Higher Levels Of Mathematics Research Articles

Students’ Perception of Declining Learner’s Enrollment in Mathematics : A Context of Universities in Nepal

The students' perception of declining learner enrollment at higher levels of mathematics is one of the significant factors to deal with them successfully. Therefore, this study aims to investigate the bachelor second-year students' perception of difficulty in subject matters, the attitude of teachers, the efficiency of subject matters and teaching methodology, the application of mathematics, and existing exam patterns. This investigation is based on the survey research design consisting of 198 respondents of mathematics of second-year students that includes 108 male and 90 female students from different colleges in Pokhara valley. A five-point Likert- scale survey questionnaire, related to independent variables was prepared with 22 structured questions and administered by the researcher to the students. This study used a descriptive research design, where the data were collected and analyzed. The finding of this study concludes that declining student enrollment in higher levels in mathematics was significantly positively correlated with the difficulty in subject matters, attitude of faculty members, efficiency in subject matters, application of mathematics, and existing exam patterns. The study also revealed that most learners positively believe that mathematics was relevant to further studies as it supported to the development of the creative, imaginative, logical, and constructive skills of learners. However, most of the respondents realized that mathematics educators did not support the weakness of learners' problems properly, and most teachers had insufficient skills to connect mathematics knowledge to learners' real lives.

Insider accounts of dyslexia from research mathematicians

Within educational research, dyslexia and other disabilities are typically conceptualized as deficits. The theory of neurodiversity encourages researchers to conceptualize cognitive differences as natural forms of human diversity with unique sets of challenges and strengths. Using neurodiversity as our theoretical framework, we analyze the experiences of five research mathematicians with dyslexia as told through personal narratives to find common strengths and challenges for dyslexic thinkers at the highest level of mathematics. We report on 4 themes: (1) highly visual and intuitive ways of mathematical thinking, (2) issues with language and translation between forms, (3) issues with memorization of mathematical facts and procedures, and (4) resilience as a strength of dyslexia that matters in mathematics. We use our participants’ insights to explore how neurodiversity, a theory of cognitive disability developed by and for neurodiverse people, could expand opportunities for research. We call for mathematics educators to consider the strengths and challenges of dyslexic learners, as well as valuing expertise from insider perspectives.

Kindergarten domain-specific and domain-general cognitive precursors of hierarchical mathematical development: A longitudinal study.

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and provided longitudinal evidence for a hierarchy of mathematics. During development, the reliance on prior skills at lower, most proximal levels becomes increasingly important in order to acquire and succeed at later and higher levels of mathematics. The study extends the Fuchs et al. (2010b) model as the mechanisms underlying 3 different hierarchical levels of mathematics all involve an interplay between domain-specific number abilities (i.e., sequence knowledge, digit comparison) and general cognitive abilities (i.e., logical reasoning, phonological awareness, working memory). The constellation of domain-specific number and domain-general cognitive mechanisms subserving mathematics at different hierarchical levels showed a high degree of similarity. However, the importance of number abilities decreases during development, whereas the importance of general cognitive abilities remains approximately equal across levels of mathematical learning. Early symbolic number skills (i.e., counting sequence knowledge, digit comparison) are subserved by general cognitive mechanisms such as working memory, phonological awareness, and rapid automatic naming processes. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

Clever girls\u2019 stories: the girl they call a nerd

In this paper, we explore the issue of gender and mathematics participation, focusing on the ways in which “clever girls” self-author within the discourse order of a high ability group, which has particular significance in the Norwegian context in which this study took place. Contrasting the cases of three girls, only one of whom (Anna) chooses to continue with a higher level of mathematics (mathematics for science), we consider the ways in which they manage being members of the “smart group”. We analyse in particular the storying of Anna as a “nerd” and the social cost of being a “clever girl” against the backdrop of a public discourse of equality of opportunity in Norway.

