Assessment of engineering mathematics in the context of distance learning

Mathematics is a crucial component of programmes on engineering, science and technology. In the context of computerised distance learning education, the subject of engineering mathematics is often delivered and assessed through a digital learning environment. This paper gives an overview of the history of distance learning education and its mathematics component. It also discusses the most popular on-line automated technologies applied to the assessment and evaluation of engineering mathematics including problems of the on-line representation of mathematical graphs and equations in the assessment material

The Influence of Teaching Instruction and Learning Styles on Mathematics Anxiety in the Developmental Mathematics Classroom

In the US, an estimated 25% of four-year college students and up to 80% of community college students suffer from a moderate to high degree of mathematics anxiety (MA) (Chang & Beilock, 2016). Many scholars have noted that mathematics anxiety can be regarded as a significant factor in determining a student's achievement and mathematics related jobs. In the existing literature body, many researchers noted that MA may stem from teaching methods that are more conventional and rule-bounded such as lecture-style classroom models. On the other hand, MA can be mitigated by inquiry-based learning classroom models where students construct knowledge through inquiry, communication, critical thinking, and group work. However, the current literature has not built the connection between different teaching styles and students' individual differences with respect to MA. The individual differences are associated with the personality of the learner, learning styles, learning speed, and needs and interests of the learner. Depending on a student's learning style and a compatible teaching style, the student may actively participate in their own learning with less mathematics anxiety. Thus, the purpose of this study is to determine the influence of different teaching styles on MA, when interacted with Kolb’s and Gregorc’s (1984) four different learning and thinking styles. The research questions investigated in this study are: 1) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on students’ mathematics anxiety levels over a fifteen-week semester of a college-level remedial mathematics course?; 2) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on mathematics anxiety levels for students with different learning and thinking styles (as defined by Kolb’s and Gregorc’s learning styles) over a fifteen-week semester?; and 3) What aspects of instructional approaches (LCM and IBL) do students with different learning and thinking styles report as being related to mathematics anxiety? The abbreviated version of the mathematics anxiety rating scale (A-MARS), Kolb’s learning styles inventory, Gregorc’s thinking styles, and Written questionnaire were used to measure students’ MA levels and identify their learning and thinking styles. The results provided evidence that IBL instruction is beneficial for the students with MA, especially with mathematics test anxiety and mathematics course anxiety. Only numerical task anxiety was not significant. Thus, student-centered learning pedagogies turned out to be an effective and engaging method for lowering MA. However, there was no evidence to support the overall relationship between the constructs of learning and thinking styles and MA levels, above and beyond the instructional approaches. Classifying students according to learning and thinking styles did not influence students’ MA levels in this study over the 15 academic weeks. Moreover, after a 15 academic weeks, students in both LCM and IBL classes responded positively to key components of LCM and IBL classroom models. This implies that both LCM and IBL approaches still are important models regardless of students’ MA levels

Large scale Open Educational Resources (OER) initiative in mathematics

A team of LaGuardia Community College math faculty designed and launched the OER (Open Educational Resources) project in Spring 2017 to allow to take mathematics courses at zero or low textbook cost. Our first pilot phase started with 10 sections in Fall 2017 using three different OER platforms: Myopenmath, Webwork and Khanacademy. One out of the three platforms, Myopenmath used in phase 1 was selected to pilot 34 sections in Spring 2018. In Fall 2018, the OER team moved to a full-scale implementation on all remedial and gateway courses of 164 sections including Fundamentals of Algebra, Intro to Algebra, Elementary Algebra Co-req STEM, College Algebra and Elementary Statistics. From Fall 2017 to Spring 2018, a total of $477,182 was saved by 5,560 LaGuardia students. By Fall 2019, the project had saved a total of$1,184,329.25 on textbook costs. In addition, the pass rates for OER courses were either better or the same when compared to non-OER courses. Furthermore, the pass rate for OER Co-req STEM was almost two times higher than the one for non- OER Co-req STEM sections

A Comparison of Student Final Grades in College Algebra Based on Face-to-Face and Online Course Modalities

