Computer Animation to teach interpolation

Students struggle with developing conceptual understanding of abstract concepts in Science, Technology, Engineering, and Mathematics (STEM) courses. Two-dimensional (2D) figures are commonly used during instruction in textbooks and multi-media presentations such as PowerPoint, or in computer animation. The use of 2D visualizations during instructions lacks opportunities for students to meaningfully explore these concepts by rotating three-dimensional (3D) visualizations and examining how the rotations impact the 2D representations. Instructions delivered using 3D visualizations have the potential to improve conceptual understanding of both concrete and abstract concepts. In this study, we employ a multiple case study methodology to examine student gestures to explore how the use of augmented reality in an immersive technology environment can impact conceptual understanding of abstract concepts in STEM education. Preliminary findings indicate that students utilize gestures that represent the visualizations in the AR application to think and reason about abstract concepts such as electric and magnetic fields. In addition, these gestures appear to be related to mental simulations that students employ during problem-solving. The benefits of employing innovative pedagogical approaches through correct gestures, visualization and cueing representations is not limited to improving conceptual understanding in STEM but promote problem solving and critical thinking. The benefits derived from integrating gestures and 3D visualizations in AR immersive technological environments suggest that using embodied learning activities have strong potential for abstract conceptual learning in STEM

Teaching mathematics in an EFL context at higher education; before, during and after the COVID-19 pandemic: a comparative study

This paper reports on a study that examined science majors' conceptions of learning experiences in first-year undergraduate science and mathematics courses. The researchers were particularly interested in factors that contribute to or hinder students' performance and decisions to persist in their degree programs. Study participants shared their conceptions during one of four focus group interviews. These data were examined to identify themes across the interviews and resulted in two major findings. The first finding was that students struggle with the amount of content in science and mathematics courses and perceive misalignment between what they learn during class and what they are assessed on for exams. The second finding indicated that students value the support that faculty and peers provide both in and outside of class. These findings suggest a need to improve on and clarify course content and assessments, and to leverage opportunities for students to interact with faculty and peers as a way to foster academic success and persistence for science majors.

Supporting students in the transition from secondary school to university is an important action to be taken in order to increase the number of people with tertiary education degrees; it has positive consequences on the citizens’ working perspective and on the national economic growth. To this purpose, in the academic year 2014/2015 the University of Turin started the Project Orient@mente, a platform of self-paced open online courses aimed to guide students in the choice of a scientific university program. This paper focuses on the design of the Realignment Course in Mathematics, provided by the platform and aimed at the self-paced review and integration of knowledge that students are required to acquire during secondary school. Materials are created and structured according to the User Experience Design for Learning, with the aim of providing a valuable learning experience to students. Contents are delivered through an accessible learning management system integrated with an advanced computing environment and an automatic assessment system. Data from the usage of the activities and from the results of the online tests are analyzed in order to validate the design choices and the coherent structure of the course.

In this chapter, a flipped model is implemented in an undergraduate mathematics course. There is a need to enhance learning experiences in STEM disciplines and college mathematics courses. The authors seek to redefine the traditional relationship of instructor as the active conveyor of knowledge and the student as the passive receiver of knowledge. They discuss their efforts to plan and prepare for the course and their experiences with its implementation. The authors started with what they wanted their students to learn in the course. Prior to coming to class, students watched video lectures and completed pre-work assignments. In class, the authors incorporated group-work through peer-instruction and lab activities, and the use of a classroom response system. They present the results of their data collection, feedback from student response surveys. Among other results, the students realized the value of preparation and took an active role in the formation of their own learning experiences.

A significant portion of mathematics education research has focused on factors that impact student pursuit of science, technology, engineering and mathematics (STEM). Low rates of STEM student enrollment combined with high drop-out rates have consistently drawn attention from educators, administrators and policy-makers at all levels. Many studies have been dedicated to the investigation of the influential factors that exacerbate this problem, and one factor that has been cited consistently is the learning experience in a specific introductory mathematics course – first-semester calculus. Research has shown strong relationships between STEM persistence and student affect in this context including their attitudes, beliefs, confidence and enjoyment related to mathematics, and between persistence and student perceptions of pedagogy in these courses. In this paper, we extend prior work by the authors by investigating the impact of three different Calculus I course settings on these relationships and find that some course structures have a moderating effect on these relationships. We present those results and indicate some possible ways to leverage pedagogical structures to improve student persistence in pursuing a STEM major.

