The effect of project-based learning on students’ statistical literacy levels for data representation

The point of this study is to define the effect of project-based learning approach on 8th Grade secondary-school students’ statistical literacy levels for data representation. To achieve this goal, a test which consists of 12 open-ended questions in accordance with the views of experts was developed. Seventy 8th grade secondary-school students, 35 in the experimental group and 35 in the control group, took this test twice, one before the application and one after the application. All the raw scores were turned into linear points by using the Winsteps 3.72 modelling program that makes the Rasch analysis and t-tests, and an ANCOVA analysis was carried out with the linear points. Depending on the findings, it was concluded that the project-based learning approach increases students’ level of statistical literacy for data representation. Students’ levels of statistical literacy before and after the application were shown through the obtained person-item maps.     

Statistical modeling to promote students’ aggregate reasoning with sample and sampling

While aggregate reasoning is a core aspect of statistical reasoning, its development is a key challenge in statistics education. In this study we examine how students’ aggregate reasoning with samples and sampling (ARWSS) can emerge in the context of statistical modeling activities of real phenomena. We present a case study on the emergent ARWSS of two pairs of sixth graders (age 11–12) involved in statistical data analysis and informal inference utilizing TinkerPlots. The students’ growing understandings of various statistical concepts is described and five perceptions the students expressed are identified. We discuss the contribution of modeling to these progressions followed by conclusions and limitations of these results. While idiosyncratic, the insights contribute to the understanding of students’ aggregate reasoning with data and models, with regards to samples and sampling.     

Technological Tools in the Introductory Statistics Classroom: Effects on Student Understanding of Inferential Statistics

While technology has become an integral part of introductory statistics courses, the programs typically employed are professional packages designed primarily for data analysis rather than for learning. Findings from several studies suggest that use of such software in the introductory statistics classroom may not be very effective in helping students to build intuitions about the fundamental statistical ideas of sampling distribution and inferential statistics. The paper describes an instructional experiment which explored the capabilities of Fathom, one of several recently-developed packages explicitly designed to enhance learning. Findings from the study indicate that use of Fathom led students to the construction of a fairly coherent mental model of sampling distributions and other key concepts related to statistical inference. The insights gained point to a number of critical ingredients that statistics educators should consider when choosing statistical software. They also provide suggestions about how to approach the particularly challenging topic of statistical inference. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014–2015 at the ‘ETSEIB'of Universitat Politècnica de Catalunya (UPC).     

Computer-Assisted Statistics Education at Delft University of Technology

Abstract

At Delft University of Technology many students experience difficulties in mastering basic concepts of probability and statistics. In the past few years the lectures have undergone a radical change—the lecture notes now contain modern data analysis techniques, like kernel density estimation, simulation, and bootstrapping. In the TWI-Stat project, a computer-aided instruction course was developed to help students become more familiar with modern statistical analysis. The course presents itself as a dynamic, interactive, personal book. Highly interactive analysis tools are available. The software will be available for MS-Windows.     

Use of Demonstrations and Experiments in Teaching Business Statistics

The aim of a business statistics course should be to help students think statistically and to interpret and understand data, rather than to focus on mathematical detail and computation. To achieve this students must be thoroughly involved in the learning process, and encouraged to discover for themselves the meaning, importance and relevance of statistical concepts. In this paper we advocate the use of experiments and demonstrations as aids to achieving these goals. A number of demonstrations are given which can be used to illustrate and explain some key statistical ideas.     

Calibration of estimator-weights via semismooth Newton method

Weighting is a common methodology in survey statistics to increase accuracy of estimates or to compensate for non-response. One standard approach for weighting is calibration estimation which represents a common numerical problem. There are various approaches in the literature available, but quite a number of distance-based approaches lack a mathematical justification or are numerically unstable. In this paper we reformulate the calibration problem as a system of nonlinear equations. Although the equations are lacking differentiability properties, one can show that they are semismooth and the corresponding extension of Newton’s method is applicable. This is a mathematically rigorous approach and the numerical results show the applicability of this method.     

