Statistics Curriculum Research Articles

DEFRAGMENTATION OF CONSTRUCTION HOLE THINKING PROCESS OF JUNIOR HIGH SCHOOL STUDENTS IN SOLVING NUMERATION LITERACY QUESTIONS

Teachers must be aware of and take action regarding students' errors in creating incomplete mathematical concepts, also referred to as construction holes, particularly when it comes to answering numeracy literacy questions. This will help students rebuild their understanding of numeracy literacy questions overall. By using diagrams to depict the answers to numeracy literacy questions both before and after the defragmentation process, this study seeks to identify the places where pupils fall short conceptually. A mixed-methods research methodology was employed for this study, which was conducted in two phases: quantitative analysis was used in the first phase, and qualitative analysis in the second. Based on the research findings, the numeracy component of the statistics curriculum is where the gaps in students' thinking processes are located. Students' thought structures can be strengthened by the use of defragmentation. When answering questions on numeracy and literacy, the defragmentation method utilized is scaffolding at level two, which consists of explaining, reviewing, and restructuring. The mean, mode, and median material in the student results contained construction holes that were later resolved through a scaffolding type that involved three steps: explaining, reviewing, and restructuring. This process helped students avoid making mistakes when answering the questions about the mean, mode, and median.

Intended Statistics Curriculum at the Elementary Level: Thailand vs. Indonesia

Mathematics occupies a central role in school education, with the mathematics curriculum serving as a critical tool for guiding curriculum reform. To identify the need for reform in specific contexts, it is necessary to examine curricula from a comparative perspective. Such an approach can yield valuable insights into the directions and priorities for curriculum reform. Accordingly, this study examined the current status of the intended statistics curriculum in Thailand and Indonesia. A qualitative content analysis was employed as the research design, with one mathematics curriculum document from Thailand and one from Indonesia purposively selected for analysis. The findings reveal that, in the domain of statistics, Indonesia introduces probability alongside statistics at the elementary level, whereas Thailand does not include probability at this stage. Furthermore, both countries place limited emphasis on incorporating a comprehensive statistical problem solving process within their curricula. It is important to note that this study focuses exclusively on the intended curriculum; further research is required to provide a more nuanced understanding.

Open Case Studies: Statistics and Data Science Education through Real-World Applications

With unprecedented and growing interest in data science education, there are limited educator materials that provide meaningful opportunities for learners to practice statistical thinking, as defined by Wild and Pfannkuch, with messy data addressing real-world challenges. As a solution, Nolan and Speed advocated for bringing applications to the forefront in undergraduate statistics curriculum with the use of in-depth case studies to encourage and develop statistical thinking in the classroom. Limitations to this approach include the significant time investment required to develop a case study—namely, to select a motivating question and to create an illustrative data analysis—and the domain expertise needed. As a result, case studies based on realistic challenges, not toy examples, are scarce. To address this, we developed the Open Case Studies (opencasestudies.org) project, which offers a new statistical and data science education case study model. This educational resource provides self-contained, multimodal, peer-reviewed, and open-source guides (or case studies) from real-world examples for active experiences of complete data analyses. We developed an educator’s guide describing how to most effectively use the case studies, how to modify and adapt components of the case studies in the classroom, and how to contribute new case studies (opencasestudies.org/OCS_Guide).

Adopting Optimal Statistical Practices: Graduate Programs.

In 2024, the Methodology Corner will briefly look at how we might foster enduring commitments from nurse education researchers to remain up-to-date on their statistical expertise and to use optimal statistical methods. The first column of the year specifically looks at how graduate programs might enrich their statistics curriculum in a manner that could foster an increasingly valid science of nursing education. [J Nurs Educ. 2024;63(3):197-198.].

