Understanding Early Mathematical Modelling: First Steps in the Process of Translation Between Real-world Contexts and Mathematics

The aim of this study is to provide data to better understand the processes of early mathematical modelling. According to this, an early mathematical modelling activity carried out by 21 Spanish schoolchildren aged 5–6 years is analysed, using the validated tool “Rubric for the Evaluation of Mathematical Modelling Processes” (REMMP). The results show that children link the content of the problem with their prior knowledge (understanding); identify the important data of the problem and simplify it (structuring); show some difficulties in substituting the elements of the real context for mathematical objects (mathematizing); use progressively mathematical objects and strategies in order to propose solutions for the problem (working mathematically); compare the solution with the initial problem (interpretation); justify the proposed model via valid arguments (validation); and also communicate the decisions taken throughout the modelling process and the concrete model obtained applied to the real context (presenting). We conclude that the description of this type of activities and the tools for their analysis could be used for grading and teaching tool in order to promote mathematic modelling in early childhood education.

Experimental Investigation and Image Processing to Predict the Properties of Concrete with the Addition of Nano Silica and Rice Husk Ash

The use of the combination of ultrafine rice husk ash (RHA) and nano silica (NS) enhances the compactness of hardened concrete, but there is still a lack of studies that address the effects of NS and RHA on the workability, mechanical properties and pore microstructure of concrete. This study mainly aims to investigate the influence of the pore size distribution in multiphysics concrete model modified by NS and RHA and to determine the workability and mechanical properties of concrete with NS and RHA. In this work, NS and RHA were used as 0, 5, 10, 15 and 20% replacements of ordinary Portland cement (OPC) in concrete grade M20. Concrete mixed with NS and RHA showed improved performance for up to 10% addition of NS and RHA. Further addition of NS and RHA showed a decrease in performance at 7, 14 and 28 days. The decrease in concrete porosity was also found to be up to 10% when adding NS and RHA to cement. Image processing was performed on the cement-based materials to describe the microstructure of the targeted material without damage. The results from the experimental and tomography images were utilized to investigate the concrete microstructure and predict its inner properties.

Understanding of Symmetry: Measuring the Contribution of Virtual and Concrete Models for Students with Different Spatial Abilities

Virtual and concrete models have been of interest in chemistry teaching to improve students’ understanding of a three-dimensional representation of chemical concepts such as symmetry. This study aims to determine the effectiveness of using concrete and virtual models on students’ understanding of symmetry. Students’ understanding was also explored in light of their spatial ability. The study was conducted using a quasi-experimental design with 62 students as participants. Two different instruments, spatial ability and understanding of symmetry tests, were employed for data collection. Data analysis was performed using the Pearson product-moment correlation and two-way variance analysis test. The results showed the virtual model’s contribution to improving students’ understanding of symmetry is higher than that of the concrete model for both students with high spatial ability (HSA) and low spatial ability (LSA). Also, the better students’ spatial ability, the better their understanding of molecular symmetry.

Discretization, the Road to Quantum Computing?

The main challenge we face in making quantum computing a reality is error control. For this reason it is necessary to study whether the hypotheses on which the threshold theorem has been proved capture all the characteristics of quantum errors. The extraordinary difficulties that we find to control quantum errors effectively together with the little progress in this endeavor, compared to the enormous effort deployed by the scientific community and by companies and governments, should make us reflect on the road map to quantum computing. In this work we analyze error control in quantum computing and suggest that discrete quantum computing models should be explored. In this sense, we present a concrete model but, above all, we propose that Quantum Physics should be taken one step further, in order to allow discretization of the quantum computing model.