Instructional Design of an Online Upper-Level Undergraduate Geometry Course Using Hands-On Pedagogy

The purpose of this study was to explore instructors' perspectives on the effect of using pen-based technology in the online mathematics courses and understand instructors' experiences in online mathematics teaching with pen-based technology. In this study, two instructors who taught online mathematics courses in fourteen weeks used digital pen as a pen-based technology. The data were obtained from semi-structured interviews and observation of online mathematics course records. The findings indicated that the use of digital pen in the online mathematics course was fairly beneficial in pedagogical and interaction aspects and it was necessary to use digital pen in online mathematics courses for displaying steps of problem solving process synchronously. It was concluded from the study that digital pen technology plays a positive role in the enhancement of interaction between the elements of an online learning environment by providing real-time feedback to students and permitting to digitize mathematical concepts. The observation findings also supported the statements of the instructors. The findings of the study have further provided some insight into how to use digital pen by an instructor in online mathematics course efficiently.

Institutions of higher learning had to adopt a flexible learning delivery due to the threat of the global health crisis in 2020. Taking advantage of the technological affordances, many universities and colleges implemented the online learning modality. However, teachers and students found themselves overwhelmed with issues of quality assurance and outcomes of online teaching and learning. In this descriptive research study, the university students’ feedback on their engagement and satisfaction in the online mathematics courses was analyzed to get a perspective on successful online learning implementation. The mediation analysis on the responses of 512 university students on a 35-item researcher-made questionnaire showed that the university students were engaged and satisfied with their online mathematics courses. The design factor had a significant effect on learner engagement and satisfaction. The human factor has a significant impact on learner engagement but no significant effect on learner satisfaction. The structural equation model further revealed that learner engagement fully mediates the relationship between human factor and learner satisfaction while partially mediating the relationship between design and learner satisfaction. The results strongly assert the need for efficient and effective instructor knowledge and facilitation, more significant class interaction, and engaging use of technology in online mathematics courses to increase learner satisfaction.

Mathematics is the engine, vehicle, driver, and language of today’s initiatives, innovations, and human endeavors. In this mathematical-driven world, the ability to perform mathematical tasks and logical reasoning is also essential in solving quotidian tasks and problems. Therefore, mathematical competency and problem-solving skills are kept as an integral component in almost every educational curriculum around the globe. However, there are numerous stumbling blocks along the way to successful teaching, conducive learning environment, and good student performances in almost all disciplines, but more prevalent and visible in mathematics. The major concerns of educators responsible for teaching mathematics and mathematics-related courses are to find effective and innovative ways to deliver mathematical content, to extend the concepts and theories beyond the classrooms, to integrate mathematics with important concepts such as gamification, data mining, learning analytics, deep learning, and effective tools such as mobile devices, learning management systems, and digital technology, and to maintain a good record of students’ performance. In online deliveries, these concerns are further escalated due to no or limited one-to-one interactions and lack of face time, to mention a few. This article investigates the efficacy and effectiveness of traditional and innovative pedagogical practices used in online mathematic courses at the University of the South Pacific (USP). It examines the interdependence of embedded activities and students’ achievement. The results indicate that these online mathematics courses were highly dominated by conventional approaches and were less interactive and engaging, resulting in lower success rates when compared to the courses from other disciplines. To recommend possible ways to enhance the quality of learning and teaching in online mathematics courses, selected online courses from the information system discipline were explored. The reasons for the high online presence in the course were investigated and activities that could lead to collaborative and active learning beyond the passive materials were data mined. The evidence drawn from the statistical analysis highlights the importance of including selected interactive and engaging activities in online learning space of mathematics courses to promote student engagement and help create a sense of community among geographically dispersed students. Overall, based on the observations and theoretical foundation from literature, it can be said that including regular and frequent active assessment strategies, such as weekly quizzes and discussion forums, could extend and promote interactive and engaging learning in online learning space.

This study aims to examine the opinions of university students about using mobile learning Technologies in an online mathematics course during the pandemic (COVID-19) period. The participant group of the study consists of 266 university students studying at a private university. In the study, a mixed research method, in which quantitative and qualitative research methods are used, was used. A questionnaire form which was "Student Opinions Regarding Using Mobile Learning Technologies in an Online Mathematics Lesson During the Pandemic Process" created by the researchers and open-ended questions were used to reveal the opinions of the students about the online mathematics lesson. According to the results of the study, one can be seen that the majority of the students make an effort and spare time to understand mathematics in online lessons who use mobile learning technologies during the Covid-19 pandemic process. In addition, they argued that the majority of the students believe that they will be successful in the exam at the end of the online mathematics lesson by using mobile learning technologies and that it is easy to follow the mathematics lesson online using mobile learning technologies during the Covid-19 pandemic process, depending on the teacher giving the lesson. In addition, they stated the inadequacy of knowledge in the field of numeracy and the lack of technical infrastructure in distance education among the difficulties experienced by the students in the online mathematics course. As learning strategies in the virtual environment, the students stated that they did it again and again, watched the live lesson videos over and over, prepared an individual study program for themselves, took notes, attended regular classes, and watched educational videos by using mobile learning technologies.

