Mathematics Courses Research Articles

Planning to Take More Mathematics Courses in High School: Who Does and Who Doesn't?

What are the most common motives invoked by 9th graders when asked about their plans to take (or not) more mathematics courses during high school? How do beliefs about math course-taking affect students’ actual planning? To what extent is planning of math course-taking associated with high school students’ socio-demographic backgrounds? The study employs data from the High School Longitudinal Survey of 2009 to examine the issue of persistence in math course-taking during high school. The study shows that almost two-thirds of 9th graders plan to do math during all their high school years, although intentions to persist in math vary across racial and especially socioeconomic backgrounds. The study also demonstrates the importance of belief constructs such as math identity, internal motivation toward math learning and math utility on math course-taking planning. A better understanding of students’ motives to engage in high school math may help develop classroom practices that emphasize the long-term benefits of math learning.

Quantitative evaluation of a theoretical-conceptual model based on affective and socio-behavioral dimensions to explain the academic performance of mathematics students.

There is evidence that suggests that affective dimensions, personality traits, as well as students' cooperative interpersonal interactions, are an important element in the students learning process. In this work we propose a theoretical model, based on evidence, that shows the direct and indirect relationships between these factors and academic performance in mathematics courses, in undergraduate and school students. To understand the type of relationships between these variables, the PANAS psychometric test of positive and negative affect, the BIG FIVE personality test and the economic decision game DUPLES GAME were applied. The study sample was 130 students between 17 and 22 years of age from undergraduate and school (M ± SD = 20.1 ± 3.99). From a path analysis, statistically significant relationships were found, for example, a direct relationship between neuroticism and positive affect, which in turn is related to academic performance. We also found a direct relationship between neuroticism and negative affect, extraversion and positive affect. This allows us to propose that some of the independent variables of the model directly and indirectly influence the academic performance of students in the subject of mathematics. Positive affect and negative affect directly affect academic performance in mathematics, neuroticism has a direct impact on negative affect and extraversion direct impact on positive affect. Consequently, there are direct and indirect relationships between personality traits and affective dimensions, which affect the academic performance of mathematics students.

Motivation in online course design using self-determination theory: an action research study in a secondary mathematics course

AbstractWith continued growth in online learning, motivation remains a key factor in persistence and achievement. Online mathematics students struggle with self-regulation and self-efficacy. As reported by Ryan and Deci (Self-determination theory: basic psychological needs in motivation, development, and wellness, Guilford Press, 2017, https://doi.org/10.3233/EFI-2004-22201), in their well-established self-determination theory, contended that satisfying the psychological needs of autonomy (involving self-regulation), competence (involving self-efficacy), and relatedness (involving a sense of belonging) creates a suitable environment for integrated extrinsic and intrinsic motivation to thrive. The purpose of this action research was to implement a self-determination theory-based online unit for mathematics students to improve their motivation levels. A convergent mixed methods action research design was employed to identify changes in the levels of autonomy, competence, and relatedness of the participants in an Algebra 2 course (n = 50) at a fully online school in the northeastern United States. Results from the motivation questionnaire and student interviews indicated a significant increase in competence and relatedness after completing the intervention. While no significant increase in autonomy was evident in the quantitative results, the qualitative findings showed some support for improved autonomy. Recommendations for online mathematics course design to support increased motivation are provided.

An idea to explore: A systematic approach for solving plasmid double-digest puzzles.

A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using puzzle-based assignments at the intersection of molecular biology and mathematics. Therefore, we should present students with a puzzle that allows them to combine knowledge and skills from these seemingly disconnected disciplines. Here, we present a method for analyzing RE digests of circular plasmids using basic geometric principles.

Teaching and learning processes for pre-service mathematics teachers: The case of systems of equations

This study aims to explore the teaching and learning processes of the school mathematics course for pre-service mathematics teachers in the case of systems of equations. Types of teaching and learning approaches and a symbol sense perspective were used as theoretical frameworks for this study. To do so, we conducted a qualitative case study, involving 35 pre-service mathematics teachers, in the form of classroom observations in one of the state universities in Bandung, Indonesia. The observations included the teaching and learning processes, a written formative test, and interviews. The results showed that the teaching and learning processes are implemented by using a deductive approach,<i> </i>and the written student work from the formative test and interviews revealed various solution strategies. From the symbol sense perspective, we conclude that the teaching and learning processes need to be enhanced to promote pre-service teachers’ procedural skills and conceptual understanding in a balanced manner.

