This study aims to improve the effectiveness of English grammar teaching in high school. Firstly, the Science, Technology, Engineering, Art, and Mathematics (STEAM) educational model is comprehensively discussed. Then, the current situation and difficulties of English grammar teaching in high school are analyzed. Finally, based on the traditional and the STEAM teaching mode, a comprehensive study on the psychological motivation of students is carried out in high school English grammar teaching. The traditional teaching model (...) had little effect on students’ psychological motivation in the process of English grammar teaching. Therefore, students’ satisfaction with English grammar teaching under the traditional teaching model is very low, especially in innovation and practice. The STEAM teaching model has greatly improved the psychological motivation of high school students in the English grammar teaching process. The overall satisfaction rate of the students with the English grammar teaching in the STEAM teaching model is 70%. This teaching model can greatly improve students’ requirements for innovation and practice. This study not only provides a reference for the improvement of English teaching in high schools but also contributes to the reform and development of education. (shrink)

This book tells a single story, in many voices, about a serious and sustained set of changes in mathematics teaching practice in a high school and how those efforts influenced and were influenced by a local university. It includes the writings and perspectives of high school students, high school teachers, preservice teacher candidates, doctoral students in mathematics education and other fields, mathematics teacher educators, and other education faculty. As a whole, this case study provides (...) an opportunity to reflect on reform visions of mathematics for all students and the challenges inherent in the implementation of these visions in US schools. It challenges us to rethink boundaries between theory and practice and the relative roles of teachers and university faculty in educational endeavors. (shrink)

ObjectivesUnder the COVID-19 prevention and control policy, online learning has been widely used. The current study aimed to identify latent profiles of self-regulated learning in the context of online mathematics learning during the recurrent outbreak of COVID-19, and examine the mechanisms underlying the relationship between self-regulated learning and online mathematics learning engagement among Chinese junior high school students using variable-and person-centered approaches.MethodsA sample of 428 Chinese junior high school students completed questionnaires on self-regulated learning, perceived academic (...) control, and learning engagement. Mplus7.0 was used to analyze the latent classes of self-regulated learning. A mediation model was conducted using the software SPSS PROCESS macro.ResultsThree profiles of self-regulated learning were identified and named as low self-regulated learning, medium self-regulated learning, and high self-regulated learning. In the mediating analysis, results of the variable-centered approach showed that perceived academic control mediated the effects of self-regulated learning on learning engagement. For the person-centered approach, we selected the low self-regulated learning type as the reference profile, and the analysis revealed that compared with the reference profile, perceived academic control partially mediated the link between the medium self-regulated learning profile and learning engagement; perceived academic control partially mediated the relationship between the high self-regulated learning profile and learning engagement.ConclusionThis study showed the heterogeneity in the online mathematics self-regulated learning patterns of Chinese junior high school students during the COVID-19 pandemic, revealing the internal mechanisms of Chinese junior high school students’ online mathematics learning engagement using variable-and person-centered approaches. Furthermore, the findings of the study have important implications for promoting online mathematics learning engagement among junior high students during the pandemic. (shrink)

This study explored and compared the perspectives of Taiwanese in-service and pre-service high school mathematics teachers regarding ideal teaching behaviours; the perspectives of a nationwide sample of students were taken as the baseline. Fourteen factors contributing to ideal teaching behaviours were identified through exploratory factor analyses. Nine factors, including idea explanation and speedy lecture, were rooted in traditional Chinese culture; five factors, including concrete representation and student activities, were influenced by Western cultures. Three teacher profiles were identified through (...) k-means clustering analysis. The perspectives of in-service teachers were dominated by a painless meaning-emphasised profile; these teachers emphasised meaningful learning for students and avoided the fast pace and demanding requirements that can cause distress in students, whereas pre-service teachers were dominated by an all-round profile, revealing their openness to all factors. Compared with... (shrink)

Many high schools offer students the opportunity to take advanced placement (AP) courses in many subjects including science and mathematics. Studies have shown that students who take these classes are more likely to succeed in college and that failure in engineering education is strongly correlated to deficiencies in mathematics and science. This article presents the background of AP classes and their impact on science, technology, engineering, and mathematics (STEM) career choices of college students. The results of this study confirm (...) that students who take AP classes in calculus and the sciences are more likely to select majors in careers such as engineering, science, mathematics, and the medical field. In this study, both minority and nonminority students who were taking AP calculus and/or science courses in high school selected STEM careers at a higher rate than other careers and males selected engineering at a higher rate than females. Females selected science and mathematics and the medical field at a higher rate than males. Furthermore, the size and location of the high school, profession of parents, and socioeconomic level of parents all affect the number of AP classes offered in high schools as well as which ethnic groups primarily take them. (shrink)

