College Mathematics Students Research Articles

Optimization Strategy for the Reform of Applied Mathematics Teaching in Higher Vocational Colleges

In the face of the impact of economic globalization and cultural diversification, higher vocational colleges must provide more diversified and intelligent multi-dimensional education services for college students to promote the rapid innovation of subject teaching and improve student-centered education and teaching concepts. Based on this background, applied mathematics, as a very important basic course in higher vocational education, must carry out all-around teaching reform to continuously improve the comprehensive quality of mathematics of contemporary college students. Therefore, based on the practical experience of applied mathematics teaching and the collation and summary of relevant references, this study explores how to optimize the reform of applied mathematics from several aspects, to further improve the quality of applied mathematics teaching and the comprehensive quality of contemporary college students in mathematics by creating a new model of applied mathematics classroom teaching in higher vocational colleges.

Looking through the New World of Mathematics: Experiences of College Students in Mathematics in the Modern World Course

This study focuses on exploring the lived experiences of college students in Mathematics in the Modern World course. Using the phenomenological qualitative research design, struggles, coping mechanisms, and insights are asked from 11 participants of the study. Results revealed that the struggles of the college students are on class interaction and resources, and learning techniques. Also, it was found out that the coping mechanisms includes technological skills, learning management, and positive attitudes. Meanwhile, their insights focused on the application of the course to the real world. Implications and recommendations are discussed.

Rigorous Thinking in Mathematics Modelling for Slow Learners

Rigorous questions in discussion learning method plays a dominant role in the successful delivery of lessons for slow learners at higher education. This study aims to propose a framework to achieve good critical thinking for slow learners through Rigorous Mathematics computational Thinking (RMcT) model. This study used qualitative approach to describe slow learner’s critical thinking by using RMcT model. The instruments used in this study were test instrument, critical thinking questionnaire, and interview guideline as supporting instrument to describe slow learner’s critical thinking through RMcT model. The subjects were college students in mathematics modelling course in mathematics education department. Based on critical thinking test results, slow learners could divide variable used in mathematics modelling. Based on questionnaire results, slow learner students build their own understanding and solve the problem based on their experience while answering the given question during learning process. In addition, the interview they feel that the instructor can mediated the problem by giving analogy to the other material. In summary, RMcT could mediate slow learner’s critical thinking as its characteristics (by using Rigorous questions). Findings are useful for designers, service providers and policy makers of special needs higher school when implementing teaching strategy to mediated real-life problems into mathematics modelling for slow learners.

College Mathematics Students' Peceptions of "Believing" Teacher Actions

College Mathematics Students' Peceptions of "Believing" Teacher Actions

Perceptions and Effects of Classroom Capture Software on Course Performance Among Selected Online Community College Mathematics Students: A Mixed Methods Research Study

Perceptions and Effects of Classroom Capture Software on Course Performance Among Selected Online Community College Mathematics Students: A Mixed Methods Research Study

Mathematical Writing Errors in Expository Writings of College Mathematics Students

<p>Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students’ procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in mathematical writing were pre-defined namely, misuse of mathematical terms, misuse of mathematical symbols, incorrect notation, incorrect grammar, incorrect capitalization, no or incorrect punctuation, vague term, incorrect term, and lack of term or phrase. This study used qualitative method of research to keep a record of errors in mathematical writing. Conducted in the College of Education Arts and Sciences of De La Salle Lipa, the study involved twelve BS Mathematics students enrolled in Advanced Calculus 1 class as respondents. Results revealed that the most committed errors done in mathematical writing are incorrect grammar and misuse of mathematical symbols. Certainly, intervention programs on mathematics writing will bring favorable outcomes. Language courses in the students’ curriculum which tackle proper grammar usage may be integrated with writing about mathematics as part of the student activities. Such will provide the students with writing experiences fitted to their discipline.</p><p> </p>

Robust and Fragile Mathematical Identities: A Framework for Exploring Racialized Experiences and High Achievement Among Black College Students