Assessing students’ attitudes and perceptions towards statistical literacy in a university system in a developing African country

Statistical literacy is important in the curriculum of every higher education institution and the sustainable development of countries. Nonetheless, low performances and student enrolment recorded in statistical education warrant investigation into plausible factors. This case study used the Students’ Attitude towards Statistics (SATS) 36-item instrument to investigate the attitudes and perceptions of 185 students, enrolled in different disciplines, towards statistics education at Chinhoyi University of Technology in Zimbabwe. Descriptive, factor reduction, and multiple regression techniques were used to summarise and extract critical covariates, and relate variables in each construct in order to explain the attitudes of students towards statistics. Thematic analysis was done for an in-depth qualitative explanation of the drivers and barriers to the teaching and learning of statistics education. The main factors which induce fear, stress, anxiety, and antipathy towards statistics include: the perceived difficulty and numerical complexity of statistics, a natural low statistics self-efficacy and self-perception, and the extremely varying statistics cognitive capabilities of students. Inadequate supporting and facilitating conditions such as modern Information Communication Technology infrastructure, and a conducive teaching and learning environment lead to low performances. Regardless, students still perceive statistics as imperative for future professions and are willing to exert enough effort provided they are motivated in statistics education. It entails a diametric paradigm repositioning of the teaching and learning of statistics, emphasising collaborative learning, the intense use of electronic learning and the assessment of statistics, and smaller-sized classes giving individualised attention to benefit weaker students. Future research needs to explore statistics curriculum development, which is lagging and may be silently responsible for the low development rate in poor African countries.

High school mathematics texts construction of statistics practices

IntroductionA robust understanding of statistics has become crucial in our data centric societies. In the school setting the teaching of statistics is situated within the mathematics curriculum in the U.S. However, many mathematics teachers often have little to no past experiences with statistics before teaching it. Given such circumstances, textbooks likely play a strong role influencing the statistics curriculum teachers enact for students. In this study, I investigate how the discourse of two common high school textbook series form what the actions are for doing statistics.MethodsFor this study I used a Foucauldian discourse analysis to inductively analyze the texts for the actions they create.ResultsOne of the main results of the study was that the actions are very routinized/algorithmic in nature. Furthermore, most actions were associated with analyzing data. I also contrast the findings of the analysis to the discourse of the field of statistics education, namely through the Guidelines for Assessment and Instruction in Statistics Education, which highlighted some significant absences including statistical questions to drive investigation and discussion of collecting data.DiscussionThe findings have implications for teacher education in terms of topics to focus teachers’ attention on and to help provide them further support with teaching to their students.

STATISTICAL THINKING AT EARLY PRIMARY SCHOOL LEVELS: CURRICULUM PERSPECTIVES IN UAE TEXTBOOKS

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.

Research on Statistics Curriculum Reform under the Influence of Public Security Big Data Technology

In the use of big data, public security mainly focuses on the key processing of data. Although it is structured, it needs to be used in many aspects. Data processing results and analysis results, but through data processing, can effectively think about the specific implementation methods. Public security data science is becoming a new public security discipline and police technical field. Under the influence of public security big data technology, there are various problems in the development of statistics education and teaching and the design of teaching courses. On the premise of combining the design of statistics-related courses and the development of teaching, this paper makes an in-depth study on the reform of statistics courses under the influence of public security big data technology, and puts forward the reform path of statistics courses. In order to improve the teaching quality of statistics course and cultivate professionals who are more in line with the development of the times.

영국의 수학교육에 대한 고찰

This study intends to suggest implications by comparing Korea's high school mathematics curriculum with the UK's high school mathematics curriculum ahead of the 2022 revision of the mathematics curriculum. The UK has revised assessments to emphasize post-16 mathematics since 2017. Accordingly, the contents of Key Stage 4, Core Maths and A-level, which correspond to the UK high school mathematics curriculum, were examined and compared with Korean high school math subjects. In the UK, mathematics education is emphasized at the high school level. In the UK national curriculum, students’ options for mathematics were expanded. In order to prepare for the future society, new mathematics subjects and evaluations were developed and implemented, and the A-level mathematics was improved. In addition, the subject-centered content was developed and continuously handled from Key Stage 3 to the high school stage, and it was structured to facilitate the internal and external connection of mathematics by linking it with the subjects of other areas. The implications of this UK high school math education for high school math education in Korea are: First, it is necessary to think about the content of learning to prepare for the future society. Second, support for math learning and development of subjects and evaluation at the same time. Third, it is necessary to improve the statistics curriculum to improve statistics education.