This study developed an instrument that measures the attitude of Filipino high school students towards mathematics, with reliable predictors and factors. Using the responses of 300 high school students from Zamboanga Sibugay, the validity and reliability of the Mathematics Attitude Scale (MAS) was tested using Exploratory Factor Analysis (EFA) and reliability analyses. The EFA showed that four-factor structures of the instrument, regarding the mathematics attitude for high school students, explained 27.48% of the variance in (...) the pattern of relationships among the items. The Average Variance Extracted (AVE), Composite Reliability, and Cronbach’s Alpha coefficients were reported. They proved that the extracted constructs have obtained and satisfied convergent validity. Thirty-three items remained in the final questionnaire after deleting the twenty-seven items with factor loadings of less than 0.4 (Students’ Perceived Motivation and Support in Learning Mathematics: twelve items; Students’ Perceived Anxiety in Learning Mathematics: ten items; Students’ Perceived Self-Efficacy in Learning Mathematics: six items; and Teachers and Parents’ Influences to Students in Learning Mathematics: five items). This study has confirmed the four-factor structure of the MAS. Educators and researchers can use the MAS to better understand the attitudes of Filipino high school students towards mathematics. (shrink)

This article reports pretest and posttest results of the infusion of engineering principles and design into an existing ninth-grade integrated science class. The results indicated that more knowledge of engineering makes attitudes of high school students more favorable toward engineering. The results of infusing engineering topics into an existing science curriculum were also compared with an earlier study of a formal 3-week engineering unit taught to ninth-grade students in another high school. The results of that comparison (...) indicated that a formal unit on engineering was more successful in improving student attitudes toward engineering than the infusion of engineering topics into an existing science unit. The article also presents information on a capstone engineering course for preservice and in-service science and mathematics teachers. That course was designed with collaboration from the colleges of engineering and education with the goal of increasing the interest of high school students in careers in engineering. (shrink)

ObjectiveTo investigate the reciprocal relationship between high school students’ academic self-efficacy and achievement in mathematics using US data from the HSLS:2009 and first follow-up longitudinal surveys, while accounting for biases in effect estimates due to unobserved heterogeneity.MethodsInstrumental Variables regressions were estimated, to derive causal effect estimates of earlier math self-efficacy on later math achievement and vice versa. Particular attention was paid to testing the validity of instruments used. Models were estimated separately by gender, to uncover gender differences in (...) effects.ResultsEvidence of robust reciprocal effects between self-efficacy and achievement for male students is presented, with the dominant effect from earlier achievement to later self-efficacy. For girls, evidence of such effects is weak. Generally, IV estimates are higher than OLS estimates for males, but not for females. As opposed to earlier correlational studies which did not find significant gender differences despite theoretical expectations for their existence, the findings support higher effects for male students. (shrink)

This study aims to find out how high the level and trends of student misconceptions experienced by high school students in Indonesia. The subject of research that is a class XI student of Natural Science (IPA) SMA Negeri 1 Anjatan with the subject matter limit function. Forms of research used in this study is a qualitative research, with a strategy that is descriptive qualitative research. The data analysis focused on the results of the students' answers on the (...) test essay subject matter limit function with the number of students by 16 (sixteen). Data collection techniques used are shaped test methods essay, interview method to students who have misconceptions, and methods of documentation of the test answers. Examination of the validity of the data using a triangulation technique that compares the data written test results with data from interviews. The results of this study can be described as follows; (1) The level of misconceptions experienced by students belonging to the category of low, amounting to 12.18%. However, students who do not understand the concept quite high at 40.38%, and the others are students who understand the concept that is equal to 47.44%. (2) The misconception most experienced students lie in subconcepts explain the meaning of limit function at one point through the calculation of values around that point, that is equal to 20.51%. The tendency misconceptions experienced by students is located on errors and operating concepts that misconceptions students that there should be no limit in the completion of the writing of the emblem and misconceptions about the limit students to conclude if the limit value of 0 is no limit to the value of the function. (shrink)

ABSTRACTThis study aimed to investigate the association of locus of control with reading and mathematics achievement of high school students with disabilities using data from the Special Educ...

Reviewed Works:Reuben Hersh, Proving is Convincing and Explaining.Philip J. Davis, Visual Theorems.Gila Hanna, H. Niels Jahnke, Proof and Application.Daniel Chazan, High School Geometry Students' Justification for Their Views of Empirical Evidence and Mathematical Proof.