I introduce the construct of fragile and robust identities for the purpose of exploring the experiences that influenced the mathematical and racial identities of highachieving Black college students in mathematics and engineering. These students maintained high levels of academic achievement in these fields while enduring marginalization, stereotyping, and other forms of racialization. Their fragile mathematical identities were manifested in the way they were motivated to achieve in order to prove false the negative expectations of others. Their robust mathematical identities were characterized by an evolving sense of self-efficacy and discovery, a growing affinity and passion for mathematics, and a desire to be a mathematically inspiring role model. Extending the work on identity development, I recommend more nuanced interpretations of the interplay of human development, racialized experiences, and distinctly race-related risk and protective factors that complicate mathematical identity formation for Black college students in mathematics and engineering fields.

Measuring students’ transition into university and its association with learning outcomes

Previously we showed how we measured pedagogy and revealed its association with learning outcomes of sixth‐form college mathematics students. In this project we followed a similar approach to the study of university transition. We particularly sought to identify the students’ perceptions of the transitional experience, and measure the association with learning outcomes. We drew on longitudinal surveys of students entering different programmes in five universities. Following them into their first year or so, allowed us to track their ‘disposition to complete the course’ and their ‘disposition to study more mathematics’, inter alia. We developed and validated two ‘fit‐for‐purpose’ measures of students’ perception of their transition, one we call ‘perception of the transitional gap/jump’ and one we call ‘degree of positive feeling about the transition’. We report some statistically and educationally significant associations between these and the students’ developing dispositions, and discuss the prospects for this approach to studying transition.

Learning Communities: Their Effects on College Mathematics Students

Learning Communities: Their Effects on College Mathematics Students

Achievement Goal Orientations of Community College Mathematics Students and the Misalignment of Instructor Perceptions

This study reports on the results of a survey of achievement goal orientations administered to a sample of 777 students enrolled in remedial and college-level mathematics courses at a community college. Results indicate that students’ achievement goal orientations are consistent with adaptive learning patterns: Students are interested in developing competence, expect and believe they can handle challenging work, avoid self-handicapping behaviors, and exhibit a positive mathematics self-concept. However, interviews with faculty members teaching the courses in which the students were enrolled revealed that instructors had a more negative perspective. This discrepancy suggests that instructors might not be taking advantage of the high confidence and motivation to learn that their students bring to the mathematics classroom.

Characterizing the Mathematics Anxiety Literature Using Confidence Intervals as a Literature Review Mechanism

ABSTRACT The authors report the contextualization of effect sizes within mathematics anxiety research, and more specifically within research using the Mathematics Anxiety Rating Scale (MARS) and the MARS for Adolescents (MARS-A). The effect sizes from 45 studies were characterized by graphing confidence intervals (CIs) across studies involving (a) adults not participating in studies focusing on remedial or entry-level mathematics students or teachers, (b) remedial mathematics and entry-level college mathematics students, (c) preservice and inservice teachers, and (d) 7–12th-grade students and rising college students. The results also illustrate how CIs can be useful in research syntheses, because CIs (a) encourage meta-analytic thinking, (b) provide information about the research precision of a literature, and (c) provide plausible estimates for parameter values even if initial research expectations are wildly wrong.

Applications of a sequence of points in teaching linear algebra, numerical methods and discrete mathematics

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, Using a sequence of number pairs as an example in teaching mathematics. Math. Comput. Educ., 39 (2005), pp. 198–205; Y. Shi, Case study projects for college mathematics courses based on a particular function of two variables. Int. J. Math. Educ. Sci. Techn., 38 (2007), pp. 555–566) have presented some interesting examples which can be used in teaching high school and college mathematics classes. In this article, we further discuss a few interesting ways to apply this sequence of points in teaching college mathematics courses such as linear algebra, numerical methods in computing, and discrete mathematics. In addition to using them in individual courses, these studies may also be combined together to offer seminars or workshops to college mathematics students. Studies like these are likely to promote student interests and get students more involved in the learning process, and therefore make the learning process more effective.

