problem Solving Research Articles

Analysis of Elements Related to Data Literacy Presented in Achievement Standards of 2022 Revised National Curriculum

With the drastic increase in the amount and types of data due to advancements in information and communication technology, the significance of data literacy has become more prominent. This study examined the elements of data literacy included in the achievement standards of the revised 2022 national curriculum, investigating how data literacy elements are reflected across various subjects such as Korean literature, mathematics, social studies, science, and practical arts. Analyzing 600 achievement standards related to data literacy, the study found that data interpretation and data-based inquiry were the main elements identified, with the application of data varying across subjects. The Korean literature focused on data communication, while mathematics stressed statistical problem-solving. An increasing trend in the ratio of data interpretation and databased inquiry was observed with higher grade levels, although it was challenging to clearly discern the learning hierarchy of data literacy elements. Through this analysis, the study suggests the necessity of systematic guidance on data literacy education in the curriculum and a deeper understanding of how data literacy elements vary by subject. This research provides foundational data on integrating data literacy into the curriculum and offers insights into how students can be supported in developing the ability to extract information from data and utilize it to solve problems.

Exploring Students’ Numerical Literacy on Statistical Problem-Solving in Indonesia

Numerical literacy is a skill that must be possessed by students. It is the ability to use numbers and mathematical symbols to solve practical problems in daily contexts. In statistics courses, it is identified that 73.3% of students could solve paired t-test problems using the SPSS 21 program, but 86.36% of these students could not understand the symbols and numbers in the output of the program. This indicates that students' numeracy literacy skills need further analysis. This study aims to analyze students' numeracy literacy by using paired t-test statistical problem-solving. The type of this research was qualitative descriptive research with a case study method. This study employed a purposive sampling technique. The subjects were 30 students of mathematics education. Data were analyzed using a triangulation technique between two assignments. This study has obtained sixth major results. First, 53.3% of students cannot write statistical hypotheses correctly. Second, 73.3% of students cannot determine the solution at the output of the SPSS 21 program. Third, 60% of students cannot conclude their answers correctly. Fourth, subjects with low numerical literacy skills could understand the meaning of the questions. Fifth, subjects with medium numerical literacy skills should get training on numeracy literacy-based questions to improve their numerical analysis skills. Sixth, subjects with medium numerical literacy skills could conclude the solution correctly and tend to reflect on the process before concluding a final solution.

Establishing the Validity and Reliability of the LOCUS Assessments

The development of assessments as part of the funded LOCUS project is described. The assessments measure students’ conceptual understanding of statistics as outlined in the GAISE PreK–12 Framework. Results are reported from a large-scale administration to 3,430 students in grades 6 through 12 in the United States. Items were designed to assess levels of understanding as well as components of the statistical problem solving process as articulated in the GAISE framework. We discuss details of how the model used to develop the LOCUS assessments guided the gathering of evidence for validity and reliability arguments. Three types of validity evidence are presented: Validity Evidence via Evidence-Centered Design, Validity and Reliability Evidence via Item Analysis, and Validity Evidence via Item Calibration.

Understanding and addressing complexity in problem solving

Complexity manifests itself in many ways when attempting to solve different problems, and different tools are needed to deal with the different dimensions underlying that complexity. Not all complexity is created equal. We find that most treatments of complexity in problem solving within both the statistical and quality literature focus narrowly on technical complexity, which includes complexity of subject matter knowledge as well as complexity in the data access and analysis of that data. The literature lacks an understanding of how political complexity or organizational complexity interferes with good technical solutions when trying to deploy a solution. Therefore, people trained in statistical problem solving are ill-prepared for the situations they are likely to face on real projects. We propose a framework that illustrates examples of complexity from our own experiences, and the literature. This framework highlights the need for more holistic problem-solving approaches and a broader view of complexity. We also propose approaches to successfully navigate complexity.

Anaysis of statistical problem solving and discussion of elementary school students in project-based learning

Anaysis of statistical problem solving and discussion of elementary school students in project-based learning

Analyzing research questions from pre-service mathematics teachers in statistical problem solving process

Analyzing research questions from pre-service mathematics teachers in statistical problem solving process

