Multimedia resources designed to support learning from written proofs: An eye-movement study

This paper presents two studies of an intervention designed to help undergraduates comprehend mathematical proofs. The intervention used multimedia resources that presented proofs with audio commentary and visual animations designed to focus attention on logical relationships. In Study 1, students studied an e-Proof or a standard written proof and their comprehension was assessed in both immediate and delayed tests; the groups performed similarly at immediate test, but the e-Proof group exhibited poorer retention. Study 2 accounted for this unexpected result by using eye-movement analyses to demonstrate that participants who studied an e-Proof exhibited less processing effort when not listening to the audio commentary. We suggest that the extra support offered by e-Proofs disrupts the processes by which students organise information, and thus restricts the extent to which their new understanding is integrated with existing knowledge. We discuss the implications of these results for evaluating teaching innovations and for supporting proof comprehension

Investigating and improving undergraduate proof comprehension

Undergraduate mathematics students see a lot of written proofs. But how much do they learn from them? Perhaps not as much as we would like – every professor knows that students struggle to make sense of the proofs presented in lectures and textbooks. Of course, written proofs are only one resource for learning; students also attend lectures and work, independently or with support, on problems. But, because mathematics majors are expected to learn much of their mathematics by studying proofs, it is important that we understand how to support them in reading and understanding mathematical arguments. This observation was the starting point for the research reported in this article. Our work uses psychological research methods to generate and analyse empirical evidence on mathematical thinking, in this case via experimental studies of teaching interventions and quantitative analyses of eye-­‐movement data. What follows is a chronological account of three stages in our attempts to better understand students’ mathematical reading processes and to support students in learning to read effectively

Matlab package for the Gait and Posture experiment from Pedestrian motion modelled by Fokker–Planck Nash games

This matlab package is set up to reproduce the results of test case 4: Gait and Posture. A readme file is included to help in the simulation and to describe the main modules of the package and the location of the input

Matlab package for the Turnwald-1C-A3 experiment from Pedestrian motion modelled by Fokker–Planck Nash games

This matlab package is set up to reproduce the results of test case 2: Turnwald 1C-A3. A readme file is included to help in the simulation and to describe the main modules of the package and the location of the input

Matlab package for the Gait and Posture experiment from Pedestrian motion modelled by Fokker–Planck Nash games

This matlab package is set up to reproduce the results of test case 4: Gait and Posture. A readme file is included to help in the simulation and to describe the main modules of the package and the location of the input

<i>cis</i>-Dioxomolybdenum(VI) complex of N-<i>o</i>-hydroxyacetophenonene-isonicotinic acid hydrazide as nosocomial anti-infectious agent: experimental and theoretical study

<p>Due to growing resistance and continuous colonization among microbes, researchers are eager to design and put forth antibiotic substances of effective anti-nosocomial infection activity. Under such purview, the current report deals with synthesis and formulation of a dioxomolybdenum(VI) complex of general formula [MoO₂(L)(H₂O)], where H₂L = N-(<i>o</i>-hydroxyacetophenone)isonicotinic acid hydrazide (H₂haina), as antibiotic compound against hospital acquired infections. The complex was characterized by elemental analysis, conductance determination, magnetic susceptibility measurements, Proton Nuclear Magnetic reonance spectroscopy (¹HNMR), Fourier-transform Infra-red spectroscopy (FTIR), mass spectrometry, thermal and electronic spectral studies. Experimental data results were compared with theoretical outcomes by invoking density functional theory-based molecular topography and conjoint spectroscopic analysis with the help of Gaussian09 software package using LANL2DZ/B3LYP combination for the cis-dioxo group of distorted octahedral complex, [MoO₂(haina)(H₂O)]. The experimental and theoretical outcomes were found in an excellent agreement with one another. The overall study reveals that the complex under investigation possesses a <i>cis</i><i>-</i>dioxo-octahedral geometry. Significant antimicrobial activity of the complex was obtained against hospital origin microbes in comparison with some selected standard commercial drugs including tetracycline and azithromycin. <i>E. Coli and Pseudomonas</i> were the microbes selected for the study.</p