Albinism in Tanzania causes fierce health-related stigma. Little research has focused on the impact of stigma reduction strategies aiming to reduce albinism related stigma. Therefore, this research assessed the impact of two short video interventions among high school students in Tanzania on their attitude towards people with albinism: a contact intervention (n = 95) and an education intervention (n = 97). A mixed method design was used. Directly before and after the interventions impact was measured among all participants (...) through the Albinism Social Distance Scale for Adolescents (ASDS-A), knowledge items, and entertainment items. After these measurements focus group discussions were conducted, 16 in total (n = 80). Both interventions caused a significant increase in the levels of correct knowledge about albinism. The education intervention entailed a significant positive change in attitude measured through the ASDS-A, whereas the contact intervention did not have a significant effect. In terms of entertainment value, the respondents were more enthusiastic about the contact intervention. The study suggests that education interventions on their own can be a successful tool in decreasing albinism related stigma. Additionally, qualitative findings show many positive outcomes for the contact intervention. Therefore, we would recommend using a combination of these two interventions, which has also proved successful in the past. However, more research on the effect of a combination of the two strategies is recommended. (shrink)

The aim of the present study was to further examine the impact over time of single‐sex and coeducational school environments on girls’ motivation in language arts and mathematics. Two cohorts comprising 340 girls from eight coeducational and two single‐sex schools were followed during a period of three academic years in a longitudinal research scheme. Data were collected with a self‐reported questionnaire including several scales: parental and teachers’ support, competence beliefs, utility‐value and achievement goals. In general, mixed‐design repeated measures analyses (...) of variance indicated no effect of the environment or of the interaction between environment and time of measurement. Significant time effects on several variables indicated a general decline of achievement motivation over time. Consequently, the multiplication of non‐mixed high schools, as proposed by some, would constitute an expensive and inefficient social policy, as far as girls’ motivation is concerned. (shrink)

This study reports the results of a survey of 405 high school students in a school district in the western United States. The data were used to determine why so many students take only the minimal science required for graduation. Key areas addressed included how science is taught; science literacy; science, technology, engineering and mathematics (STEM); science, technology, and society (STS); and who influences students to take science. Results were directed at how to motivate more students to (...) continue science study beyond the required courses and how to improve the prospect of more students choosing STEM majors in higher education. Key conclusions included that no new science courses are needed to increase enrollments, but existing courses need to be taught differently, specifically with more labs and activities that create more interest and relevance for students. Furthermore, students need more awareness of good reasons for taking science. Last, science instruction must improve. (shrink)

In the first centenary of Cantor's death, we discuss how to introduce his life, his works and his theories about mathematical infinity to today's students. Keywords: proper and improper infinite, cardinal number, countable set, continuum, continuum hypothesis. Sunto Nel primo centenario della scomparsa di Cantor, si discute come presentare la sua vita, le sue opere e le sue teorie sull’infinito agli studenti di oggi. Parole chiave: infinito proprio e improprio, numero cardinale, numerabile, continuo, ipotesi del continuo.

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e., sequent) isomorphisms corresponding to the high‐school identities, we show that one can obtain a more compact variant of a proof system, consisting of non‐invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalization procedure. (...) Moreover, for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non‐invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first‐order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism. (shrink)

As part of the laboratory activities designed for the students of the second year of the Mathematical High School by the research group in Mathematics Education of the Department of Mathematics of the University of Salerno, the theme “From Archimedes and the oxen problem to Pell’s equation” has been designed. The course has not yet been delivered to students and in this paper the didactic path to be developed in the classroom will be described. The students initially (...) will retrace the various solution approaches proposed over the centuries. Subsequently, with a heuristic approach, they will tackle the resolution of the proposed problem by exploiting properties related to the theory of numbers. With the help of some schedules, provided by the teachers-tutors, they will conjecture and argue by answering questions aimed at stimulating didactic reflection. This workshop path involves processes such as exploring and conjecturing through the articulation of different ways of working (individual and in groups), manual and digital. (shrink)