Effectiveness of seminar-case learning for use in practice teaching of statistics for undergraduates majoring in preventive medicine: a prospective cluster-randomized controlled trial

BackgroundThe seminar-case learning (SCL) method is a case-oriented teaching model, with teachers and students as the main body of teaching, characterized by communication, interaction, and mutual inspiration. This study explored the effects of the SCL method versus traditional lecture-based learning (LBL) in the statistics curriculum for undergraduate students majoring in preventive medicine. Research questions were: 1) whether the scores of students in the experimental group (the SCL model) were higher than those in the control group (the LBL model); 2) whether the students’ satisfaction in the experimental group was better than that in the control group; and 3) whether the self-report benefit of students in the experimental group was better than that in the control group.MethodsWe conducted a two-armed cluster-randomized education intervention trial in practice teaching of health statistics among undergraduates majoring in preventive medicine. Two administrative classes (classes 1–4 and classes 5–8) were divided into the experimental group and the control group according to the principle of drawing lots. The students in two groups received the same statistical theory course. For the arrangement of statistical practice course, the experimental group adopted the SCL model, and the control group used the LBL model. The teaching effect was evaluated via an examination and an anonymous questionnaire survey.ResultsScores for noun explanation questions in the experimental group showed no statistical significance with that of the control group(U = 2911.0, P = 0.964). The scores of single choice, calculation, and case analysis questions, and the total scores were significantly higher than that of the control group (P < 0.05). Students’ satisfaction with arrangements of the practice course in the experimental group (92.41%) was significantly higher than that of in the control group (77.03%), the difference was statistically significant (χ2 = 7.074, P = 0.008). The self-report benefit of students in the experimental group was better than that in the control group (P < 0.05).ConclusionAs an effective method of high-quality education, the SCL model is worthy of further promotion in the practice teaching of preventive medicine.

A Comparative Study of the Probability and Statistics Curricula in the High School Mathematics Textbooks of Vietnam and Germany

An international comparative study of mathematics textbooks is essential in identifying trends in international mathematics education, developing textbooks and improving the quality of teaching and learning in mathematics. This study analyses and compares the contents of the probability and statistics curricula in the high school textbooks of Vietnam and Germany. It highlights the similarities and differences in the contents and the way they are presented, consolidated and deepened in textbooks of the two countries. The probability and statistics curricula in Vietnamese textbooks are much less than that of German textbooks. The Vietnamese textbooks focus on the mathematical content whereas the German textbooks focus on applications of the content in real life. Vietnamese textbooks tend to force students to accept probability and statistics knowledge while German textbooks encourage students to explore knowledge. Because of this, contexts relating to the contents in German textbooks are more detailed and more natural. German textbooks mainly use an inductive approach to present the contents whereas Vietnamese textbooks often use a deductive approach. In addition, German textbooks unlike those of Vietnam, always take advantage of realistic situations in exploring the contents, encourage co-operative learning and promote statistical reasoning by implementing several project works and provide an opportunity for practical experience and experiment by using the simulations of probability and statistics situations. The comparison shows the strengths of probability and statistics contents in German textbooks that Vietnamese textbooks can learn for the development of textbooks in future.

COMPUTES: DEVELOPMENT OF AN INSTRUMENT TO MEASURE INTRODUCTORY STATISTICS INSTRUCTORS’ EMPHASIS ON COMPUTATIONAL PRACTICES

&#x0D; The influx of data and the advances in computing have led to calls to update the introductory statistics curriculum to better meet the needs of the contemporary workforce. To this end, we developed the COMputational Practices in Undergraduate TEaching of Statistics (COMPUTES) instrument, which can be used to measure the extent to which computation practices—specifically data, simulation, and coding practices—are included in the introductory statistics curriculum. Data from 236 instructors were used in a psychometric analysis to evaluate the latent structure underlying instructors’ response patterns and understand the quality of the items. We also examined whether computational practices are being emphasized differently across institutional settings. Results suggest that the latent structure is best captured using a correlated multidimensional model and that most items were contributing information to the measurement process. Across institutional settings, curricular emphasis related to data and simulation practices seem quite similar, while emphasis on coding practices differs.&#x0D;

