Mathematical Game Research Articles

Effects of Mathematical Games Strategy on the Achievement of Students in High School Geometry

Mathematical games have become an interesting area in educational research. The study was conducted to determine the effects of games on achievement in geometry. It was done in one of the public high schools in the Division of Nueva Vizcaya, Philippines. Quasi-experimental design, specifically the pretest-posttest control group design was adopted using two intact groups of fourth year students with 39 students each as the subjects of the study. The first group was assigned as the experimental group adopting the mathematical games strategy in teaching while the second group as the control group employing the traditional way of teaching. A 60-item multiple choice teacher-made test was the main instrument in the study. The test provided the scores for the pretest and posttest for the two groups of respondents. The test underwent a series of steps of validation and later on the reliability coefficient was determined at 0.91 using the KR20. The study found that the students who were exposed to mathematical games strategy obtained higher achievement scores compared to students taught using the traditional method. As a result, the researcher recommends the use of mathematical games strategy in presenting and discussing lessons for the purpose of achieving higher grades in Geometry.

Sharing Behaviors in Educational Games: A Framework for EEDU Elements Mathematics Game

Sharing Behaviors in Educational Games: A Framework for EEDU Elements Mathematics Game

New Research and Practice in the Field of Youth and the Media

In this section we present examples of current research projects related to young people and media. Each of these projects uses media to improve the knowledge of the user. There are examples of games to encourage interaction between young people and elders (ChronoLeap) at the same time as providing young people with information about how science and technology have developed. There are games to increase children’s awareness of the environment (Virtual Sprouts and Citizen Science) and interactions with that environment to promote healthy life styles (Virtual Sprouts). Other examples include games to introduce children and young people to science (Educational Game Environments group) and mathematics (Mathematics Games for Children) in stimulating and attractive ways. We also include one example (PlatinuMath) of a game designed to help teachers improve their own awareness of mathematical concepts with the aim of contributing to those teachers’ classroom practice. Finally, we include one instance of recent television research (Rechov Sumsum) demonstrating how media can improve children’s awareness of people with disabilities and provide children with more accurate and positive beliefs about other people. All these are recent or current research programs, and we have included links for those readers who would like to find out more about them.

Design of robust water exchange networks for eco-industrial symbiosis

The field of industrial ecology promotes the establishment of resource exchange networks in eco-industrial parks (EIPs) as an approach toward resource conservation. Previous studies have shown that full blown resource integration can be encouraged through the exchange of common utilities such as energy and water. Different approaches such as mathematical programming, pinch analysis and game theory have been used to identify the optimal network designs, which can simultaneously reduce the utilization of freshwater resources and the generation of wastewater streams. Since water exchange in an EIP involves multiple independently operating plants, information exchange between the participants is not completely transparent and multiple future scenarios are expected to happen as the fate and plans of other participants are not completely divulged. These future scenarios may bring about changes in the capacity or characteristic of industrial processes and may also involve the entry of additional companies and the closure of previously operating ones. Such aspects have not been fully addressed in previous studies. A robust optimization model is thus developed in this work to determine the optimal network design which can effectively operate in anticipation of multiple probable scenarios. Case studies are solved to demonstrate the capability of the model.

When Does Overuse of Antibiotics Become a Tragedy of the Commons?

BackgroundOver-prescribing of antibiotics is considered to result in increased morbidity and mortality from drug-resistant organisms. A resulting common wisdom is that it would be better for society if physicians would restrain their prescription of antibiotics. In this view, self-interest and societal interest are at odds, making antibiotic use a classic “tragedy of the commons”.Methods and FindingsWe developed two mathematical models of transmission of antibiotic resistance, featuring de novo development of resistance and transmission of resistant organisms. We analyzed the decision to prescribe antibiotics as a mathematical game, by analyzing individual incentives and community outcomes.ConclusionsA conflict of interest may indeed result, though not in all cases. Increased use of antibiotics by individuals benefits society under certain circumstances, despite the amplification of drug-resistant strains or organisms. In situations where increased use of antibiotics leads to less favorable outcomes for society, antibiotics may be harmful for the individual as well. For other scenarios, where a conflict between self-interest and society exists, restricting antibody use would benefit society. Thus, a case-by-case assessment of appropriate use of antibiotics may be warranted.

