College Mathematics Education Research Articles

Exploration of cultivating students' autonomous problem-solving ability in college mathematics teaching

With the continuous development of information technology and the arrival of globalization, the demand for talents in society is becoming increasingly urgent. At the same time, talents from all walks of life also need to continuously improve their ability to independently solve problems in order to adapt to the requirements of the rapidly developing era. College mathematics education also faces the challenge of cultivating students' ability to solve problems independently. This situation makes it difficult for the traditional teaching mode that focuses on "teaching" and "training" to meet the needs of cultivating high-quality talents. Therefore, this article explores the cultivation of students' autonomous problem-solving ability in college mathematics teaching.

Digital Twin for Math Education: A Study on the Utilization of Games and Gamification for University Mathematics Education

Gamification has emerged as a promising strategy for engaging students and enhancing learning outcomes across various disciplines, including education. It involves incorporating game-like elements into non-game contexts to motivate and engage users. Extensive research has demonstrated the positive impact of gamification on student engagement, motivation, and learning outcomes in diverse subjects, including mathematics. Nevertheless, there is a paucity of research on the effectiveness of gamification in mathematics education. To bridge this gap, we investigated the effects of gamification in college mathematics education, with a specific emphasis on students from liberal arts backgrounds who may lack foundational mathematical knowledge. In this work, we designed and implemented a gamified mathematics course tailored for liberal arts students in a Korean university. Leveraging digital twin technology for game and gamification, we created an immersive learning environment that allows students to visualize mathematical concepts through games, pair gamification factors on physical and virtual worlds, and engage in interactive problem-solving activities. The effectiveness of this gamified course in improving students’ engagement, motivation, and learning outcomes was thoroughly evaluated. Digital twin technology, in conjunction with gamification, holds immense potential to revolutionize the way mathematics is taught and learned, making it more accessible, interactive, and engaging for students from diverse educational backgrounds.

ANALYSIS OF UNDERGRADUATE STUDENTS’ METACOGNITIVE AWARENESS BASED ON CLASS LEVEL

Metacognitive awareness is essential not only for school level learners, but also for higher level students. They are still experiencing the process of learning and the assumptions about what they learn still exist in their minds. Therefore it can lead to metacognitive awareness with different levels. However, metacognitive awareness based on class level is still yet to be explored. In this study, the level of undergraduate students’ metacognitive awareness according to class level was identified. The participants were 31 college mathematics education students per group from first, second, and third-years at a state university in Indonesia. The data were collected through the Metacognitive Awareness Inventory. The data were analyzed as numbers, mean scores and percentages on every participants. The findings showed that class level had no effect on level of students’ metacognitive awareness. It also indicated that although there are no students who have very low metacognitive awareness, but the higher the class level, the lower their average of metacognitive awareness. These findings suggest that there should be attention from teachers as well as efforts to enhance students' metacognitive awareness. Article DOI: https://dx.doi.org/10.20319/pijtel.2019.31.164172 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Research Problems in Community College Mathematics Education: Testing the Boundaries of K-12 Research

The purpose of this commentary is to articulate the need to investigate problems of mathematics instruction at community colleges. We briefly describe some features of this often-ignored institution and the current status of research. We also make an argument for how investigations of instruction in this setting can both advance our understanding of this particular context and give practitioners tools to deal with pressures from policymakers to show short-term results. This work is the result of a collaborative effort between community college practitioners and researchers, responding to the needs of their work in mathematics education.

모바일 선형대수학 스마트폰 콘텐츠 개발과 활용

대학 수학교육에서 선형대수학은 가장 중요한 과목 중 하나이다. 21세기 향상된 정보 기술이 선형대수학 수업에 적용된다면, 학생들의 선형대수학 내용에 대한 이해는 한층 더 향상될 것이다. 우리는 학생들의 관심을 높이고 보다 효율적으로 학습 목표에 도달하는데 기여하고자 웹상의 무료 수학 프로그램인 'Sage'(http://sagemath.org)를 활용한 교수학습 환경을 구축하고 그 콘텐츠를 개발하였다. 특히, 2009년 저자는 PC 환경 외에 휴대폰의 인터넷 기능을 통하여 Sage 명령어를 사용할 수 있는 단순모듈 콘텐츠를 개발하였다. 본 논문에서는 스마트폰을 이용하여 대부분의 Sage 기능을 활용할 수 있도록 개발한 모바일 Sage를 소개하고, 학생들의 자기주도적인 선형대수학 학습을 위해 개발한 모바일 선형대수학 스마트폰 콘텐츠(강의록, 동영상강의, 문제와 풀이, 공학적 도구)를 소개한다. Linear Algebra are arguably the most popular math subjects in colleges. We believe that students' learning and understanding of linear algebra can be improved substantially if we incorporate the latest advanced information technologies in our teaching. We found that the open source mathematics program 'Sage' (http://sagemath.org) can be a good candidate to achieve our goal of improving students' interest and learning of linear algebra. In particular, we developed a simple mobile content which is available for Sage commands on common cell phones in 2009. In this paper, we introduce the mobile Sage which contains many Sage functions on a smart-phone and the mobile linear algebra content model(lecture notes, and video lectures, problem solving, and CAS tools) and it will be useful to students for self-directed learning in college mathematics education.

Study on College Mathematics Education and Teaching Strategies

In order to improve the quality of college mathematic education, cultivating rational thinking of people, and improving the quality of nation, this paper make a comprehensive and systematic survey and analysis on college mathematic education. Results show that the team-constructer and quality of students in university have been changed, and it is not optimistic for mathematic learning of students. For the above problems, it is important and necessary to adjust the teaching content, improving teaching methods and means, promoting the cultural ideas and history of mathematics, and show humanistic concern to students.

Mathematical Literacy and College Mathematics Education

Mathematics, being an important part of human culture, plays a significant role in both spiritual life and material life of people. Mathematical literacy is one of the most basic scientific literacies, which is of far-reaching importance to cultivate mathematical literacy of students in college mathematics education. This paper elaborates the contents of mathematical literacy, discusses the necessity of cultivating mathematical literacy of college students, and proposes effective approaches of improving the literacy of college students.

Review: A New Era in Collegiate Mathematics Education Research: Good Learning of College Mathematics: Can We Recognize, Understand, Foster, and Document It?

Research in college mathematics education is neither new (Suydam, 1975) nor unusual (Becker & Pence, 1994). However, the literature of this field is still very scattered, with many of the articles published in journals that mathematicians do not usually read. Although in recent years a few books have appeared that deal with college mathematics, books that collect papers devoted to research in the field are certainly needed.

Teachers', Principals', and University Faculties' Views of Mathematics Learning and Instruction as Measured by a Mathematics Inventory

Differences and similarities among the views of secondary mathematics teachers (n=199), high school principals (n=160), and college mathematics education professors (n=117), as reflected by responses on an inventory concerned with cognitive and affective aspects of mathematics learning and instruction, were examined. The response patterns of each group analyzed by factor analysis or analysis of variance methods were found to have some unique characteristics: however, teachers were found to be more similar to principals than to college professors in both factor structure and individual item responses. Implications of this finding for the transmission of innovation in instruction are discussed.