Building and Teaching a Statistics Curriculum for Post-Doctoral Biomedical Scientists at a Free-Standing Cancer Center

In the past decade, the cancer research community has made considerable progress in characterizing the genomic features of human tumors. Knowledge of molecular drivers of cancer has therefore increased greatly. Although the oncology community hoped that this would lead to more effective therapies, our ability to translate laboratory cancer research into clinical success has been remarkably low –only 5% of the agents demonstrated to have anticancer activity in laboratory studies went on to achieve success in phase III clinical trials. Many factors are responsible for this high percentage of failures. In addition to the biological difficulties of generalizing lab animal treatments to humans, other factors involved in driving this low rate include misuse or misunderstanding of statistical design and analysis concepts, interpretation and reporting methods. Recognizing the seriousness of these widely prevalent and correctable issues, the National Institutes of Health has called for the full engagement of the entire biomedical research enterprise to implement the resources needed to improve and sustain the statistical rigor and successful translation of preclinical cancer research. To this end, we developed a statistics curriculum for early-career preclinical cancer researchers (i.e., postdoctoral researchers) conducting laboratory research at Memorial Sloan Kettering Cancer Center as well as the broader research community. Our proposed curriculum was delivered over an eight-week period with one 60-90-minute class per week and included hands-on activities with experimental designs, data analysis and participatory dialogues. We developed an evaluation of the curriculum and have plans to make all resources available to the broader statistics and cancer research communities. In this column, we discuss our efforts to build such a statistics curriculum for post-doctoral biomedical scientists at a free-standing cancer center. We share experiences in the development of the curriculum and provide insights from the perspective of students, their laboratory leads, and collaborative biostatisticians.

Introducing Statistical Inference: Design of a Theoretically and Empirically Based Learning Trajectory

This paper comprises the results of a design study that aims at developing a theoretically and empirically based learning trajectory on statistical inference for 9th-grade students. Based on theories of informal statistical inference, an 8-step learning trajectory was designed. The trajectory consisted of two similar four step sequences: (1) experimenting with a physical black box, (2) visualizing distributions, (3) examining sampling distributions using simulation software, and (4) interpreting sampling distributions to make inferences in real -life contexts. Sequence I included only categorical data and Sequence II regarded numerical data. The learning trajectory was implemented in an intervention among 267 students. To examine the effects of the trajectory on students’ understanding of statistical inference, we analyzed their posttest results after the intervention. To investigate how the stepwise trajectory fostered the learning process, students’ worksheets during each learning step were analyzed. The posttest results showed that students who followed the learning trajectory scored significantly higher on statistical inference and on concepts related to each step than students of a comparison group (n = 217) who followed the regular curriculum. Worksheet analysis demonstrated that the 8-step trajectory was beneficial to students’ learning processes. We conclude that ideas of repeated sampling with a black box and statistical modeling seem fruitful for introducing statistical inference. Both ideas invite more advanced follow-up activities, such as hypothesis testing and comparing groups. This suggests that statistics curricula with a descriptive focus can be transformed to a more inferential focus, to anticipate on subsequent steps in students’ statistics education.

Computational skills by stealth in introductory data science teaching

AbstractIn 2010, Nolan and Temple Lang proposed “integration of computing concepts into statistics curricula at all levels.” The unprecedented growth in data and emphasis on data science has provided an impetus to finally realizing full implementations of this in new statistics and data science programs and courses. We discuss a proposal for the stealth development of computational skills in students' exposure to introductory data science through careful, scaffolded exposure to computation and its power. Our intent is to support students, regardless of interest and self‐efficacy in coding, in becoming data‐driven learners, who are capable of asking complex questions about the world around them, and then answering those questions through the use of data‐driven inquiry. Reference is made to the computer science and statistics consensus curriculum frameworks the International Data Science in Schools Project (IDSSP) recently published for secondary school data science or introductory tertiary programs, designed to optimize data‐science accessibility.