Supplementary education has been always a topic of discussion in academia. In most of developing countries, students lack of a solid education in mathematics. In particular, freshmen engineering students have shown deficiencies in the areas of arithmetic, algebra and trigonometry, which are prerequisites for entry-level mathematics courses. In this paper, we focus on freshmen engineering students enrolled in the first calculus course offered by Universidad Galileo in Guatemala. We show how the deficiencies from high school education were detected, and then, we present the improvement obtained by our students as a result of a hands-on based supplementary course. Such a course was focused on developing problem solving and operatory skills in the previous mentioned areas. In contrast to classic supplementary approaches, our course was offered concurrently with the calculus course and its grade was part of the main course grade distribution. The course design and execution details are also addressed. In order to analyze the impact of our supplementary course we split the class into two groups based on the abilities they presented in a diagnostic test conducted at the beginning of the academic period. At the end of the term, we repeated the same diagnostic test in order to compare the impact of such a supplementary class. Our main result showed that, even though we could not level up the two groups of study, we were able to reduce the academic breach between them by 34%. In addition, we present all the statistical analysis and comparisons between different tests we ran throughout the study. We conclude the discussion with the future improvements to implement in order to achieve better results.

Note from the EditorsToo often, biology has been considered by both students and faculty as the ideal major for the scientifically inclined but mathematically challenged, even though the advantage of quantitative approaches in biology has always been apparent.Increasingly, biologists are utilizing mathematical skills to create simulations or manage and query large data sets.The need for basic mathematical and computer science (CS) literacy among biologists has never been greater.But does this require a fundamental change in the organization of the undergraduate biology curriculum?What is the utility of math/CS in different areas of biology?How can we best provide math/CS instruction to biologists so that the utility is appreciated?Do all biology students require a stronger math/CS foundation, or only those interested in research careers?Given the speed at which technology changes, what is the best preparation?Three different points of view are offered below.Dr. Roger Brent, President and Director of the Molecular Sciences Institute, reflects on the "innumeracy" common among biologists and argues that significant insights into biological problems may be gained from better mathematical intuition.

Choosing and Adapting Technology in a Mathematics Course for Engineers Jenna Tague, Ohio State University Jenna Tague is a mathematics education doctoral student at The Ohio State University. She received her B.S. and M.S. in mathematics from Bucknell University and Colorado State University, respectively. Research interests include mathematics for engineering students and problem solving. Miss Jennifer Czocher, Ohio State University Jennifer Czocher is a doctoral candidate in mathematics education at Ohio State University. Her research interests are mathematical modeling and mathematical thinking in STEM disciplines. Prof. Gregory Richard Baker, Ohio State University Ms. Amanda Roble, Ohio State University

In Mastery-Based Assessment (MBA), students have multiple attempts to meet standards set via course learning outcomes (Collins et al. [2019]. Mastery-based testing in undergraduate mathematics courses. PRIMUS, 29(5), 441–460. https://doi.org/10.1080/10511970.2018.1488317), often as it pertains to lower-stakes assessments like homework or quizzes. This mixed methods case study focuses on evaluating an implementation of MBA in an introductory proof class for undergraduates at a private R1 university in order to assess its impact on learning and student experience. In spring 2023, the first author taught two classes of such a course simultaneously; one heavily using MBA and the other using a traditional assessment scheme. Both classes were given common examinations and submitted regular reflections. The distributions of examination scores from each class were analysed in several ways, including the difference in performance between the midterm and final examinations. Student reflection data were inductively coded, and analysed for emergent themes. Findings suggest: (a) there was no significant difference in the distributions of examination scores between the classes; (b) there was no significant difference in the relative performance of students between the two examinations between the classes; (c) students had a strongly positive perception of MBA. We believe longer-term studies into ‘hybrid’ assessment featuring mastery-based and traditional assessment practices in tandem are warranted.