The purpose of the present study was to investigate the effect and use of distributed practice in the context of self-regulated mathematical learning in high school. With distributed practice, a fixed learning duration is spread over several sessions, whereas with massed practice, the same time is spent learning in one session. Distributed practice has been proven to be an effective tool for improving long-term retention of verbal material and simple procedural knowledge in mathematics, at least when the (...) practice schedule is externally guided. In the present study, distributed practice was investigated in a context that required a higher degree of self-regulation. In total, 158 secondary school students were invited to participate. After motivational and cognitive characteristics of the students were assessed, the students were introduced to basic statistics, a topic of their regular curriculum. At the end of the introduction, the students could sign up for the study to further practice this content. Eighty-seven students did so and were randomly assigned either to the distributed or to the massed practice condition. In the distributed practice condition, they received three practice sets on three different days. In the massed practice condition, they received the same three sets, but all on one day. All exercises were worked in the context of self-regulated learning at home. Performance was tested two weeks after the last practice set. Only 44 students finished the study, which hampered the analysis of the effect of distributed practice. The characteristics of the students who completed the exercises were analyzed exploratory: The proportion of students who finished all exercises was significantly higher in the massed than in the distributed practice condition. Within the distributed practice condition, a significantly larger proportion of female students completed the exercises compared to male students. Additionally, among these female students, a larger proportion showed lower concentration difficulty. No such differential effects were revealed in the massed practice condition. Our results suggest that the use of distributed practice in the context of self-regulated learning might depend on learner characteristics. Accordingly, distributed practice might obtain more reliable effects in more externally guided learning contexts. (shrink)

Statistics and probability enabled students to better understand, process, and evaluate massive amounts of quantitative data that existed and had a probabilistic sense in uncertain situations. The research article aimed to elucidate the performance and self-efficacy as predictors of students' achievement in the statistics and probability courses. The study utilized a descriptive-predictive research method and was conducted at Sto. Tomas National High School, involving a sample of 263 grade 11 senior high school students. The gathered data (...) were analyzed using descriptive measures and multiple regression analysis. The study's results revealed that the performance in General Mathematics was very satisfactory, while self-efficacy was high. Moreover, the level of achievement in Statistics and Probability was very satisfactory. It was also revealed that both General Mathematics performance and self-efficacy had a positive and significant relationship with Statistics and Probability achievement. Through regression analysis, it was discovered that General Mathematics performance was the strongest predictor that influenced achievement in Statistics and Probability. The study identified a significant predictive model for Statistics and Probability achievement. These findings could provide valuable guidance to teachers in enhancing the achievement of senior high school students in Statistics and Probability. (shrink)

Autonomous learning capacity is a key competency that supports teachers’ professional development. In this study, a stratified sampling method was used to recruit 396 junior and senior high school mathematics teachers in T city, one of the provincial city in China. A questionnaire with high reliability and validity developed prior to the study by the researchers was employed to measure their autonomous learning capacity and differences across groups. Twelve teachers were then selected for interviews. The results showed (...) satisfactory overall performance. By subdimension, teachers’ performance was the best in the development of study plans, followed by evaluation of learning outcomes, while they needed improvement in learning habit formation and proficiency in using learning methods. Furthermore, the analysis of differences across groups indicated that for autonomous learning capacity, female teachers were significantly better than their male peers; junior high school teachers were better compared to those in senior high school; teachers aged 41–50 underperformed those aged 51 and above; teachers who work in rural areas and townships did not perform worse than urban teachers; and those with doctoral degrees did not demonstrate considerable advantage over others. There were no significant differences in the overall autonomous learning capacity across years of teaching and job title groups. However, in the subdimensions, those with 21–30 years of teaching experience had lower proficiency in using learning methods and evaluation of learning outcomes, and teachers with senior titles did not demonstrate expected advantages in learning habit formation. (shrink)

The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students . The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying (...) methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving. (shrink)

One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of (...) class='Hi'>mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

This is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material. This textbook is essential reading (...) for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school. (shrink)

Stimulating, thought-provoking analysis of a number of the most interesting intellectual inconsistencies in mathematics, physics and language. Delightful elucidations of methods for misunderstanding the real world of experiment (Aristotle’s Circle paradox), being led astray by algebra (De Morgan’s paradox) and other mind-benders. Some high school algebra and geometry is assumed; any other math needed is developed in text. Reprint of 1982 ed.