Escola e sociedade de consumidores: um estudo com crianças "catadoras"

O artigo apresenta resultados de uma pesquisa cujo objetivo foi analisar os significados atribuídos à "catação" de resíduos sólidos recicláveis por um grupo de alunos de uma escola municipal de São Leopoldo que tinham sua existência vinculada a essa atividade. O material de pesquisa foi composto por entrevistas, feitas com oito crianças, desencadeadas por seus desenhos e registros em diário de campo. O estudo tem como referencial teórico o pensamento de Michel Foucault, as ideias do "Segundo" Wittgenstein e a obra de Zygmunt Bauman. A análise possibilitou inferir que aquelas crianças: a) participavam da catação, sobretudo, porque desejavam consumir, estando integrados à sociedade de consumo via uma "inclusão diferenciada"; e b) praticavam jogos de linguagem matemáticos que possuíam especificidades, mesmo que guardassem semelhanças de família com aqueles que constituem a matemática escolar.

Using the Elements of Manufacturing Systems Management in the Calculation of the Implementation of a Serial‐Modular Industrial Robot within a Flexible Work Cell Designed for Special Applications

AbstractIn this paper, the authors propose a basic design of a flexible work cell with a parallel organization, destined for the spot welding of AAV carcasses. The cell is serviced by three industrial TTR robots that perform spot welding operations on the carcasses flowing on the conveyor belt to each of the robots performing this operation. This paper presents economic issues on the value of the robots comprised by the system, the calculus of the entire FWC value, the determination of the FWC static configuration, and evaluates the overall profitability of the cell using elements pertaining to the mathematical game theory and the graph theory, as well. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dealing with the Problem of the Differences in Students’ Learning Styles in Physics Education via the Brain Based Teaching Approach

The primary focus of this study was to investigate the impact of games activities in mathematics classes. The study incorporated a pre-post approach that involved surveys to assess students' perceptions of psychosocial features of the learning environment, academic efficacy and students' enjoyment of mathematics lessons. A sample of 90 students from three colleges in the United Arab Emirates participated in the study. After the initial collection of quantitative data, Jeopardy!-type games were introduced to 90 students over a six-week period. The findings suggest that, during exposure to games, students experienced an improvement in the three psychosocial features of the learning environment (teacher support, involvement and personal relevance) and also academic efficacy and enjoyment of mathematics lessons. The results of this study offer potential opportunities for mathematics educators to incorporate the use of mathematical games in the curriculum as a practical way to improve classroom environments and students' attitudes.

The effect of mathematical games on on-task behaviours in the primary classroom

A challenge for primary classroom teachers is to maintain students’ engagement with learning tasks while catering for their diverse needs, capabilities and interests. Multiple pedagogical approaches are employed to promote on-task behaviours in the mathematics classroom. There is a general assumption by educators that games ignite children’s on-task behaviours, but there is little systemically researched empirical data to support this claim. This paper compares students’ on-task behaviours during non-digital game-playing lessons compared with non-game-playing lessons. Six randomly selected grade 5 and 6 students (9–12 year olds) were observed during ten mathematics lessons. A total of 2,100 observations were recorded via an observational schedule and analysed by comparing the percentage of exhibited behaviours. The study found the children spent 93 % of the class-time exhibiting on-task engagement during the game-playing lessons compared with 72 % during the non-game-playing lessons. The game-playing lessons also promoted greater incidents of student talk related to the mathematical task (34 %) compared with the non-game-playing lessons (11 %). These results support the argument that games serve to increase students’ time-on-task in mathematics lessons. Therefore, it is contended that use of games explicitly addressing the mathematical content being taught in a classroom is one way to increase engagement and, in turn, potential for learning.

Gaming Your Mathematics Course: The Theory and Practice of Games for Learning

Learning through play is fundamental to humans and to many other animals. Game Based Learning is an interactive pedagogy that has as its foundation the tenet that games, by their very nature, increase learning through positive emotional experience. This article introduces readers to what games in mathematics classes have the potential to do, including to decrease anxiety, increase motivation, and deepen learning through immersive gaming. The article then connects this theory to practice, providing examples of both computer and non-computer games in introductory middle school, high school and college mathematics. The article analyses how these games work, and makes the distinction between intrinsic games, in which the concept being taught is an integral part of the game, and extrinsic games which can be used for a variety of classes and topics, and tend to be more about review than about learning new concepts.

