Based on the current situation of advanced mathematics curriculum teaching, this study first constructs a blended learning model for advanced mathematics based on SPOC through literature research ...from three aspects: curriculum design, teaching implementation, and learning evaluation. And designs a specific blended teaching case combined with the "definite integral concept". Then, we conducted a purposeful sampling in a public school called Qinghai Normal University and selected 82 students from two first-year classes majoring in biotechnology as the research objects, and carried out an 18-week empirical study with experimental control. Finally, the final grades and teaching evaluation questionnaires of students in advanced mathematics were collected for data processing and analysis. The research results showed that students in the SPOC blended learning class had better math scores than those in the traditional teaching class, and blended learning could narrow the gap in students' math proficiency. At the same time, the questionnaire survey found that students believe that blended learning in advanced mathematics courses has abundant resources, frequent interaction and communication, and can improve learning efficiency. However, traditional advanced mathematics learning puts a lot of pressure, and they are busy taking notes in the classroom and cannot respond to the teacher's questions in time.
Based on the current situation of advanced mathematics curriculum teaching, this study first constructs a blended learning model for advanced mathematics based on SPOC through literature research ...from three aspects: curriculum design, teaching implementation, and learning evaluation. And designs a specific blended teaching case combined with the "definite integral concept". Then, we conducted a purposeful sampling in a public school called Qinghai Normal University and selected 82 students from two first-year classes majoring in biotechnology as the research objects, and carried out an 18-week empirical study with experimental control. Finally, the final grades and teaching evaluation questionnaires of students in advanced mathematics were collected for data processing and analysis. The research results showed that students in the SPOC blended learning class had better math scores than those in the traditional teaching class, and blended learning could narrow the gap in students' math proficiency. At the same time, the questionnaire survey found that students believe that blended learning in advanced mathematics courses has abundant resources, frequent interaction and communication, and can improve learning efficiency. However, traditional advanced mathematics learning puts a lot of pressure, and they are busy taking notes in the classroom and cannot respond to the teacher's questions in time.
To understand the quantile regression model, research on a statistical analysis of advanced mathematics teaching quality evaluation was proposed. In the research, based on the test bank and ...questionnaires, statistical analysis was applied to examine the quality of the test bank and investigate the factors affecting the teaching quality, to understand the students’ scores, find the main factors affecting the teaching quality and use them to analyze the students’ learning status and learning quality. This will help teachers understand and grasp the students’ learning process and improve their teaching ability. And it can provide a theoretical basis for qualitative and quantitative analysis to further improve the high quality.
There has been significant growth in the literature base exploring questions of teaching in undergraduate mathematics. In this paper we synthesize the literature on the teaching of proof-based ...undergraduate mathematics, drawing on 104 published reports from a range of countries and research traditions. We primarily differentiate the papers into those which explore lecture-based pedagogy and student-centered pedagogy. For each type of instruction, we focus on three categories of findings from the literature: description of instruction, instructor beliefs and rationales, and the relationship between instruction and students (cognitive, participatory, affective, and equity oriented). Much is known about the enactment of lecture-based teaching, including instructors’ cognitive and affective goals. The student-centered literature focuses on tensions and challenges implementing curricula with a greater focus on participatory goals. Overall, there are few studies that attempt to link instructors’ classroom activity and students’ learning. Similarly, attention to equity is relatively lacking in the extant research.
•In the lecture setting, we have a rich understanding of what mathematicians do and why, but only limited work on its influence on student activity and outcomes.•In the student-centered setting, we have evidence of affective and participation benefits to students, but more work is needed on the teachers’ role.•We propose a framework by which to conduct research on teaching in advanced mathematics in both lecture-based and student-centered formats.
Numerous studies have delved into the role of spaced learning in factual memory retention. However, there is a limited understanding of the spacing effect in acquiring problem-solving skills, ...particularly in advanced mathematics. In this study, 68 female collegiate scholars were randomly assigned to either spaced or massed learning groups. Both groups engaged in solving advanced mathematical problems, specifically those related to implicit function derivation, using worked examples. Results indicated comparable performance immediately after a 5-minute interval, but the spaced learning group demonstrated superior outcomes during a prolonged assessment after one week. Importantly, the spacing effect was observed irrespective of participants' prior mathematical performance. These findings underscore the effectiveness of spaced example-based learning in sustaining advanced mathematical knowledge among female collegiate scholars. The study concludes by discussing its limitations and proposing directions for future research.
Abstract
The application of mathematics permeates different fields, especially in the field of economics. The connection between economics and mathematics is indispensable. It can also be said that ...the problems and research in the economic field are inseparable from the support of mathematics. This paper explores the connection between advanced mathematics and economics and its application in economics through the literature review method. Through example studies, the paper finds that only by choosing appropriate mathematical methods for different economic problems can economic problems be solved effectively.
•We examined the direct and indirect relationships between linguistic skills and fifth-grade mathematics.•Phonological skills and grammatical ability were related to geometric and fraction skills via ...arithmetic.•Academic vocabulary was directly related to geometric skills.•Verbal reasoning was directly related to fraction skills.
The current study investigated the direct and indirect relations between basic linguistic skills (i.e., phonological skills and grammatical ability) and advanced linguistic skills (i.e., academic vocabulary and verbal reasoning), on the one hand, and fifth-grade mathematics (i.e., arithmetic, geometry, and fractions), on the other, taking working memory and general intelligence into account and controlling for socioeconomic status, age, and gender. The results showed the basic linguistic representations of 167 fifth graders to be indirectly related to their geometric and fraction skills via arithmetic. Furthermore, advanced linguistic skills were found to be directly related to geometry and fractions after controlling for arithmetic. It can be concluded that linguistic skills directly and indirectly relate to mathematical ability in the upper grades of primary education, which highlights the importance of paying attention to such skills in the school curriculum.
•Mathematicians discussed common teaching practices as determined by research in undergraduate math education.•Analysis of participants’ responses reveal goals and orientations that account for their ...use of these common teaching practices.•Some goals, like preparing future mathematicians, have so far received limited attention in the math education research literature.•Recommendations are made for math educators that wish to change the teaching practices of mathematicians.
Despite mathematics educators’ research into more effective modes of teaching, lecture is still the dominant mode of instruction in undergraduate mathematics courses. Surveys suggest this is because most mathematicians believe this is the best way to teach. This paper answers a call by mathematics education researchers to explore mathematicians’ needs and goals concerning teaching. We interviewed eight mathematicians about findings in the mathematics education research literature concerning common pedagogical practices of instructors of advanced mathematics classes: “chalk talk,” the presentation of formal and informal content, and teacher questioning. We then analyzed the responses for resources, orientations, and goals that might influence the participants to engage in these practices. We describe how participants believed common lecturing practices allowed them to achieve their goals and aligned with their orientations. We discuss these findings in depth and consider what implications they may have for researchers that aim to change mathematicians’ teaching practices.
Abstract
This year, online imparting has become a popular topic. Due to the novel coronavirus pneumonia outbreak, schools in China have to stop the students’ return to school and the behavior of ...imparting under the school’s line. It is because of the emergence of network imparting platform jointly produced by many schools that students can hear the imparter’s lecture in their own home as usual. Higher mathematics has always been a science subject for college students 1. We know that the learning of offline higher mathematics is very difficult. In this paper, based on the application of network imparting platform, the imparting of higher mathematics course is explored, and the conclusion is drawn.
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