ENVISIONING CHANGE IN THE STATISTICS-EDUCATION CLIMATE

The African Data Initiative started as a crowd-sourced campaign to improve the teaching of statistics in African universities. The analysis of climate data provides one suitable context to illustrate ideas that lead to a radical new form of teaching. The problem within the context comes first, the technicalities are largely reduced – mathematics is supported by meta knowledge and backed up by modelling; calculations are reduced by user-friendly software that is also used by experts. The problems are treated similarly to research questions and the results are often easier to interpret, making sense as potential answers in their context. The criteria of this approach are compared to the framework proposed by W. G. Cobb to reform statistics education in the light of the latest developments in statistics, driven by the huge increase of data. Implementation details are presented around three components: case studies, data, and the required skills. Together, these three components describe an alternative education pathway centred around statistical problem solving. The focus on interpretations of results within a real context enables software, mathematical thinking and modelling to play a supportive role, which flattens the prerequisites of complex methods and encourages their use across all levels of education.
 First published February 2020 at Statistics Education Research Journal Archives

Statistical reasoning levels and error analysis of prospective mathematics teacher students

This paper describes the level of statistical reasoning and the difficulties and errors that occur in statistical problem-solving in prospective mathematics teacher students at STKIP PGRI Jombang. This research is a qualitative study with a case study strategy, the case study in the process of solving statistical problems carried out by the subject. The research subjects were the 69 students at third-semester of Mathematics Education Program STKIP PGRI Jombang who had taken descriptive statistics. The results of this study indicate that students are not found at the idiosyncratic level, most of them are at the transitional and quantitative level, while the analytical level is still a minority

Data Scraping, Ingestation, and Modeling: Bringing Data from cars.com into the Intro Stats Class

New tools have made it much easier for students to develop skills to work with interesting data sets as they begin to extract meaning from data. To fully appreciate the statistical analysis cycle, students benefit from repeated experiences collecting, ingesting, wrangling, analyzing data and communicating results. How can we bring such opportunities into the classroom? We describe a classroom activity, originally developed by Danny Kaplan (Macalester College), in which students can expand upon statistical problem solving by hand-scraping data from cars.com, ingesting these data into R, then carrying out analyses of the relationships between price, mileage, and model year for a selected type of car.

Embedding and assessing project based statistics

Traditional approaches to learning and teaching in statistics often involves the passive absorption of information through lectures, a focus on mathematical theory and assessments which test mastery of procedures. This often results in students struggling to apply their statistics knowledge in practical and authentic contexts particularly within final year projects and in the workplace. For some time, statistics educational literature has recommended shifting the focus of teaching and assessment from theory to statistical problem solving, application based statistics using real-life scenarios, and effective communication of statistics. This research has led to the production of guidelines for statistics educators from the American Statistical Association.This paper discusses how educational literature and guidelines have been used to implement changes in the teaching of a first year probability and statistics module for mathematics undergraduates at Sheffield Hallam University. Changing to project based learning with a focus on active learning, effective decision making and communication enabled students to successfully undertake an open group project by the end of their first year. In addition, attendance, engagement and understanding were noticeably improved. The rationale, challenges and benefits to changing the focus of the course and also the teaching style are discussed.

INTRODUCTORY STATISTICS: PREPARING IN-SERVICE MIDDLE-LEVEL MATHEMATICS TEACHERS FOR CLASSROOM RESEARCH

In this study, we examined how in-service middle-level mathematics teachers used statistics in their own classroom research. Using an embedded single-case design, we analyzed a purposefully selected sample of nine teachers’ classroom research papers, identifying several themes within each phase of the statistical problem solving process to summarize how teachers 1) planned studies and collected data, 2) analyzed data, and 3) interpreted results. The results illustrate the varying ways in which teachers used statistics to make data-based decisions about their classrooms, revealing teachers’ early development in their statistical thinking and suggesting that teachers’ required knowledge of statistics is multi-faceted, requiring both a pedagogical component and statistical knowledge for the teaching profession. Such findings have important implications for how we, as teacher educators, can best meet teachers’ professional needs. First published November 2018 at Statistics Education Research Journal Archives

فاعلیة التشارک الإلکترونی فی تنمیة مهارات حل المشکلة الإحصائیة وعمق التعلم لدى طلاب التعلیم الفنى التجارى The Effectiveness of E-Collaboration on Developing Statistical Problem Solving Skills and Deep Learning among Business Secondary School Learners

