Mathematical Basis Research Articles

2015 개정 교육과정에 따른 <기본 수학> 교과서의 선분의 중점 지도에 관한 분석

Objectives The purpose of this study is to analyze whether to introduce coordinates that midpoint on the line seg-ment and the learning contents that show different description methods of the <Basic Mathematics> textbooks according to the 2015 revised curriculum. Methods To do this, seven <Basic Mathematics> textbooks according to the 2015 revised curriculum were analyzed. Results First, only three of seven <Basic Mathematics> textbooks introduce the coordinates of the midpoint of the line segment. Two of these were introduced in the coordinate plane, and the other one was provided to the auxil-iary space as a hint to solve the equation problem of the circle. Second, three of the seven <Basic Mathematics> textbooks presented a problem to be solved using the coordinates of the midpoint of the line segment. In the equation of the straight line, it is presented as a problem of finding a perpendicular bisector of a line segment, and in the equation of the circle, it was presented as a problem of finding an equation of a circle given both end points of the diameter. Third, the method of describing the contents of the symmetric movement about the straight line    was different depending on whether or not it was introduced into the coordinates of the center. Conclusions Changes in the curriculum due to the nature of the mathematics subject not only affect the teaching and learning methods of that part, but also the teaching methods of other parts. Therefore, it is necessary to con-tinuously study the learning contents and changes in teaching and learning materials such as textbooks according to changes in the curriculum.

Investigation of the Concept Images of Mathematics Educators and Preservice Mathematics Teachers Regarding Slope, Rate of Change, and Derivative

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service elementary mathematics teachers who successfully completed the Calculus 1 course at a state university, and four pre-service elementary mathematics teachers who successfully completed the Calculus 1 and Calculus 2 courses participated in the study. In order to determine the concept images of the participants about the concepts of slope, rate of change and derivative, the participants were asked semi-structured interview questions prepared by the researcher and application questions including the second stage questions. The audio recordings obtained from the interviews were transcribed and then the second stage questions were applied to the participants. The second stage questions were received in writing from the participants and analysed by the researcher through descriptive content analysis. As a result of this study, mathematics educators were able to use the concept images they had in the first stage questions in the second stage questions. On the other hand, pre-service elementary mathematics teachers were able to use the concept images they had in the first stage questions in the second stage questions.

Creating Digital Storytelling as Digital Materials in Mathematics Education

The digitalization of stories through technology-supported software has created the concept of digital stories. In recent years, researchers have been making efforts to investigate the effects of digital stories that have started to be used as digital materials in education. This study aims to evaluate the digital stories created by preservice mathematics teachers for mathematics courses, their experiences in the process of creating digital stories, and their views on the use of digital storytelling as digital materials in mathematics courses. This qualitatively designed study was conducted with the participation of 49 preservice elementary mathematics teachers and lasted 7 weeks. It was found that the digital stories created by the participating preservice teachers were moderately acceptable. Participants characterized digital storytelling as materials that are interesting, support teaching, and provide visual richness. They also stated that they intended to use digital storytelling when they begin working as teachers. However, due to the time-consuming nature of the process, most participants stated that they would use ready-made digital stories instead of creating them themselves. Additionally, the results of this study provide information about the experiences of preservice teachers regarding the process of creating digital storytelling.

A Survey on Ring Theory for its Mathematical Foundation and Applications

The origin of the ring theory can be dated to the early 19th century. With the rapid development of technology, more and more complex engineering problems and computer problems need to obtain support and results from more basic mathematics theory. Hence, based on this demand, the researcher discovered that ring theory is a very noteworthy math theory for solving the complicated problems above. This paper investigated the ring theory and related articles based on number theory and corresponding applications, which produces and results in a literature review in this particular direction.