Assessment of numeracy in sports and exercise science students at an Australian university

ABSTRACTThe effect of high school study of mathematics on numeracy performance of sports and exercise science (SES) students is not clear. To investigate this further, we tested the numeracy skills of 401 students enrolled in a Bachelor of Health Sciences degree in SES using a multiple-choice survey consisting of four background questions and 39 numeracy test questions. Background questions (5-point scale) focused on highest level of mathematics studied at high school, self-perception of mathematics proficiency, perceived importance of mathematics to SES and likelihood of seeking help with mathematics. Numeracy questions focused on rational number, ratios and rates, basic algebra and graph interpretation. Numeracy performance was based on answers to these questions (1 mark each) and represented by the total score (maximum = 39). Students from first (n = 212), second (n = 78) and third (n = 111) years of the SES degree completed the test. The distribution of numeracy test scores for the entire cohort was negatively skewed with a median (IQR) score of 27(11). We observed statistically significant associations between test scores and the highest level of mathematics studied (P < 0.05), being lowest in students who studied Year 10 Mathematics (20 (9)), intermediate in students who studied Year 12 General Mathematics (26 (8)) and highest in two groups of students who studied higher-level Year 12 Mathematics (31 (9), 31 (6)). There were statistically significant associations between test scores and level of self-perception of mathematics proficiency and also likelihood of seeking help with mathematics (P < 0.05) but not with perceived importance of mathematics to SES. These findings reveal that the level of mathematics studied in high school is a critical factor determining the level of numeracy performance in SES students.

Analysis of Mathematical Connection Ability and Mathematical Disposition Students of 11th Grade Vocational High School

The purpose of this research was to described mathematical connection ability, mathematical disposition students of eleventh grade Vocational High School. This research also was to described mathematical connection ability reviewed by mathematical disposition and mathematical disposition reviewed by mathematical connection ability. The social situation was students of eleventh grade Eight Vocational High School. The subject in this research was students in the level of capacity to mathematical connection ability and mathematical disposition was three students in XI RPL 2 Eight State Vocational High School of Semarang. The result showed a description (1) mathematical connection ability level of students were medium; (2) mathematical disposition level of students were medium; (3) students had high mathematical connection ability level tendency to construct mathematical disposition level better than students had medium and low mathematical connection ability level; (4) students had high mathematical disposition level tendency to construct mathematical connection ability level better than students had medium and low mathematical disposition level.

Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be proficient at all mathematics skill subdomains compared toWhite advanced mathematics students. Interestingly, African American students who take calculus as their highest level of mathematics in high school have similar achievement levels as White advanced mathematics students who have trigonometry/pre-calculus as their highest level of mathematics in high school.

Does prior knowledge of economics and higher level mathematics improve student learning in principles of economics?

Using the instrumental variable two stage least square (IV2SLS) and generalised method of moments (IVGMM) estimations, this paper investigates the relative importance of a wide range of variables on student performance in multiple choice and short answer questions in a first year principles of economics (PE) subject. The multi-year data set provides detailed demographic and performance characteristics of 2186 students enrolled in a major multi-campus university. Results from IVGMM and IV2SLS estimation indicate that higher levels of mathematics and economics taken prior to university are associated with significantly improved student performance in PE. Results also indicate that prior economics knowledge has more influence than prior mathematics knowledge on student performance in PE. Students with better understanding of mathematics perform significantly better in multiple choice questions. On the other hand, prior mathematics knowledge does not significantly affect the marks in short answer questions.

About Use and Misuse of Statistics in Education: On Mathematics Exams at General Matura in Slovenia

Exact mathematical methods, in particular statistical, are used everywhere in science. But for proper application of any method, certain assumptions are necessary, which is often neglected. Traditionally, mathematical exam at General Matura in Slovenia is obligatory. At present, it can be passed either on the basic or on the higher level, opening an interesting and natural question about equating grades at the two levels. A related and more challenging problem is to compare the scores at Vocational Matura with the scores at General Matura. We emphasize that the methodology used has to be chosen very carefully. It is shown that the application of the Rasch model for equating grades at Basic and Higher Level of Mathematics at General Matura exam in [Hauptman, Metodoloski zvezki 7 (2010) 167-181] is not justified.