Undergraduate Students’ Logical Consistency in Mathematical Thinking: Implications for Teaching and Learning

This paper introduces the concept of logical consistency in students’ thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students’ evaluation of mathematical statements and accompanying arguments. Beyond its utility as an assessment tool, this paper also underscores the potential of the LinC instrument as an instructional aid, effective for identifying students who may inadvertently overlook logical contradictions within their mathematical assertions. Furthermore, this paper outlines a practical classroom activity based on the LinC instrument format. This activity is tailored to enhance students’ capacity for reasoning with logical consistency, specifically in proof-oriented mathematics courses. We hope this activity helps instructors address and mitigate logical inconsistencies in students’ thinking throughout their classroom activities.

Designing Student Worksheets (LKM) Based on the Rigorous Teaching and Learning (RTL) Model

This research aims to design Student Worksheets (LKM) for the Discrete Mathematics course, where the LKM design is structured so that the LKM can be used in the Rigorous Teaching and Learning (RTL) learning model. The results of the lecturers' reflections found that the main problem lies in the content of the material in textbooks which is not interesting, students are often unable to understand the textbooks they own, especially in solving the questions given. This has implications for 1) lack of motivation to learn, 2) lack of understanding of the material, 3) fear of expressing opinions, and 4) lectures are less effective and less enjoyable. Therefore, teaching materials need to be packaged appropriately according to the substance and conditions of students in LKM. The research design used in this research is Thiagarajan's 4-D development model. This model is a system of educational development approaches that are carried out in 4 sessions, namely Define or Introduction where in this session preliminary analysis, student analysis, and needs analysis are carried out, Design or Planning where in this session what is done is format selection, initial design and design preparation, Develop or Development where in this session validation and limited trials are carried out, as well as Disseminate or Disseminate where in this session the LKM is given to the teaching lecturers. This research produces an LKM that is used in Discrete Mathematics courses.

The study of an innovative Eéducationnel practice in Greek students: The flipped learning

The purpose of this paper is to compare the effectiveness of using flipped teaching against traditional teaching, with active learning techniques, in physics and mathematics courses. The study was conducted on 100 middle and high school students who were first subjected to traditional teaching (control group) and then subjected to flipped teaching (experimental group). To check the effectiveness of the two methods, the students were submitted to an assessment test in the lesson taught with the two methods. To test the existence of a statistically significant difference between the performance of the two groups, the independent sample t-test and ANOVA test were used for continuous variables. In addition, multiple logistic regression analysis with Odds Ratios was used to predict student achievement depending on the teaching method used. The results of the study showed that there is no statistically significant difference in the average performance of students with the two teaching methods.

Assessment in Online Mathematics and Statistics Courses During COVID-19: Insights from Students and Teaching Staff at a Canadian University

Assessment in Online Mathematics and Statistics Courses During COVID-19: Insights from Students and Teaching Staff at a Canadian University

Success in Asynchronous Courses Through Increasing Student’s Social Presence

Online education has fundamentally altered the educational landscape, enhancing accessibility and flexibility for learners. However, a notable limitation of asynchronous learning modalities is the diminished interpersonal engagement inherent in traditional face-to-face pedagogical contexts. This empirical inquiry investigates the impact of deliberately integrating highly interactive instructional activities within online asynchronous developmental mathematics courses. Three principal thematic categories emerged through the iterative design process of these activities. Each category is delineated and exemplified, followed by exploring course policies conducive to student achievement in interactive learning contexts. Following a grounded theory approach, this study scrutinizes course outcomes alongside student and instructor evaluations at the semester’s end. Findings suggest incorporating social interactive activities yields positive effects on course outcomes.

Verification of Taylor's theorem

Multivariate function calculus is an important part of mathematical analysis courses, and most conclusions can be found and generalized in univariate calculus. However, the biggest difficulty in teaching multivariate calculus lies in its abstraction, such as Taylors theorem, multiple integral regions drawing, and integral variable transformation. At the same time, ordinary differential equations are also one of the basic courses of the profession, and dynamic systems based on ordinary differential equations have extensive applications in mathematical models of continuity problems and optimal control problems. Software such as Mathematica, Python, Matlab, etc. can solve similar problems. Therefore, this article will use the visualization and computational capabilities of Mathematica to validate important definitions and conclusions in multivariate calculus, and compare the differences among the three software in solving approximate numerical solutions of dynamic systems of ordinary differential equations from different perspectives.