TESTING THE EFFECTIVENESS OF MATHEMATICAL GAMES AS A PEDAGOGICAL TOOL FOR CHILDREN’S LEARNING

In an effort to engage children in mathematics learning, many primary teachers use mathematical games and activities. Games have been employed for drill and practice, warm-up activities and rewards. The effectiveness of games as a pedagogical tool requires further examination if games are to be employed for the teaching of mathematical concepts. This paper reports research that compared the effectiveness of non-digital games with non-game but engaging activities as pedagogical tools for promoting mathematical learning. In the classrooms that played games, the effects of adding teacher-led whole class discussion was explored. The research was conducted with 10–12-year-old children in eight classrooms in three Australian primary schools, using differing instructional approaches to teach multiplication and division of decimals. A quasi-experimental design with pre-test, post-test and delayed post-test was employed, and the effects of the interventions were measured by the children’s written test performance. Test results indicated lesser gains in learning in game playing situations versus non-game activities and that teacher-led discussions during and following the game playing did not improve children’s learning. The finding that these games did not help children demonstrate a mathematical understanding of concepts under test conditions suggests that educators should carefully consider the application and appropriateness of games before employing them as a vehicle for introducing mathematical concepts.

Teaching modeling skills using a massively multiplayer online mathematics game

One important challenge in mathematics education is teaching modeling skills. We analyze the logs from a game-based learning system used in a massively multiplayer online tournament. Students had to detect an input---output pattern across 20 rounds. For each round, they received an input and had 2 minutes to predict the output by selecting a binary option (2 points if correct, ?1 otherwise), or writing a model (4 points if model prediction was correct, ?4 otherwise), or refraining (1 point). Thousands of 3rd to 10th grade students from hundreds of schools simultaneously played together on the web. We identified different types of players using cluster analysis. From 5th grade onwards, we found a cluster of students that wrote models with correct predictions. Half of the 7th to 10th grade students that detected patterns were able to express them with models. The analysis also shows diffusion within the teams of modeling strategies for simple patterns.

A teachable-agent-based game affording collaboration and competition: evaluating math comprehension and motivation

This paper presents an educational game in mathematics based on an apprenticeship model using a teachable agent, as well as an evaluative study of how the game affects (1) conceptual understanding and (2) attitudes towards mathematics. In addition, we discuss how collaborative and competitive affordances of the game may affect understanding and motivation. 19 students played the game in pairs once a week during math lessons for 7 weeks (the game-playing group) while another 19 students followed the regular curriculum (the control group). Math comprehension scores increased significantly for the game-playing group but not the control group (p < 0.05). However, there was no significant difference in attitude change between the two groups. Post hoc analyses indicated that game-playing primarily affected students’ confidence in explaining math to a peer, but not their enjoyment of doing so. Collaborative and competitive activities seem to carry a strong motivational influence for students to play the game.

EFFECTIVENESS OF USING GAMES IN TERTIARY-LEVEL MATHEMATICS CLASSROOMS

The primary focus of this study was to investigate the effectiveness of games when used in tertiary-level mathematics classes in the United Arab Emirates. Our study incorporated a mixed-method approach that involved surveys (to assess students’ perceptions of the learning environment and attitudes towards mathematics), interviews, observations of classes and narrative stories. A sample of 90 students from 3 tertiary-level institutions in Abu Dhabi participated in the study. In-depth qualitative data provided information about the introduction and use of games in mathematics. A narrative, based on classroom observations of students playing Jeopardy!-type mathematics games, provided insights into games in action in the classrooms. The data were analysed to examine students’ interactions during the games and to triangulate, clarify and explain students’ responses to the learning environment and attitude questionnaires. To examine pre–post differences in students perceptions of the learning environment and their attitudes, 2 questionnaires were administered to students before and after the introduction of games. Pre–post differences for 3 of the 6 learning environment scales (Teacher Support, Involvement, Personal Relevance) and both attitude scales (Enjoyment of Mathematics Lessons and Academic Efficacy scales) were statistically significant. Information obtained from interviews with students and teachers were used to explain the pre–post differences.

Differentially positioned language games: ethnomathematics from a philosophical perspective

This paper discusses a new philosophical perspective for ethnomathematics which articulates Ludwig Wittgenstein’s and Michel Foucault’s theoretical notions. It is conceived as a theoretical toolbox which allows the analysis of, on the one hand, the mathematical language games of different forms of life and their family resemblances and, on the other hand, the Eurocentric discourses of academic and school mathematics and their effects of truth. Based on fieldwork done in rural forms of life in the south of Brazil, examples of the use of this perspective are presented. The paper analyzes language games of those different forms of life and the school mathematics discipline, highlighting the complex network of learning and powers that makes other mathematics than that known as the mathematics be positioned “in a void” in school curricula.

