Relationship of Mathematics Self-efficacy and Competence with Behaviors and Attitudes of Engineering Students with Poor Mathematics Preparation

Abstract

This mixed methods research study focuses on two relevant factors in students' decisions to pursue and complete an engineering major: mathematics preparation and mathematics self-efficacy. This study describes the relationship of mathematics self-efficacy on engineering students' performance, behavior, and attitudes in their first college mathematics courses. Participants completed a mathematics self-efficacy survey (n=408); 11 were selected to be interviewed. A grounded theory approach was used to examine participants' behaviors and attitudes in college mathematics courses, their mathematics self-efficacy beliefs, and how these beliefs aligned with their mathematics competence. Interview participants reported relatively high mathematics self-efficacy, but many revealed a mismatch between their mathematics self-efficacy beliefs and mathematics competence levels. Participants who had a balance between these two factors reported being more likely to spend extra time working to overcome their mathematics deficiencies and seeking extra help. However, participants with a mismatch reported being more likely to procrastinate and put little effort into improving their mathematics competence, blaming external factors for their struggles. Despite showing different behaviors and attitudes, all participants reported being likely to continue taking mathematics courses required for their major even after failing their first college mathematics course.

Advantages of Using the CAS Mathematica in a Study of Supplementary Chapters of Probability Theory

“…In order to get over this psychological obstacle, it is necessary to perform explanatory work and to use supplementary stimulating measures, e.g. additional rating points for students using the interactive templates (Morán-Soto, Benson, 2018). Again arises the problem of motivation playing the key role in education outcomes.…”

“…Typical difficulties associated with learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses of data (Holmes, 2003). In terms of another difficulty influencing the choice of an education strategy, it is possible that many students have not trained enough in mathematics in general; students' fear before certain STEM subjects should also be taken into account (Fatikhova, Sayfutdiyarova, 2017;Morán-Soto, Benson, 2018). In order to overcome these difficulties, students ought to learn computer-based methods of data analysis.…”

Using Computer Algebra Systems as a Tool for Disclosure of Interdisciplinary Linkages in Courses of Probabilistic Disciplines

“…Кроме того, зачастую отдельная часть потока не в состоянии провести математические выкладки в принципе в силу отсутствия у них необходимых навыков или же из-за забывания материала, пройденного на первых курсах. Это становится особенно очевидным при обучении магистрантов, группы которых очень разнородны по своему составу и полученному ранее образованию [5]. Поэтому при решении задач могут быть использованы персональные компьютеры, планшеты или смартфоны, на которые установлены специальные комплексы программ.…”

“…Несмотря на то, что вероятностные дисциплины являются необходимыми  PEDAGOGICAL SCIENCES (13.00.00)  элементами математического образования возникают ситуации, когда отсутствующие базовые знания теории вероятностей не позволяют студентам успешно освоить математическую статистику или теорию случайных процессов [4][5][6].…”

“…Отметим особый статус вероятностных дисциплин, идеология и дидактика преподавания которых существенно отличаются от других дисциплин математического цикла [4]. Как известно, теория вероятностей является аксиоматической теорией, такое построение дисциплины трудно для восприятия студентами технического направления, не имеющих достаточной подготовки по таким дисциплинам, как математическая логика, функциональный анализ, теория графов [5,6].…”