STEM department chairs’ perspectives on navigating teaching culture to influence instructional change: a four-frames model analysis

Academic departments have been highlighted as key targets to sustainably transform the learning environments of postsecondary science, technology, engineering, and mathematics (STEM) courses in the United States. Despite STEM department chairs playing a critical role in shaping their unit, few studies have characterized how chairs view the teaching culture within their department and how cultural features influence instructional change. This study addressed this gap by applying the four-frames model for organizational change to analyze interviews conducted with 14 STEM department chairs at one research-intensive institution in the United States. The department chairs identified several challenges to supporting and advancing teaching culture. These challenges were mostly related to the structures and symbols frames and included an institutional emphasis on research over teaching, inadequate methods to evaluate effective teaching, and weak teaching feedback mechanisms available to faculty. The chairs also described how they leverage their power to affect people and thereby influence the teaching culture. For example, they strategically position teaching as an important aspect of the departmental culture during hiring processes and elevate certain groups of faculty who have demonstrated interest and efficacy in teaching. This study contributes to the literature by providing a rich description of the teaching culture in STEM departments at a research-intensive institution from the perspective of department chairs. This unique focus on department chairs helps identify opportunities for instructional reforms that are grounded in the reality of the departmental environment and provides a framework for considering how change might occur in STEM departments at research-intensive institutions. The opportunities identified emphasize the importance for department chairs to consider and leverage all four frames to enact instructional change.

Cultural Transitions in Mathematical Discourse: Unveiling Mathematical Writing Hurdles during the Rite of Passage

This qualitative case study delves into the intricate landscape of mathematical writing challenges faced by first-year university students undergoing the critical transition from school-level to university-level mathematical discourse. Conducted at a prominent South African university, the research, employing a purposive sampling technique, engaged thirty first-year mathematics students. Guided by the community of practice theory by Lave and Wenger, alongside van Gennep’s rite of passage analytical lens, the study sought answers to the question: What are the mathematical writing challenges encountered by first-year university students during their rite of passage period? Thematic analysis, informed by Adu's (2019) coding framework, was utilized to systematically examine common themes and patterns within the qualitative data. The findings illuminated key hurdles during this transitional phase, prominently including the inconsistency in working with mathematical notations, erroneous use of universal and existential quantifiers, and a notable confusion between the acts of illustrating and proving in mathematical contexts. In response to these challenges, the study advocates for the explicit incorporation of mathematical writing instruction to scaffold students during this rite of passage. Furthermore, it recommends a shift in the emphasis of first-year mathematics courses—suggesting a redirection from a content-centric approach to one that prioritizes the cultivation of students' new identities. This entails focused attention on teaching the customs, traditions, and adept ways of constructing and articulating mathematical proofs in the university context. The implications of this study extend beyond the immediate challenges identified, offering actionable recommendations to enhance the pedagogical strategies employed in the crucial transition period for first-year mathematics students.

The Effect of Mathematics Teaching with Mobile Augmented Reality Technology on Secondary School Students’ Attitudes and Academic Achievements

Nowadays, the prevalence of augmented reality technology is increasing day by day, along with the benefits it provides in many fields from shopping to education, from medicine to the automotive sector. This technology, which allows the real environment to interact with the virtual environment, has been used in many studies in the literature. In this research, the seventh-grade mathematics course, which was processed with augmented reality applications, was conducted. The effects of classroom students’ academic achievements, attitudes toward mathematics lessons, and augmented reality applications were examined. For this purpose, a quasi-experimental design with a pre-test, and post-test control group was used. The research was conducted with a total of 60 students, including 30 in the experimental group and 30 in the control group. A total of 10 lesson hours were applied, including 5 hours per week. Among the quantitative data collection tools, achievement tests, mathematics attitude scales, and augmented reality applications attitude scales were used in the research. As a result of the research, it was found that the course conducted with augmented reality application has a positive effect on the academic achievements of students. However, it was found that there was no significant difference in their attitudes towards mathematics courses. The written opinions received from the students show that the students find the lesson more entertaining and want to use it in other lessons as well.

Augmented Reality in Mathematics Education: A Systematic Review

The aim of this study is to explore the application of augmented reality technology in mathematics education. To accomplish this, papers related to Augmented Reality (AR) and mathematics, indexed in the Web of Science, ERIC, and SCOPUS databases from January 2010 to June 2024, were analysed. The review process identified a total of 645 items: 415 from the Web of Science, 113 from the ERIC, and 117 from the SCOPUS. Following the application of our relevance criteria, unrelated articles were removed, resulting in a final selection of 96 articles for examination in this study. The findings indicate a year-on-year increase in publications, reflecting the growing prominence of AR in the field. However, there seems to be a recent trend of stabilization, which may be temporary. Also, most of these studies were conducted with middle school or university students. Based on the reviewed papers, there is a trend that AR applications are generally prepared for the geometry and measurement topics of mathematics courses. Although there are some limitations such as insufficient technical infrastructure, operating system incompatibility, and the shift of attention to software rather than content, AR can positively affect students’ attitudes and interest towards mathematics, motivation, spatial ability, creative thinking skills, high-level strategy use, and self-efficacy.

