An Online-Based Edu-Escape Room: A Comparison Study of a Multidimensional Domain of PSTs with Flipped Sustainability-STEM Contents

The use of active and flipped methodologies has increased in recent years. Here, gamification uses typical elements of a game in different contexts, including that of education. Specifically, Escape Room games used as educational tools have potential for teaching–learning, and they can be beneficial because they can improve students’ motivation and emotions toward learning. This is particularly valuable in science, technology, engineering and mathematics (STEM) courses, where the cognitive factor and multidimensional domain are closely connected. This research presents an online-based Edu-Escape Room with science and sustainability contents as an educative tool in a STEM course. With the intervention proposed, we analyze how this tool influences the multidimensional domain (attitudes, self-efficacy and emotions) of pre-service teachers (PSTs). According to attitude and self-efficacy analysis, it is observed that most of the items analyzed show an increase in self-efficacy and more positive attitudes after the intervention. In particular, Question 11 (Q11) indicates a significant difference. Concerning the results for emotion, the positive emotions “joy”, “satisfaction” and “fun” are significantly increased after the intervention. However, the negative emotions “nervousness”, “frustration” and “concern” also increase, partly due to the game characteristics. The proposed activity had a medium effect on items with significant differences except for the emotion “frustration”, where the intervention had a large effect according to effect size (ES) analysis. According to the principal component analysis (PCA), the attitudes, self-efficacy and emotions of the PSTs are positively correlated, and the influence of the proposed activity shows a significant improvement in these variables. Finally, the structural equation modeling partial least squares (SEM-PLS) analysis showed the effects that the instruction has on the PSTs’ emotions and also that they had a significant effect on the positive attitudes towards and self-efficacy in science. Therefore, there are multiple benefits in the multidimensional domain of PSTs of having implemented the proposed online-based Edu-Escape Room.

Behavior of blow-up solutions for quasilinear parabolic equations

We study the quasilinear parabolic equation $(|u|^{q-1}u)_t-\Delta_p\,u=0$ in a multidimensional domain $(0,T)\times\Omega$ under the condition $u(t,x)=f(t,x)$ on $(0,T)\times\partial\Omega$, where the boundary function $f$ blows-up at a finite time $T$, i.e., $f(t,x)\rightarrow\infty$ as $t\rightarrow T$. For $p\geqslant q>0$ and the boundary function $f$ with power-like behavior, the upper bounds of weak solutions of the problem are obtained. The behavior of solutions at the transition from the case where $p>q$ to $p=q$ is investigated. A general approach within the method of energy estimates to such problems is described.

On the number of integer points in a multidimensional domain

We provide a new upper estimate for the modulus of the difference |Λ ∩ 𝓢| − voln(𝓢)/det Λ, where 𝓢 ⊂ ℝn is a set of volume voln(𝓢) and Λ ⊂ ℝn is a complete lattice with determinant det Λ. This result has an important practical application, for example, in estimating the number of integer solutions of an arbitrary system of linear and nonlinear inequalities.