The review of the literature on the role of instructional strategies in online mathematics learning addresses the following major areas and their related subsets: motivation and academic success; online learning and andragogy; and instructional design and learning strategies. It is noted that the hypothesis that motivational strategies promote achievement and success in online mathematics courses is supported by recent investigators who suggested the need to research the effectiveness of incorporating motivational strategies in the implementation of online instructional designs (Bellon & Oates, 2002; Kelsey & D’Souza, 2004; Patall, et al., 2008; Sanacore, 2008; Skinner, 2005). Additionally, the limited role documented on motivation in online mathematics courses by both mathematicians and educators is included. Next, discussions of online learning, andragogy and learning theories, learners’ characteristics and heuristics in interpersonal and cognitive tools are addressed. Lastly, laying the foundation of theory into practice, considerations for instructional designs are included along with suggestions for design and implementation of learning strategies.

Enrollment in online remedial mathematics courses has increased in popularity in institutions of higher learning; however, students unskilled in self-regulated learning (SRL) find online remedial mathematics courses particularly challenging. We investigated the role of SRL, specifically motivation, emotion, and learning strategies, in students’ learning experiences in a remedial online mathematics course. With an online survey of 229 college students, we found that student motivation explained a small portion of variance in achievement; whereas student motivation and emotion explained a significant portion of variance in satisfaction. In addition, significant differences in motivation and emotion were found in passing and nonpassing students; however, learning strategies did not influence student achievement and satisfaction. Implications for teaching and learning in self-paced online remedial mathematics courses are discussed.

The purposes of this study were to investigate (a) the effects of volition support (VoS) on students’ motivation, effort regulation, and performance as well as (b) the perceptions of students about VoS in an online mathematics course offered at a community college. VoS was developed based on the theories of and research on volition (e.g., Corno in, Educ Res 22(2): 14–22, 1993; Gollwitzer in, Am Psychol 54: 493–503, 1999; Keller in, Technol Instr Cognit Learn 6(2): 79–104, 2008). VoS consists of the four stages: (1) goal initiation (“Want it”), (2) goal formation (“Plan for it”), (3) action control (“Do it”), and (4) emotion control (“Finish it”). A virtual change agent was designed into VoS to provide the support to students. Results indicated that the experimental group provided with VoS showed higher effort regulation and performance than a comparison group without VoS although there was no difference in motivation. Findings and implications for design of and research on VoS interventions are discussed.

With the rapid advancement of generative artificial intelligence (GenAI), teaching and learning in higher education are undergoing profound transformations. As a foundational competency for students in the digital age, pathways to foster online mathematics learning power require exploration. Although teacher support is recognized as a critical factor, the mechanisms through which it might foster students’ new digital competencies, thereby contributing to online mathematics learning power within the context of intelligent technologies remain underexplored. This study aims to construct a multiple mediation model to examine how perceived teacher support predicts online mathematics learning power through two pathways: AI literacy (the ability to leverage artificial intelligence for mathematical cognition) and the use of cognitive tools (e.g., MATLAB, GeoGebra). A questionnaire survey was conducted among 758 undergraduates enrolled in online mathematics courses at a comprehensive university in eastern China. The instruments included scales for perceived teacher support, AI literacy, cognitive tools, and online mathematics learning power. Data were analyzed using structural equation modeling and bootstrap sampling to examine direct and mediating effects. The results confirm that within the generative artificial intelligence context, perceived teacher support directly predicts students’ online mathematics learning power while also indirectly predicts it by fostering AI literacy and cognitive tools proficiency. This reveals the mechanisms linking environmental support, digital competencies, and learning outcomes. This study suggests that educators adopt a teaching strategy integrating direct support, AI literacy cultivation, and cognitive tool guidance. This entails incorporating AI literacy and cognitive tools training into online mathematics course design within supportive learning environments. Doing so can effectively develop student competencies and prepare them for the intelligent era.

This study analyzed the level of stress experienced by students during online mathematics courses. Some students conveyed the conditions during the class. Some of them gave suggestions, such as using various learning media alternately. This study aimed to know the level of academic stress on students when attending online mathematics lectures and find solutions to the difficulties of online mathematics lectures. This study used a descriptive quantitative approach with the sample of 143 students. Data were analyzed using a descriptive statistical formula. The instrument used is a questionnaire adapted from D.A.S.S. 42 issued by the Psychology Foundation of Australia. Data collection was carried out using a Likert-type scale that was tested for its validity and reliability. Based on data analysis, most of the students experienced stress in the normal-level category. They enjoy learning mathematics using various kinds of learning media.