Grasha–Riechmann Teaching Styles have a high potential to be applied in Mathematics especially to help increase teacher educators’ knowledge. However, very little attention has been paid to the study of identifying the teaching style patterns of Mathematics teachers at the primary school National-Type Chinese Primary Schools or Sekolah Jenis Kebangsaan Cina SJKC. There is increasing concern about how this teaching style related to the teaching experience. This study aims to identify the patterns of Grasha–Riechmann Teaching Styles among primary (...) school Mathematics teachers and the relationship between Grasha–Riechmann Teaching Styles with teaching experience. The quantitative approach through a survey was applied to 97 Mathematics teachers of SJKC Kepong, Kuala Lumpur using the simple random sampling method. The instrument was adapted from the Grasha–Riechmann Teaching Styles Questionnaire, which measures five teaching styles such as Personal Model Teaching Style, Expert Teaching Style, Formal Authority Teaching Style, Delegator Teaching Style, and Facilitator Teaching Style. The patterns showed that the Personal Model Teaching Style is the most dominant, and the Facilitator Teaching as the least dominant style. The Spearman’s Rho Correlation also reported a very weak significant correlation between Grasha–Riechmann Teaching Styles with the teachers’ Mathematics teaching experience, specifically for Expert, Formal Authority, and Facilitator Teaching Styles. The study provides practical implications for educators’ professional development to diversify the training of teachers by experience and adapt them to the needs of student learning in primary school. These findings trigger ideas to get a better understanding by other demographic variables such as gender, age, and complexity of Mathematics subject. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy in the School Music ProgramBennett ReimerWho is philosophy of music education for? Several groups of people immediately spring to mind. First, it is for those of us in music education who produce it and consume it as a major or important responsibility in our work—people like members of our Special Research Interest Group at MENC. Second, teachers of music education courses at the undergraduate and graduate levels (...) who deal with it either in a full course or series of courses or seminars devoted to philosophy, or as one part of courses devoted to other topics (as I believe is most often the case.) Third, school music teachers, many of whom have taken or are taking such courses (and many who have not) who are expected to have some level of acquaintance, however rudimentary, with philosophical issues so as to be able to cope with them, as when writing curriculum guides, or explaining to other teachers, administrators, school boards, and parents why music education is valuable and deserves support. If we stretch it, we might include among those who need to be involved with philosophy of music and music education all educational professionals, since all, in one way or another, exert some sort of influence on the fortunes of music education. But that begins to strain a bit at the edges.No doubt there are other constituencies that can be identified. But one that has not been conceived as requiring substantive encounters with philosophical issues of music is that of students in schools, K-12. We all assume that philosophy can and should play a major role in determining what is most valuable for students to learn in their study of music. But seldom has it been argued, to my [End Page 132] knowledge, that philosophical issues should be addressed in all programs of music education intended to produce people who are, in any convincing sense, musically educated.My premise is that philosophical reflection relating to music and to the teaching and learning of music should be foundational in school music programs. Further, philosophy needs to be present in our programs in three distinctive ways, reflecting common practices of education in America and all over the world. That is, as integral in the general music education of all students, as a component of all elective offerings, and as one particular, focused offering among the electives available to all students.My position is that what we call "general music" (which, as we know, goes by a variety of names around the world including just "music") is not complete; in fact is invalid, if it does not provide philosophical challenges of the same level of complexity, and the same degree of authenticity, as everything else we believe all students should know and be able to do in music. What we call the "music elective program," or the "music specialization program," is incomplete, in fact is invalid, if philosophical matters are not addressed as they relate to the particularities of each elective offered. And, in addition, philosophy needs to be a standard elective offering, taught with the same level of expertise by specialist teachers as we now routinely make available in performance and in the meager smattering of other electives we manage to offer.What? Philosophical thinking for all children, even in the primary grades, and as electives starting perhaps at the middle school or high school level? Electives taught by music educators whose specialization is the teaching of philosophy of music to youngsters? Am I serious? After all, even those of us who are devoted to it as a major aspect of our professionalism are constantly at the edges of our competence given the deep challenges philosophy presents to our intellect. And I expect children—all children—to be able to deal with it authentically?Well, we could ask precisely the same questions about, say, mathematics, and science, and history, and social studies, all the ways of thinking which constitute the basic learnings in all grades of our schools. As educators we know better than to conceive the nature of those subjects as only apparent at the level of professional work in them. We recognize the obvious: while at... (shrink)

