Mathematical Knowledge Research Articles

Assessing the prior knowledge of students in physics minors

The number of students who give up science and engineering in the first semesters is regrettably high. While there is empirical evidence of the relationship between (lack of) prior knowledge in mathematics and dropout among students with a compulsory minor in physics, there are - to our knowledge - no studies on the relevance of prior knowledge in physics. Therefore, we constructed a knowledge test and statistically validated the results of two pilot studies in consecutive semesters with students from different physics minor programs (n = 643). In this article, we briefly introduce the structure of the test, consisting of three sections (knowledge of facts, knowledge of meaning, application of knowledge) and the corresponding test parameters. Furthermore, we summarise the first empirical results using descriptive methods. For this purpose, violin plots were created to analyze similarities or differences in the response behaviour of the subgroups. Moreover, an analysis of classical statistics was carried out, e.g. pairwise Mann-Whitney-U tests for comparing sample subgroups.Our results show that subgroups in the overall sample significantly differ in their test results depending on their faculty affiliation.

Unlocking the secrets of students’ mathematical literacy to solve mathematical problems: A systematic literature review

Mathematical literacy is the ability to use mathematical knowledge in real-life situations, making it an essential component of education because of its importance in solving everyday problems. Mathematical literacy is also part of the Program for International Student Assessment (PISA) global assessment. Because of the importance of the subject, this Systematic Literature Review (SLR) investigated the relationship between students’ mathematical literacy and their ability to solve mathematical problems. This SLR uses the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) approach was used, and articles published from January 2013 to August 2023 were obtained from databases including ERIC (342), ProQuest (1,329), and Scopus (27). Following PRISMA, a total of 20 articles were included in the review. Of the 20 articles, most were conducted on junior high school students in Turkey. The majority of reviewed studies found students to have a low level of mathematical literacy, which caused difficulties in formulating problems. The examined studies also revealed several internal and external factors affecting mathematical literacy. Problems used by PISA were the most frequently employed to measure students’ mathematical literacy in the reviewed studies.

Research on Integrated Teaching of Mathematical Units from the Perspective of HPM

In recent years, unit holistic teaching has been continuously focused on as an effective way to implement core competencies. This teaching method takes a global perspective, organizes teaching content from a unit perspective with systematic thinking, and emphasizes the improvement of students' basic abilities and the development of core competencies. At the same time, teaching based on the history of mathematics is highly valued, HPM (History and Pedagogy of Mathematics) entered the mathematics classroom teaching. HPM teaching can transform science oriented mathematics into education oriented mathematics, thereby maximizing the educational value of the history of mathematics. HPM teaching coincides with unit teaching. This article conducts in-depth research on the overall teaching of mathematical units, sorts out the development of mathematical history, explores the historical background of mathematical knowledge, calculates the evolution process, and effectively integrates mathematical history resources into unit teaching design. The introduction of M-perspective can effectively enrich the content of mathematics teaching, enhance students' interest in learning, deepen their cognitive depth, and help cultivate students' innovative thinking ability in mathematics. Explore the overall teaching implementation strategy of mathematical units, propose corresponding teaching suggestions, and provide reference for mathematics educators.

Mathematical Model Applied for Hotel Recommendation System with Machine Learning

Abstract: the purpose of this paper is to promote the value of Albanian tourism creating a Hotel Recommendation System applying a Mathematical Model. The data of one hundred and one hotels, loaded from two excel files in CSV format are implemented in the Spyder IDE and processed by code, using Mathematical and Machine Learning knowledge. The code recommends ten best hotels as output. There is made a combination of Machine Learning methods and techniques with the concepts of probability, statistics, algebra and geometry. The main methodological approach taken in this study is Content-Based Filtering.