Bringing Visual Inference to the Classroom

In the classroom, we traditionally visualize inferential concepts using static graphics or interactive apps. For example, there is a long history of using apps to visualize sampling distributions. The lineup protocol for visual inference is a recent development in statistical graphics that has created an opportunity to build student understanding. Lineups are created by embedding plots of observed data into a field of null (noise) plots. This arrangement facilitates comparison and helps build student intuition about the difference between signal and noise. Lineups can be used to visualize randomization/permutation tests, diagnose models, and even conduct valid inference when distributional assumptions break down. This article provides an overview of how the lineup protocol for visual inference can be used to build understanding of key statistical topics throughout the statistics curriculum. Supplementary materials for this article are available online.

What Makes a Good Statistical Question?

The statistical problem-solving process is key to the statistics curriculum at the school level, post-secondary, and in statistical practice. The process has four main components: formulate questions, collect data, analyze data, and interpret results. The Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education (GAISE) emphasizes the importance of distinguishing between a question that anticipates a deterministic answer and a question that anticipates an answer based on data that will vary, referred to as a statistical question. This article expands upon the Pre-K-12 GAISE distinction of a statistical question by addressing and identifying the different types of statistical questions used across the four components of the statistical problem-solving process and the importance of interrogating these different statistical question types. Since the publication of the original Pre-K-12 GAISE document, research has helped to clarify the purposes of questioning at each component of the process, to clarify the language of questioning, and to develop criteria for answering the question, “What makes a good statistical question?”

진화전략(Evolution Strategy)을 활용한 최대ㆍ최소 탐구과정 및 코딩환경 연구

The purpose of this study is to develop a curriculum of school mathematics and artificial intelligence regarding max-min problems. We also developed a coding environment for a designed curriculum that can be accessed and utilized at codingmath.org without any additional installation. The curriculum uses an evolution strategy-based gradient descent method founded on a school probability and statistics curriculum with an experiment using dice; this curriculum is designed to work when the function is not differentiable and is ultimately linked to a calculus-based gradient descent method. The coding environment, in which even middle school students can visualize the min-max problem of f(x,y), uses a three-dimensional function graph with minimal coding inputs and explores the gradient descent process using a two-dimensional Python animation. This study, which is an attempt to combine mathematical problem solving and computational thinking in the context of max-min problems, further discusses ideas regarding the ways to integrate AI and coding in mathematics education.

The Relevance of Statistical Knowledge for Teaching to Health Care Professionals: Reflections on a COVID-19 Press Briefing

Statistics is an important component of the knowledge base for health care professionals. In this essay, it is argued that statistical knowledge for teaching (SKT) should be considered an important component of their preparation as well. Health care professionals often must help others understand the statistical basis for recommendations they make. A COVID-19 press briefing is used to illustrate the need for SKT when making high-stakes recommendations related to public health. It is conjectured that efforts to educate the public during the press briefing would have been enhanced if the presenters had deeper knowledge of the general public’s common statistical thinking patterns, the typical statistics curriculum experienced by members of their audience, and contemporary tools for teaching statistics. The importance of such knowledge to support smaller-scale individual interactions is also discussed. A call for SKT-centered partnerships between educational researchers and medical researchers is made; such partnerships could be mutually beneficial to the development of both fields and to society at large.

Spatial Data in Undergraduate Statistics Curriculum

In this article we present and discuss the importance and relevance of the inclusion of spatial data analysis as part of the undergraduate statistics curriculum. Given its usefulness and applicability across a range of disciplines, spatial data are a topic that should receive more emphasis within undergraduate statistics curricula. There exist many topical and intriguing spatial datasets from different areas of research that can bring fruitful discussions into the classroom including the environment, medicine, and political science. Spatial data can be incorporated at any level of study, from lower to upper division courses, as well as graduate-level courses in Mathematics and Statistics. This article will focus on its role in undergraduate statistics curricula, and present topics that can be included in an introductory course, a mathematical course in statistics, and an elective course in spatial data analysis. Supplemental materials for this article are available online.