Online (web-based) courses emerged at the beginning of the twenty-first century. While this new pedagogic paradigm (PP) holds a promise of better learning and training, it comes with challenges as traditional PPs are not suited to the new settings which highly differ from the physical classroom methods. We studied three online PPs (Synchronous, Asynchronous, and Asynchronous with an audience) and their influence on the students learning process and achievements during an academic mathematics course that was conducted online. 168 students took an exam and answered a questionnaire regarding their learning preferences, experience, and habits after experiencing one of these PPs. We found that students who studied according to the asynchronous with an audience PP achieved a higher score in the exam, regardless of their initial level than students who learned by either the synchronous or asynchronous PPs. In addition, we developed a personalized model based on machine learning methods that match an online PP for each student to maximize the student’s score in the exam. In the case of an academic mathematical course, the online PP had a major influence on the students’ scores in the exam. We found that students with high grades in previous courses preferred synchronous learning, which indicates the importance of picking the right online PP for each student. Our model provides a novel tool for the pedagogic community to personalize online learning by recommending the PP that could be most suitable for each student.

The digitalization system that continues to roll has brought changes to the learning system, where face-to-face learning is replaced by an online system. On the one hand, learning experiences to acquire critical thinking (CT) skills as one of the essential skills of the 21st century must also be encouraged. The objective of this study is to assess students’ CT skills in terms of cognitive style by implementing the problem-based e-learning (e-PBL) model in mathematics courses. This study is an evaluative study with an experimental approach, where as many as 28 students as research samples were taken purposively from Mandalika University of Education, Indonesia. A set of instruments was prepared to measure every aspect of CT and cognitive style, including descriptive and statistical data analysis so that the results of the CT assessment were found. In general, the results of the CT evaluation show that e-PBL is effective in improving students’ CT skills, so this is a recommendation to use e-PBL widely and intensively.

The purpose of this study is to explore how to effectively integrate ideological and political education into the mathematics curriculum by proposing a "combination of classroom teaching, practical training projects, and competition activities". By organically combining classroom teaching, practical training projects, and competition activities, it promotes students' learning of mathematical knowledge while enhancing their sense of social responsibility and professional ethics. Research results show that this model has significantly improved students' mathematics performance, especially in terms of basic knowledge and modelling ability. At the same time, by participating in mathematical modelling competitions and practical training, students have demonstrated strong teamwork spirit and innovation ability, and their professional ethics have been significantly improved. Through questionnaires and interviews, the feedback results show that students attach great importance to the practical value of the curriculum and ideological and political education. Finally, the research suggests that the integration of ideological and political elements into more mathematics courses should be explored in the future, in order to improve the quality of education and cultivate high-quality talents with a sense of social responsibility and professional ethics.

The application of mathematics has become an important task of mathematics education. Mathematical modeling is a bridge between mathematics and the real world, a mathematical abstraction of real problems, and a higher level of comprehensive literacy. It can effectively improve students’ comprehensive practical ability and their ability to acquire knowledge independently, and at the same time, it is conducive to students’ achievement of other core mathematical literacy goals. Therefore, it is very necessary to apply the thought of mathematical modeling in mathematics classes of colleges and universities. It is found that the specific method and case implementation of applying mathematical modeling idea to classroom teaching is not thorough enough. The purpose of this paper is to study the method of integrating mathematical modeling into higher mathematics teaching in applied universities under the epidemic situation. In this article, through classroom practice and take the questionnaire research method, from the Angle of subjective and objective respectively from students’ mathematical modeling ideas on the improvement of their teaching and learning situation, etc to investigate, using mathematical modeling thought teaching can change students’ attitude and understanding of mathematics, and the ability to change students mathematics study, help students to set up the correct view of mathematics and mathematics learning concept. The proportion that “modeling ideas can stimulate learning interest” is above 40%.

There are new educational approaches that are moving towards student-centred teaching and learning. One of them is challenge-based education, where students acquire and develop disciplinary knowledge and competencies by collaborating on solving real-life problems. Hence, in this paper, we report on a study of applied mathematics students’ learning experiences in the context of challenge-based education in a higher education mathematics course. Using a case study approach, we investigate how students perceive the role of the different resources to help them solve real-life problems during a one-week challenge-based modelling course. We collected data, from four groups of students (5–7 students each) who worked together and interacted with their mathematics supervisors and problem owners. Results show (1) the crucial importance of using and integrating different resources, such as social resources (e.g. mathematics supervisors and problem owner), for such learning environments to link mathematics to an authentic situation and develop the skills of an ‘applied mathematician in the real world’; (2) the relevance of mathematical knowledge in creating models to solve real-life challenges.