Cauchy’s Residue Theorem and Its Application

One of the key theorems in complex analysis, Cauchy’s Residue Theorem, which refers to the integral value of an analytic function along any simple closed contour surrounding an isolated singularity in a certain ring domain divided by 2πi, will greatly simplify the process of computing integrals on contour surrounding singularities. In the field of basic mathematics, the Cauchy’ Residue Theorem plays a key role in the integral calculation of analytic functions, nonuniform complex functions and the argument principle, which establishes a connection between a curve’s winding number and the quantity of zeros and poles inside the curve. Furthermore, Residue Theorem can combine with various subjects, including electromagnetism. This paper gives an overview of the Cauchy’s Residue Theorem and its application. Firstly, it talks about the definition and proof of the Cauchy’ Residue Theorem, along with the definition of residue. Then two examples of using Residue Theorem to integrate functions will be given. Finally, this paper involves application of Residue Theorem in trigonometric sum identities and a remark on the method.

Literary and Arithmetic Schools of Uktus Factory (1735–1742): A Historical Analysis

This article examines the activities of the schools established at the Uktus Factory, initiated by the proactive policies of V.N. Tatischev during his tenure as the head of the factories (1734–1739), aimed at engaging children from all factory residents in formal education. The study establishes enrollment figures for the schools over three-year intervals, details collective recruitment efforts, and presents the total number of students taught literacy and basic mathematics, alongside an analysis of the social and age demographics of the pupils. It demonstrates that during the establishment of a network of factory schools in 1735–1736, the movement of skilled workers to other factories due to production needs rarely interrupted children’s education, often resulting in a turnover of students at Uktus. The article characterizes the teacher, exiled Nikita Afanasyev, highlighting his proactive approach to enhancing the organization of literacy instruction. It identifies key dates regarding the commencement of arithmetic education at the Uktus Literary School in Yekaterinburg, the founding of the arithmetic school at the Uktus Factory, and the appointment of top students from the Yekaterinburg school to teach Uktus children under the supervision of teachers Fyodor Sannikov and Afanasy Kichigin. The reasons for the closure of the schools at the Uktus Factory in autumn 1742 and the sharp decline in student enrollment from 1743 onwards are also analyzed.

Derivation of Power Density Equation of Hydro Turbine: Mathematical Basis of Osmosis Energy to Rotate a Reaction Turbine

Derivation of Power Density Equation of Hydro Turbine: Mathematical Basis of Osmosis Energy to Rotate a Reaction Turbine

The importance of Method 300 to improve the mathematical foundation of first-year STEM Brazilian undergraduates

This research explores strategies to support first-year STEM Brazilian undergraduates in two programs, computer science and mathematics, through partnerships among faculty and student members and the implementation of an active methodology known as “Method 300” within an elementary mathematics course. The primary goal of these initiatives was to enhance the academic performance of freshmen. In Method 300, for students to benefit from grade improvements, they must assist each other, regularly attend team meetings, and commit to the activities that constitute the method. The method was implemented only during the first half of the course, fortunately it also implicated into the second part of the course, showing that a tenth of the students who performed poorly at the beginning achieved satisfactory and excellent performance in the last assessment, even though the content was more complex. According to the assessment system of the whole course, by monitoring students who initially had poor academic performance, it was found that half of them achieved satisfactory performance by the end of the course, which contributed to a final approval rate above 73% of all students. The condition of student heterogeneity is crucial for the effective application of Method 300; without it, this could become a potential limitation to its successful implementation. In addition to this strategy, the course was supported by voluntary extracurricular tutors, although these were underutilized by the freshmen, prompting us to consider new ways of providing support. These results suggest that future research in this field should focus on improving students’ academic performance by systematically replicating Method 300 in other courses for freshmen students.

Basic aspects of IOL calculation

IOL calculation can now be considered a solved problem. However, the problem of sharing the knowledge of the underlying physical and mathematical basics is still unsolved. Also, the necessary hard- and software tools for an IOL calculation approximating the accuracy of prescribed glasses are not yet generally available. The aim of this survey is a clarification of the basics and of some historical pitfalls that still lead to persisting misunderstandings.