The incoming statistical knowledge of undergraduate majors in a department of mathematics and statistics

Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics education), students who are presumably better prepared in terms of mathematics and statistics than the average university student, have of introductory statistics. This case study found that these students enter college with common statistical misunderstandings, lack of knowledge, and idiosyncratic collections of correct statistical knowledge. Moreover, they also have a wide range of beliefs about their knowledge with some of the students who believe that they have the strongest knowledge also having significant misconceptions. More attention to these statistical building blocks may be required in a university introduction statistics course.     

浅谈蒙特卡罗法在概率统计教学中的应用

在概率统计教学中利用蒙特卡罗法设计适当的模拟实验,结合多媒体在课堂教学中实时演示,能很好地加深学生对概率统计概念、思想的理解,进而培养学生的统计思维能力.     

Electronic Resources: The Ohio State University EESEE Project

Electronic resources aid in the teaching and learning of statistics by providing data that may be used interactively by teachers and students. By interacting with the data students are encouraged to discover knowledge and thereby gain a deeper understanding of statistical concepts. The Electronic Encyclopedia of Statistical Examples and Exercises (EESEE) is an electronic resource that includes over 80 'real-world' examples about the uses and abuses of statistics. These examples are drawn from published and printed media and the diverse range of subject-matter areas make it suitable for use in any statistics course.     

A pathway from Bayesian statistical analysis to superstatistics

Superstatistics and Tsallis statistics in statistical mechanics are given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by Mathai’s pathway model and further both components are replaced by Mathai’s pathway models. This produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics. It is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier. Those integrals are also connected to Krätzel integrals in applied analysis, inverse Gaussian densities in stochastic processes, reaction rate integrals in the theory of nuclear astrophysics and Tsallis statistics in nonextensive statistical mechanics. The final results are obtained in terms of Fox’s H-function. Matrix variate analogue of one significant specific case is also pointed out.     

User-friendly statistical concepts for process monitoring

Many standard statistical process control techniques involve sophisticated mathematical concepts, which are frequently misunderstood and misused by their users. This means, as this paper argues, that the techniques, and the terminology and concepts underlying them, are inappropriate for their intended uses and users. The paper considers the areas of the statistical background which cause difficulties. It goes on to describe some alternative concepts, techniques and terminology, which are likely to be conceptually simpler and more ‘user-friendly’ (and in some cases more accurate and robust). None of the ideas require users to be familiar with the standard deviation. We also suggest that the approach of reengineering the conceptual background to suit the context of users and uses may be appropriate to other areas of practical statistics and OR. The paper identifies some general principles for achieving this.     

A systematic methodology to assess the impact of human factors in ship design

Evaluating ship layout for human factors (HF) issues using simulation software such as maritimeEXODUS can be a long and complex process. The analysis requires the identification of relevant evaluation scenarios; encompassing evacuation and normal operations; the development of appropriate measures which can be used to gauge the performance of crew and vessel and finally; the interpretation of considerable simulation data. Currently, the only agreed guidelines for evaluating HFs performance of ship design relate to evacuation and so conclusions drawn concerning the overall suitability of a ship design by one naval architect can be quite different from those of another. The complexity of the task grows as the size and complexity of the vessel increases and as the number and type of evaluation scenarios considered increases. Equally, it can be extremely difficult for fleet operators to set HFs design objectives for new vessel concepts. The challenge for naval architects is to develop a procedure that allows both accurate and rapid assessment of HFs issues associated with vessel layout and crew operating procedures. In this paper we present a systematic and transparent methodology for assessing the HF performance of ship design which is both discriminating and diagnostic. The methodology is demonstrated using two variants of a hypothetical naval ship.     

