An alternative teaching method of conditional probabilities and Bayes' rule: an application of the truth table

This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities—especially the ones that involve Bayes' rule—with the help of such traditional approaches as formula use or conversion to natural frequencies. The truth table approach is an alternative method for explaining the concept and calculation procedure of conditional probability and Bayes' rule.     

The classroom as a stage and the teacher's role

Teaching is a profession in which teachers are accustomed to being in the spotlight. In this paper we meet “Tina”¹—a newly employed teacher at a Norwegian public junior high school—who is engaged on an hourly basis to teach Arts and Crafts, including a seventh-grade class which has been called “challenging” by other members of the staff. Enthusiastic, committed, and focused educators who can serve as role models for their students are much in demand at this school. Her own challenge is to find a good balance between the many cultural roles she has to perform in an inclusive education—one that works toward a goal of servicing an integrated student body—as manager, administrator of materials, initiator, facilitator, reflection partner, and mentor. In this paper we describe how she shapes a learning environment characterized by clear and unambiguous signals about what is acceptable behavior, while at the same time insisting on creativity and originality in art work. The guiding question is: How does the teacher achieve the double task of keeping order and maintaining creativity?The study is based on ethnographic field work conducted over several months in the Arts and Crafts class of “Berge” school. We describe how the children try to sabotage the tasks, and analyze critical episodes using sociocultural theory. With its emphasis on cultural and creative activities, the Arts and Crafts subject provides a special opportunity for what sociocultural theory calls using mediating artefacts or elements (mediated action²). What makes the subject particularly interesting is that it is not only a matter of using linguistic mediation, but rather also mediation based on external factors, such as the use of specific objects or model learning.     

Teaching Classic Probability Problems with Modern Digital Tools

This article is written to share teaching ideas about using commonly available computer applications—a spreadsheet, The Geometer's Sketchpad, and Wolfram Alpha—to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors’ work with prospective economists, mathematicians, and teachers. The historical contexts include the problem of the division of stakes (14^th century), the problem of the Grand Duke of Tuscany (17^th century), and the problem of co-primality of two natural numbers chosen at random (19^th century). The suggested use of computers can be extended to other probability contexts to achieve at least two goals: to make complex mathematical ideas more accessible and to emphasize the importance of experimental evidence as a means of conceptual development in mathematics for all student populations.     

On Latent Change Model Choice in Longitudinal Studies

An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R ² indexes associated with repeatedly followed measures in longitudinal studies. In addition to facilitating evaluation of local model fit, the approach is helpful for purposes of differentiating between plausible models stipulating different patterns of change over time, and in particular in empirical situations characterized by large samples and high statistical power. The procedure is also applicable in cross-sectional studies, as well as with general structural equation models. The method is illustrated using data from a nationally representative study of older adults.     

Detection of Differential Item Functioning with Nonlinear Regression: A Non‐IRT Approach Accounting for Guessing

In this article we present a general approach not relying on item response theory models (non‐IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non‐IRT approach, NLR can be seen as a proxy of detection based on the three‐parameter IRT model which is a standard tool in the study field. Hence, NLR fills a logical gap in DIF detection methodology and as such is important for educational purposes. Moreover, the advantages of the NLR procedure as well as comparison to other commonly used methods are demonstrated in a simulation study. A real data analysis is offered to demonstrate practical use of the method.     

Relationship Between Client-Learning Style and Preference for Counselor Approach

A client-counselor matching model based on Kolb's experiential learning theory was examined. A questionnaire, which included Kolb's Learning Style Inventory (LSI) and four counselor approach profiles, was completed by 205 counseling clients. The clients indicated which counselor they preferred. The following four preference patterns were predicted: concrete learners—experiential approach, abstract learners—rational approach, active learners— behavioral approach, and reflective learners—client-centered approach. The results did not confirm the hypothesized four-way model, although limited support for the matching concept was evident when only two counselor approaches were considered. Clients who preferred directive counselors were more abstract learners. Clients preferring nondirective counselors were more concrete learners. Overall, clients preferred the rational counselor approach. A nonclient comparison group (n = 75) preferred the client-centered approach.     

