Preservice Teachers’ Understandings of the Relation Between a Fraction or Integer and Its Decimal Expansion: Strength and Stability of Belief

Abstract

In an earlier study of preservice elementary and middle school teachers’ beliefs about repeating decimals, Weller, Arnon, and Dubinsky (2009) reported on a comparison of the mathematical performance of 77 preservice teachers who completed an APOS-based instructional unit with 127 preservice teachers who completed traditional instruction. The purpose of the current study, based on 47 interviews conducted 4 months after the instruction, during which time there was no further instruction on this topic, is to determine the strength and stability (over time) of the students’ beliefs, to uncover thinking that did not arise in the earlier study, and to see whether the interviews yield similar comparative results. The interviews did uncover changes in student thinking. The students who received the APOS-based instruction developed stronger and more stable (over time) beliefs that a repeating decimal is a number; a repeating decimal has a fraction or integer to which it corresponds; a repeating decimal in general equals its corresponding fraction or integer; and, in particular, In addition, a number of indices and categories were developed that may prove useful in other studies consisting of the comparison of interview and questionnaire data involving a large number of interview subjects.     

Hyaluronan Synthase and Hyaluronidase Expression in Serous Ovarian Carcinoma is Related to Anatomic Site and Chemotherapy Exposure

The present study investigated the expression and clinical role of hyaluronan synthases (HAS1-3) and hyaluronidases (Hyal1-3) in serous ovarian carcinoma. HAS and HYAL mRNA expression was analyzed in 97 tumors (61 effusions, 27 primary carcinomas, 9 solid metastases) using PCR and further studied for association with clinicopathologic parameters, including survival. HAS1 mRNA was overexpressed in effusions compared to primary carcinomas and solid metastases (p < 0.001), and an alternatively spliced HAS1 was expressed only in effusions. HAS2 mRNA was overexpressed in solid metastases and primary carcinomas compared to effusions (p = 0.043), and HAS3 mRNA was overexpressed in primary carcinomas and effusions compared to solid metastases (p = 0.008). HYAL1 mRNA was absent in all specimens, whereas HYAL2 was expressed as two splice variants, of which HYAL2-var2 was overexpressed in solid metastases compared to effusions and primary carcinomas (p < 0.001). HYAL3 mRNA was expressed as wild-type and variant 1–3 form, the latter more highly in primary carcinomas and effusions compared to solid metastases (p = 0.006). HAS1 mRNA was overexpressed in pre- compared to post-chemotherapy effusions (p < 0.001), with opposite finding for HYAL2-var1 and HYAL3-WT (p = 0.016 and p = 0.024, respectively). Higher HYAL2-var1 and HAS1 splice variant mRNA expression in effusions was associated with longer (p = 0.033) and shorter (p = 0.047) overall survival, respectively. These data are the first to document a role for HAS and Hyal members in tumor progression in ovarian carcinoma, as evidenced by their differential expression as function of anatomic site and chemotherapy exposure, with a possible prognostic role for patients with malignant effusions.     

The effect of evaporation on size and shape evolution of faceted gold nanoparticles on sapphire

We studied the size and shape evolution of about 180 faceted gold nanoparticles attached to a sapphire substrate during annealing at 950 °C in air. We employed the scanning force microscopy and interrupted annealing techniques to track the changes in size and shape of individual nanoparticles. The height of all single-crystalline nanoparticles was constant up to the longest cumulative annealing time of 65 h. The lateral dimensions of ∼20% of all nanoparticles shrunk during anneals, while all three dimensions of the remaining 80% of nanoparticles remained constant. Only the nanoparticles with the height below the average (for all particles) were laterally shrinking. We formulated a kinetic model relating the lateral shrinkage of the nanoparticles to the evaporation of Au atoms adsorbed on sapphire. We also assumed that the process controlling particles shrinkage is the slow self-diffusion of Au atoms along the lateral facets of the nanoparticles toward the substrate. The model predicted a power law dependence of the shrinkage rate on the particle height, with the exponent n = 3. The corresponding exponent determined from the experimental data was n = −2.9 ± 0.3, in excellent agreement with the theory. The low value of the effective self-diffusion coefficient along the lateral facets determined with the aid of our model (3.2 ± 0.2 × 10⁻¹⁷ m² s⁻¹) was attributed to the difficulties of step nucleation on atomically flat facets.     

Capillary-driven motion of nanoparticles attached to curved rigid substrates

We considered the shape and crystallographic orientation evolution of nanoparticles attached to a curved rigid substrate at elevated temperatures at which the particle atoms move by diffusion along the particle surface and along the particle–substrate interface. We employed a variational method for calculating the chemical potential of the atoms of nanoparticles located at the particle–substrate interface. This chemical potential can be determined by calculating the change of total surface and interface energy of the system caused by two infinitesimal orthogonal translations and one rigid rotation of the particle. Once the distribution of the chemical potential along the particle–substrate interface is known, the kinetics of particle movements can be determined by coupling diffusion fluxes along the particle surface and particle–substrate interface. We illustrate the general theory by analyzing the particle movements on the surface step, on the sinusoidally patterned substrate, and within the corner formed by two intersecting planar surfaces. We also show that the developed theory can be applied to the analysis of burrowing of rigid ceramic nanoparticles into the metal substrate.     