Teaching Reform of Public Mathematics Basic Courses--Taking Electronic Information Engineering Major as an Example

Teaching Reform of Public Mathematics Basic Courses--Taking Electronic Information Engineering Major as an Example

Examining TPACK Enactment in Elementary Mathematics with Various Learning Technologies

As schools continue to invest more resources into learning technologies and their infrastructure, there is a need to consider ways to support teachers’ professional learning related to the appropriate uses of learning technologies. The construct of TPACK continues to provide a framework for the field to help make sense of the knowledge and skills related to effectively integrating learning technologies into teaching. The article includes three vignettes that describe research-aligned enactments of TPACK using three different learning technologies: an internet-based activity focused on lower-level fluency, an internet-based simulation/game on budgeting, and an internet-based open-ended tool. The three vignettes suggest that TPACK can be enacted regardless of the learning technologies and that the culture and context of schools greatly influences whether and how teachers integrate technology into their mathematics teaching.

Training of HOTS integration in elementary school level mathematics teaching as an effort to strengthen state defense awareness

Strengthening state defense awareness could be supported by the existence of educators from remote and border areas who have adequate performance of high-order thinking skills (HOTS). Currently, HOTS has not been consistently introduced in mathematics learning for teachers in remote areas. This study is a part of the teachers’ development program concerned with delivering effective methods in teaching mathematics at the elementary school level and gaining teachers’ State Defense Awareness to provide educators’ perspectives regarding HOTS implementation in mathematics learning in remote areas of Indonesia. Data was collected by giving questionnaires to the teachers as pre-tests and post-tests. The results showed that the teachers of some remote areas recognized the advantages as well as the difficulties of HOTS integration in learning activities. Teachers' understanding of applying HOTS in mathematics teaching could be slightly increased through comprehensive training regarding HOTS. It was also found that teachers from remote and border areas are still required to be more encouraged to implement and develop HOTS in mathematics learning through training in education research activities.

Detailed Late Pliocene-Quaternary sedimentation history and diagenesis processes in the eastern part of the Norwegian-Greenland Basin based on mathematical statistical methods

As a result of univariate regression analysis, quantitative parameters on the distribution of Mn/Al and Mn/Fe ratios in the sections of the studied holes of ODP Leg 151 were obtained. On the basis of correlation analysis data with Pearson matrix construction and classical factor analysis with varimax rotation, a division of rather homogeneous Upper Pliocene-Quaternary sediments was carried out with the allocation of 3 main factors that characterize the history of sedimentation and diagenesis in the Norwegian-Greenland Basin. The boundaries between lithostratigraphic subdivisions are drawn on a strict mathematical basis. It is established that the nature and degree of intensity of diagenesis processes in this region were influenced by the following main factors: sedimentation environments in the Norwegian-Greenland Basin in the Late Pliocene-Quaternary time; grain-size and chemical composition of the studied sediments; total organic carbon content in the sediments; sedimentation rates.

The Numerically Leveled Performance Assessment Framework (NLPAF): A Literature-Based Evaluation of Acceptability

ABSTRACT The purpose of this study is to present a literature-based, initial “evaluation of acceptability” (American Educational Research Association et al., 2014, p. 7) of the Numerically Leveled Performance Assessment Framework (NLPAF). Its results enable confidence in continuing its use in the authors’ professional development work and in making it available to professional developers and researchers. The authors developed the NLPAF to guide elementary mathematics teachers enrolled in a professional development program in constructing performance assessments they then administer up to three times annually to their students. These assessments measure growth across time in mathematical proficiency relating to the domain of whole number operations most prominent in the curriculum standards for the grade level taught. Numerically leveled refers to the process teachers learn and apply to estimate the size and numerical complexity of computations to be used in designing performance tasks for their students’ unique levels.

Perception of the elementary mathematics teachers about assessment for learning: a case study of Sukkur IBA community colleges, Sindh, Pakistan

This study aims to explore the perceptions of elementary mathematics teachers regarding assessment for learning (AfL). The participants of this study included three elementary mathematics teachers, each with over 5 years of teaching experience at Sukkur IBA community colleges and schools in Sindh, Pakistan. These participants were selected using purposive sampling techniques. A qualitative exploratory case study research approach was used, with data collected through semi-structured interviews and observations. To ensure the trustworthiness of the study, the interview guide and observation checklist were reviewed by experts. The data were analyzed using thematic analysis. The findings of this study revealed that teachers had a limited understanding of the concept of assessment for learning. Based on these results, the study recommends several measures: the initiation of an assessment literacy program, an increase in class time, reducing the number of students per class, using moveable chairs to enhance classroom flexibility, and making amendments to the assessment policy.

