The Case of a Multiplication Skills Game: Teachers’ Viewpoint on MG’s Dashboard and OSLM Features

Educational games and digital game-based learning (DGBL) provide pupils interactive, engaging, intelligent, and motivating learning environments. According to research, digital games can support students’ learning and enhance their motivation to learn. Given the central role teachers play in the learning process, their perceptions of DGBL play a significant role in the usage and effectiveness of game-based learning. This paper presents the main findings of an online research on primary school teachers’ attitudes toward DGBL. Furthermore, the research investigates teachers’ opinions about the functionalities provided by the implemented Multiplication Game (MG) and the newly incorporated teacher dashboard. The MG is an assessment and skills improvement tool that integrates an adaptation mechanism that identifies student weaknesses on the multiplication tables and in its latest version also supports a strong social parameter. Students can be informed about their own progress as well as the progress of their peers in an effort to examine if social interaction or competition can increase players’ motivation, which is a subject that raised some concerns in the teaching community. The paper describes the functional options offered by the MG dashboard and documents the outcomes of an online survey conducted with the participation of 182 primary school teachers. The survey indicated the potential usefulness of MG and the benefits it can offer as a learning tool to improve pupil multiplication skills and help teachers identify individual pupil skills and difficulties and adapt their teaching accordingly. The analysis applied has found a correlation between teachers’ perceptions about MG and their view on using digital games in general.

Arithmetical Advice

This chapter presents advice on how to avoid simple mistakes when performing mental calculations at high speed. It includes a method to speed up the rate at which you recite your multiplication tables. This can save fractions of a second, which, in an exam with many such multiplications, can be crucial. It urges neat handwriting, and shows the superfluity of zeros at the end, or decimal points in the middle of a number, provided you make estimates before calculating an answer. It presents a quick look at factors, which can slash seconds from the time it take to multiply and divide, and introduces the art of shunting.

Robot Tutoring of Multiplication: Over One-Third Learning Gain for Most, Learning Loss for Some

In the design of educational robots, it appears to be undecided as to whether robots should show social behaviors and look human-like or whether such cues are insignificant for learning. We conducted an experiment with different designs of social robots built from the same materials, which is unique in robotics research. The robots rehearsed multiplication tables with primary school children in Hong Kong, which is a user group not easily or often accessed. The results show that affective bonding tendencies may occur but did not significantly contribute to the learning progress of these children, which was perhaps due to the short interaction period. Nonetheless, 5 min of robot tutoring improved their scores by about 30%, while performance dropped only for a few challenged children. We discuss topics, such as teaching language skills, which may be fostered by human likeness in appearance and behaviors; however, for Science, Technology, Engineering, and Mathematics (STEM)-related subjects, the social aspects of robots hardly seem to matter.

Robot Tutoring Multiplications: Over One-Third Learning Gain for Most, Learning Loss for Some

In the design of educational robots, it seems undecided whether robots should show social behaviors and look human-like or that such cues are indifferent to learning. We conducted an experiment with different designs of social robots, rehearsing the multiplication tables with primary school children in Hong Kong. Results show that affective bonding tendencies may occur but did not significantly contribute to the learning progress of these children, perhaps due to the short interaction period. Nonetheless, 5 minutes of robot tutoring improved their scores with about 30% and only for a few challenged children, performance dropped. We discuss that topics such as teaching language skills may be fostered by human likeness in appearance and behaviors but that for STEM-related subjects, the social aspects of robots hardly matter.

Can We Explain Students’ Failure in Learning Multiplication?

Teaching multiplication is a compulsory topic in elementary education mathematics programs. Much time is dedicated to teaching multiplication tables and algorithms, obtaining mediocre results. Recent investigations in neuroscience suggest that our way of teaching is not congruent with how the brain works and, as such, important changes should be made in teaching of numerical facts and algorithms. Additionally, other kinds of calculation, like mental calculation and calculations with a calculator, have not yet reached the level of importance of their use in education that citizens require in a contemporary society.

A complete classification of three-dimensional algebras over ℝ and ℂ — (visiting old, learn new)

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a completely elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results with those given by mathematicians in the 19th century and this century.

Formation of orthogonal latin squares by index structuring of n-set multiplication tables

Objective. Formation of structurally perfect orthogonal Latin squares by the method of index ordering of the multiplication table elements of n-sets based on the multiplication table. Methods. Orthogonal Latin squares are formed by the method of index structuring of n-set multiplication tables. Results. A method is proposed for constructing structurally perfect orthogonal Latin squares of pairs of indexed finite sets of odd dimension, based on the index ordering of an nxn-array of elements in the multiplication table. A distinctive feature of the proposed method for constructing structurally perfect orthogonal squares from elements of two indexed sets of the same dimension is the use by the authors of the method of permutations of elements of the original nxn-matrix configurations, with the formation of index-ordered or index-structured combinatorial configurations. Conclusion. The use of the method for constructing a family of orthogonal Latin squares for pairs of indexed finite sets of the same odd dimension by the elements forming their multiplication table by the method of index structuring based on the principle of functional dependency of the index values on pairs of set elements and index values on pairs of elements from its environment allows creating a specific class orthogonal configuration, which, in terms of element indices, easily demonstrates their orthogonality.