X. Wang

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the history of mathematics by combining the objectives of high school mathematics curriculum in China. This framework includes six dimensions: the harmony of knowledge, the beauty of ideas or methods, the pleasure of inquiries, the improvement of capabilities, the charm of cultures, and the availability of moral education. The results show that this framework better explained the all-educational values of the history of mathematics that all teaching cases showed. Therefore, the framework can guide teachers to better integrate the history of mathematics into teaching.

The resource constraint project scheduling problem has attracted growing attention since the last decades. Precedence constraints are considered as well as resources with limited capacities. During the project, the same resource can be required by several in-process jobs and it is compulsory to ensure that the consumptions do not exceed the limited capacities. In this paper, several criteria are involved, namely makespan, total job tardiness, and workload balancing level. Our problem is firstly solved by the non-dominated sorting genetic algorithm-II as well as the recently proposed NSGAIII. Giving emphasis to the selection procedure, we apply both the traditional Pareto dominance and the less documented Lorenz dominance into the niching mechanism of NSGAIII. Hence, we adopt and modify L-NSGAII to our problem and propose L-NSGAIII by integrating the notion of Lorenz dominance. Our methods are tested by 1350 randomly generated instances, considering problems with 30–150 jobs and different configurations of resources and due dates. Hypervolume and C-metric are considered to evaluate the results. The Lorenz dominance leads the population more toward the ideal point. As experiments show, it allows improving the original NSGA approach.

A geometric lattice is the lattice of closed subsets of a closure operator on a set which is zero-closure, algebraic, atomistic and which has the so-called exchange property. There are many profound results about this type of lattices, the most recent one of which, due to Czédli and Schimdt, says that a lattice L of finite length is semimodular if and only if L has a cover-preserving embedding into a geometric lattice G of the same length. The goal of our paper is to offer the following result: a lattice of finite length is semimodular if and only if every cell in L is a 4-element Boolean lattice and the 7-element non-distributive atomistic lattice having 3 atoms is not a cover-preserving sublattice of L.

In a world awash with data, the ability to think and compute with data has become an important skill for students in many fields. For that reason, inclusion of some level of statistical computing in many introductory-level courses has grown more common in recent years. Existing literature has documented multiple success stories of teaching statistics with R, bolstered by the capabilities of R Markdown. In this article, we present an in-class data visualization activity intended to expose students to R and R Markdown during the first week of an introductory statistics class. The activity begins with a brief lecture on exploratory data analysis in R. Students are then placed in small groups tasked with exploring a new dataset to produce three visualizations that describe particular insights that are not immediately obvious from the data. Upon completion, students will have produced a series of univariate and multivariate visualizations on a real dataset and practiced describing them.

A short-lived but important movement in seventeenth-century English natural philosophy—which scholars call “magnetical philosophy” or “magnetical cosmology”—sought to understand gravity (both terrestrial and celestial) by analogy with magnetism. The movement was clearly inspired by William Gilbert’s De magnete (1600) and culminated with Robert Hooke’s prefiguring of the universal principle of gravitation, which he personally communicated to Isaac Newton in 1679. But the magnetical cosmology, as professed by those in the movement, differed from Gilbert’s philosophy in highly significant ways. Proponents never accepted Gilbert’s animistic account of magnets and seem tacitly to have accepted a belief in action at a distance that Gilbert himself rejected. This essay argues that Francis Bacon (1561–1626) had already provided just the adaptations to Gilbert’s philosophy that the later thinkers adopted, including an important endorsement of action at a distance, and that he should be recognized as playing an important role in the movement.

In the current study, late Chinese–English bilinguals performed a facial expression identification task with emotion words in the task-irrelevant dimension, in either their first language or second language. The investigation examined the automatic access of the emotional content in words appearing in more than one language. Significant congruency effects were present for both L1 and L2 emotion word processing. Furthermore, the magnitude of emotional face-word Stroop effect in the L1 task was greater as compared to the L2 task, indicating that in L1 participants could access the emotional information in words in a more reliable manner. In summary, these findings provide more support for the automatic access of emotional information in words in the bilinguals’ two languages as well as attenuated emotionality of L2 processing.

This study examines the effects of teachers' speech and hand gestures on the task performances of students with Attention‐Deficit/Hyperactivity Disorder. Forty‐five 7½‐year‐old students clinically diagnosed with ADHD participated in the study. The students were asked to solve three sets of puzzles. The teachers supported the students in the tasks by using three different scaffolding modalities: speech‐only, gesture‐only and speech in conjunction with gestures. The results indicate that when the teachers used the scaffolding that contained gesture components, the ADHD students were more responsive, focused longer on the tasks and were more successful in completing the tasks. Moreover, teachers' representational and deictic gestures were found to be the most effective gestures in scaffolding. This study suggests that when teachers' hand gestures are used together with speech, they are a powerful pedagogical means to engage ADHD children in tasks.

One of the major divergences between dynamical systems theory and symbolism lies in their views on the role of representation in cognition. From the perspective of development, the cognitive development could be divided into three levels: sensorimotor, imagery representation and linguistic representation. It is claimed that representation is not a sufficient condition though it is necessary for cognition. However, it does not mean that the authors agree with the notion of strong coupling in dynamicism that completely rejects representation.

A series of features of the contemporary globalization of human society, especially its dual positive arid negative effects, shows that contemporary globalization has great significance for the survival and development of mankind as a whole. From the point of view of its deep axiological significance, globalization has resulted in the formation of common human interests that manifest themselves negatively as the emergence of various global problems. The formation of common human interests and the emergence of global problems in turn have objectively introduced a specific norm of value to contemporary global society. This norm of value requires people in the contemporary global society to take common human interests as their value orientation when dealing with the relationship between the human being and the world, if they are to solve various contemporary global problems and make possible the continued survival of mankind and the sustainable development of human society.