The advantages of algebra for learning proof

Calls to expand proof beyond geometry are usually based on the general benefits of proving for students, but this essay argues that proof should be extended to algebra because the representational systems in algebra are well suited for understanding the generality and deductive flow of proofs

Who should learn proving and why: An examination of secondary mathematics teachers’ perspectives

Reasoning-and-proving is a crucial part of students’ mathematical experiences in secondary school. There is scholarly debate, however, on the extent to which proving at the secondary level needs to be formal and whether all students should be held to disciplinary standards of rigor. In this study, we investigated the notion of “proof for all” from the perspective of secondary mathematics teachers. We analyzed, using the framework of practical rationality, the justifications teachers gave for whether or not all students should learn proof. Based on interviews with twenty-one secondary teachers from a socioeconomically-diverse set of schools, we found that teachers differ in their opinions of who should learn proving but they were similar in their feelings of obligation toward individual student learning; some teachers cited obligations to individual students as a justification for teaching proving to all students and others cited those obligations as a justification for not teaching proving to some students. We also share teachers’ perspective with regard to their obligations to the discipline, educational institutions, interpersonal dynamics among students, and the worldly relevance of mathematics education

Evaluation of multiple variate selection methods from a biological perspective: a nutrigenomics case study

Genomics-based technologies produce large amounts of data. To interpret the results and identify the most important variates related to phenotypes of interest, various multivariate regression and variate selection methods are used. Although inspected for statistical performance, the relevance of multivariate models in interpreting biological data sets often remains elusive. We compare various multivariate regression and variate selection methods applied to a nutrigenomics data set in terms of performance, utility and biological interpretability. The studied data set comprised hepatic transcriptome (10,072 predictor variates) and plasma protein concentrations [2 dependent variates: Leptin (LEP) and Tissue inhibitor of metalloproteinase 1 (TIMP-1)] collected during a high-fat diet study in ApoE3Leiden mice. The multivariate regression methods used were: partial least squares “PLS”; a genetic algorithm-based multiple linear regression, “GA-MLR”; two least-angle shrinkage methods, “LASSO” and “ELASTIC NET”; and a variant of PLS that uses covariance-based variate selection, “CovProc.” Two methods of ranking the genes for Gene Set Enrichment Analysis (GSEA) were also investigated: either by their correlation with the protein data or by the stability of the PLS regression coefficients. The regression methods performed similarly, with CovProc and GA performing the best and worst, respectively (R-squared values based on “double cross-validation” predictions of 0.762 and 0.451 for LEP; and 0.701 and 0.482 for TIMP-1). CovProc, LASSO and ELASTIC NET all produced parsimonious regression models and consistently identified small subsets of variates, with high commonality between the methods. Comparison of the gene ranking approaches found a high degree of agreement, with PLS-based ranking finding fewer significant gene sets. We recommend the use of CovProc for variate selection, in tandem with univariate methods, and the use of correlation-based ranking for GSEA-like pathway analysis methods

Exploiting genomics for antimicrobial resistance surveillance at One Health interfaces.

The intersection of human, animal, and ecosystem health at One Health interfaces is recognised as being of key importance in the evolution and spread of antimicrobial resistance (AMR) and represents an important, and yet rarely realised opportunity to undertake vital AMR surveillance. A working group of international experts in pathogen genomics, AMR, and One Health convened to take part in a workshop series and online consultation focused on the opportunities and challenges facing genomic AMR surveillance in a range of settings. Here we outline the working group's discussion of the potential utility, advantages of, and barriers to, the implementation of genomic AMR surveillance at One Health interfaces and propose a series of recommendations for addressing these challenges. Embedding AMR surveillance at One Health interfaces will require the development of clear beneficial use cases, especially in low-income and middle-income countries. Evidence of directionality, risks to human and animal health, and potential trade implications were also identified by the working group as key issues. Addressing these challenges will be vital to enable genomic surveillance technology to reach its full potential for assessing the risk of transmission of AMR between the environment, animals, and humans at One Health interfaces.

Examining Population Structure through the Use of Surname Matrices: Methodology for Visualizing Nonrandom Mating

The analysis of nonrandom mating using the frequency of marital isonymy indirectly measures the degree of population structure. However, population structure is the result of all matings in a population. Difficulties with large surname matrices have resulted in data being summarized into a single statistic or collapsed into brief tables, with considerable loss of information. By using sophisticated computer graphing procedures and displays, it is possible to directly analyze the mating structure of a community. If P is a vector of proportions for each male surname i (i = 1, 2, 3, ..., n), Q a similar vector of female surnames j (j = 1, 2, 3, ..., m), then the expected frequency matrix E of each possible mating is P x Q. The difference D between the observed frequency matrix O and the expected matrix is O — E. The D matrix is graphed with the x axis containing the male surnames, the y axis the female surnames, and the z axis the difference values dij. Negative values represent negative nonrandom mating and positive values positive nonrandom mating. From 5417 marriages (1840-1963) in the M idlands of Tasmania, those between spouses having 1 of 194 core names were extracted. We analyze these marriages utilizing the new technique and examine the surface of the graph and statistical analysis of its finer structure. Among the results was the dem onstration of frequency-dependent selection of surnames. This finding has significant implications for microevolution of hum an populations, as surnames have existed for possibly 700 years