المستخلص: هدف البحث الحالى إلى تطوير تدريس مقرر الإحصاء بالتعليم الفنى التجارى من خلال إعداد تصور مقترح للتشارک الإلکترونى فى حل المشکلات الإحصائية، وقياس فاعليته فى تنمية مهارات حل المشکلة الإحصائية وعمق التعلم. ولتحقيق هذا الهدف فقد تم استخدام مزيج من إجراءات منهج البحث الوصفى، ومنهج البحث التطويرى، وشبه التجريبى. ولتحديد ولقياس المتغيرات التابعة، تم تحليل محتوى وحدات علم الإحصاء وطرق جمع البيانات والعرض الجدولي والبياني للبيانات الإحصائية ـــ مقاييس النزعة المرکزية ــــ ومقاييس التشتت) بمقرر الإحصاء للصف الثانى الثانوى التجارى نظام الثلاث سنوات، ثم صمم الباحثون التصور المقترح للمهام التعليمية المصاغة فى صورة مشکلات إحصائية، وتحديد بيئة التشارک الإلکترونى من خلال تطبيقات جوجل درايف، اختبار لقياس المعارف المرتبطة بالمهارات الإحصائية، اختبار لقياس مهارات حل مشکلة الإحصائية، ومقياس لعمق التعلم، وقد تم تطبيق هذه الأدوات على عينة من طلاب الصف الثانى الثانوى التجارى بالتعليم الفنى التجارى نظام الثلاث سنوات، بلغ حجمها (33) طالبة کمجموعة تجريبية و(33) کمجموعة ضابطة، وقد أظهرت نتائج التجريب وجود فرق ذو دلالة إحصائية بين طلاب المجموعة التجريبية والضابطة فى اختبار المعارف واختبار مهارات حل المشکلة الإحصائية، وعمق التعلم، وهذا الفرق لصالح المجموعة التجريبية؛ مما أکد فاعلية التشارک الإلکترونى فى تنمية مهارات حل المشکلة الإحصائية وعمق التعلم، وفى ضوء ما توصل إليه البحث من نتائج قدم البحث مجموعة من التوصيات والمقترحات التربوية لتعميم نتائجه. Abstract: This research amid at developing the teaching of business secondary school statistical curriculum through a suggested framework of e-collaboration in solving statistical problems and measure its effectiveness on acquiring statistical, developing statistical problem solving and deep learning skills. To achieve this objective, a mixed method approach of descriptive, developmental and quasi-experimental methodologies was applied. To measure the impact of the independent variable on the dependent variables in this research, the content of statistical course in the second year of business secondary school was analyzed, specifically, data presentation and illustration methods, measurements of central tendency, and measurement of variance units. Based on the content analysis results, researchers deigned an e-collaborative learning strategy and utilized Google drive applications. In addition, test of solving statistical problems and deep learning scale were also developed and validated. These instrumentations were applied on a sample of the second year business secondary school learners. This sample was randomly and equally distributed into two groups (33 as experimental group and 33 as control group). After application of the treatment variable (e-collaborative learning strategy), the findings showed a significant impact for the new e-collaborative strategy on acquiring statistical problem solving skills and improving the deep learning skills. The difference was in favor of the experimental group. Based on these results, a set of educational recommendation were suggested to generalize the outcomes of this research in different business education context and courses.

統計的問題解決過程における「知識の活用」の評価に関する研究:― 統計的確率を用いて判断を行う授業におけるカード型知識の活用評価ツールの可能性―

統計的問題解決過程における「知識の活用」の評価に関する研究:― 統計的確率を用いて判断を行う授業におけるカード型知識の活用評価ツールの可能性―

Development of Humanistic Statistics Learning Devices Based one Inquiry and Mind Mapping Models

The purpose of this research are: (1) to determine the characteristic of humanistic statistics learning, (2) to obtain a humanistic statistics learning tools based on valid, practical, and effective inquiry and mind mapping learning model. The research method uses 4D Thiagarajan which has been modified to 3D, namely: define, design, and develop. Implementation of the development and humanistic statistics learning tool trials using Inquiry and Mind Mapping learning model show that learning tools used in statistical learning activities were practical and effective. The trial shows an increase of students’ statistical problem-solving ability using humanistic learning based on Inquiry and Mind Mapping learning model. The improvement of statistical problem-solving on Inquiry learning model is better than humanistic statistics learning using Mind Mapping learning model.

2B3-G5 問題解決の枠組みと統計的思考力の育成 : 「データの分析」の授業の視点(初等・中等教育における統計的思考力を育成する実践研究と今後の展開へ向けて,自主企画課題研究,次世代の科学力を育てる-社会とのグラウンディングを求めて-)

2B3-G5 問題解決の枠組みと統計的思考力の育成 : 「データの分析」の授業の視点(初等・中等教育における統計的思考力を育成する実践研究と今後の展開へ向けて,自主企画課題研究,次世代の科学力を育てる-社会とのグラウンディングを求めて-)

Application of Six Sigma Methodology in Glazing and Printing Processes: The Case of Lanka Wall Tiles PLC