As community colleges emerge from the COVID-19 pandemic there may be a tendency to rely on technology to facilitate more online coursework. Online education has been a fixture of higher education since the mid-1990s, but there’s always been a question as to whether it is effective as traditional, face-to-face coursework. This is especially important in College Algebra, already viewed as a barrier course for many students. If more students take College Algebra online, will the results be as good as students taking the course in a classroom? The purpose of this quantitative causal-comparative study is to identify the relationship between course modality and final grade percentage, after accounting for instructor and curriculum effects for college algebra courses taught both online and face-to-face. Previous research studied this question, but a consensus about the efficacy of online education was mixed. Some studies found that online students perform worse than face-to-face students in college algebra (Amro, 2014; Amro et al., 2015; Driscoll, 2012). Other studies found no difference between the modalities (Araeipour, 2013; Harrington et al., 2016; Huang, 2016). Research by Burch and Kuo (2010) and Graham and Lazari (2018) discovered online students perform better than face-to-face students. This study considered the question through the lens of Moore’s Theory of Transactional Distance, which examines the distance between the learner and instructor, course content, interface, and other learners as a psychological distance rather than a spatial distance. Using one instructor teaching both online and face-to-face courses using the same materials was an attempt to keep transactional distance as a constant, mitigating instructor and curriculum effects that could impact a study comparing modalities. Previous research that accounted for the instructor and course materials found no significant difference in outcomes based on modality. This study looked at final grade percentages in College Algebra courses taught by one instructor with both online and face-to-face sections over the course of the 2017-2018 school year. Data were supplied by a two-year institution located in rural Arkansas. In addition to looking for the relationship between modality and final grade percentages, the study looked for relationships between gender and final grades, a student’s age and final grades, as well as an interaction between online students and their age or gender on final grade percentages. Findings indicated there was no significant relationship between the course modality and final grade percentages. Additionally, there was no relationship between gender or age and final grades based on modality. However, one significant relationship the study found was that when women took online algebra, they scored over 15 points lower than men taking online algebra. There was no interaction between a student’s age and taking an online college algebra course. Further research should expand on the notion of accounting for Transactional Distance while looking at the relationship between course modality and final grade percentages and expand the study to disciplines outside of college algebra. Finally, research should investigate whether the relationship changed after the COVID-19 pandemic altered perceptions and implementation of online courses

A Comparison of Student Final Grades in College Algebra Based on Face-to-Face and Online Course Modalities

As community colleges emerge from the COVID-19 pandemic there may be a tendency to rely on technology to facilitate more online coursework. Online education has been a fixture of higher education since the mid-1990s, but there’s always been a question as to whether it is effective as traditional, face-to-face coursework. This is especially important in College Algebra, already viewed as a barrier course for many students. If more students take College Algebra online, will the results be as good as students taking the course in a classroom? The purpose of this quantitative causal-comparative study is to identify the relationship between course modality and final grade percentage, after accounting for instructor and curriculum effects for college algebra courses taught both online and face-to-face. Previous research studied this question, but a consensus about the efficacy of online education was mixed. Some studies found that online students perform worse than face-to-face students in college algebra (Amro, 2014; Amro et al., 2015; Driscoll, 2012). Other studies found no difference between the modalities (Araeipour, 2013; Harrington et al., 2016; Huang, 2016). Research by Burch and Kuo (2010) and Graham and Lazari (2018) discovered online students perform better than face-to-face students. This study considered the question through the lens of Moore’s Theory of Transactional Distance, which examines the distance between the learner and instructor, course content, interface, and other learners as a psychological distance rather than a spatial distance. Using one instructor teaching both online and face-to-face courses using the same materials was an attempt to keep transactional distance as a constant, mitigating instructor and curriculum effects that could impact a study comparing modalities. Previous research that accounted for the instructor and course materials found no significant difference in outcomes based on modality. This study looked at final grade percentages in College Algebra courses taught by one instructor with both online and face-to-face sections over the course of the 2017-2018 school year. Data were supplied by a two-year institution located in rural Arkansas. In addition to looking for the relationship between modality and final grade percentages, the study looked for relationships between gender and final grades, a student’s age and final grades, as well as an interaction between online students and their age or gender on final grade percentages. Findings indicated there was no significant relationship between the course modality and final grade percentages. Additionally, there was no relationship between gender or age and final grades based on modality. However, one significant relationship the study found was that when women took online algebra, they scored over 15 points lower than men taking online algebra. There was no interaction between a student’s age and taking an online college algebra course. Further research should expand on the notion of accounting for Transactional Distance while looking at the relationship between course modality and final grade percentages and expand the study to disciplines outside of college algebra. Finally, research should investigate whether the relationship changed after the COVID-19 pandemic altered perceptions and implementation of online courses

Web-Based Homework versus Paper-Based Homework in United Arab Emirates Secondary Mathematics

This study investigated whether Web-based homework (WBH) in mathematics is a method of homework delivery more suitable than traditional paper-based homework (PBH) for United Arab Emirates (UAE) secondary students in Abu Dhabi. Few studies have addressed delivery methods for mathematics homework outside of a context where homework is considered usual practice. The study centres in the UAE because of its culturally distinctive attitudes towards homework completion and reportedly low levels of self-efficacy among Emirate students. If homework completion and performance were to increase, WBH could offer opportunities to enrich student learning and engagement in mathematics. This study used the WBH tools Myimaths and GeoGebra in selected school years. The research questions for this study were as follows: (1) Do students interact more with WBH than with PBH? (2) What are student perceptions of their learning with WBH and PBH? The sample consisted of approximately 2,000 students. The data for this two-group, pre-and post-test control group design was collected over three years, covering school years 2012 to 2015. As a measure of interaction, a Pearson Chi-square test suggested that student homework completion was significantly higher in the WBH group. The result led to the rejection of the null hypothesis for the first research question, suggesting that students do interact more with WBH than with PBH. Analysis of the student survey and interview transcript notes indicated that students perceived they spent more time practicing mathematics using the WBH tools due to the immediate feedback offered by the tools. Furthermore, they were encouraged by the feedback to review their mistakes and revise their thinking, subsequently resubmitting their WBH to get a higher score. Student perceptions in this study were that the availability of multiple homework submissions was a motivating factor that contributed to them spending more time practicing mathematics. Students reattempted the homework tasks that led to the possibility of them revising certain mathematical concepts and procedure while in pursuit of a higher homework score. Though WBH is limited in terms of written explanations and partial credit scores for correct mathematical procedures, in comparison to PBH, student interview perceptions in this study were that the WBH tools used facilitated positive interaction effects. The effects described were improved levels of motivation, positive peer communication, higher rates of homework completion and an improvement in their mathematics homework performance