Strategies to Reduce Pathological Fear in Mathematics among Secondary School Students in Adamawa State, Nigeria

The purpose of this study is to identify causes of pathological fear in Mathematics among secondary school students in Adamawa State, Nigeria. The study also examines strategies that could be adopted to reduce pathological fear in Mathematics among students. Three research questions and a hypothesis tested at a = 0.05 level of significant were formulated to guide the study. A research questionnaire on Pathological Fear in Mathematics Questionnaire (PFMATQ) was used in collecting data from 250 senior secondary school students. They were selected by stratified random sampling technique from five educational zones in Adamawa State. Mean, standard deviation and t-test were used to analyses the data generated. The study reveals that causes of pathological fear in Mathematics among others include: parental indoctrination that Mathematics is difficult, the Mathematics teacher factor and the abstract nature of Mathematics. Strategies that could be adopted to reduce pathological fear in Mathematics among others include; the use of mathematical games; uses of heuristic method of teaching and use of relevant set induction techniques. It is recommended that parents should stop indoctrinating their children that Mathematics is difficult; they should keep away their unpleasant experiences about Mathematics and present favorable ones to encourage them to develop interest in Mathematics. Recommendations were outlined.

Toward a deeper understanding of the relationship between interaction constraints and visual isomorphs

Interaction and manual manipulation have been shown in cognitive science literature to play a critical role in problem solving. Given different types of interactions or constraints on interactions, a problem can appear to have different degrees of difficulty. While this relationship between interaction and problem solving has been well studied in the cognitive science literatures, the visual analytics community has yet to exploit this understanding for analytical problem solving. In this paper, we hypothesize that constraints on interactions and constraints encoded in visual representations can lead to strategies of varying effectiveness during problem solving. To test our hypothesis, we conducted a user study in which participants were given different levels of interaction constraints when solving a simple mathematic game called number scrabble. Number scrabble is known to have an optimal visual problem isomorph, and the goal of this study is to learn if and how the participants could derive the isomorph and to analyze the strategies that the participants utilize in solving the problem. Our results indicate that constraints on interactions do affect problem solving, and that although the optimal visual isomorph is difficult to derive, certain interaction constraints can lead to a higher chance of deriving the isomorph.

Assessing the effectiveness of a 3‐D instructional game on improving mathematics achievement and motivation of middle school students

AbstractThis research study assessed the effectiveness of a three‐dimensional mathematics game, DimensionM, through a pretest–posttest control group quasi‐experimental design. Participants consisted of 437 eighth graders. The classrooms were randomly assigned either to the treatment group that utilized DimensionM as a supplement to regular classroom instructions or to the control group that received regular class instructions without any computer activities. The results of the analysis on the pretest–posttest data revealed that the DimensionM game increased mathematical knowledge acquisition in algebra and maintained student motivation to learn. The findings suggest that the implementation of DimensionM in mathematics education can greatly benefit middle school students learning algebra.Practitioner NotesWhat is already known about this topic Evaluations on the effectiveness of instructional games are known in the community of both practitioners and experienced researchers in educational research. What this paper adds This paper specifically added to the literature by evaluating the effectiveness of the novel instructional game, the DimensionM game, on increasing middle school student mathematical knowledge acquisition in algebra and maintaining student motivation to learn. Implications for practice and/or policy The study results suggested that the implementation of DimensionM in mathematics education can benefit middle school students' learning of algebra and can be helpful to maintain their motivation in learning.

Hexaflexagons

SummaryThis is a reprint of Martin Gardner's very first “Mathematical Games” column (which appeared December 1956 in Scientific American). Here Gardner introduces flexagons (paper polygons folded from straight or crooked strips of paper which have the fascinating property of changing their faces when they are “flexed”), discusses their history prior to World War II, and explains how to make several hexaflexagons. The reprint, part of a special issue of The College Mathematics Journal devoted to “Martin Gardner's Mathematics,” is followed by two contemporary papers that describe some of the ways that the study of flexagons has developed since 1956. Susan Goldstine and Ethan Berkhove provided vital assistance editing all three flexagon papers.

The Secretary Problem from the Applicant's Point of View

SummaryA 1960 “Mathematical Games” column describes the problem, now known as the Secretary Problem, which asks how someone interviewing candidates for a position should maximize the chance of hiring the best applicant. This note looks at how an applicant should respond, if they know the interviewer uses this optimal strategy. We show that all but the very top applicants have the best chance of being hired if they arrange to be the last person interviewed.