Applıcatıon Desıgns to Measure the Mathematıcal Reasonıng Skılls of Teacher Candidates

Mathematical reasoning can be defined as the ability of individuals to approach situations they encounter from a mathematical perspective, to investigate the cause and effect, to make sense of the situation, and to make reasoning that will help reach a logical conclusion by using mathematical concepts and symbols. The purpose of the research is to evaluate the mathematical application designs of primary school teacher candidates studying at Khoja Akhmet Yassawi International Kazakh-Turkish University in order to measure the mathematical reasoning skills of primary school students. For this purpose, at the primary school level, teacher candidates will be asked to (a) identify and use appropriate reasoning, (b) recognize and use mathematical knowledge / patterns / structures / general properties, (c) recognize different representations of the same data, (d) predict, (e) Developing logical arguments regarding the solution, (f) Deciding on the correctness of the solution/result, (g) Making generalizations, and (h) Solving non-routine problems. In this respect, the research was designed in the case study pattern, one of the qualitative research methods. The study group of the research includes a total of 16 teacher candidates representing different grade levels. Typical case sampling method was used to select the teacher candidates in the study group. Pre-service teachers were asked to develop application designs in which they could evaluate the mathematical reasoning sub-dimensions mentioned above. In the research, the theoretical framework was scanned, and an application was carried out to 16 teacher candidates and at the end of the application, the teacher candidates were able to design questions for all their reasoning skills. When the questions they prepared were evaluated, it was seen that the question objectives met some of those stated in the literature.

Integration of Islam and Mathematics: Religious and Mathematics Education In Grand Mosque of West Sumatra

The study aimed to determine the integration of religion and mathematics education within the context of the Grand Mosque of West Sumatra, with a specific focus on its potential impact on mathematics learning. The study was undertaken at the Grand Mosque of West Sumatra. The research methodology employed in this study is descriptive qualitative research utilising an ethnographic approach. Data gathering methods include literature review, direct observation, documentation analysis, and conducting interviews. Data analysis techniques include data reduction, data presentation, and conclusion. The findings of this study indicate that the Grand Mosque serves as a multifaceted institution encompassing several functions such as a place of worship, a platform for preaching, an educational hub, a centre for character development, a catalyst for moral and social advancement, a hub for economic empowerment, and a destination for religious tourism. The Grand Mosque serves as a conducive environment for the acquisition of mathematical knowledge due to the presence of several mathematical principles embedded within the worship activities, as well as within the physical structure and courtyard of the Mosque. The Grand Mosque incorporates mathematical ideas such as multipli-cation, parallel lines, straight lines, curves, triangles, rhombuses, rectangles, trapezoids, congruence, and social arithmetic. According to the data above, it can be inferred that the West Sumatra Grand Mosque serves as a venue for religious and mathematical education. Consequently, this establishment holds potential as a resource for students to acquire knowledge in religious studies and develop a comprehensive understanding of mathematical principles.

Study and Analysis of Some Real Life Applications of Exponential Function

The exponential function as a mathematical concept plays an important role in the Corpus of mathematical knowledge, but unfortunately Students have problems grasping it. Paper exposes examples of exponential function application in a real-world (life).One of the most prevalent applications of exponential functions Involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded Interest to radioactive decay and Newton's law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential grown and decay in the context of some of the applications. In the preceding section, we examined a population growth problem in which the population grew at a fixed percentage each year. In that case, we found that the population can be described by an exponential function. A similar analysis will show that any process in which a quantity grows by a fixed percentage each year (or each day, hour etc.) can be modeled by an exponential function. Compound Interest is a good example of such a process. Other applications of exponential function are bacterial growth, bacterial decay, population decline, are obtained in this project.

