Understanding what you are doing: A new angle on CAS?

Powerful Computer Algebra Systems (CAS) are often used only with reluctance in early undergraduate mathematics teaching, partly because of concerns that they may not encourage students to understand what they are doing. In this exploratory study, a version of a CAS that has been designed for secondary school students was used, with a view to considering the value of this sort of student learning support for first year undergraduate students enrolled in degree programs other than mathematics. Workshops were designed to help students understand aspects of elementary symbolic manipulation, through the use of the Algebra mode of an algebraic calculator, the Casio Algebra FX 2.0. The Algebra mode of this calculator allows a user to undertake elementary algebraic manipulation, routinely providing all intermediate results, in contrast to more powerful CAS software, which usually provides simplified results only. The students were volunteers from an introductory level unit, designed to provide a bridge between school and university studies of mathematics and with a focus on algebra and calculus. The two structured workshop sessions focussed respectively on the solution of linear equations and on relationships between factorising and expanding; attention focussed on using the calculators as personal learning devices. Following the workshops, structured interviews were used to systematically record student reactions to the experience. As a result of the study, the paper offers advice on the merits of using algebraic calculators in this sort of way

Graphics calculators in the mathematics curriculum: Integration or differentiation?

Graphics calculators are examples of powerful technologies that we want our students to learn to use well. However if we use them in our courses only for learning, students will not regard them with due importance because they are not integrated into the assessment. On the other hand, if graphics calculators are integrated into both learning and assessment there are risks associated with students becoming calculator dependent, issues of equity arise associated with calculator access and there may be problems with setting an appropriate examination. We discuss this dilemma in the light of our experiences and the reactions of our students over the last two years

Graphics calculators and assessment

Graphics calculators are powerful tools for learning mathematics and we want our students to learn to use them effectively. The use of these hand held personal computers provides opportunities for learning in interactive and dynamic ways. However, it is not until their use is totally integrated into all aspects of the curriculum that students regard them with due importance. This includes their use in all kinds of assessment tasks such as assignments, tests and examinations as well as in activities and explorations aimed at developing students’ understanding. The incorporation of graphics calculators into assessment tasks requires careful construction of these tasks. In this paper, discuss issues of equity relating to calculator models, levels of calculator use and the purpose and design of appropriate tasks. We also describe a typology we have developed to assist in the design and wording of assessment tasks which encourage appropriate use of graphics calculators, but which do not compromise important course objectives

Graphics calculator use in examinations: accident or design?

As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be used to help design examinations in which students are permitted to use graphics calculators as well as to interrogate existing examination practice

Symbolic manipulation on a TI-92: New threat or hidden treasures?

The availability of hand held devices that can undertake symbolic manipulation is a recent phenomenon, potentially of great significance for both the algebra and calculus curriculum in the secondary and lower undergraduate years. The significance to date of symbolic manipulation for mathematics is described, and parallels drawn with the significance of arithmetic skills for the primary school. It is suggested that, while symbolic manipulation is central to mathematics, many students develop only a restricted competence with the associated mathematical ideas. The Texas Instruments TI-92 is used to suggest some potential beneficial uses of technology that involves symbolic manipulation

Optimizing PiB-PET SUVR change-over-time measurement by a large-scale analysis of longitudinal reliability, plausibility, separability, and correlation with MMSE

AbstractQuantitative measurements of change in β-amyloid load from Positron Emission Tomography (PET) images play a critical role in clinical trials and longitudinal observational studies of Alzheimer's disease. These measurements are strongly affected by methodological differences between implementations, including choice of reference region and use of partial volume correction, but there is a lack of consensus for an optimal method. Previous works have examined some relevant variables under varying criteria, but interactions between them prevent choosing a method via combined meta-analysis. In this work, we present a thorough comparison of methods to measure change in β-amyloid over time using Pittsburgh Compound B (PiB) PET imaging.MethodsWe compare 1,024 different automated software pipeline implementations with varying methodological choices according to four quality metrics calculated over three-timepoint longitudinal trajectories of 129 subjects: reliability (straightness/variance); plausibility (lack of negative slopes); ability to predict accumulator/non-accumulator status from baseline value; and correlation between change in β-amyloid and change in Mini Mental State Exam (MMSE) scores.Results and conclusionFrom this analysis, we show that an optimal longitudinal measure of β-amyloid from PiB should use a reference region that includes a combination of voxels in the supratentorial white matter and those in the whole cerebellum, measured using two-class partial volume correction in the voxel space of each subject's corresponding anatomical MR image

Prediction of Streptococcus uberis clinical mastitis risk using Matrix-assisted laser desorption ionization time of flight mass spectrometry (MALDI-TOF MS) in dairy herds

The purpose of this study was to evaluate whether the risk of Streptococcus uberis clinical mastitis at cow level could be predicted from the historical presence of specific strains of S. uberis on dairy farms. Matrix-assisted laser desorption ionization time of flight mass spectrometry was used to identify S. uberis isolates potentially capable of contagious transmission. Data were available from 10,652 cows from 52 English and Welsh dairy farms over a 14 month period, and 521 isolates of S. uberis from clinical mastitis cases were available for analysis. As well as the temporal herd history of clinical mastitis associated with particular S. uberis strains, other exposure variables included cow parity, stage of lactation, milk yield, and somatic cell count. Observations were structured longitudinally as repeated weekly measures through the study period for each cow. Data were analyzed in a Bayesian framework using multilevel logistic regression models. Similarity of mass spectral profiles between isolates of S. uberis from consecutive clinical cases of mastitis in herds was used to indicate potential for contagious phenotypic characteristics. Cross validation showed that new isolates with these characteristics could be identified with an accuracy of 90% based on bacterial protein mass spectral characteristics alone. The cow-level risk in any week of these S. uberis clinical mastitis cases increased with the presence of the same specific strains of S. uberis in other cows in the herd during the previous 2 weeks. The final statistical model 29 indicated there would be a 2 to 3 fold increase in the risk of S. uberis clinical mastitis associated with particular strains if these occurred in the herd 1 and 2 weeks previously. The results suggest that specific strains of S. uberis may be involved with contagious transmission, and predictions based on their occurrence could be used as an early warning surveillance system to enhance the control of S. uberis mastitis

The Eyes Have It: Sex and Sexual Orientation Differences in Pupil Dilation Patterns

Recent research suggests profound sex and sexual orientation differences in sexual response. These results, however, are based on measures of genital arousal, which have potential limitations such as volunteer bias and differential measures for the sexes. The present study introduces a measure less affected by these limitations. We assessed the pupil dilation of 325 men and women of various sexual orientations to male and female erotic stimuli. Results supported hypotheses. In general, self-reported sexual orientation corresponded with pupil dilation to men and women. Among men, substantial dilation to both sexes was most common in bisexual-identified men. In contrast, among women, substantial dilation to both sexes was most common in heterosexual-identified women. Possible reasons for these differences are discussed. Because the measure of pupil dilation is less invasive than previous measures of sexual response, it allows for studying diverse age and cultural populations, usually not included in sexuality research