Development of an attitude-towards-using-mathematics scale for high-school students and an analysis of student attitudes

ABSTRACT

This research has been carried out in two stages and has two main objectives. The first aim of the study is to develop a Likert-type scale which is used to determine the attitudes towards the use of mathematics in real life. The second aim is to examine the attitudes of high school students about the use of mathematics in real life according to different variables used in the developed scale. The research was carried out according to the correlational research method, and the participants comprise the sample of 340 and 356 students for the scale development and implementation stages of the study, respectively. As a result of the research, a structure consisting of 23 items and three sub-factors was determined for the scale. In the second stage of the study, it was observed that the student attitudes were at the level corresponding to the ‘undecided’ option of the scale, and they differed significantly according to gender and grade level variables. In addition, it was found that there was a positive and significant relationship between the students’ attitudes towards the use of mathematics and their mathematics achievement.     

Finding the needles in the haystack: efficient intelligence processing

As a result of communication technologies, the main intelligence challenge has shifted from collecting data to efficiently processing it so that relevant, and only relevant, information is passed on to intelligence analysts. We consider intelligence data intercepted on a social communication network. The social network includes both adversaries (eg terrorists) and benign participants. We propose a methodology for efficiently searching for relevant messages among the intercepted communications. Besides addressing a real and urgent problem that has attracted little attention in the open literature thus far, the main contributions of this paper are two-fold. First, we develop a novel knowledge accumulation model for intelligence processors, which addresses both the nodes of the social network (the participants) and its edges (the communications). Second, we propose efficient prioritization algorithms that utilize the processor’s accumulated knowledge. Our approach is based on methods from graphical models, social networks, random fields, Bayesian learning, and exploration/exploitation algorithms.     

Statistical characteristics of an integrated oceanographic data processing system

Integration of special- and general-purpose application packages is considered as an efficiency improving technique, A package integration system is defined and its statistical characteristics are computed. Parallel and sequential package integration systems are analyzed. A real-life system, developed on the basis of sequential integration principles is described. This is a computer-aided oceanographic data processing system for the ES OS environment, which includes preprocessing and data preparation programs, a number of special-purpose application packages, and interfaces between these packages.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 113–122, 1987.     

An effective computer modelling approach to the study of aeroelastic characteristics of an aircraft composite wing with high aspect ratio

Static aeroelastic and flutter characteristics of an aircraft composite wing with high aspect ratio were analysed by an effective Computational Fluid Dynamics and Computational Structure Dynamics coupled method. Effects of stiffness distribution on aeroelastic characteristics were considered. Honeycomb core sandwich composite was considered to be equivalent to an orthotropic material by stiffness and inertance equivalent method to allow highly efficient numerical simulation, which was used for analysis of bending and torsional stiffness distribution. The results showed that the redistributed aerodynamic load leads to a decrease of pressure difference between the upper and lower airfoils. The flutter speed of the composite wing is near 0.64 Ma. Both bending and torsional stiffness increases with a small increase of beam size. Stiffness of the wing root has a major influence generally on the static aeroelastic characteristics. Both the lift coefficient and the loss percent decrease with a small increase of beam size. Effects of stiffness distribution on frequency are not obvious. Flutter speed remains close to the initial value when the beam size is changed.     

The mathematical beliefs and behavior of high school students: Insights from a longitudinal study

There is a documented need for more research on the mathematical beliefs of students below college. In particular, there is a need for more studies on how the mathematical beliefs of these students impact their mathematical behavior in challenging mathematical tasks. This study examines the beliefs on mathematical learning of five high school students and the students’ mathematical behavior in a challenging probability task. The students were participants in an after-school, classroom-based, longitudinal study on students’ development of mathematical ideas funded by the United States National Science Foundation. The results show that particular educational experiences can alter results from previous studies on the mathematical beliefs and behavior of students below college, some of which have been used to justify non-reform pedagogical approaches in mathematics classrooms. Implications for classroom practice and ideas for future research are discussed.     

Mathematical modelling and study of the consolidation of an elastic saturated soil with an incompressible fluid by FEM

The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the stability of the method as well as the estimation of the error by using semi-discretization in time. Finally, we then solved this one by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data.     

Student enrichment in mathematics: a case study with first year university students

ABSTRACT

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an enrichment programme. Following the intervention, students completed a questionnaire and a few were interviewed to establish their experiences of the enrichment programme. We discuss the successes and pitfalls of the intervention and report on the impact it had on the participants.     

A study of an arbitrary Stokes flow past a fluid coated sphere in a fluid of a different viscosity

A general method to discuss the problem of an arbitrary Stokes flow (both axisymmetric and non-axisymmetric flows) of a viscous, incompressible fluid past a sphere with a thin coating of a fluid of a different viscosity is considered. We derive the expressions for the drag and torque experienced by the fluid coated sphere and also discuss the conditions for the reduction of the drag on the fluid coated sphere. In fact, we show that the drag reduces compared to the drag on a rigid sphere of the same radius when the unperturbed velocity is either harmonic or purely biharmonic, i.e., of the form ${r^2\vec{\textbf{v}}}$ , where ${\vec{\textbf{v}}}$ is a harmonic function. Previously Johnson (J Fluid Mech 110:217–238, 1981), who considered a uniform flow showed that the drag on the fluid coated sphere reduces compared to the drag on the uncoated sphere when the ratio of the surrounding fluid viscosity to the fluid-film viscosity is greater than 4. We show that this result is true when the undisturbed velocity is harmonic or purely biharmonic, uniform flow being a special case of the former. However, we illustrate by an example that the drag may increase in a general Stokes flow even if this ratio is greater than 4. Moreover, when the unperturbed velocity is harmonic or purely biharmonic, and the ratio of the surrounding fluid viscosity to the fluid-film viscosity is greater than 4 for a fixed value of the viscosity of the ambient fluid, we determine the thickness of the coating for which the drag is minimum.     

