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.     

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.     

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...     

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.     

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.     

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.     

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.     

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.     

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 difficulties experienced with mathematics by engineering students in higher education

This paper describes a study undertaken to investigate the problem of the lack of mathematical expertise demonstrated by polytechnic engineering students. The study is based on a multiple‐choice diagnostic mathematics test, designed for the purpose, which was taken by incoming engineering students over a period of five years. The test aims to identify particular areas of difficulty. These difficulties are analysed and suggestions are made regarding their cause and alleviation. It has been confirmed that there is cause for concern at the overall mathematical ability of the students and it has been possible to identify certain areas of mathematics which appear to be difficult to a large proportion of students. It has also been possible to identify some of the common errors made by students in certain topic areas. Some suggestions have been made regarding the implications for teaching.     

Stepping beyond high school mathematics: a case study of high school women

The Summer Explorations and Research Collaborations for High School Girls (SEARCH) Program, held annually since 2004 at Mount Holyoke College in the US, was created for talented high school girls to explore mathematics beyond that taught in high school. Our study, which focuses on factors that facilitate or inhibit the pursuit of higher level mathematics by girls, is centered on the 2006 SEARCH Program. We present a combination of qualitative and quantitative data drawn from student journals written during SEARCH, program evaluations written at the end of SEARCH, post-program interviews, and comparisons with two peer group samples. From this data we point to important factors, such as developing a mathematical voice, gaining a broader view of advanced mathematics, being challenged in a supportive atmosphere, and having a positive stance toward risk-taking, that may help to maintain the interest of talented girls in advanced mathematical studies.     

Knowledge-based improvement: simulation and artificial intelligence for identifying and improving human decision-making in an operations system

The performance of most operations systems is significantly affected by the interaction of human decision-makers. A methodology, based on the use of visual interactive simulation (VIS) and artificial intelligence (AI), is described that aims to identify and improve human decision-making in operations systems. The methodology, known as ‘knowledge-based improvement’ (KBI), elicits knowledge from a decision-maker via a VIS and then uses AI methods to represent decision-making. By linking the VIS and AI representation, it is possible to predict the performance of the operations system under different decision-making strategies and to search for improved strategies. The KBI methodology is applied to the decision-making surrounding unplanned maintenance operations at a Ford Motor Company engine assembly plant.     

Academic maturity of students in an extended programme in mathematics

ABSTRACT

This paper focuses on the students who are registered in the University of Pretoria’s academic development programme, named the Four-year Programme (FYP). The programme was introduced as a gateway for students who are underprepared but have the potential to succeed and then continue their studies into the mainstream science programmes. Our research focuses on measuring the change in the academic maturity of these students. In the theoretical framework that we developed, academic maturity is subdivided into two components namely non-subject based maturity and subject based maturity (mathematical maturity). This paper focuses on measuring non-subject based academic maturity. The survey used for this purpose is called the Student Academic Readiness Survey (STARS), taken at the beginning of the year and after the first semester respectively. The results of the surveys are compared to measure the change in students’ views. Results show that in all constructs there is a surprising decline in students’ perceptions regarding their own abilities over the first semester at university. We use the Dunning–Kruger effect to explain this unexpected decline, in that students seem to develop a more realistic view of their own maturity, which in itself can be seen as a growth in academic maturity.     

Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid

We consider the controlled motion in an ideal incompressible fluid of a rigid body with moving internal masses and an internal rotor in the presence of circulation of the fluid velocity around the body. The controllability of motion (according to the Rashevskii–Chow theorem) is proved for various combinations of control elements. In the case of zero circulation, we construct explicit controls (gaits) that ensure rotation and rectilinear (on average) motion. In the case of nonzero circulation, we examine the problem of stabilizing the body (compensating the drift) at the end point of the trajectory. We show that the drift can be compensated for if the body is inside a circular domain whose size is defined by the geometry of the body and the value of circulation.