基于JAF软件的数字测图方法研究

介绍了一种新的数字测图方法———基于JAF软件测图法。这种方法在外业测量时可以摆脱控制点坐标的束缚,提高外业的工作效率。通过以往常用方法与基于JAF软件测图法的对比以及对这种新方法的工作原理、外业操作方法与步骤、内业数据处理的论述,全面地介绍了基于JAF软件测图法。     

Kuwaiti Science Teachers’ Beliefs and Intentions Regarding the Use of Inquiry-Based Instruction

To improve the quality of education, the Kuwaiti Ministry of Education has encouraged schools to implement inquiry-based instruction. This study identifies psychosocial factors that predict teachers’ intention to use inquiry-based instruction in their science classrooms. An adapted model of Ajzen’s (1985) theory of planned behaviour—the Science Adoption Model—was used to study Kuwaiti science teachers’ beliefs. Four hundred and ninety-six teachers from all the government primary schools in Kuwait completed a questionnaire. The data were analysed using the Statistical Package for the Social Sciences (SPSS) to statistically examine the relationships among the constructs of the model. It was found that teachers’ attitudes towards using inquiry-based instruction significantly predicted their capacity to create and deliver inquiry-based lessons. Although Kuwaiti science teachers held positive beliefs about the implementation of inquiry-based instruction, many factors limited their use of this approach in their science classroom. One clear implication from this study is that educators need to overtly consider teachers’ beliefs as inquiry-based instruction reform is implemented.     

Models of Decisionmaking Processes for Multiple-Choice Test Items: An Analysis of Spatial Ability

Latent class models of decisionmaking processes related to multiple-choice test items are extremely important and useful in mental test theory. However, building realistic models or studying the robustness of existing models is very difficult. One problem is that there are a limited number of empirical studies that address this issue. The purpose of this paper is to describe and illustrate how latent class models, in conjunction with the answer-until-correct format, can be used to examine the strategies used by examinees for a specific type of task. In particular, suppose an examinee responds to a multiple-choice test item designed to measure spatial ability, and the examinee gets the item wrong. This paper empirically investigates various latent class models of the strategies that might be used to arrive at an incorrect response. The simplest model is a random guessing model, but the results reported here strongly suggest that this model is unsatisfactory. Models for the second attempt of an item, under an answer-until-correct scoring procedure, are proposed and found to give a good fit to data in most situations. Some results on strategies used to arrive at the first choice are also discussed     

Designing customizable reading modules for a high school literature classroom

This design case follows an ongoing collaboration between an instructional technologist and a high school literature teacher promoting reading comprehension through modules that provide visually interesting display of text on a computer screen along with cognitive tools. The modules were found to boost comprehension of specific content in even one use, and over time, overall reading skills were improved. Specific examples from the design and development process of this collaboration are shared here to illustrate decisions made in the face of common constraints—limited time, funding, and technical know-how—that emerged from theory and pilot studies. Teacher educators and their instructional-technology collaborators can use the information from this design and research process to harness the potential of ubiquitous software in affordable, replicable, and pedagogically sound ways.     

Model Selection in Structural Equation Models With Continuous and Polytomous Data

Recently, analysis of structural equation models with polytomous and continuous variables has received a lot of attention. However, contributions to the selection of good models are limited. The main objective of this article is to investigate the maximum likelihood estimation of unknown parameters in a general LISREL-type model with mixed polytomous and continuous data and propose a model selection procedure for obtaining good models for the underlying substantive theory. The maximum likelihood estimate is obtained by a Monte Carlo Expectation Maximization algorithm, in which the E step is evaluated via the Gibbs sampler and the M step is completed via the method of conditional maximization. The convergence of the Monte Carlo Expectation Maximization algorithm is monitored by the bridge sampling. A model selection procedure based on Bayes factor and Occam's window search strategy is proposed. The effectiveness of the procedure in accounting for the model uncertainty and in picking good models is discussed. The proposed methodology is illustrated with a real example.     

Comparison of 3D reconstructive technologies used for morphometric research and the translation of knowledge using a decision matrix

The use of three‐dimensional (3D) models for education, pre‐operative assessment, presurgical planning, and measurement have become more prevalent. With the increase in prevalence of 3D models there has also been an increase in 3D reconstructive software programs that are used to create these models. These software programs differ in reconstruction concepts, operating system requirements, user features, cost, and no one program has emerged as the standard. The purpose of this study was to conduct a systematic comparison of three widely available 3D reconstructive software programs, Amira^®, OsiriX, and Mimics^®, with respect to the software's ability to be used in two broad themes: morphometric research and education to translate morphological knowledge. Cost, system requirements, and inherent features of each program were compared. A novel concept selection tool, a decision matrix, was used to objectify comparisons of usability of the interface, quality of the output, and efficiency of the tools. Findings indicate that Mimics was the best‐suited program for construction of 3D anatomical models and morphometric analysis, but for creating a learning tool the results were less clear. OsiriX was very user‐friendly; however, it had limited capabilities. Conversely, although Amira had endless potential and could create complex dynamic videos, it had a challenging interface. These results provide a resource for morphometric researchers and educators to assist the selection of appropriate reconstruction programs when starting a new 3D modeling project. Anat Sci Educ 6: 393–403. © 2013 American Association of Anatomists.     