Utilization of Photomath Among Grade 7 Junior High School Students

This study investigates the efficacy of introducing the Photomath mobile app into the mathematics curriculum for Grade 7 students. The study takes a mixed-methods approach, combining quantitative analysis and qualitative observations to assess Photomath's impact on students' learning results. The study intends to offer light on how Photomath affects students' mathematical knowledge, problem-solving abilities, and overall academic achievement via the lens of educational technology. The quantitative component entails examining pre- and post-intervention assessment scores and comparing the performance of students who used Photomath to those who used standard teaching methods. In addition, surveys and interviews are used to collect qualitative data about students' perspectives, attitudes, and experiences using Photomath. This dual-method approach enables a more nuanced assessment of the complex implications of incorporating this technology into the Grade 7 mathematics curriculum. The study's findings are intended to contribute not only to scholarly discussions on technology-assisted learning, but also to practical issues for educators and legislators. By investigating the efficacy of Photomath at a specific grade level, the study hopes to shed light on the possible benefits and drawbacks of using similar instructional tools. Finally, this investigation aims to inform evidence-based decisions on the use of technology to improve mathematics teaching for Grade 7 pupils.

Mathematics as an Important Tool in Managing Human Health: Implication on COVID-19 Outbreak

Mathematics plays a crucial role in human lives in terms of calculation with the use of numbers and different operations. Human health needs proper attention and error-free calculations. It is imperative for the people in the health sector to have the knowledge and skills required by the health workers based on a different area to carry out the job properly. The application of various skills in Mathematics is needed during the outbreak of any strange disease to protect people's lives and reduce the rapid spread of such disease. In this article, the history of the past pandemic, and COVID-19 were discussed. The Post COVID -19, and the skills needed were explained. The roles of Mathematics knowledge in the COVID -19 were highlighted, and the roles of Mathematics knowledge and skills in the Health sector were explained. It was therefore concluded, that, Mathematics serves as an important tool in health, and the health workers must possess basic knowledge of the skills required in different health fields. It was recommended that the healthcare professionals must undergo in-service training in the required Mathematics skills relevant to their specific area of specialization to avoid the error that can increase the mortality rate. Regular training is needed in the technology used to carry out successfully the test and practical aspects of their work with zero or minimal error.

Mathematics students’ self-reported resources used for solving real-life problems in a challenge-based modelling course

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.

Reinforcing Protein Biochemistry: A Two-Week Experiment Studying Iron(III) Binding by the Transferrin Protein through Stoichiometric Determination, Stability Analysis, and Visualization of the Binding Site.

The two-week protein biochemistry experience described herein focuses on reinforcing key biochemical concepts and achieving significant learning domain accomplishments for students (Content Knowledge, Logical Mathematical Reasoning, Visualization, Information Literacy, and Knowledge Integration) and valuable teaching opportunities for instructors. The experience encompasses an exploration of the transport protein serum transferrin as an important regulator of Fe(III) biochemistry and incorporates techniques to assess protein-metal stoichiometry and protein stability and to perform molecular visualization. Students gain practical experience in utilizing spectrophotometric analysis for constructing stoichiometric curves, in performing urea-PAGE, and in applying the PyMOL program to evaluate metal coordination at a protein binding site and the associated protein structural change. The learning and teaching accomplishments provide valuable skills that can be extended into research and translated to other teaching formats.

The Development Of Mathematics In Philosophy And The School Of Formalism Contained In The Philosophy Of Mathematics.

The philosophy of mathematics, with its many contradictions and paradoxes regarding systematic truths, contributes to the creation of a systematic and absolute foundation of mathematical knowledge, with the aim of preserving that foundation. This research aims to answer the question of what efforts are needed to overcome the crisis, contradictions and paradoxes in mathematics, as well as introduce the philosophical foundations of mathematics that are currently often used in the teaching and development of mathematics. The research method used is descriptive research using Systematic Literature Review (SLR). In particular, the emergence of formalism in mathematics education is also a reaction to formalism's attempt to impose the thinking of mathematicians on all humanity, thus forcing mathematics to be presented deductively. Therefore, as a suggestion, mathematics education should pay more attention to the diversity of abilities and potential of individual learners, realize that learners are not as smart as teachers, and that undergraduate and graduate students are not as smart as teachers.