Undergraduate Engineering Majors' Beliefs About Mathematics

This study examined the mathematics beliefs of college students in 10 undergraduate mathematics classes at a large engineering school in the Midwest. The beliefs of 254 engineering majors were measured by the Indiana Mathematics Belief Scales and compared to the beliefs of elementary education majors and remedial college mathematics students obtained from earlier studies using the same instrument. The results were interpreted in terms of the students' daily attitudes towards their mathematics classes and corresponding academic and demographic parameters. The study showed that in many respects, the beliefs of the engineering majors were not that different from the other populations. The correlations among beliefs for the engineering group tended to be higher although there were relatively few significant correlations between belief and background variables. Attitude data were collected across a full semester for the engineering majors. The relatively modest day‐to‐day variation in those attitudes suggests that they are based on deeply seated beliefs.

Procedural Explanations in Mathematics Writing

This study analyzes the procedural explanations written by remedial college mathematics students. Relevant literatures suggest that six communication activities might be key in effective procedural explanations in mathematics writing: (a) orienting the learner, (b) providing kernels or definitions of concepts and procedures, (c) using exemplars or worked examples, (d) providing descriptions of the process or procedure, (e) solidifying learner understanding, and (f) facilitating linguistic control of mathematical terms. Using this framework, 18 practices or types of difficulties were discovered in students' written explanations. Independent experts consistently evaluated student explanations more highly when the explanations contained arithmetic or algebraic exemplars, described specific actions and their meanings, linked new with prior knowledge, and used descriptive language; experts evaluated student explanations more negatively when students displayed difficulties reasoning with kernels, reasoning with exemplars, or with describing processes.

Case study projects for college mathematics courses based on a particular function of two variables

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, Mathematics and Computer Education, 39(3), 198–205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry, calculus, and linear algebra. In this paper, this study is generalized further to develop a few interesting case study proposals that can be used for student projects in college mathematics courses such as real functions, analytic geometry, and complex variables. In addition to using them in individual courses, these studies may also be combined to offer seminars or workshops to college mathematics students. Projects like these are likely to promote student interest and get students more involved in the learning process, and therefore make the learning process more effective.

Dispositions of college mathematics students

The paper considers the dispositions of college students in mathematics courses towards mathematics. Disposition is looked at as a measure of the attitude of students towards mathematics and their beliefs about mathematics. Effective mathematics teaching involves more than the teaching of mathematical concepts and procedures: it also includes helping students develop their dispositions towards mathematics. An important component in the reform of the programme at the authors' university was an understanding of students' dispositions and attitudes towards mathematics. This study focused on beliefs and attitudes of students at the college level. Students in a variety of mathematics courses were surveyed. Several variables, such as academic major, mathematical background and gender were used to classify the students who were surveyed. Students' initial attitudes were assessed and changes in their attitudes identified over the course of one semester.

Factors involved in linking representations of functions

This article focuses on the intertwining between the flexibility in moving from one representation to another, and other aspects of knowledge and understanding. During the first phase of data collection, 152 college mathematics students who were also prospective secondary mathematics teachers completed an open-ended questionnaire. In the second phase, an additional ten subjects were interviewed after responding to the questionnaire. The results illustrate how knowledge about different representations is not independent, but is interconnected with knowledge about different approaches to functions, knowledge about the context of the presentation and knowledge of underlying notions.

An Introduction to Combinatorial Group Theory and the Word Problem

(1997). An Introduction to Combinatorial Group Theory and the Word Problem. Mathematics Magazine: Vol. 70, No. 1, pp. 3-10.

College Students' Attitudes toward Mathematics

Three samples of college students in mathematics ( n = 292), psychology ( n = 66), and other fields ( n = 76) chose two out of 14 statements concerning mathematics and mathematicians to indicate their attitudes toward mathematics. Three items describing mathematics as good mental exercise and valuable mental training were selected by more than 55% of the students in all three samples. The over-all similarity in attitudes toward mathematics among the three samples is quite high. These results suggest that mathematics is highly valued by these college students.