Six Sigma is a data-driven process of thinking to create new knowledge and skills for business process improvement. It is a buzz word in the business community today as Six Sigma thinking has gained widespread popularity as a part of business process improvement methodology. This paper presents the results of applying Six Sigma methodology at Lanka Wall Tiles PLC in the areas of glazing and printing operations. The company in its process re-engineering project identified glazing and printing operations as the main processes in which defects occur regularly. In order to address the issue of production defects a five-step DMAIC framework, viz. Define, Measure, Analyze, Improve and Control, was applied. In the define stage, the size of the problem was gauged after mapping the process by means of the SIPOC (Supplier, Input, Process, Outputs, Customer) model. In the measurement and data analysis stages, a set of carefully chosen statistical methods and problem solving techniques of Six Sigma system were applied to uncover the sources of variations (SOV). Data was collected from both the past records of production and by observation of the process for a period of 21 days. Data analysis was done using tools and techniques such as quality function deployment (QFD), control charts, cross tabulation, cause and effect diagrams and Pareto charts. A detailed analysis of the data revealed the major sources of variations for which homegrown solutions were found and implemented by the project team at the improvement stage. A cautious application of DMAIC over a period of two months resulted in a gradual and steady reduction of defects by a significant 3.3 percent giving rise to savings of approximately LKR 3.36 million per month for the company. It further revealed that the methodical and systematic application of the Six Sigma system using the thinking process of DMAIC enabled the team to identify sources of variations that had been undetected for a long period of time. The success of the experiment paves the way for further studies as well as the application of Six Sigma methodology in the manufacturing environments of all production units of the company.

The Statistical Content of Elementary School Mathematics Textbooks

This study reports on the statistical content of five U.S. textbook series written for elementary students in grades 1-5. The researchers examined 17,688 pages and coded 7445 statistical tasks to determine (1) the distribution of statistical topics within textbooks, and (2) the relative emphasis on the phases of the statistical problem solving process (Formulate Questions, Collect Data, Analyze Data, and Interpret Results). Different series contained markedly different distributions of statistical content: two series located most statistical content near the end of the text, whereas two other series located statistical tasks more uniformly throughout the textbook. A large majority of statistical tasks required students to Analyze Data, with a heavy emphasis on the activities of reading displays and performing mathematical calculations.

An Analysis of the Statistical Content in Textbooks for Prospective Elementary Teachers

We analyzed the statistical content within mathematics textbooks used in courses for preparing elementary teachers. Six textbooks commonly used in the United States comprised our sample. Each task in statistical sections was analyzed using both the levels of the GAISE framework (Franklin et al. 2007) and phases of the statistical problem solving process (Formulate Questions, Collect Data, Analyze Data, and Interpret Results). Tasks within the Analyze Data phase were also classified as creating or reading a display, performing a mathematical computation, or using statistical reasoning beyond mathematical computations. The majority of statistical tasks in each book required data analysis. Two textbooks primarily consisted of tasks addressing statistical concepts beyond computations, while three series focused on graphical displays and computational procedures.

The effects of collaborative practice on statistical problem solving: Benefits and boundaries

In recent years, understanding the effects of collaboration on learning and memory has emerged as a major topic of investigation. Findings from applied educational research and from basic cognitive research demonstrate a complex view of how collaboration affects learning. The present laboratory study bridged these two domains of research to address the question of how collaborative learning affects statistical problem solving. After viewing a lecture, participants completed two statistics tests. They either completed the tests collaboratively and then individually, or completed both tests individually. Results showed an immediate benefit of collaboration, but this benefit did not persist on a subsequent individual test. Repeated practice by those who worked individually increased performance to the level of those who had previously collaborated. These results were qualified by gender as females showed a consistent benefit from prior collaboration on the post-collaborative test, particularly on conceptual problems. Implications for education are discussed.

What Should We Grow in Our School Garden to Sell at the Farmers’ Market? Initiating Statistical Literacy through Science and Mathematics Integration

ABSTRACT Statistical literacy is essential to scientific literacy, and the quest for such is best initiated in the elementary grades. The Next Generation Science Standards and the Common Core State Standards for Mathematics set forth practices (e.g., asking questions, using tools strategically to analyze and interpret data) and content (e.g., statistics) to guide the development of statistical literacy. This article portrays how statistical literacy can be initiated at the upper elementary level through integrated science–mathematics instruction in an authentic context: project-based learning focused on a farmers’ market project and school gardening. The shared classroom examples illustrate how to scaffold students’ understanding of statistical questions and develop their ability to formulate good survey questions. Science practices and science and mathematics content extend to analyzing, interpreting, and representing data as well as structure and function. This article helps teachers find an appropriate balance between offering students the freedom to explore on their own and providing them with guidance to achieve the goal of enhancing the statistical problem solving process. Student learning is extended through seed germination and related experimentation, raising produce, and vending at a local farmers’ market.