Proposition Research Articles

ANALISIS PENALARAN MATEMATIS SISWA SMA KELAS XI DALAM MENYELESAIKAN SOAL BARISAN DAN DERET ARITMETIKA DITINJAU DARI GAYA BELAJAR HONEY-MUMFORD

This study aims to describe the mathematical reasoning in students of class XI MIPA 5 SMAN 4 Jember in solving arithmetic sequences and series in terms of the learning styles of activists, reflectors, theorists, and pragmatists. This type of research is descriptive qualitative research. The research subjects were eight students based on the Honey-Mumford learning style. The instruments used in this study were learning style questionnaires, mathematical reasoning tests, and interview guidelines. The results of this study are Activist Students in solving arithmetic sequences and arithmetic sequences capable of presenting mathematical statements verbally and in writing but are incomplete, constructing and establishing conjectures, carrying out mathematical manipulations, giving reasons or evidence for the correctness of solutions, and making conclusions from statements, but incomplete. Reflector students are able to present mathematical statements verbally and in writing, construct and determine conjectures, carry out mathematical manipulations but are not careful in writing the methods used, provide reasons or evidence for the correctness of the solution, and make conclusions from statement, but takes a long time. Theorist students are able to present mathematical statements verbally and in writing, construct and determine conjectures, carry out mathematical manipulations, provide reasons or evidence for the correctness of the solution, and make conclusions from statements. Pragmatic students are able to present mathematical and verbal statements, construct and determine conjectures, carry out mathematical manipulations, provide reasons or evidence for the correctness of the solution, and make conclusions from statements.

The Relationship Between Proof and Certainty in Mathematical Practice

Many mathematics educators believe a goal of instruction is for students to obtain conviction and certainty in mathematical statements using the same types of evidence that mathematicians do. However, few empirical studies have examined how mathematicians use proofs to obtain conviction and certainty. We report on a study in which 16 advanced mathematics doctoral students were given a task-based interview in which they were presented with various sources of evidence in support of a specific mathematical claim and were asked how convinced they were that the claim was true after reviewing this evidence. In particular, we explore why our participants retained doubts about our claim after reading its proof and how they used empirical evidence to reduce those doubts.

Evaluating Simultaneous Impact of Slag and Tire Rubber Powder on Mechanical Characteristics and Durability of Concrete

In this experimental study, the impact of Portland cement replacement by ground granulated blast furnace slag (GGBFS) and micronized rubber powder (MRP) on the compressive, flexural, tensile strengths, and rapid chloride migration test (RCMT) of concrete were assessed. In this study, samples with different binder content and water to binder ratios, including the MRP with the substitution levels of 0%, 2.5% and 5%, and the GGBFS with the substitution ratios of 0%, 20% and 40% by weight of Portland cement were made. According to the results, in the samples containing slag and rubber powder in the early ages, on average, a 12.2% decrease in the mechanical characteristics of concrete was observed, nonetheless with raising the age of the samples, the impact of slag on reducing the porosity of concrete lowered the negative impact of rubber powder. Regarding durability characteristics, the RCMT results of the samples were enhanced by using rubber powder because of its insulation impact. Moreover, adding slag into the MRP-included mixtures results in a 23% reduction in the migration rate of the chloride ion averagely. At last, four mathematical statements were derived for the mechanical and durability of concrete containing the MRP and GGBFS utilizing the genetic programming method.

Pulmonary rehabilitation in patients with interstitial pneumonia, the pro position

Pulmonary rehabilitation in patients with interstitial pneumonia, the pro position

Задачи логистики: классификация и методы решения

The article provides definitions of logistics tasks and their classification. Some mathematical statements of logistics problems and methods of their solution are also given. In particular, the following combinatorial optimization problems are described: the traveling salesman problem, the resource allocation problem, the transportation problem, the maximum flow problem.

Методические функции примеров и контрпримеров в когнитивно-рефлексивном стиле понимания высшей математики

The problem of methodological functions of examples and counterexamples in cognitive-reflexive problem situations in the study of meaningful sections of higher mathematics has not been specifically studied in terms of understanding mathematics. On the one hand, examples and counterexamples help to comprehend the abstract formulation of mathematical definitions, and on the other hand, with their help you can test the mathematical statement for its truth. The article analyzes the essence of the counterexample as the most important cognitive-reflective concept of mathematical knowledge. Its educational role in cognition is methodically underestimated not only by non-mathematicians, but even by teachers of higher mathematicians.