Computational logic and the social

For centuries, the highest level of mathematics has been seen as an isolated creative activity, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. ‘Crowdsourcing’ pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers, using programs designed to verify hardware, check proofs that are just too long and complicated for any human to comprehend. ‘Social machines’ are new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity. This paper outlines a research agenda for a new vision of a mathematics social machine, a combination of people, computers, and archives to create and apply mathematics, and places it in the context of verification research, computational logic and Roy Dyckhoff’s pioneering work on computer proof.

THE MOVING FRICTION CONE APPROACH FOR THREE-DIMENSIONAL CONTACT SIMULATIONS

A finite element contact approach based on the Moving Friction Cone (MFC) formulation is presented herein. The formulation is based on the contact constraint described using a single gap vector. Such a simplification, in comparison with the standard approach where normal and tangential gap vectors are used, results in significantly simpler, shorter and faster element code. The associated penalty is formulated to include large deformations and displacements. Within this approach a triangular contact element is developed using a high abstract mathematical level of symbolic description. Using this technique, a consistent linearization is obtained which leads to quadratic rates of convergence. Furthermore, the new technique results in algorithmic robustness, fast evaluation time, as well as a compact element code.

Japanese precious metals manufacturer refocuses

Using the instrumental variable two stage least square (IV2SLS) and generalised method of moments (IVGMM) estimations, this paper investigates the relative importance of a wide range of variables on student performance in multiple choice and short answer questions in a first year principles of economics (PE) subject. The multi-year data set provides detailed demographic and performance characteristics of 2186 students enrolled in a major multi-campus university. Results from IVGMM and IV2SLS estimation indicate that higher levels of mathematics and economics taken prior to university are associated with significantly improved student performance in PE. Results also indicate that prior economics knowledge has more influence than prior mathematics knowledge on student performance in PE. Students with better understanding of mathematics perform significantly better in multiple choice questions. On the other hand, prior mathematics knowledge does not significantly affect the marks in short answer questions.

Personnel Preparation and Secondary Education Programs For Gifted Students

The advent of the new millennium has created a new willingness to accept change as a natural event. Change in the way we prepare personnel to work with gifted students is one that is needed (Gallagher, 2000). The education of gifted students has been a part of the American scene for over seven decades. During that time, the focus of these special efforts has been mainly on the elementary and middle school levels (Clark, 1997; Gallagher & Gallagher, 1994; Maker & Nielson, 1996). The education of gifted students at the secondary level has been comprised of acceleration (moving the student more rapidly through the secondary program), advanced placement or honors courses, and, occasionally, special schools like the North Carolina School of Math and Science or the Illinois Academy of Science and Mathematics (Kolloff, 1997). Rarely have secondary education teachers had special preparation for meeting the needs of gifted students or even for working with a specialist in gifted education who could provide them with technical assistance on this topic. Is There a Need for Personnel Preparation? Certainly many secondary school teachers believe that the rigorous curriculum that they present to bright students in their classes should be enough to meet the academic needs of these students. However, there is a variety of evidence to suggest that gifted students are often being shortchanged in their secondary education programs. Gallagher, Harradine, and Coleman (1997) surveyed 871 gifted students in nine school systems (K-12) in North Carolina, asking them about their experiences in these public school programs. In response to the question as to whether their academic subjects were challenging, 20-40% of the secondary gifted students surveyed answered No, and many added comments that they were bored by the pace and the nature of the instruction that they received. Students who call for a more rigorous challenge are a surprise to many administrators who are used to students trying to avoid schoolwork, often in rather creative ways. Yet, these gifted students were asking for more complex and sophisticated content and for ways where they could work more independently in mastering important, if difficult, content. An education wake up call for educators came with the results of the Third International Math and Science Study, which compared American students with students of 20 or more foreign countries (TIMSS, 1997). American students were far from outstanding in their performance, particularly at the higher levels of mathematics (precalculus) and science. These results were a direct challenge to United States secondary programs, particularly programs for bright students. Even at schools such as the North Carolina School of Science and Math (NCSSM), a review of the school program found that the instructors' understanding of gifted students or methods to stimulate their creative and critical thinking was a weakness in an otherwise outstanding program (Gallagher, Coleman, & Staples, 1989). What and Who Should Be the Focus of Training? There are two groups in the secondary programs that need distinctive instruction: the classroom teacher and the specialist in gifted education who can provide support to the classroom teacher. First let us consider specialists in gifted education and what their role should be. They should operate to aid the classroom teacher with technical assistance, meaning providing access to special materials, demonstrations, and advice. They should be the windows to the broader world of instruction and knowledge about gifted students and their learning. The specialists in gifted education should also provide services for middle schools, and these individual should have credentials in gifted education. They should play an analogous role to the specialist in learning disabilities, whose task is to provide access to special materials and methods and to aid the classroom teacher in creating an effective learning environment for children with special needs. …

