What are possible Sources of Common and Persistent Student Errors in Algebra and Calculus?

Research shows that college students make numerous algebra and other prerequisite content-related errors in Calculus courses. Most of these errors are common, persistent, and often observed in simple mathematical tasks. This qualitative study is an attempt to identify the potential sources of such errors. Based on our observations of student errors, we wrote a Precalculus and a Calculus test and administered them in twelve sections of four different undergraduate mathematics courses for which either Precalculus, Calculus I or both were a prerequisite. The tests were announced on the first day of the class and administered the following week. All the questions on the test were True or False questions. Based on our experience as college mathematics instructors, we assumed that many students would perceive the True answers as False and the False as True. Therefore, if students’ selected a given answer, mathematical statement, process or solution as True, they were asked to justify why that was not False and vice-versa. They were instructed to provide logical explanations and avoid plugging in numbers to check for correctness. Analysis of data using grounded theory approach resulted in the following three possible external sources of common and persistent student errors: a) Difficulty with symbols and/or lack of attendance to the meaning of those symbols, b) Instructional practices, and c) Lack of knowledge. We will provide examples to illustrate how such errors could have originated from these sources.

Examination of Classroom Teacher’s Experiences Regarding Mathematics Courses Taught through Distance Education throughout the COVID-19 Pandemic Period

The aim of this study is to investigate the experiences of teachers regarding online primary school mathematics courses throughout the pandemic period. In this respect, the teachers were examined about the efficiency of distance education during the course sessions, the activities that involve the student, its positive and negative aspects, the utilized materials, portals, websites, the situation of students embodying the concepts, the extent to which they maintained the assessment, the difficulties they encountered within the process, as well as their suggestions. In the study, it was seen that teachers had both positive and negative views on distance education. The participant teachers in the study utilized different portals and websites throughout the distance education process. The majority of those teachers had the opinion that the methods used in mathematics courses through distance education assisted students in learning the concrete concepts. In the study, suggestions were made to enhance the efficiency of the mathematics courses along with distance education.

Exploring New PLTL Modalities, Forging New Alliances

This essay focuses on rethinking and reimagining elements of a PLTL program, and on the new modalities to meet challenges of online undergraduate mathematics courses and rising demands for flexible student support. It examines advantages and challenges as found in the Integrated PLTL and Virtual Peer-Led Mathematics Study Groups, including issues such as meeting protocols, and the selection and training of peer leaders. Finally, it discusses an alliance with the college’s mathematics education program, which allows the PLTL program to draw on senior prospective teachers to co-organize and facilitate virtual study groups supporting undergraduate mathematics courses.

How can we illustrate the usefulness of the differential calculus course taught in a technical university

Working in a challenging academic environment as mathematics professors for the Technical University of Civil Engineering Bucharest, we thought to find a teaching strategy that, in addition to the required standard, but also has the standard of attractiveness and accessibility. Why? This is due to the fact that our students have a very nonhomogeneous level of knowledge and logical-mathematical skills. That's how we came up with the idea of organizing each lesson in our courses in a gradual way, and completing them with an informal part. On the other hand, we set out to collaborate with professors working in the departments of other natural sciences or in engineering departments, enriching the mathematics courses with technical applications. This has led to write several didactic works, which also include such applications. Proving the usefulness of this courses, our new work offers two such technical applications for the mathematical analysis course, taught in the first semester and dedicated to the differential calculus of functions having one or several variables. More precisely, we present in a gradual way, two applications solved by using the mathematical modelling: a problem belonging to electricity and then, the cruising speed problem. The gradual presentation begins, for each of these problems, with the necessary notions (organized in the form of two dictionaries, for Math and for Physics, respectively), continues with the statement of the problem, with the solution methodology, and finally, with the solution itself. Our presentation will provide students with a model of logical (mathematical) approach, useful to them in the courses of other natural sciences and of engineering disciplines that they will study later. In addition, it will prove them why mathematics is a fundamental discipline for the engineering education.