It has become a fact that fluency and competency in utilizing the advancement of technology, specifically the computer and the internet is one way that could help in facilitating learning in mathematics. This study investigated the effects of Dynamic Geometry Software (DGS) and Computer Algebra Systems (CAS) in teaching Mathematics. This was conducted in Zamboanga del Sur National High School (ZSNHS) during the third grading period of the school year 2015-2016. The study compared the achievement and attitude (...) towards Mathematics between those students taught with DGS and CAS and those students who were taught without DGS and CAS. A quasi-experimental pretest-posttest control group design was used with two groups which was matched according to their mathematical level. An achievement test was developed and administered to assess the students’ achievement in Mathematics. Aiken’s attitude scale was also used to assess the students’ attitude towards Mathematics. The data were treated with One-Way Analysis of Covariance (ANCOVA) and t-test at 0.05 level of significance. The study revealed a significant difference between the mathematics achievement between students taught with DGS and CAS and those who were taught without it. The integration of DGS and CAS in Mathematics lessons leads to better academic achievement result compared with that of the conventional method of teaching. Moreover, there was no significant difference on the attitude level of the students between the two groups. (shrink)

Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory. An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability (...) of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills. All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers. As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book. (shrink)

Microgames are rapidly gaining increased attention and are highly being considered because of the technology-based media that enhances students’ learning interests and educational activities. Therefore, this study aims to develop a new construct through confirmatory factor analysis, to comprehensively understand the factors influencing the use of microgames in mathematics class. Participants of the study were the secondary school teachers in West Java, Indonesia, which had a 1-year training in microgames development. We applied a quantitative approach to collect the data (...) via online questionnaires through google form. Structural Equation Modelling with AMOS software was used to analyze the proposed model. Empirical results confirmed the perceived easy to use and subjective norm influence relationship with teachers’ microgame usage behaviors and intentions. In this condition, SN was found to have the initial significant influence on behavioral intention, as attitude, BI, and facilitating conditions also correlated with the actual use of microgames. Furthermore, the largest influential factor was BI, with the results subsequently showing that TPACK had no significant influence on the actual use of microgames. This report is expected to help bridge the gap across several previous studies, as well as contribute to the explanation and prediction of the factors influencing the teachers’ mathematical utilization of the study’s program. Besides this, it also helps to increase the use of microgames in teaching and learning activities. (shrink)

The present research investigates gender gaps in the results of secondary school exit exams in mathematics in Poland in 2015. The analysis shows that, in the basic level exam, males are highly overrepresented at the upper end of the score distribution. The same pattern did not exist in the extended-level Matura. Two explanations are offered here. The differences are driven by gender self-selection in high school programs. Students who decide on maths-related tracks have more maths lessons than (...) other students. Secondly, a student who takes the extended Matura also has to take the basic Matura exam. As a result, the population of students taking the basic Matura is highly differentiated in terms of maths competence and motivation. Additionally, the analysis of differential item functioning shows that only a few items were flagged as having DIF. (shrink)

This book provides an overview of behavioral decision theory and related research findings. In brief, behavioral decision theory is a general term for descriptive theories to explain the psychological knowledge related to decision-making behavior. It is called a theory, but actually it is a combination of various psychological theories, for which no axiomatic systems, such as the utility theory widely used in economics, have been established; it is often limited to qualitative knowledge. However, as suggested in the studies of H. (...) A. Simon, who won the Nobel Prize for Economics in 1978, and D. Kahneman, who won the prize in 2002, the psychological methodology and knowledge of behavioral decision theory have been applied widely in such fields as economics, business administration, and engineering, and are expected to become more useful in the future. This book explains various behavioral decision theories related to decision-making processes. Numerous models have been proposed to explain the psychological processes related to such a selection of decision strategies, and this book also introduces some new models that are useful to explain decision-making processes. The book concludes with speculation about the future of modern behavioral decision theories while referring to their relation to fields associated with neuroscience, such as neuroeconomics, that have been developed in recent years. In addition, each chapter includes a bibliography that can be referred to when studying more details related to behavioral decision theory. Reading this book requires no advanced expertise; nonetheless, an introductory knowledge of psychology, business administration, and economics, and approximately a high school graduate’s level of mathematics should facilitate the reader’s comprehension of the content. (shrink)

This book discusses in dialogue form the basic principles of mathematics and its applications including the question: What is mathematics? What does its specific method consist of? What is its relation to the sciences and humanities? What can it offer to specialists in different fields? How can it be applied in practice and in discovering the laws of nature? Dramatized by the dialogue form and shown in the historical movements in which they originated, these questions are discussed in their full (...) complexity, yet are easily comprehended. The first dialogue, whose chief actor is Socrates, leads the reader to the source of modern mathematics in Athens in the 5th Century BC. The second dialogue, featuring Archimedes, takes place during the siege of Syracuse in 212 BC and shows the birth of applied mathematics. The third dialogue occurs in the year 1633 in Rome, its chief character being Galileo Galilei who fully realized the central importance of the mathematical method in discovering the laws of nature. Intended as supplemental reading for philosophy of mathematics courses at the high school or college level it will be of interest to both specialists and non-specialists in mathematics. Alfréd Rényi was born in Budapest Hungary in 1921. He studied mathematics and physics at the University of Budapest and received his Ph. D. from the University of Szaged in 1945. Since 1950 he has been Director of the Mathematical Research Institute of the Hungarian Academy of Sciences and since 1952 a professor at the University of Budapest. Dr. Renyi was a visiting professor at Michigan State University in 1961, at the University of Michigan in 1964 and at Stanford University in 1966. His main fields of research are probability theory, mathematical statistics and information theory, and he has also worked in analytic number theory as well as in various branches of analysis, combinatorial analysis and geometry. (shrink)

Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has (...) become the enabling science behind the complexity of contemporary knowledge, from gene interpretation to bank risk. Mathematical understanding is all the more necessary for future jobs, as well as remaining, as ever, a prophylactic against the more corrosive philosophical views emanating from the humanities. (shrink)

Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and the imagination, it profiles the development of logic from ancient to modern times and compellingly examines the nature of logic and its philosophical implications. No prior knowledge of logic is necessary; readers need only an acquaintance with high school mathematics. The author emphasizes understanding, rather than technique, and focuses on such topics as the (...) historical reasons for the formation of Aristotelian logic, the rise of mathematical logic after more than 2,000 years of traditional logic, the nature of the formal axiomatic method and the reasons for its use, and the main results of metatheory and their philosophic import. The treatment of the Gödel metatheorems is especially detailed and clear, and answers to the problems appear at the end. (shrink)

The Trends in International Mathematics and Science Study shows that US school students have a lower level of achievement than students from many East Asian countries. Therefore, media, researchers and policy‐makers in the United States have often argued that US competitiveness in mathematics and science will decline. This paper aims at verifying this conclusion by analysing data on medallists at the International Olympiads for high school students. The analysis suggests that US competitiveness may not be endangered.

This study aimed to investigate the longitudinal trends in mathematical competencies of Grade 8 students in a public high school located in Zamboanga del Sur, Philippines. The study collected data over a period of six academic years, allowing for a comprehensive analysis of students' performance in 16 distinct mathematical competences of basic education curriculum. These topics include, but are not limited to, special products and factors, factoring, and basic concepts of probability. Using a quantitative research design, (...) the study analyzed both numerical and secondary data to identify patterns or trends in students' mathematical competencies. Trends were analyzed through regression analysis using slopes. The significance of these trends was then evaluated using t-tests for the standard error of slopes. The statistical analysis revealed significant upward trends in certain mathematical topics, indicating an improvement in the students' competencies over the six academic years. However, certain topics displayed downward or stable trends, indicating areas for improvement in the teaching methods used for these topics. The study highlights the importance of flexible and adaptable approaches to mathematics education. It emphasizes the need for constant evaluation and improvement of teaching methods to enhance student learning outcomes. The findings of this study provide valuable insights for educators and policymakers to guide evidence-based decision-making and improve the quality of mathematics education in the new normal setup. Implications and future research directions are incorporated in the study. (shrink)

The article describes a capstone engineering course for preservice and inservice secondary science and mathematics teachers and shows teacher attitudes toward engineering before and after the course and results of a comparison with a convenience sample. It also gives the results of the attitudes of high school student experimental and control groups toward engineering in a pretest-posttest design. Four findings were made: (a) The science and mathematics preservice and inservice teacher attitudes toward engineering became more favorable after the (...) capstone course; (b) the attitudes of the convenience sample of secondary graduate students were less favorable toward engineering than they were among the treatment group in the capstone course; (c) the attitudes of the experimental group of high school students became significantly more favorable toward engineering after a 3-week unit on engineering; and (d) the attitudes of the experimental group became significantly more favorable toward engineering than did those of the control group after the 3-week unit. (shrink)