Sustaining Active Learning in Undergraduate Precalculus: Results and Challenges of a Course Redesign

Addressed toward course coordinators and departmental leaders interested in redesigning undergraduate mathematics courses with a focus on active learning, this report provides an update on progress in redesigning the Precalculus course offered by the Department of Mathematics at the University of Maryland, College Park, following initial indicators of success. We begin by discussing our team’s challenges due to the COVID-19 pandemic and our attempts to navigate these challenges. We then provide results related to student achievement, self-efficacy, and STEM intentions, in addition to addressing the remaining goals of the redesign.

Integration of Augmented Reality and Modeling Techniques in Dynamic Systems for Teaching Theorems and Demonstrations in University Mathematics Courses: A Differential Equations-Based Approach and Its Applications.

Teaching theorems and proofs in mathematics at the university level poses a considerable challenge due to their high abstraction and conceptual complexity. Augmented reality (AR) emerges as an innovative tool that transforms learning by facilitating the visualization and understanding of complex mathematical concepts, particularly in the realm of differential equations, which are fundamental for modeling dynamic systems. This technology allows students to interact with three-dimensional representations, enhancing their comprehension and analytical skills by visualizing the effects and solutions of equations in real time. Despite technological advancements in education, traditional teaching methods remain static and abstract, limiting the assimilation of concepts. The research employed a quantitative approach and a documentary methodology to analyze the effectiveness of integrating AR and modeling techniques, providing data that evidences their positive impact on academic performance. A thorough review of relevant literature was conducted, consolidating a theoretical framework that highlights the importance of these emerging technologies. The findings suggest that implementing AR in the classroom not only improves knowledge retention but also enriches the discussion on mathematics education in higher education.

Impact of the Pandemic on the University of Oklahoma’s STEM Mathematics Pathway

Using an organizational development framework, we consider different aspects related to first-year mathematics courses leading to STEM fields. We use the Weisbord six-box model to describe how the pre-pandemic structures and mechanisms helped our instructors weather COVID-19 and how changes were implemented to cope with the challenges faced. Certain practices adopted at the height of the pandemic are still in place, while others are not. We share this information as well as some of the innovations that were used to build relationships and provide informal rewards, two key aspects that are often overlooked. We also share some of the documented trends, continued challenges, and lessons learned.

An engineering design-based mathematics activity example based on STEM approach in middle school: Cold storage design

Engineering design practices in STEM education focus on reflecting the discipline-specific work of engineers in a manner that is suitable for the student level and course learning objectives. Using an engineering design context also facilitates student identification of global problems and feasible solutions to address such problems. In this article, within the framework of STEM approach, an engineering design activity that can be applied in middle school mathematics course is presented. Additionally, examples of students’ experiences of the engineering design-based mathematics activity are given. The "Cold Storage Design Activity" was executed in a classroom setting, and the implementation process underwent examination and evaluation. 12 eighth-grade students from a middle school in Turkey took part in the implementation. The middle school were able to successfully perform an engineering design process and effectively overcome challenges through teamwork. The results of the activity show that middle school students are excited and eager to participate in a design activity.

Teaching strategies based on augmented reality for the understanding of theorems and proofs in mathematics courses for higher education students

The object of this study is to explore how teaching strategies based on increased reality can improve the understanding of theories and demonstrations in mathematics courses for higher education students. Realized an exhaustive revision of the academic literature relative to the use of the increased reality in the teaching of mathematics. We identify and analyze studies that investigate the impact of reality increased in the understanding of abstract mathematical concepts, as well as in the motivation and compromise of students. In addition, we will examine specific applications of increased reality used in educational contexts to teach theorems and demonstrations. The results reveal that the teaching strategies are based in reality and offer many benefits for the understanding of theorems and demonstrations in mathematics courses for higher education students. These benefits include improved visualization of abstract concepts, greater interaction and active participation, adaptability to the individual needs of students, immediate feedback and greater motivation and compromise. In combination, these results suggest that the increased reality has the potential to significantly transform the form into which one teaches and learns the mathematical concepts in higher education institutions.