Модальный структурализм и проблема интеграции

Modal structuralism attempts to solve the problems of Platonism in the philosophy of mathematics. First, the paper presents the view that modal structuralism emerges out of Benacerraf’s arguments against Pla-tonism and set-theoretic reductionist realism. Putnam’s account is showed to be another source of influ-ence on modal structuralism. Second, the basic ideas of modal structuralism are reviewed, with special at-tention paid to how the translation of mathematical statements into modal sentences helps to avoid the set-theoretic grounding of such statements. However, since possible worlds are conceived as set-theoretic entities, the translation itself faces the problem of potential circular explanation. To solve the problem, Hellman suggests taking modalities as primitives, but his solution faces additional issues. Two of them are an unclear metaphysical status of the possible structures mathematicians make statements about and an obscure epistemic access mathematicians have to these structures. In order to avoid these issues, the paper suggests combining modal structuralism with modal normativism. According to the latter, modal statements are not about objects or facts but about linguistic rules. Since modal normativists interpret the possible structures as non-metaphysical entities, the problem of epistemic access to such structures trans-forms into the problem of the agent’s knowledge of the semantic rules of mathematical language. It is al-so pointed out that modal normativism might solve another set of structuralist problems, not specifically concerned with modalities, e.g., the problem of objects’ dependence on the structures in which they are embedded.

Зависимость комплексной гарантированной водоотдачи от регулирующего объема водохранилища

The purpose of the study is to generalize the methodology for solving one of the common engineering problems solved in the development of basin schemes and water management projects, assessment of the parameters of reservoirs of complex purpose. The article analyzes the methodology of construction and practical use ofthe dependence of the complex reservoir guaranteed output onthecalculated hydrological characteristics, the reservoir usable storageand water resourcesprovision for requirements coverage. The role of reservoirs for the development of the integrated use schemesand reservoir water resources using rules to solve the most important water management problems is shown. The engineering and mathematical statement of the problem is formulated. The representativeness of long-term hydrological series by their duration is analyzed, when the relative errors of parameters are put in accordance with the serieslength. It is shown that consideration of the in-series connection (coeffi cient of autocorrelation) and an increase in changeability by 30% leadto the increase in the minimum required duration by several times. On the example of specifi c water objects, the Tsimlyanskiy hydroelectric complex and the cascade of reservoirs of the upper Tobol, the practical application of the generalized method and simulation modeling of the long-term water balance is considered. A variant of water supply scheme to the defi cient areas of Donbass with the involvement of the Severskiy Donets resources for their long-term regulation in the Krasnopavlovsky reservoir (currently not used as a regulating capacity) is presented. Based on the analyzing dependence «capacity-yield», an assessment of additional guaranteed water resources was obtained. With regard to the transboundary section line on the Tobol River, the assessment of the real water yield was obtained by simulation modeling according to the authors’ methodology. The expediency of using simulation and optimization modeling is discussed. The relevance of the topic is noted in connection with the cross-sections topologyand the reservoirsregulating capacity that have been changing for decades. It is rec ommended to discuss the raised issues at conferences and in publications.

ДЕЯТЕЛЬНОСТЬ ШКОЛЬНИКОВ ПРИ ИЗУЧЕНИИ МАТЕМАТИЧЕСКИХ УТВЕРЖДЕНИЙ И СПОСОБОВ ИХ ДОКАЗАТЕЛЬСТВА

ДЕЯТЕЛЬНОСТЬ ШКОЛЬНИКОВ ПРИ ИЗУЧЕНИИ МАТЕМАТИЧЕСКИХ УТВЕРЖДЕНИЙ И СПОСОБОВ ИХ ДОКАЗАТЕЛЬСТВА

What are possible Sources of Common and Persistent Student Errors in Algebra and Calculus?

Research shows that college students make numerous algebra and other prerequisite content-related errors in Calculus courses. Most of these errors are common, persistent, and often observed in simple mathematical tasks. This qualitative study is an attempt to identify the potential sources of such errors. Based on our observations of student errors, we wrote a Precalculus and a Calculus test and administered them in twelve sections of four different undergraduate mathematics courses for which either Precalculus, Calculus I or both were a prerequisite. The tests were announced on the first day of the class and administered the following week. All the questions on the test were True or False questions. Based on our experience as college mathematics instructors, we assumed that many students would perceive the True answers as False and the False as True. Therefore, if students’ selected a given answer, mathematical statement, process or solution as True, they were asked to justify why that was not False and vice-versa. They were instructed to provide logical explanations and avoid plugging in numbers to check for correctness. Analysis of data using grounded theory approach resulted in the following three possible external sources of common and persistent student errors: a) Difficulty with symbols and/or lack of attendance to the meaning of those symbols, b) Instructional practices, and c) Lack of knowledge. We will provide examples to illustrate how such errors could have originated from these sources.

