Advanced Students Of Mathematics Research Articles

Teacher characteristics as predictors of mathematics attitude and perceptions of engaged teaching among 12th grade advanced mathematics students in the U.S

ABSTRACT The present study examined the 2015 Trends in International Mathematics and Science Study “Advanced” data to examine how the educational credentials of maths teachers and other teacher characteristics were related to attitude towards advanced mathematics and perceptions of engaged teaching among 12th-grade students enrolled in advanced mathematics courses in the U.S. As attitudinal outcomes in this study, two measures of attitude towards mathematics were employed – the Students Like Learning Advanced Mathematics scale and the Students Value Advanced Mathematics scale, and one measure of student perception of engaged teaching – the Students’ Views on Engaging Teaching in Advanced Mathematics Lessons. A set of multilevel regression analyses were conducted predicting each of these aforementioned outcomes. No statistically significant effects on the attitudinal outcomes were observed for teacher variables. Positive effects were noted for parental education on students’ valuing of advanced mathematics. A prominent finding was that higher levels of parental education were associated with higher student levels of valuing mathematics, which likely reflects a family/home culture that implicitly or explicitly places high value on science and mathematics. Identifying factors that might facilitate positive attitude is important to increase the likelihood that students will choose, and be retained in, mathematics and STEM education and careers.

Students’ understanding of the number line / Estudiantes pensando en la recta numérica

We studied the conceptions of students coming from secondary education and university regarding the number line as a representation of real numbers. In the context of a wider questionnaire, 307 students were presented with a task consisting of two verbal items and one graphic item related to the number line. The students were all at different levels in their study of mathematics (in the third, fourth or fifth year of secondary education, or at the beginning or advanced stage of a university degree in mathematics, biology or physical education). A gradient in the depth of the students’ conceptions, associated with the level of their studies in mathematics, was found. This gradient extends from the estrangement of facing the problem or a conception of a drawn or physical matter line, which was associated with students with a lower level of mathematical studies, passing through a vision centred around potential numeric density or a line containing points (discrete), up to an instrumental conception of the line as supportive of magnitudes in advanced students of biology and focusing on continuity sustained by advanced students of mathematics.

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.

Increasing Problem Solving Skills in Fifth Grade Advanced Mathematics Students

Increasing Problem Solving Skills in Fifth Grade Advanced Mathematics Students

Increasing Problem Solving Skills in Fifth Grade Advanced Mathematics Students

Because No Child Left Behind (NCLB) calls for every student to make gains during every school year, even advanced students who are already performing at the top must make these gains. Teachers need to find areas to target with advanced students. One area that could be targeted to strengthen is problem solving skills. Research shows that daily practice and strategy instruction in problem solving skills will increase students’ problem solving abilities. I dedicated 5-10 minutes per day to problem solving practice and strategy instruction for a five week period. Pre- and post-assessment data were collected using confidence surveys constructed by the teacher and problem solving tests to show growth from the beginning to the end of the study. Results indicate that although confidence in problem solving did not show notable increases, there was evidence indicating an increase in problem solving skills both in correct answers and strategy knowledge.

Conditional inference and advanced mathematical study

Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one’s ability to reason logically. In this paper we explore this view by directly comparing the inferences drawn from abstract conditional statements by advanced mathematics students and well-educated arts students. The mathematics students in the study were found to endorse fewer invalid conditional inferences than the arts students, but they did not endorse significantly more valid inferences. We establish that both groups tended to endorse more inferences which led to negated conclusions than inferences which led to affirmative conclusions (a phenomenon known as the negative conclusion effect). In contrast, however, we demonstrate that, unlike the arts students, the mathematics students did not exhibit the affirmative premise effect: the tendency to endorse more inferences with affirmative premises than with negated premises. We speculate that this latter result may be due to an increased ability for successful mathematics students to be able to ‘see through’ opaque representations. Overall, our data are consistent with a version of the formal discipline view. However, there are important caveats; in particular, we demonstrate that there is no simplistic relationship between the study of advanced mathematics and conditional inference behaviour.

Of connections and fields - I

We describe some instances of the appearance of Chern’s mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These applications range from magnetic monopoles in electrodynamics to instantons in quantum chromodynamics to the geometric phase of quantum mechanics. The first part of this article is elementary and addressed to a general reader. The second part is somewhat more demanding and is addressed to advanced students of mathematics and physics.

A Simple Introduction to Integral Equations

Integral equations are equations in which the unknown function appears inside a definite integral. They are closely related to differential equations. Initial value problems and boundary value problems for ordinary and partial differential equations can often be written as integral equations (see [7] for an introduction to the technique), and some integral equations can be written as initial or boundary value problems for differential equations. Problems that can be cast in both forms are generally more familiar as differential equations, owing to the larger collection of analytical procedures for solving differential equations. Many applications are best modeled with integral equations, but most of these problems require a lengthy derivation. A relatively simple example is the model for population dynamics, with birth and death rates that depend on age. This model was first formulated in 1922 by Alfred J. Lotka [8], who is best known for the LotkaVolterra predator-prey population model. A similar model has been used to model the spread of the HIV virus among IV drug users [4]. A simple age-dependent population model will be developed at the end of this article. Integral equations are also important in the theory and numerical analysis of differential equations; this is where the mathematics student is most likely to encounter them. For example, Picard's existence and uniqueness theorem for first-order initial value problems is conveniently proved using integral equations [1]; the proof is constructive and can be used to formulate a method for numerical solution of initial value problems. Systematic study of integral equations is usually undertaken as part of a course in functional analysis (see [6]) or applied mathematics (see [9]). This advanced setting is required for a full appreciation of integral equation theory, but it makes the subject accessible only to the advanced student. By contrast, several of the important results in the theory of integral equations can be demonstrated using nothing more than elementary analysis, and the elaboration of this statement is the goal of the present discussion. In fact, all but one of the results presented here will be derived using nothing more than the material presented in a standard advanced calculus course. This gives less advanced students of mathematics a chance to encounter some integral equation concepts that play an important role in the theory and application of continuous mathematics.

Proof Practices and Constructs of Advanced Mathematics Students

AbstractProof has traditionally been seen as an important aspect of the advanced mathematics curriculum. The study reported here examines the proof practices and constructs of a group of students educated within a ‘post‐Cockcroft’ mathematics curriculum. It finds that although, in the spirit of the reformed curriculum, students are actively involved in developing mathematical ideas, this is within a restricted mode in which ideas of enquiry have become largely instrumentalised. In particular, validation is primarily and predominantly empirical, and there is little concern for illumination and systematisation.

An ‘integrating’ application of mathematics

This paper presents a coherent application of several mathematical tools and concepts in an area of financial analysis. As an educational tool, the example demonstrates the usefulness of seemingly obscure mathematics to non‐mathematical students, and provides an interesting case study or exercise to more advanced students of mathematics.

Report on the Training of Teachers of Mathematics

Teachers of mathematics will be interested in a report on “The Training of Teachers of Mathematics” published in a recent issue of The American Mathematical Monthly.1 The report was prepared by a group of ten mathematicians serving as a Commission on the Training and Utilization of Advanced Students of Mathematics.2 In December, 1934, it was presented to the Trustees of the Mathematical Association of America by whom it was accepted and approved. The following excerpts from the report may serve to indicate its character.