Towards an ecological mathematics

Mathematics plays a fundamental role in ecological research, yet its uses remain strikingly separate from advances in the environmental social sciences and humanities. In this paper, I work to address this impasse and outline the motivation and scope for an ‘ecological mathematics’, an approach to doing mathematics in environmental research which foregrounds relationship, embodiment and human difference. I begin by tracing the historical emergence of mathematics in ecology, noting how life processes have been conceptualised in a way which forces them to fit the ideals of mathematical models transplanted from the physical sciences. I then investigate the cultural factors shaping the evolution of mathematical thought, eliciting a malleability in how mathematical knowledge relates to the more-than-human world. This provides a place from which to rethink the role of abstraction in ecological thought, and develop mathematical methods grounded in ecological concepts. Drawing on ethnographic and perceptual accounts of space and time, I work with topological concepts from both mathematics and the social sciences to suggest a new correspondence between these subjects, elaborating a way of employing mathematical techniques which enliven, rather than deaden, the ecologies under study. The paper concludes with important philosophical clarifications to the approach of an ecological mathematics.

Taptana Cañari In the Teaching of Number Systems

Purpose: The teacher's work is of paramount importance, as only they shape individuals for society. Students present problems in their learning, and to work on these irregularities. This operational complexity gives the true value that the Taptana has as an intercultural didactic resource. Theoretical Framework: The work includes a theoretical framework with pedagogical, didactic, and ethno-scientific relevance, as the educational unit is located in a Kichwa-Spanish cultural context, where members of different communities integrate between the two cultures to share and enrich each other through their productive and social activities. Methods: The starting point is the Cañari Taptana, where participatory and cooperative didactic processes will be used to structure quantities based on 10, 20, 5, 2, and any other base, as well as multi-base transformations. Results and Conclusion: The knowledge refers to the existing analogy between the Mayan system (vigesimal), the base-5, with the base-2, applied in intelligent calculating machines that exist in today's society; structure and handling of the taptana. Improves the structuring of quantities in different bases, and their axiomatic relationship to build other numbering systems with the application of the redesigned taptana Cañari Research implications: This aspect is related to the value of their identity, knowing the history of their ancestors, projecting it into daily activities, in their religious festivities, in the communal work; ethnomathematical and mathematical knowledge. Originality/value: Design and construction of different types of taptana to enrich the teaching resources of teachers in the mathematics area. to have a significant impact on students' learning and their attitude towards mathematics.

VẬN DỤNG CHỦ ĐỀ STEM TRONG DẠY HỌC THEO DỰ ÁN Ở HỌC PHẦN THỰC TẬP ĐIỆN TỬ

The trend of educational innovation from a content approach to a competency approach raises the need to innovate teaching methods. For new innovation, learners need guidance and supports in practical activity. The ultimate goal of project-based learning is specific circuit, for applying knowledge to solve daily problems. Teaching STEM topics is to improve knowledge and skills in science, technology, engineering, and mathematics for learners. For Electronic Practice course, lessons are structured as projects to meet the requirement of STEM education. The article suggests that the knowledge and skills acquired through project-based teaching surpass those obtained through traditional teaching methods. In addition, it proposes experimenting with implementing project-based STEM method in the Electronics Practice course with three lessons specifically designed by integrating individual lessons. The STEM project-based teaching process for the lesson “Design and Assemble the regulator Power 5V DC” is presented, analyzed, and designed with completely new questionnaires. This will be a reference for lecturers while teaching the Electronics Practice course to innovate teaching methods to keep up with current development speed.

Multivariable calculus textbook representation of non-cartesian coordinates: a misalignment between multivariable calculus textbook content and upper-division physics application

Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.