Stability of an aneurysm in a membrane tube filled with an ideal fluid

Theoretical and Mathematical Physics - The stability of standing localized structures formed in an axisymmetric membrane tube filled with fluid is studied. It is assumed that the tube wall is...     

Flows of an incompressible fluid with linear vorticity

All the flows of an incompressible fluid, for which the vorticity of the velocity field is linear with respect to the spatial variables, are described.     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

绍兴市区中学生情绪障碍与生命早期应激相关性研究

目的调查绍兴市区中学生生命早期应激及情绪障碍的发生情况,并探讨两者的相关性。方法对绍兴市区6所中学的518例初中生和468例高中生以生命早期应激问卷（ELSQ）调查生命早期应激发生情况;根据有无生命早期应激及其数量,共分成6组：初中生高应激组（应激数量≥3个,75例）、低应激组（应激数量1~2个,279例）、对照组（无应激,164例）和高中生高应激组（应激数量≥3个,92例）、低应激组（应激数量1~2个,260例）、对照组（无应激,116例）,以抑郁自评量表（SDS）和焦虑自评量表（SAS）分别评定各组的情绪障碍情况。结果绍兴市中学生焦虑、抑郁症状等情绪障碍的发生率分别为16.73%和31.54%,初中生的抑郁症状发生率高于高中生,而高中生的焦虑症状发生率高于初中生;绍兴中学生生命早期应激发生率为71.60%,以家庭暴力、遭受欺凌、与父母分离及家庭冲突发生率最高;初中生经历自己患重大疾病、遭受欺凌、情感虐待或忽视、家庭暴力、家庭灾祸等应激事件容易出现焦虑、抑郁,而高中生在经历家庭冲突、与父母分离、家庭暴力、遭受欺凌、亲人死亡、情感虐待或忽视及家庭成员重大疾病等应激事件时更易出现焦虑、抑郁;生命早期应激与中学生情绪障碍的发生有相关性,特别是抑郁情绪与ELS数量更有显著相关性。结论高达2/3以上的青少年存在生命早期应激,生命早期应激与中学生焦虑、抑郁密切相关,生命早期应激可能是导致中学生出现情绪障碍的重要影响因素。     

Oscillation of membranes in an incompressible fluid

This article considers the problem of natural oscillations of membranes in an unbounded incompressible fluid. The article contains a qualitative analysis of the equations used and upper and lower bounds are obtained for the natural frequencies of the membrane. Translated fromDinamicheskic Sistemy. Vol. 12. pp. 23–29, 1993.     

Equations of an effective model of an anisotropic elastic medium with cracks filled with a fluid

For a periodic layered medium in which every period consists of an elastic anisotropic layer and a fluid homogeneous layer, an effective model is derived by averaging. This model describes wave propagation and has two phases. The equations of this model are deduced in the case of the general anisotropy and in some special cases. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 175–191. Translated by L. A. Molotkov.     

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.     

Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains

In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder (rd) where (r, , z) denotes the cylindrical co-ordinates in ³ is considered. The motion is with swirl (i.e. the -component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. [9] that for the problem without swirl (f _q = 0 in (f)) in the whole space, as the flux constant k tends to 1) dist(0z, A) = O(k ^1/2); diam A = O(exp(–c ₀ k ^3/2));2) k^1/2)_k converges to a vortex cylinder U _m (see (1.2)).We show that for the problem with swirl, as k , 1) holds; if m q + 2 then 2) holds and if m > q + 2 it holds with U _q+2 instead of U _m. Moreover, these results are independent of f ₀, f _q and d > 0.     

The origin of vortices in an ideal fluid

Translated from Matematicheskie Zametki, Vol. 48, No. 3, pp. 128–133, September, 1990.     

A study of the solvability of the generalized equation of filtration of an inhomogeneous fluid

We study the existence of solutions of the generalized equation of filtration of an inhomogeneous fluid and prove that they are unique. We study the smoothness properties of the solutions when the right-hand sides of the equation belong to various spaces.This work is carried out using the machinery of rigged Hilbert spaces and energy inequalities.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 77–84.     

Gender, technology and attitude towards mathematics: a comparative longitudinal study with Mexican students

In this paper the results of a comparative longitudinal study investigating changes in girls’ and boys’ attitudes towards mathematics, and self-confidence in mathematics are presented. A 5-point Likert scale, AMMEC, was used to measure attitudes towards mathematics (AM), computer-based mathematics (AMC), and self-confidence in mathematics (CM). A total of 430 students using technology for mathematics and 109 students not using it were monitored for 3 years. At the beginning of the study, the participants were aged about 13 years. The statistical analyses of the data showed few gender differences in the way students’ attitudes and self-confidence changed over the 3 years. Significant gender differences favouring boys were found in attitudes towards mathematics in grades 8 and 9 for the group using technology. For the group using technology, significantly more boys than girls got high scores in attitudes towards computer-based mathematics in grade 7. Significantly, more girls using technology than girls not using it got high scores in grade 8. The use of technology did not have a positive impact on students’ self-confidence. Regardless of whether they used computers or not, from grades 7 to 9, there was a decrease in the self-confidence in mathematics of both boys and girls. To enrich these results and detect possible gender differences in the way attitudes were constructed, 12 girls and 13 boys were interviewed at the end of the study. The analysis of the arguments they presented to explain and justify their attitudes towards mathematics, computer-based mathematics, and their self-confidence in working in mathematics provided evidence of important gender differences in the ways in which boys and girls construct their attitude, indicating how their constructions reflect the gender stereotypes within Mexican society.