Revisiting the fitting of the Nelson–Siegel and Svensson models

The Nelson–Siegel and the Svensson models are two widely used models for the term structure of interest rates. These models are quite simple and intuitive, but fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, we provide a novel mathematical analysis of the fitting problem based on parametric optimization. We formulate the fitting problem as a separable nonlinear least-squares problem, in which the linear parameters can be eliminated. We provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation itself and cannot be tackled by choosing a particular optimization algorithm. Our stability analysis provides novel insights that we use to show that some of the ill-conditioning can be avoided, and that a suitably chosen penalty approach can be used to address the remaining ill-conditioning. Numerical results indicate that this approach has the expected impact while being independent of any choice of a particular optimization algorithm. We further establish smoothness properties of the reduced objective function, putting global optimization methods for the reduced problem on a sound mathematical basis.

“Our Voyage with Knowing and Teaching Elementary Mathematics”

From the Archives highlights articles from NCTM’s legacy journals, previously discussed during MTLT Teacher Talk.

DEFINING THE ROLE OF EDUCATIONAL PLATFORMS IN MATHEMATICS IN THE EFFECTIVE TRAINING OF FUTURE MATHEMATICS TEACHERS

The present study analyzes the results of a survey of teachers and students designed to identify the preferences and needs of universities in using educational platforms in mathematics to study the subject «Elementary Mathematics». The aim of the study was to determine the preferred characteristics and functionality of mathematics learning platforms that can contribute to effectivelearning and increase interest in mathematics for future mathematics teachers. To achieve this goal, questionnaires were developed, which were distributed among mathematics teachers and first-year students in the specialty «Mathematics» when teaching the subject «Elementary Mathematics» and third and fourth-year students when teaching the subject «Methods of teaching mathematics». The questionnaires included questions about preferences in using educational platforms in mathematics, the level of comfort andperception of educational material when working with technologies, preferred learning formats and expected learning outcomes. The analysis of the obtained results allowed us to identify the key principles that should be taken into account when using educational platforms in mathematics to study the subject «Elementary Mathematics» at the university. Following these principles contributes to the use of educational platforms in mathematics, and as a result, to improving the quality of mathematical education at the university and improving the learning ability of future mathematics teachers.

Secret sharing in a special linear group

Objectives. The problem of developing the mathematical foundations of modular secret sharing in a special linear group over the ring of integers is being solved.The relevance of the problem is reduced to the fact that a large number of requirements are imposed on secret sharing schemes. These include the ideality of the scheme, the possibility of verification, changing the threshold without the participation of the dealer, the implementation of a non-threshold access structure and some others. Every secret sharing scheme developed to date does not fully satisfy all these requirements. It only has a certain configuration of these properties. The development of a scheme on a new mathematical basis is intended to expand the list of these configurations, which creates more opportunities for the user in choosing the optimal option.Methods. Group theory, modular arithmetic and theory of secret sharing schemes are used.Results. A fundamental domain with respect to the action of the main congruence subgroup by right shifts in the special linear group of second-order matrices over the ring of integers is constructed. On this basis, methods for modular secret sharing and its threshold restoration are proposed.Conclusion. A rigorous mathematical justification is given for the correctness of the algorithms for generating partial secrets and restoring the main secret in the special linear group over the ring of integers. These results will be used to study the configuration of secret sharing properties in this group.

Implementing Equitable Practice-Based Teacher Education to Advance Rural STEM Teacher Candidates’ Pedagogical and Content Knowledge

This longitudinal three-year study explored implementation of practice-based teacher preparation incorporating high-leverage teaching practices to advance PCK. Participants included teacher candidates (n = 45) who completed elementary science and mathematics methods courses at a rural Midwestern university. Students engaged in teaching rehearsals to explore STEM concepts and equitable teaching practices. Data from surveys and student reflections revealed an increase in teacher candidates' perceptions of their knowledge and competence of teaching science and math content equitably.