Search for: All records

In engineering, students’ completion of prerequisites indicates an understanding of fundamental knowledge. Recent studies have shown a significant relationship between student performance and prior knowledge. Weak knowledge retention from prerequisite coursework can present challenges in progressive learning. This study investigates the relationship between prior knowledge and students’ performance over a few courses of Statics. Statistics has been considered as the subject of interest since it is the introductory engineering course upon which many subsequent engineering courses rely, including many engineering analysis and design courses. The prior knowledge was determined based on the quantitative and qualitative preparedness. A quiz set was designed to assess quantitative preparedness. The qualitative preparedness was assessed using a survey asking students’ subjective opinions about their preparedness at the beginning of the semester. Student performance was later quantified through final course grades. Each set of data were assigned three categories for grouping purposes to reflect preparedness: 1) high preparedness: 85% or higher score, 2) medium preparedness: between 60% and 85%, and 3) weak preparedness: 60% or lower. Pearson correlation coefficient and T-test was conducted on 129 students for linear regression and differences in means. The analysis revealed a non-significant correlation between the qualitative preparedness and final scores (p-value = 0.29). The data revealed that students underestimated their understanding of the prerequisites for the class, since the quantitative preparedness scores were relatively higher than the qualitative preparedness scores. This can be partially understood by the time gap between when prerequisites were taken and when the course under investigation was taken. Students may have felt less confident at first but were able to pick up the required knowledge quickly. A moderately significant correlation between students’ quantitative preparedness and course performance was observed (p -value < 0.05). Students with high preparedness showed > 80% final scores, with a few exceptions; students with weak preparedness also showed relatively high final scores. However, most of the less prepared students made significant efforts to overcome their weaknesses through continuous communication and follow-up with the instructor. Despite these efforts, these students could not obtain higher than 90% as final scores, which indicates that level of preparedness reflects academic excellence. Overall, this study highlights the role of prior knowledge in achieving academic excellence for engineering. The study is useful to Civil Engineering instructors to understand the role of students’ previous knowledge in their understanding of difficult engineering concepts. 

ABSTRACT In recent years, breakthroughs in methods and data have enabled gravitational time delays to emerge as a very powerful tool to measure the Hubble constant H0. However, published state-of-the-art analyses require of order 1 yr of expert investigator time and up to a million hours of computing time per system. Furthermore, as precision improves, it is crucial to identify and mitigate systematic uncertainties. With this time delay lens modelling challenge, we aim to assess the level of precision and accuracy of the modelling techniques that are currently fast enough to handle of order 50 lenses, via the blind analysis of simulated data sets. The results in Rungs 1 and 2 show that methods that use only the point source positions tend to have lower precision ($10\!-\!20{{\ \rm per\ cent}}$) while remaining accurate. In Rung 2, the methods that exploit the full information of the imaging and kinematic data sets can recover H0 within the target accuracy (|A| < 2 per cent) and precision (<6 per cent per system), even in the presence of a poorly known point spread function and complex source morphology. A post-unblinding analysis of Rung 3 showed the numerical precision of the ray-traced cosmological simulations to be insufficient to test lens modelling methodology at the percent level, making the results difficult to interpret. A new challenge with improved simulations is needed to make further progress in the investigation of systematic uncertainties. For completeness, we present the Rung 3 results in an appendix and use them to discuss various approaches to mitigating against similar subtle data generation effects in future blind challenges. 

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H 0 = 73.3 −1.8 +1.7 km s −1 Mpc −1 , describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H 0 . We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H 0 . Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H 0 = 74.5 −6.1 +5.6 km s −1 Mpc −1 . Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H 0 = 67.4 −3.2 +4.1 km s −1 Mpc −1 . This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H 0 . While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H 0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H 0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.