Gerrit H. Stols

Teachers' beliefs and their intention to use interactive simulations in their classrooms

In this pilot study, we sought to examine the influence of the beliefs of Grade 10 to 12 physical science teachers on their intended and actual usage of interactive simulations (Physics Education Technology, or PhET) in their classrooms. A combination of the Theory of Planned Behaviour, the Technology Acceptance Model and the Innovation Diffusion Theory was used to examine the influence of teachers’ attitudes, subjective norms and perceived behavioural control on their intention to use simulations in their classrooms. Using regression and factor analyses, it was found that beliefs about the perceived usefulness and the pedagogical compatibility of PhET have a signif icant effect on teachers’ attitude towards the use of the simulations in their classrooms. The expectations of the teachers’ colleagues contribute to the subjective norm of these teachers. The regression and partial correlation result also highlights the importance of teachers’ general technology proficiency. Although we were not able to confirm a direct link between attitudes, subjective norm, perceived behavioural control, and the teachers’ behaviour intention we show the influence of behaviour intention on the actual use of the simulations with an accuracy of 70.83%.

Erratum to: The individualisation of a dog bite mark: a case study highlighting the bite mark analysis, with emphasis on differences between dog and human bite marks

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Reconstruction of Deformed Bite Marks Using Affine Transformations

Abstract:  Bite marks inflicted on animate and inanimate objects will undergo a certain degree of deformation. This fact remains one of the biggest stumbling blocks when analyzing evidence for court presentation. It has been demonstrated that the reliability of pattern association analysis will not be affected by minimal degrees of warping, shrinkage, and distortion. In this study, affine transformations were applied to bite marks to establish if minimal distortions would affect the mathematically determined relationships of the defined features. In a real case study, it was then tested whether the distorted bite mark matched the dentition of the perpetrator by applying an affine transformation. This was confirmed to be the case. Affine transformations will thus not affect the relationships of the individual features found in bite marks. The numerical calculations validate the reliability of pattern association analysis in the presence of minimal amounts of warping, shrinkage, and distortion.

The application of affine transformations in matching distorted forensic samples with a common origin

The practice of forensic odontology regularly requires the forensic dental expert to establish a degree of concordance between two objects, one or both of which have undergone minimal degrees of warping, shrinkage and distortion collectively described as deformations. These comparisons can be between the suspects or victims dentition and bite marks on inanimate objects/skin, two radiological images, palatal rugae patterns, dental arches, lip prints and other unique scenarios which are presented in forensic odontological cases. This paper will define the mathematical concept of affine transformation as it pertains to forensic matters and explains how it can be applied to a case study involving pattern deformations. Although the deformation of the evidence may be minimal in extent, it creates a measure of uncertainty when expert evidence is given in court cases. Any metric discrepancy caused by deformation of the evidence will necessitate the application of pattern association and negate the use of metric analysis. It has been shown that a pattern association analysis of evidence will not be affected by minimal amounts of deformation. The mathematical limits of these deformations which will significantly affect the comparisons have not yet been determined. In the case study presented the deformations were considered minimal and thus explainable by a pattern association analysis. The mathematical concepts will empower the expert to explain to a court of law how two samples which were not a perfect match, could in fact be deformed equivalents of common origin.

The use of a tablet PC for instruction : a theoretical framework

Abstract This article is about my own journey and my reflections during my first month of using technology for instruction. The context was the use of a tablet PC and the possibilities that it creates for teaching mathematics to pre-calculus and calculus pre-service teaching students. This study attempts to understand, from the inside, the use computers for instruction, which is why the lecturer himself was also the principal researcher in this study. The advantage of using my own practice as a site for studying the processes of integrating technology into teaching is that it offers special possibilities for insight into and understanding of the thinking and emotions involved. This research may be seen as a special case of a qualitative case study. After three months of using technology for instructional purposes, I tried to make sense of my own journey by analysing my reflections using the Theory of Planned Behaviour as a theoretical framework. It was found that this theory, after some adaptations, might be used to clarify and understand my own use of technology for instruction.

An analysis of Grade 11 learners’ levels of understanding of functions in terms of APOS theory

ABSTRACT This article reports on a study of six Grade 11 learners’ levels of understanding of concepts related to the function definition and representation. Task-based clinical interviews were used to elicit the learners’ interpretations and reasoning when working with these function-related concepts. Indicators for Action–Process–Object–Schema (APOS) theory conception levels were formulated and used to categorise learners’ written and interview responses into conception levels of understanding of the function concept. According to the South African Curriculum Assessment Policy Statement (CAPS) curriculum, Grade 11 learners are expected to be operating at the object and schema levels after instruction. however, the results indicated that learners were operating at the action and process levels as their understanding was characterised by vague definitions of function-related concepts and memorisation of procedures for translating between symbolic and graphical representations.

An Application of the Rasch Measurement Theory to an Assessment of Geometric Thinking Levels

The purpose of this study is to apply the Rasch model to investigate both the Van Hiele theory for geometric development and an associated test. In terms of the test, the objective is to investigate the functioning of a classic 25-item instrument designed to identify levels of geometric proficiency. The dataset of responses by 244 students (106 for a pre-test and 138 for a post-test) of whom 76 sat both the pre-test and the post-test. The summary item statistics do not show statistically discernible differences between observed and expected scores under the Rasch model (chi-square statistic). The Rasch analysis confirms to a strong extent the Van Hiele theory of geometric development. The study identifies some problematic test items as they only require knowledge of a specific aspect of geometry instead of testing geometric reasoning. In terms of the Van Hiele theory, the Rasch analyses identified as problematic some items about class inclusion, an issue that has also been raised in other studies.