The current manuscript is a reflective case study that describes the emerging design of the author's first online mathematics course. The case study addresses how expectations associated with teaching in a live setting can raise conflicts in designing online courses. The author reframes the conflicts into questions; explores the questions and related resources; and describes one possible model for an online mathematics course. Student feedback on the written materials, teaching, and assessment developed for the online course are discussed.

The transition from high school to university-level mathematics is often accompanied by significant challenges. During the COVID-19 pandemic, these difficulties were further exacerbated by the abrupt shift to online learning. In response, educators increasingly turned to gamification—“a process of enhancing a service with affordances for gameful experiences in order to support users’ overall value creation”—as a strategy to address the limitations of remote instruction. In this study, we designed a gamified environment for a first-year Number Theory course. The system was constructed using targeted game elements such as leaderboards, optional challenge exams, and recognition for elegant solutions. These features were then integrated into a comprehensive point-based assessment system, which accounted for weekly quizzes and active participation. Following a quasi-experimental design, this study compared two groups of pre-service mathematics teachers: the class of 2017 (N = 62), which received traditional in-person instruction (control group), and the class of 2020 (N = 61), which participated in an online, gamified version of the course (experimental group). Both groups were taught by the same lecturer, using identical content, concepts, and similar tasks throughout the course. Academic performance was measured using midterm exam results. While no significant difference emerged on the first midterm in week 6 (their average percentages were 50% and 51%), the experimental group significantly outperformed the control group on the second midterm at the end of the term (their average percentages were 65% and 49%). These results suggest that a thoughtfully designed, gamified approach can enhance learning outcomes in an online mathematics course.

Perceived learning is seen as a key measure of actual learning and an essential element of course assessment. This research investigated how learning engagement mediates the relationship between learning self-efficacy and perceived learning in online mathematics courses. Using a predictive correlational approach, the study analyzed the impact of three aspects of learning engagement on the link between learning self-efficacy and perceived learning. A survey was conducted with a randomly selected sample of 605 students enrolled in online mathematics classes in Guangzhou. Structural Equation Modeling (SEM) with AMOS version 24.0 was employed to test the proposed model. The results from the maximum likelihood estimation showed that the measurement model for learning self-efficacy, engagement, and perceived learning fit well. The findings revealed that learning self-efficacy directly influences all three aspects of learning engagement in an online mathematics setting. Additionally, there was a direct relationship between learning self-efficacy and perceived learning, with all three dimensions of learning engagement partially mediating this connection. Overall, these results underscore the significance of improving student self-efficacy and engagement to enhance online learning experiences and outcomes.

This article is drawn from a dissertation (Holt, 2020) that describes, based on the teaching presence component of the community of inquiry (CoI) theoretical framework, the lived experiences of mathematics instructors while establishing teaching presence in online higher education mathematics courses. Teaching presence is necessary for achieving learning outcomes and student satisfaction. This article describes how mathematics instructors establish teaching presence in online higher education mathematics courses. The participants for this study were faculty members from a public university system. Data were collected from face-to-face and online mathematics course syllabi and in-depth, semistructured interviews. The interview data were subjected to a phenomenological analysis, and the syllabi were subjected to content analysis.

At our Historically-Black University, about 89% of first-year students place into developmental mathematics, negatively impacting retention and degree completion. In 2012, an NSF-funded learning enrichment project began offering the introductory and developmental mathematics courses on-line over the summer to incoming science, technology, engineering and mathematics (STEM) majors at no cost. Passing rates for the summer on-line classes were around 80%, and students in the on-line classes scored equivalently on the common departmental final exams as students taking the classes in the traditional format. For students who passed the on-line classes, their performance in the following classes (College Algebra and Trigonometry) exceeded that of students who progressed to those courses by taking the traditional series of in-person courses. Three years of data show that students who started college with an on-line mathematics course in a summer bridge program had a higher first year GPA, a better first year retention rate and earned significantly more credits in their first year than the overall population of STEM students. These results suggest that offering introductory mathematics courses on-line as part of a freshman bridge program is an effective, scalable intervention to increase the academic success of students who enter college under-prepared in mathematics. The positive results are particularly exciting since the students in our project were 87% minority.

The authors discuss the outcomes of a traditional and online mathematics course in the Mid-Atlantic United States. In the undergraduate Algebra course being investigated, the researchers used a matched pair design to determine whether technology infusion had positive effects on successful acquisition of mathematics skills. They also researched whether there was a pass/fail rate difference between the technology-enhanced class and the face-to-face class. The results indicated that there appeared to be a relationship between the instructional method and the pass/fail rate when comparing the traditional class and the technologyenhanced class.