Using Quality Management Tools to Enhance Feedback from Student Evaluations

Statistical tools found in the service quality assessment literature—the T² statistic combined with factor analysis—can enhance the feedback instructors receive from student ratings. T² examines variability across multiple sets of ratings to isolate individual respondents with aberrant response patterns (i.e., outliers). Analyzing student responses that are outside the “normal” range of responses can identify aspects of the course that cause pockets of students to be dissatisfied. This fresh insight into sources of student dissatisfaction is particularly valuable for instructors willing to make tactical classroom changes that accommodate individual students rather than the traditional approach of using student ratings to develop systemwide changes in course delivery. A case study is presented to demonstrate how the recommended procedure minimizes data overload, allows for valid schoolwide and longitudinal comparisons of correlated survey responses, and helps instructors identify priority areas for instructional improvement.     

Pedagogical approaches for e-assessment with authentication and authorship verification in Higher Education

Checking the identity of students and authorship of their online submissions is a major concern in Higher Education due to the increasing amount of plagiarism and cheating using the Internet. The literature on the effects of e-authentication systems for teaching staff is very limited because it is a novel procedure for them. A considerable gap is to understand teaching staff' views regarding the use of e-authentication instruments and how they impact trust in e-assessment. This mixed-method study examines the concerns and practices of 108 teaching staff who used the TeSLA—Adaptive Trust-based e-Assessment System in six countries: the UK, Spain, the Netherlands, Bulgaria, Finland and Turkey. The findings revealed some technological, organisational and pedagogical issues related to accessibility, security, privacy and e-assessment design and feedback. Recommendations are to provide a FAQ and an audit report with results, to raise awareness about data security and privacy, to develop policies and guidelines about fraud detection and prevention, e-assessment best practices and course team support.     

Minimizing the Influence of Item Parameter Estimation Errors in Test Development: A Comparison of Three Selection Procedures

In test development, item response theory (IRT) is a method to determine the amount of information that each item (i.e., item information function) and combination of items (i.e., test information function) provide in the estimation of an examinee's ability. Studies investigating the effects of item parameter estimation errors over a range of ability have demonstrated an overestimation of information when the most discriminating items are selected (i.e., item selection based on maximum information). In the present study, the authors examined the influence of item parameter estimation errors across 3 item selection methods—maximum no target, maximum target, and theta maximum—using the 2- and 3-parameter logistic IRT models. Tests created with the maximum no target and maximum target item selection procedures consistently overestimated the test information function. Conversely, tests created using the theta maximum item selection procedure yielded more consistent estimates of the test information function and, at times, underestimated the test information function. Implications for test development are discussed.     

Controversial Conversations in Science: Incorporating the Science “Sex Box”

Science classrooms—and science textbooks—are proving to be challenging spaces for education that contradicts abstinence-only-until-marriage (AOUM) sex education. However, science educators can teach against this knowledge in a way that is critical of oppressive language. In fact, having explicit dialogue about gender identities and sexual orientation can help uncover oppressive cultural attitudes and help science educators challenge universal views of the human body. This article examines two narratives that use a pedagogic practice to help them teach in AOUM environments. The first narrative discusses personal experiences of the author as a science teacher and the dilemmas faced by including what I call a “sex box” in a life science class. The second narrative discusses an excerpt from a research study conducted with life science teachers in which a participant uses this same method. The purpose of this discussion is to help expose the science classroom as a place to have meaningful discussions, even with policies and cultures that do not support the discussion of safe sex for minority human sexualities.¹ This article suggests future science teachers and present teachers alike can advocate for the incorporation of national standards that counteract overtly discriminatory policies.     

Yelavarthy Nayudamma

This is not the profile or an account of the scientific contributions of an individual but a sharing of personal experience with a visionary, missionary and grass-root researcher — Yelavarthy Nayudamma — who made the Central Leather Research Institute (CLRI) rise to glory. His is a life that raises the hopes and aspirations of youth from small towns. His contributions are part of a living legacy. His research on the shrinkage¹ phenomena of leather and the theory of tanning has stood the test of time. His leadership qualities carry many lessons for leaders of scientific establishments for generations to come. The League of Nations heeded as Nayudamma spoke for the cause of developing nations and for connecting science to development. Theory and practice for him were like two eyes essential for depth vision. For many who knew him he is a living inspirational spirit — his legacy lives long after his passing away in a tragic air crash in 1985.     

Teacher education students' reflections on how problem‐based learning has changed their mental models about teaching and learning

Abstract

Students develop robust mental models of teaching and learning during their school years, and as such, often teach as they were taught—possibly perpetuating practices that limit intellectual inquiry in classrooms. This paper reports on an analysis, using a conceptual framework and NUD?1ST software, of a cohort of 3rd‐year teacher education students' reflections on changes in their mental models following their experiences in a problem‐based learning (PBL) topic. Results provide evidence that students do report changing mental models in areas such as (a) the value of case studies for engaging with subject content, motivating learning, and connecting theory with practice; (b) self‐reflection and peer collaboration for cognitive and professional growth; and (c) processes of inquiry for developing self‐regulated learning practices.