Level of awareness in radiation protection of radiologic technologists in selected hospitals in Cavite

The researchers used the descriptive survey research method. Using convenience sampling technique, a total of 76 radiologic technologists were included in the study. The researchers used an adopted questionnaire as research instrument. The statistical tools used were frequency, percentage, mean, standard deviation, t-test of uncorrelated means and f-test. Based on the findings, the following conclusions are drawn: (1) Out of the total population of 76 radiologic technologists, majority of the respondents are within the age group of 26 to 35 years old, male and with 2-5 years length of service; (2) The radiologic technologists were aware to a very high extent on the radiation protection for the patient and the general public. Regarding radiation protection of the worker, the respondents were aware to high extent. The level of awareness of the respondents on radiation protection is interpreted as aware to a very high extent in general; (3) The level of awareness of the respondents on radiation protection of the patient, general public and worker when they are grouped according to age had no significant difference; (4) The level of awareness of the respondents on radiation protection of the general public and worker has no significant difference when they are grouped according to gender. However, the level of awareness of the respondents on radiation protection of the patient when they are grouped according to gender has a significant difference. The male respondents are more aware on radiation protection of the patient than the female respondents; (5) The level of awareness of the respondents on radiation protection of patients and the general public has no significant difference when they are grouped according to length of service. However, the level of awareness of the respondents on radiation protection of the worker has a significant difference when they are grouped according to length of service. Radiologic technologists whose length of service is 2-5 years are more aware on radiation protection of the worker than those who belong to one (1) year and below and more than five (5) years length of service

Believers of fortune telling: Who are they?

The purpose of this study is to characterize the believers of fortune telling. Believers was describe in terms of four areas, namely: (1) The demographic and psychological profile, (2) fortune telling method the believers predominantly subscribe to, )3) objectives of the believers for consulting and lastly, (4) the extent to which they abide to the advices given to them. A survey was employed to 90 participants (42 males, 48 females) with ages raging from 20-65 years old. The results show that males and females cater to fortune telling and yet most of the participants have internal locus of control. The method mostly preferred is palmistry. Reason for consulting is to help them understand things and give them control over their lives. Main issue early adults consult is about love life, for middel adults, they are concern with business and family matters. Both groups do not have full compliance to the advices given to them

Analysis of Monoglycerides, Diglycerides, Sterols, and Free Fatty Acids in Coconut (Cocos nucifera L.) Oil by 31P NMR Spectroscopy

Phosphorus-31 nuclear magnetic resonance spectroscopy (31P NMR) was used to differentiate virgin coconut oil (VCO) from refined, bleached, deodorized coconut oil (RCO). Monoglycerides (MGs), diglycerides (DGs), sterols, and free fatty acids (FFAs) in VCO and RCO were converted into dioxaphospholane derivatives and analyzed by 31P NMR. On the average, 1-MG was found to be higher in VCO (0.027%) than RCO (0.019%). 2-MG was not detected in any of the samples down to a detection limit of 0.014%. On the average, total DGs were lower in VCO (1.55%) than RCO (4.10%). When plotted in terms of the ratio [1,2-DG/total DGs] versus total DGs, VCO and RCO samples grouped separately. Total sterols were higher in VCO (0.096%) compared with RCO (0.032%), and the FFA content was 8 times higher in VCO than RCO (0.127% vs 0.015%). FFA determination by 31P NMR and titration gave comparable results. Principal components analysis shows that the 1,2-DG, 1,3-DG, and FFAs are the most important parameters for differentiating VCO from RCO

Perception of the utilization of e-books in the learning enhancement of the nursing students of De La Salle Health Sciences Institute

The method of research used in this study was a quantitative, non-experimental, descriptive research design. The sample population was composed of 143 selected nursing students of De La Salle Health Sciences Institute. Convenience sampling was utilized. The research instrument that was used was adapted and modified from unpublished undergraduate study of Del Rosario (2003). Data was analysed using percentage, mean, standard deviation, t-test, and Analysis of Variance (ANOVA). Most of the respondents were 19 years old and above, female, 4th year nursing students and have a monthly income above PhP40,001. The respondents had high perception that utilization of e-books enhances their learning. The perception on the utilization of e-books in the learning enhancement of the respondents was the same regardless of age, gender, college level and monthly family income