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body‐based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the cognitive relevance of particular body states to associated math concepts. We test competing models of action‐cognition transduction to investigate the cognitive relevance of directed actions to students’ mathematical reasoning in the area of geometry. The hypotheses we test include (1) that cognitively relevant directed actions have a (...) direct effect on performance (direct cognitive relevance hypothesis), (2) that cognitively relevant directed actions lead to more frequent production of gestures during explanations, which leads to improved performance (mediated cognitive relevance hypothesis), and (3) that performance effects of directed actions are influenced by the presence or absence of gesture production during mathematical explanations (moderated cognitive relevance hypothesis). We explore these hypotheses in an experiment where high school students (N = 85) evaluated the truth of geometry conjectures after performing cognitively relevant or cognitively irrelevant directed actions while playing a movement‐based video game. Contrary to the direct and mediated cognitive relevance hypotheses, we found no overall differences in performance or gesture production between relevant and irrelevant conditions. Consistent with the moderated cognitive relevance hypothesis, cognitive relevance influenced mathematical performance, as measured by the accuracy of students’ intuitions, insights, and the validity of their proofs, provided that students produced certain kinds of gestures during mathematical explanations (i.e., with explanatory gestures as the moderator). Implications for theories of grounded and embodied cognition and the design of embodied forms of educational interventions are discussed. (shrink)

The present study explores the application of advanced statistical techniques to predict the academic performance of students in the area of mathematics. Through the use of logistic regression models, decision trees, and neural networks, data from 500 high school students in public institutions were analyzed. The results show that advanced statistical techniques allow a more accurate prediction of academic performance, with a success rate of 87% in neural network models. These findings suggest that the integration of these tools (...) can facilitate the early identification of students at risk of low achievement and improve educational interventions. (shrink)

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. (...) The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community. (shrink)

These are notes designed to bring the beginning student of the philosophy of quantum mechanics 'up to scratch' on the mathematical background needed to understand elementary finite-dimensional quantum theory. There are just three chapters: Ch. 1 'Vector Spaces'; Ch. 2 'Inner Product Spaces'; and Ch. 3 'Operators on Finite-Dimensional Complex Inner Product Spaces'. The notes are entirely self-contained and presuppose knowledge of only high school level algebra.

When I was a teenager growing up in Los Angeles in the early 1940s, my dream was to become a mathematical physicist: I was fascinated by the ideas of relativity theory and quantum mechanics, and I read popular expositions which, in those days, besides Einstein’s The Meaning of Relativity, was limited to books by the likes of Arthur S. Eddington and James Jeans. I breezed through the high-school mathematics courses (calculus was not then on offer, and my (...) teachers barely understood it), but did less well in physics, which I should have taken as a reality check. On the philosophical side I read a mixed bag of Bertrand Russell, John Dewey and Alfred Korzybski (the missionary for “General Semantics” in Science and Sanity, a mish-mash of the theory of types, non-. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created devoted to (...) "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirme to be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

The aim of the present study was to conduct an analysis of TIMSS (Trends in International Mathematics and Science Study) 2003 database and to determine how negative school factors, such as aggression, are associated to the mathematical and science achievement of students. The analyses were conducted separately for national and international data. National analyses for Slovenia show significant associations between math and science achievement and the experience of aggressive behaviour. Students who experienced aggressive behaviour scored lower in math (...) and science, both in the fourth and in the eighth grade. The results of the regression analysis show that negative factors, such as aggressive behaviour, are good predictors of educational achievement in Slovenia. International analyses for the selected countries (high? and low?achieving countries from the whole TIMSS population) confirm that this type of finding is culturally impartial as well as valid for the level of achievement both in math and in science. (shrink)

ABSTRACT As a culture-specific phenomenon, academic dishonesty remains an under-researched domain. The purpose of this study was to voice teachers’ perceptions of: the influential factors contributing to AD, the consequences of AD for the quality of teacher–student relationships, and the specific strategies for regulating TSR. Using a qualitative phenomenological design, we attempted to present a detailed description of teachers’ lived experiences regarding the above aims. The participants were English language and Mathematics teachers with different personal and professional characteristics working in (...) public high schools of Iran. Data was collected through intensive semi-structured interviewing and analyzed by a five-step approach applied to phenomenology in psychological research. Data analysis revealed three general themes regarding teachers’ perceptions with several components. We found that the lack of attention and intrinsic motivation were the prominent perceived factors with consequences for TSR. Also, personal talk and active supervision were the common techniques that teachers utilized with students who commit AD to manage and control the TSR quality. The results were discussed with reference to teachers’ academic discipline, gender, and teaching experience. (shrink)

Because Bertrand Russell adopted much of the logical symbolism of Peano, because Russell always had a high regard for the great Italian mathematician, and because Russell held the logicist thesis so strongly, many English-speaking mathematicians have been led to classify Peano as a logicist, or at least as a forerunner of the logicist school. An attempt is made here to deny this by showing that Peano's primary interest was in axiomatics, that he never used the mathematical logic (...) developed by him for the reduction of mathematical concepts to logical concepts, and that, instead, he denied the validity of such a reduction. (shrink)