Grain growth inhibition in thin nanocrystalline Au films by grain boundary diffusion and oxidation of Ti

We studied grain growth in thin nanocrystalline Au films deposited on a sapphire substrate with and without an ultrathin Ti underlayer (adhesion promoter). The samples were annealed at 200 °C for 2 h in air. The reference thin Au film without a Ti underlayer exhibited significant grain growth during annealing, whereas no changes in microstructure of the Au layer were observed in the Au/Ti bilayers. This stabilization of the microstructure of the Au layer was attributed to thermal grain boundary grooves on the Au surface filled with Ti oxide. The grooves exhibited an elongated morphology characterized by a low apparent dihedral angle value, atypical for thermal grain boundary grooves in pure metals. We demonstrated that grooves with this morphology are very efficient in pinning grain boundary motion. We also developed a quantitative model of grain boundary grooving coupled with grain boundary interdiffusion in thin bilayer films. The model predicted the formation of long, narrow grooves at the grain boundaries, which are very efficient in suppressing grain growth in nanocrystalline thin films.     

Factors associated with implementation of preventive care measures in patients with diabetes mellitus

BACKGROUND: There is only limited information on the extent to which physicians' characteristics affect the level of care and implementation of guidelines in patients with diabetes mellitus. OBJECTIVE: To identify physician characteristics associated with implementation of measures for preventive care in patients with diabetes mellitus and the distribution of implementation of these measures among them. PATIENTS AND METHODS: A retrospective chart audit of 519 patients eligible for health maintenance organization insurance on December 31, 1994, representing patients with diabetes receiving care from 22 primary care physician-providers of a managed care medical group in suburban North Los Angeles, Calif, and seen by physicians between January 1993 and December 1994. A short retroactive questionnaire for participating physicians was also used. The outcome measures were (1) measurement of serum high-density lipoprotein cholesterol; (2) urinalysis for the detection of proteinuria; and (3) ophthalmology referral for dilated fundus examination. RESULTS: Over a period of 2 years 78% of the patients had a high-density lipoprotein cholesterol determination, 80% had a test for proteinuria, and 62% were referred to an ophthalmologist. After adjustment for patient pool differences, physicians who were perceived by the administration of the medical group as "fast," based on a blinded evaluation of their number of patient encounters per unit time, had an odds ratio of 0.60 (95% confidence interval [CI], 0.37-0.95; P=.03) to obtain a high-density lipoprotein cholesterol determination in their patients and an odds ratio of 0.53 (95% CI, 0.32-0.87; P=.01) to test their patients for proteinuria. In patients requiring insulin, of fast physicians, the odds ratio for a referral for ophthalmology screening was 0.25 (95% CI, 0.07-0.85; P= .03). Duration of time in practice of over 15 years and disagreement with practice guidelines were associated with better outcomes. There was no association between physician sex, internal medicine training, or number of patients with diabetes in the practice and the implementation of outcomes. There was a highly significant association between the implementation of an outcome and the implementation of the other 2, resulting in a nonhomogeneous distribution of health care delivery. Physicians' estimate of their rate of implementation of outcomes, as assessed by the questionnaires, overestimated their actual performance while being in proportion with the documented rates. Most physicians took responsibility for the nonimplementation, accepting that it was an oversight on their part as opposed to an encounter with patient resistance. CONCLUSIONS: Most physicians believe that the lack of implementation of the measures for preventive care in patients with diabetes mellitus is an oversight. The oversight is more prevalent in the practices of busy physicians. The result is a nonhomogeneous distribution of health care. Computer reminders might be the solution.     

Protein turnover in the hypertrophying kidney

To establish whether altered proteolysis contributes to the increase in protein content in hypertrophying kidneys, we studied protein turnover in proximal renal tubules isolated from rats with three forms of renal hypertrophy, diabetes mellitus (DM), ammonium chloride-induced acidosis and compensatory renal growth (CRG). We found that in DM and in chronic acidosis the normal balance in protein turnover is altered due to attenuated proteolysis and accelerated protein synthesis. Together this favors an increase in kidney protein content. In contrast, in CRG, the increase in protein content is entirely due to increased protein synthesis. Thus, the changes in protein turnover leading to the net gain in kidney protein content in renal hypertrophy depends on the cause of hypertrophy.     

A bacteriophage reagent for Salmonella: molecular studies on Felix 01

Felix 01 (F01) is a bacteriophage originally isolated by Felix and Callow which lyses almost all Salmonella strains and has been widely used as a diagnostic test for this genus. Molecular information about this phage is entirely lacking. In the present study, the DNA of the phage was found to be a double-stranded linear molecule of about 80 kb. 11.5 kb has been sequenced and in this region A + T content is 60%. There are relatively few restriction endonuclease cleavage sites in the native genome and clones show this is due to their absence rather than modification. A restriction map of the genome has been constructed. The ends of the molecule cannot be ligated although they contain 5' phosphates. At least 60% of the genome must encode proteins. In the sequenced portion, many open reading frames exist and these are tightly packed together. These have been examined for homology to published proteins but only 1 to 17 shows similarity to known proteins. F01 is therefore the prototype of a new phage family. On the basis of restriction sites, codon usage and the distribution of nonsense codons in the unused reading frames, a strong case can be made for natural selection that reacts to mRNA structure and function.