The use of simulation and case study†

Although statistics is a rational subject, it does not follow that students can or do learn statistics in a rational way. Students learn statistics in the pattern‐forming mode more than in the rational mode. The paper describes and compares the two modes, and identifies three conditions that prevent or discourage learning in the rational mode. The diagnosis of pattern‐forming de‐emphasizes mathematical derivations and proofs as a means of allowing students to understand statistical concepts. The primary recommendation is that the teacher should deliberately manipulate the pattern‐forming process. The underlying idea is for the teacher to view the process for what it means to the student.     

Developing a statistical modeling framework to characterize Year 7 students’ reasoning

Some researchers advocate a statistical modeling approach to inference that draws on students’ intuitions about factors influencing phenomena and that requires students to build models. Such a modeling approach to inference became possible with the creation of TinkerPlots Sampler technology. However, little is known about what statistical modeling reasoning students need to acquire. Drawing and building on previous research, this study aims to uncover the statistical modeling reasoning students need to develop. A design-based research methodology employing Model Eliciting Activities was used. The focus of this paper is on two 11-year-old students as they engaged with a bag weight task using TinkerPlots. Findings indicate that these students seem to be developing the ability to build models, investigate and posit factors, consider variation and make decisions based on simulated data. From the analysis an initial statistical modeling framework is proposed. Implications of the findings are discussed.     

A Study Comparing the Efficacy of a Mole Ratio Flow Chart to Dimensional Analysis for Teaching Reaction Stoichiometry

Reaction stoichiometry calculations have always been difficult for students. This is due to the many different facets the student must master, such as the mole concept, balancing chemical equations, algebraic procedures, and interpretation of a word problem into mathematical equations. Dimensional analysis is one of the main ways students are taught to solve these problems. However, this methodology does not provide all students with a complete understanding of how to solve these problems. Introduction of alternative problem solving techniques, such as proportional reasoning, can help to improve student understanding. The mole ratio flow chart (MRFC) is a logistical sequence of steps that incorporates molar proportions. Students are able to begin analysis of a problem from many different starting points using this MRFC method. Analyses of data collected indicate that MRFC users performed as well on exam problems covering reaction stoichiometry calculations as students using dimensional analysis. Further, class sections exposed to both dimensional analysis and MRFC methods scored as well on exam problems as class sections exposed only to dimensional analysis. These results indicate that the MRFC is a viable alternative method for teaching reaction stoichiometry calculations and for helping to create a more complete understanding of the subject.     

Picturing student beliefs in statistics

Statistical skills and statistical literacy have emerged as important areas in education. While it has a rich mathematical basis, successful understanding and application of statistics incorporates other types of knowledge. In a similar way, beliefs about statistics can be described using the same framework as beliefs about mathematics, but statistical beliefs bring other aspects as well. This article describes a project for investigating student beliefs in statistics through the creation of pictures of understanding. It presents a classification of statistical concepts and attitudes which are motivated by research in statistical literacy and then shows how these can be refined to be more reliably applied in practice.     

A multidisciplinary graduate level project-based programme in applied statistics

The use of a project-based approach for designing a one-year graduate level programme in applied statistics is addressed. The pedagogical approach, academic setting, and learning activities are described in a multidisciplinary context. Some comments on implementation of such a programme based on the results from five successive graduating classes at the University of Veracruz (1994–2000) are included.     

From Classroom to Online Teaching: Experiences in Improving Statistics Education

This study used reflective practitioner methodology to investigate how to improve the quality of statistical education. During the study, this methodology, curricula, pedagogical practices, assessment and a framework for learning to learn statistics were all developed as means of improving the quality of statistical education. Also documented was the move from being a classroom teacher of statistics to a teacher who is developing learning resources for online delivery to students. For a classroom teacher, flexible delivery has meant drawing on the sights, sounds, movement, quiet and live shows. By contrast, the online teacher feels the constraints of translating activity based programs to technologically based programs. As more students have chosen to rely on online materials rather than classroom activities, the focus of improving quality has been extended to the enrichment of online resources, so that the learning experience is not second to that of the classroom.