Mathematics Teachers’ Activation of Online Homework Via Madrasati Platform During Corona Pandemic and Its Relationship to Some Variables

This study aimed to identify the mathematics teachers’ activation of online homework via Madrasati Platform during COVID-19 Pandemic in general education stages. A questionnaire tool was designed and used to collect quantitative and qualitative data, from (135) math teachers who participated in the study. A mixed design method was used for data analysis. The results indicated a high percentage of online homework activation via Madrasati Platform according to the opinions of the mathematics teachers. The results also showed that there are statistically significant differences between mathematics teachers activation of online homework according to the gender variable (male and female) in favor of females. But there are no statistically significant differences according to the school stage variable (elementary, middle, and high). The results also indicated that there were some obstacles of online homework, such as: the weakness of internet speed, high cost of its infrastructure, limited follow-up of parents of their children to complete online homework. The teachers suggested some proposals to develop online homework management via Madrasati Platform, such as: development of the virtual platform so that it considers the nature of mathematics in terms of using the integration of some software, such as: GeoGebra and others. The study presented a set of future research proposals, which are an extension of the current study

Interactive and multimedia contents associated with a system for computer-aided assessment

This paper presents a research study addressing the development, implementation, evaluation and use of Interactive Modules for Online Training (MITO) of mathematics in higher education. This work was carried out in the context of the MITO project, which combined several features of the learning and management system Moodle, the computer-aided assessment for mathematics STACK, the mathematical software GeoGebra, several packages from the type-setting program LaTeX, and tutorial videos. A total of 1962 students participated in this study. Two groups of students taking a Calculus course were selected for a deeper analysis. In regard to usability and functionality, the results indicate that MITO scored well in almost all aspects, which is fundamental for their introduction into formal university courses. The analysis of the data reveals that the use of MITO educational contents by students mainly occurs about one week and a half prior the evaluations. Moreover, there is a strong correlation between the results of online assessments on MITO in a continuous assessment model and the final grade on the course

The Effectiveness of Blended Instruction in Core Postsecondary Mathematics Courses

Most students in U.S. universities are required to take a collection of core courses regardless of their degree or major. These courses are known as general education courses. The general education requirements typically include at least one mathematics course. Unfortunately each year hundreds of thousands of students in the US do not succeed in these general education mathematics courses causing them to act as a barrier to degree completion. Low student success rates in these courses are pervasive, and it is well documented that the U.S. needs to improve student success and retention in general education mathematics courses. In this paper, we compare the impact of a new instructional style on student retention and success in three general education mathematics courses. The new instructional style, that we have dubbed the Memphis Mathematics Method (MMM), is a blended learning instructional model, developed in conjunction with the National Center for Academic Transformation (NCAT). Our control consists of conventional lectures using identical syllabuses. The data contains 12,261 enrollments in College Algebra, Foundations of Mathematics, anq Elementary Calculus over the Fall 2007 to Spring 2010 terms at the University of Memphis. Our results show the MMM was positive and significant for raising success rates particularly in Elementary Calculus. In addition, the results show the MMM as a potential vehicle for closing the achievement gap between black and white students in such courses

Персональне освітнє середовище – як один із трендів сучасної освіти

To meet the needs of the modern information society one must constantly improve the education system. The effectiveness of teaching today’s students fully depends on the implementation and use in the study of modern information and communication technologies, including network services that allow you to create an appropriate pedagogy and technology support base of modern information systems for educational purposes, and effectively organize the electronic learning university environment. An analysis of e-learning environments of modern domestic and foreign universities demonstrates quite a high level of qualitative and quantitative indicators of the implementation of electronic resources for educational purposes. However, despite the relatively high level of organization and content of university portals, the creation and implementation of students‘ personalized e-learning environment, which in turn is based on personalization in a global network, student-centered learning, which acts as a basis for the formation of ICT and key competencies of modern student, is still an open issue. The selfspontaneous creation of personalized e-learning environment does not cover the training needs of students, but is only partially able to satisfy them, as knowledge students cannot improve the quality of both formal and informal learning. This paper focuses on the study of students‘ ICT competencies and their ability to use information and communication technologies to carry out information activities in their professional field. The authors also discuss the results of studies on personalized and adaptive learning, based on consideration of learning styles. Based on a statistical analysis of the pedagogical experiments, some recommendations are suggested for technology training for teachers and students in order to to improve training efficiency