Digital curriculum resources in mathematics education: foundations for change

In this conceptual review paper we draw on recent literature with respect to digital curriculum resources (DCR); we briefly outline and explain selected theoretical frames; and we discuss issues related to the design, and the use (by teachers and students) of digital curricula and e-textbooks in mathematics education. The results of our review show the following. Firstly, whilst there are some contrasting tendencies between research on instructional technology and research on DCR, these studies are at the same time predominantly framed by socio-cultural theories. Secondly, whilst there seems to be a continuing demarcation between the design(er) and the use(r), there is at the same time an emerging/increasing understanding that design continues in use, due to the different nature and affordances of DCR (as compared to traditional text curriculum resources). Thirdly, there is an apparent weakening of traditional demarcations between pedagogy and assessment, and between summative and formative assessment techniques, due to the nature and design of the automated learning systems. Fourthly, there is an increasing need for understanding the expanded space of interaction associated with the shift from static print to dynamic/interactive DCR, a shift that has the potential to support different forms of personalised learning and interaction with resources. Hence, we claim that DCR offer opportunities for change: of understandings concerning the design and use of DCR; of their quality; and of the processes related to teacher/student interactions with DCR—they provide indeed the foundations for change

Evolving students’ conceptions about responsible entrepreneurship : a classroom experiment

Following Neck and Corbett’s (2018) call to look at what goes on inside the entrepreneurship classroom, this paper proposed to dive into a three-hour lesson on responsible entrepreneurship, focusing on the point of view of both the teacher who develops learning activities and the students who, we hope, learn from our teachings. This exercise led us to detail a sequence of learning activities easily reproducible in other teaching contexts. The analysis of the definitions produced by the students before and after the lesson allows us to demonstrate the relevance of this lesson to enrich their conceptions about responsible entrepreneurship by associating it with sustainable development, in the complexity of its three constituent pillars

Word problems versus image-rich problems: an analysis of effects of task characteristics on students’ performance on contextual mathematics problems

This article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems

Development and Characterisation of a Gas System and its Associated Slow-Control System for an ATLAS Small-Strip Thin Gap Chamber Testing Facility

A quality assurance and performance qualification laboratory was built at McGill University for the Canadian-made small-strip Thin Gap Chamber (sTGC) muon detectors produced for the 2019-2020 ATLAS experiment muon spectrometer upgrade. The facility uses cosmic rays as a muon source to ionise the quenching gas mixture of pentane and carbon dioxide flowing through the sTGC detector. A gas system was developed and characterised for this purpose, with a simple and efficient gas condenser design utilizing a Peltier thermoelectric cooler (TEC). The gas system was tested to provide the desired 45 vol% pentane concentration. For continuous operations, a state-machine system was implemented with alerting and remote monitoring features to run all cosmic-ray data-acquisition associated slow-control systems, such as high/low voltage, gas system and environmental monitoring, in a safe and continuous mode, even in the absence of an operator.Comment: 23 pages, LaTeX, 14 figures, 4 tables, proof corrections for Journal of Instrumentation (JINST), including corrected Fig. 8b

Results of the REFLEX (Return Flux Experiment) Flight Mission

The numerous problems occurring in this first flight of the REFLEX experiment, both in the spacecraft and with the instrument package, seriously constrained the acquisition and analysis of data and severely limited the interpretation of the data that were obtained. Of these, the ambient helium measurements appear to be the most promising. They are summarized and discussed in Appendix A. Further analyses could be attempted to establish the correct values for the energy centers as they varied during the mission. In addition, an extensive laboratory recalibration on a high-speed beam system could in principle provide corrections to be used in analyzing and interpreting the returned data set. The unknown malfunction which generated the energy drift needs to be understood and corrected before the REFLEX experiment is reflown; some hardware modification, or at least retuning, is likely to be required

The Nucleon-Nucleon Interaction in a Chiral Constituent Quark Model

We study the short-range nucleon-nucleon interaction in a chiral constituent quark model by diagonalizing a Hamiltonian comprising a linear confinement and a Goldstone boson exchange interaction between quarks. The six-quark harmonic oscillator basis contains up to two excitation quanta. We show that the highly dominant configuration is $\mid s^4p^2[42]_O [51]_{FS}>$ due to its specific flavour-spin symmetry. Using the Born-Oppenheimer approximation we find a strong effective repulsion at zero separation between nucleons in both $^3S_1$ and $^1S_0$ channels. The symmetry structure of the highly dominant configuration implies the existence of a node in the S-wave relative motion wave function at short distances. The amplitude of the oscillation of the wave function at short range will be however strongly suppressed. We discuss the mechanism leading to the effective short-range repulsion within the chiral constituent quark model as compared to that related with the one-gluon exchange interaction.Comment: 31 pages, LaTe

Supersymmetry in models with strong on-site Coulomb repulsion - application to t-J model

A supersymmetric way of imposing the constraint of no double occupancy in models with strong on-site Coulomb repulsion is presented in this paper. In this formulation the physical operators in the constrainted Hilbert space are invariant under local unitary transformations mixing boson and fermion representations. As an illustration the formulation is applied to the $t-J$ model. The model is studied in the mean-field level in the J=0 limit where we show how both the slave-boson and slave-fermion formulations are included naturally in the present approach and how further results beyond both approaches are obtained.Comment: 12 pages, Latex file, 1 figur