The effectiveness of the Blackboard Elements During Corona Pandemic in Light of the Quality Assurance and Accreditation Standards from the Viewpoint of Faculty Members: A Case Study of the Mathematics Department at Umm Al-Qura University

The study aimed to identify the effectiveness of the Blackboard elements during Coronavirus pandemic in light of the quality assurance and accreditation standards from the viewpoint of faculty members at the Mathematics Department, Umm Al-Qura University. To achieve the objectives of the study, the descriptive analytical method was used. The study sample consisted of (45) members of the teaching staff in the mathematics departments of Umm Al-Qura University, who taught mathematics courses during Coronavirus pandemic. The questionnaire, which consisted of (33) items, was used to collect relevant data. The results of the study indicated that the effectiveness of the four components of the Blackboard that were studied during the Corona pandemic in light of the standards of quality assurance and accreditation was at a medium degree of (3.32), while the effectiveness component of cloud storage on the Blackboard got the highest score (3.68). The effectiveness component of the digital library on the Blackboard got the lowest score among the four elements (3.11). These results suggested the need to increase attention to the requirements of achieving quality assurance and work to raise them in higher education institutions for interactive mathematics courses, as the lack of interest in them may have affected the results and outcomes of mathematics students. The study concluded with a number of recommendations, including supporting the elements of the Blackboard and using them in the educational process, developing and evaluating them in the light of quality standards; conducting further studies on the use of the Blackboard; providing all facilities for the success of the educational process; and seeking to achieve quality and accreditation requirements whenever possible.

Examination of Classroom Teacher’s Experiences Regarding Mathematics Courses Taught through Distance Education throughout the COVID-19 Pandemic Period

The aim of this study is to investigate the experiences of teachers regarding online primary school mathematics courses throughout the pandemic period. In this respect, the teachers were examined about the efficiency of distance education during the course sessions, the activities that involve the student, its positive and negative aspects, the utilized materials, portals, websites, the situation of students embodying the concepts, the extent to which they maintained the assessment, the difficulties they encountered within the process, as well as their suggestions. In the study, it was seen that teachers had both positive and negative views on distance education. The participant teachers in the study utilized different portals and websites throughout the distance education process. The majority of those teachers had the opinion that the methods used in mathematics courses through distance education assisted students in learning the concrete concepts. In the study, suggestions were made to enhance the efficiency of the mathematics courses along with distance education.

Um Estudo Analítico das Práticas Formativas no Estágio Supervisionado das Licenciaturas em Matemática

Resumo Este artigo tem como objetivo analisar as práticas formativas apresentadas em um conjunto de dissertações e teses que versam sobre o Estágio Curricular Supervisionado na Licenciatura em Matemática. O corpus desse trabalho compreende 19 dissertações e teses publicadas no período compreendido entre os anos de 2001 a 2015. Esses trabalhos foram classificados em três categorias: prática-reflexiva, estratégias metodológicas e compartilhamento de ações. Esse trabalho caracteriza-se como uma metanálise e teve como base uma revisão bibliográfica em bases de dados públicas. Ao retomar esses trabalhos publicados como objetos de estudo, estamos valorizando o que foi pesquisado e sistematizado por esses autores e autoras, como também abrindo possibilidades para novas contribuições e propostas formativas ancoradas no que foi apresentado. Deste modo, os resultados indicam que cada categoria privilegia determinadas características formativas, como também tendem a valorar a relação professor-aluno de maneira diferente, além de esperarem um fazer docente também distinto. Os dados também nos sugerem um movimento formativo que saiu de uma proposição em relação ao professor em formação que parte da postura reflexiva e caminha para uma reflexão centrada na ação da relação teoria-prática. Em última instância, vemos uma valoração dos conceitos de compartilhamento e mediação em que estes são agregados ao processo, passando pela necessidade de um aprofundamento teórico e conceitual do conhecimento matemático. Palavras-chave: Estágio Supervisionado. Licenciaturas em Matemática. Práticas Formativas. AbstractThis article aims to analyze the formative practices presented in a set of dissertations and theses that deal with the Internship in Mathematics courses. The corpus of this work comprises 19 dissertations and theses published in the period from 2001 to 2015. These works were classified into three categories: reflective-practice, methodological strategies and sharing of actions. This work is characterized as a meta-analysis and was based on a bibliographic review in public databases. By resuming these published works as objects of study, we are valuing what was researched and systematized by these authors, as well as opening possibilities for new contributions and training proposals anchored in what was presented. Thus, the results indicate that each category favors certain formative characteristics, as well as they tend to value the teacher-student relationship differently, in addition to expecting a different teaching profession. The data also suggest a formative movement that came out of a proposition in relation to the teacher in training that starts from the reflexive posture and moves towards a centered reflection on the action of the theory-practice relationship. Ultimately, we see an appreciation of the concepts of sharing and mediation in which they are added to the process, going through the need for a theoretical and conceptual deepening of mathematical knowledge. Keywords: Internship. Mathematics Courses. Teacher Education.