Rearranging equations to develop physics reasoning

Researchers generally agree that physics experts use mathematics in a way that blends mathematical knowledge with physics intuition. However, the use of mathematics in physics education has traditionally tended to focus more on the computational aspect (manipulating mathematical operations to get numerical solutions) to the detriment of building conceptual understanding and physics intuition. Several solutions to this problem have been suggested; some authors have suggested building conceptual understanding before mathematics is introduced, while others have argued for the inseparability of the two, claiming instead that mathematics and conceptual physics need to be taught simultaneously. Although there is a body of work looking into how students employ mathematical reasoning when working with equations, the specifics of how physics experts use mathematics blended with physics intuition remain relatively underexplored. In this paper, we describe some components of this blending, by analyzing how physicists perform the rearrangement of a specific equation in cosmology. Our data consist of five consecutive forms of rearrangement of the equation, as observed in three separate higher education cosmology courses. This rearrangement was analyzed from a conceptual reasoning perspective using Sherin’s framework of symbolic forms. Our analysis clearly demonstrates how the number of potential symbolic forms associated with each subsequent rearrangement of the equation decreases as we move from line to line. Drawing on this result, we suggest an underlying mechanism for how physicists reason with equations. This mechanism seems to consist of three components: narrowing down meaning potential, moving aspects between the background and the foreground and purposefully transforming the equation according to the discipline’s questions of interest. In the discussion section we highlight the potential that our work has for generalizability and how being aware of the components of this underlying mechanism can potentially affect physics teachers’ practice when using mathematics in the physics classroom.

Differential cognitive correlates in processing symbolic and situational mathematics

AbstractSymbolic and situational mathematics are the two major representations of mathematical knowledge. Although previous literature has studied the relationship between the two from the perspective of teaching practice, learning effectiveness and behavioural performance, there is still a lack of empirical psychological research on cognitive mechanisms to explore the psychological processes of the two. The current study investigated the relationship between symbolic and situational mathematics by determining the differences in cognitive correlates between the two in fourth‐grade children. Their symbolic and situational mathematics abilities were assessed using symbolic and situational enumeration tests under the same conditions. Several types of general cognitive abilities, language processing and academic achievements were also examined. Results showed that both situational and symbolic mathematics are crucial for mathematical achievement. Arithmetic computation is closely correlated with symbolic mathematics, whereas spatial processing and inductive reasoning ability are uniquely correlated with situational mathematics. The results suggest that situational and symbolic mathematics have separate cognitive correlates, which means the two are distinct in terms of psychological processing.

Integrating the Case Studies Pedagogy and the Anthropological Theory of Didactics to Enhance the Teaching and Learning of Algebra in Undergraduate STEM Education

Methodology case studies plays a pivotal role in STEM education, especially in teaching undergraduate algebra. This article emphasizes the power of real-world scenarios and active pedagogy, a student-centered approach that makes abstract algebraic ideas tangible. The Anthropological Theory of Didactics (ATD) is spotlighted as a perspective that treats mathematical knowledge as a cultural artifact, embedding mathematics concepts deeply within cultural and historical contexts. By comparing active pedagogy with ATD, the article unveils a compelling overlap that values the significance of context in learning. Students don't just engage actively but also delve into the cultural essence of mathematical problems, gaining a profound understanding. Addressing the hurdles undergraduates face in transitioning from high school algebra to university level, the article suggests activities that merge active pedagogy and ATD. This holistic approach has the potential to transform algebra education into a more engaging, relevant, and culturally resonant experience.

Enabling teachers to enact core elements of mathematics in the classroom: a retrospective design-research analysis of interrelated course conceptions and their development phases

Mathematics education in secondary schools should not only provide content knowledge but also an understanding of the fundamental processes by which new mathematical knowledge is created – students should experience how mathematics ‘works’ as a discipline. Initiating this, however, has been shown to be a major challenge for teachers. We therefore undertook a developmental project to design courses that would better prepare pre-service teachers for this task. In this article, we conduct an analysis of the project from a design-research perspective, which provides as a result the theoretical output of the project in the form of an articulated design principle.