Promoting uncertainty to support preservice teachers’ reasoning about the tangent relationship

Including opportunities for students to experience uncertainty in solving mathematical tasks can prompt learners to resolve the uncertainty, leading to mathematical understanding. In this article, we examine how preservice secondary mathematics teachers’ thinking about a trigonometric relationship was impacted by a series of tasks that prompted uncertainty. Using dynamic geometry software, we asked preservice teachers to compare angle measures of lines on a coordinate grid to their slope values, beginning by investigating lines whose angle measures were in a near-linear relationship to their slopes. After encountering and resolving the uncertainty of the exact relationship between the values, preservice teachers connected what they learned to the tangent relationship and demonstrated new ways of thinking that entail quantitative and covariational reasoning about this trigonometric relationship. We argue that strategically using uncertainty can be an effective way of promoting preservice teachers’ reasoning about the tangent relationship.     

Spasmodic dysphonia and vocal fold paralysis:Outcomes of voice problems on work-related functioning

Patients at a university voice disorder clinic diagnosed with spasmodicdysphonia (SD, n = 68) or vocal fold paralysis (VFP, n = 57) reported vocal symptoms and adverse work outcomes in contrast to a nondisordered group (ND, n = 68). Patients with SD most frequently cited symptoms of effortfulness (57%) and weakness (54%), VFP cited hoarseness (70%) and weakness (60%), while the nondisordered reported hoarseness (28%). SD and VFP produced greater (p<.05) adverse work outcomes than the nondisordered in the past (SD: 65%, VFP: 41%, ND: 3%), potential future (SD: 78%, VFP: 65%, ND: 19%), and current job performance (SD: 64%, VFP: 46%, ND: 2%). These disorders significantly disrupt socioeconomic outcomes and research is needed to improve functional ability and quality of life.     

Ethanol-induced crack healing in poly(methyl methacrylate)

The crack healing induced by ethanol in poly(methyl methacrylate) (PMMA) has been studied at temperatures of 40–60°C. Crack healing occurs because the effective glass transition temperature of PMMA is reduced to below the test temperature by ethanol plasticization. It is found that crack closure rate is constant at a given temperature. The fracture strength of healed PMMA is lower than that of the original samples. By comparing the fracture stress with the morphology of the crack edge on the PMMA surface, we found that a high degree of swelling is responsible for the incomplete recovery of mechanical strength. The fractography of the completely healed sample shows a very different fracture morphology from that of virgin PMMA. The transport of ethanol in PMMA also is studied. At lower temperatures, transport is described by ideal Case II behavior. As the temperature increases, the kinetics shift from ideal Case II to anomalous behavior. The first stage of crack healing is controlled by Case I transport. © 1994 John Wiley & Sons, Inc.     

Sun-reactive Skin Type in 4912 French adults participating in the SU.VI.MAX study

Phototype classifications were initially developed in an attempt to predict the skin reactions of patients to phototherapy and are now widely used to advise individuals with regard to sun protection. A transversal study was conducted on the SU.VI.MAX cohort to estimate the frequency of sun-reactive skin features in a large, general adult population-based sample, and to describe the associations between these features. The data were collected 3 years after the beginning of the SU.VI.MAX nutritional intervention study on 4912 volunteers (2868 women aged 35-60 years and 2044 men aged 45-60 years). A multiple correspondence analysis was performed to study the associations between the features. The results showed that these features correspond to a one-dimensional phenomenon, which allowed us to establish a score to summarize skin sensitivity to sun exposure. Furthermore, we found a link between gender and phototype using the Césarini classification (phototype > or = IV: 37% of women, 47% of men). The analysis of the relationship with sun-reactive skin features and the score revealed the same trend. Phenotypic evaluation appears to be a good estimator of skin sensitivity to sun exposure for clinical screening or for use in research, and is easy to collect at a lower cost. Moreover, the sun sensitivity difference between gender should be considered in education about photoprotection.     

Photocatalytic coatings for environmental applications

A series of nano- and micronparticle-grade anatase and rutile titanium dioxide pigments have been prepared with various densities of surface treatments, particle size and surface area. Their photocatalytic activites have been determined in a series of paint films by FTIR, chalking, color, gloss change and weight loss after artifical weathering. The pigments have also been examined by rapid assessment methodologies using photodielectric microwave spectroscopy, 2-propanol oxidation and hydroxyl analysis. The microwave response under light and dark cycles provides an extended timescale probe of charge-carrier dynamics in the pigments. Pigment particle size, surface area and properties clearly play an important role in dispersion and any polymer-pigment interactions. Photooxidation studies on several types of paint films show a clear demarcation between nanoparticle- and pigmentary-grade titanium dioxide, with the former being more active because of their greater degree of catalytic surface activity. The photosensitivity of titanium dioxide is considered to arise from localized sites on the crystal surface (i.e. acidic OH), and occupation of these sites by surface treatments inhibits photoreduction of the pigment by ultraviolet radiation; hence, the destructive oxidation of the binder is inhibited. Coatings containing 2-5% by weight alumina or alumina and silica are satisfactory for general-purpose paints. If greater resistance to weathering is desired, the pigments are coated more heavily to about 7-10% weight. The coating can consist of a combination of several materials, e.g. alumina, silica, zirconia, aluminum phosphates of other metals. For example, the presence of hydrous alumina particles lowers van der Waals forces between pigments particles by several orders of magnitude, decreasing particle-particle attractions. Hydrous aluminum oxide phases appear to improve dispersibility more effectively than most of the other hydroxides and oxides. Coated nanoparticles are shown to exhibit effective light stabilization in various water- and oil-based paint media in comparison with conventional organic stabilizers. Hindered piperidine stabilizers are shown to provide no additional benefits in this regard, often exhibiting strong antagonism. The use of photocatalytic titania nanoparticles in the development of self-cleaning paints and microbiological surfaces is also demonstrated in this study. In the former case, surface erosion is shown to be controlled by varying the ratio of admixture of durable pigmentary-grade rutile (heavily coated) and a catalytic-grade anatase nanoparticle. For environmental applications in the development of coatings for destroying atmospheric pollutants such as nitrogen oxide gases (NO(X)), stable substrates are developed with photocatalytic nanoparticle-grade anatase. In this study, porosity of the coatings through calcium carbonate doping is shown to be crucial in the control of the effective destruction of atmospheric NO(X) gases. For the development of microbiological substrates for the destruction of harmful bacteria, effective nanoparticle anatase titania is shown to be important, with hydrated high surface area particles giving the greatest activity.     

1,2-dioxines containing tethered hydroxyl functionality as convenient precursors for pyran syntheses

A new method for the construction of tetrahydropyrans derived from readily available 1,2-dioxines containing a tethered hydroxyl moiety is described. The reaction proceeds via a base-catalyzed rearrangement of the 1,2-dioxines to either the isomeric cis or trans gamma-hydroxy enones followed by intramolecular oxa-Michael addition of the tethered hydroxyl group.     

Persistent interactions between hydroxylated nanoballs and atactic poly(2-hydroxyethyl methacrylate)(PHEMA)

The incorporation of self-assembled nanoparticles, a.k.a. hydroxylated nanoballs, into poly(2-hydroxyethyl methacrylate)(PHEMA) gives rise to a cross-linked network/hydrogel with enhanced interfacial interaction, whereas its inclusion in poly(methyl methacrylate)(PMMA) results in plasticization.