The cross product of two vectors is notjust another vector ‐‐ a major misconception being perpetuated in calculus and vector analysis textbooks

The vast majority of calculus textbooks perpetuate the misconception that the cross product of two vectors is simply another vector. This is despite the fact that scientists have known for over a century that such a representation creates major inadequacies in our description of various branches of physics. Unless it is our intent to force students to unlearn false ideas when they progress to higher levels of mathematics ‐‐ namely, the cross product of vectors does not transform according to the laws of tensors ‐‐ a much different picture should be presented. Fortunately, instead of the traditional short‐sighted definition, the cross product of two vectors can be easily explained, by starting from the perspective of dyadics. The concept of multiplication of vectors now has a simple geometrical picture that encompasses both the dot and cross products in any number of dimensions in terms of orthogonal unit vector components. By this approach the limitation of such an entity to exactly a three‐dimensional space that does not allow for one of the three metric motions (reflection in a mirror) may be discarded and an appreciation of the intrinsic difference between true vectors and pseudo‐vectors is developed.

Perceptions of the relevance of mathematics and science: Further analysis of an Australian longitudinal study

The media portray girls' achievement in mathematics and science as equal to or better than male performance. This paper reports on a longitudinal study based on Years 7–12. One of the disturbing features of these data is the extremely poor perceptions that students, both male and female, have of performance in mathematics and science in the earlier years of high school. These data suggest the need to examine students' changing perceptions in the transition years from primary school to high school. Despite there having been substantial improvement in girls' perceptions of how they have performed in mathematics and science, proportionately fewer females elect to undertake studies at the higher levels of mathematics, physics and chemistry. The data suggest that year 9 is crucial. The perspective that girls have unequivocally arrived has been challenged.

An awareness of epistemological assumptions: the case of gender studies

Perceptions of differences in the participation and achievement of girls and boys in school science and mathematics have given rise to considerable curriculum research and professional development. This research, and the practices arising from it, has aimed at increasing the participation of girls in ‘non‐traditional’ school subjects, with the ultimate goal of enhancing girls’ post‐school options. Mathematics and science have been seen as critical in this respect, particularly the higher levels of mathematics and the physical sciences. This research and professional development have contributed to our understanding of the issues and have no doubt affected the post‐school options of some girls. However, there is also dissatisfaction at the lack of significant change that has flowed from this work. A more critical analysis is now emerging, leading to a deeper questioning of the assumptions that underlie research and development in the field. Ironically, at the same time there are reports that funding for re...

Functional Integration – Theory and Applications

Jean-Pierre Antoine and Enrique Tirapegui (eds) 1980 New York: Plenum vii + 355 pp price $24.50 The individual articles in this collection cover a range of topics from quantum field theory to control theory. They are all at a high mathematical level, suitable for research workers in probability or theoretical physics.