КОМПЬЮТЕРНАЯ АНИМАЦИЯ НА УРОКАХ АЛГЕБРЫ В 7-х КЛАССАХ: РЕЗУЛЬТАТЫ ЭКСПЕРИМЕНТАЛЬНОЙ РАБОТЫ

Statement of the problem. The article deals with the problem of visualization in teaching mathematics using animated drawings. The purpose of the article is to present the analysis of the experimental work on computer animation in the GeoGebra environment as a means of improving mathematical education at school. Research methodology. The methodological foundations of the research include activity-based, informational and visual approaches to teaching mathematics, a synthesis of the author’s work experience in testing computer animation at school. Research results. The results of the experimental work confirmed the expediency of using computer animation in the process of teaching algebra in the 7th grade (educational activity of students increased, as well as interest in research work and quality of mastering mathematical knowledge and skills). Conclusion. The use of computer animation in math lessons at school increases the level of understanding and assimilation of mathematical knowledge by providing clear illustrations of mathematical concepts and statements. The analysis of experimental work using the animation capabilities of computer environments shows an increase in the technological equipment of modern mathematics teachers, which help them achieve higher educational results.

A historical method approach to teaching Kepler’s 2nd law


 Kepler’s 2nd law, the law of the areas, is usually taught in passing, between the 1st and the 3rd laws, to be explained “later on” as a consequence of angular momentum conservation. The 1st and 3rd laws receive the bulk of attention; the 1st law because of the paradigm-shift significance in overhauling the previous circular models with epicycles of both Ptolemy and Copernicus, the 3rd because of its convenience to the standard curriculum in having a simple mathematical statement that allows for quantitative homework assignments and exams. In this work I advance a method for teaching the 2nd law that combines the paradigm-shift significance of the 1st and the mathematical proclivity of the 3rd. The approach is rooted in the historical method, indeed, placed in its historical context, Kepler’s 2nd is as revolutionary as the 1st: as the 1st law does away with the epicycle, the 2nd law does away with the equant. This way of teaching the 2nd law also formulates the “time=area” statement quantitatively, in the way of Kepler’s equation, M = E – e sin E, (relating mean anomaly M, eccentric anomaly E, and eccentricity e), where the left-hand side is time and the right-hand side is area. In doing so, it naturally paves the way to finishing the module with an active learning computational exercise, for instance, to calculate the timing and location of Mars’ next opposition. This method is partially based on Kepler’s original thought, and should thus best be applied to research-oriented students, such as junior and senior physics/astronomy undergraduates, or graduate students.

Analytical Solution of Stationary Coupled Thermoelasticity Problem for Inhomogeneous Structures

A mathematical statement for the coupled stationary thermoelasticity is given on the basis of a variational approach and the contact boundary problem is formulated to consider inhomogeneous materials. The structure of general representation of the solution from the set of the auxiliary potentials is established. The potentials are analyzed depending on the parameters of the model, taking into account the restrictions associated with additional requirements for the positive definiteness of the potential energy density for the coupled problem in the one-dimensional case. The novelty of this work lies in the fact that it attempts to take into account the effects of higher order coupling between the gradients of the temperature fields and the gradients of the deformation fields. From a mathematical point of view, this leads to a change in the roots of the characteristic equation and affects the structure of the solution. Contact boundary value problems are formulated for modeling inhomogeneous materials and a solution for a layered structure is constructed. The analysis of the influence of the model parameters on the structure of the solution is given. The features of the distribution of mechanical and thermal fields in the region of phase contact with a change in the parameters, which are characteristic only for gradient theories of coupled thermoelasticity and stationary thermal conductivity, are discussed. It is shown, for example, that taking into account the additional parameter of connectivity of gradient fields of deformations and temperatures predicts the appearance of rapidly changing temperature fields and significant localization of heat fluxes in the vicinity of phase contact in inhomogeneous materials.

A Joint Assessment of Reasoning about General Statements in Mathematics and Biology

This contribution belongs to a larger empirical study that focuses on issues related to the implementation of inquiry-based learning and formative assessment in science and mathematics education, while it also refers to the issue of STEM education. Here, we discuss the two topics from the perspective of professional preparation of primary school teachers. We employ an educational tool called Concept Cartoons and perceive it as a common diagnostic tool for investigating modes of reasoning about general statements in arithmetic, geometry and biology. The presented qualitative exploratory empirical study maps and codes various kinds of reasoning that can be identified with the tool and investigates possibilities of a joint coding procedure. As a result, it provides a conversion table between various modes of reasoning in the three subject domains. The arisen code categories cover the field of generic examples, including the initial stages so that they can be used for scaffolding the process of learning the foundations of deductive reasoning. The joint approach to reasoning in mathematics and biology shows how argumentation and formative assessment can be understood equally and developed simultaneously in both school subjects. It helps us to see how the two school subjects can be integrated didactically.

Analysis of Students' Mathematical Reasoning Ability with the Constructivism Approach through Mobile Learning System

Aims: To analyze the mathematical reasoning ability of mathematics education students.
 Study Design: Qualitative research with a descriptive approach.
 Place and Duration of Study: The population of all 3rd-semester mathematics education students at Bung Hatta University who take geometry courses is 25 students.
 Methodology: This research is qualitative research with a descriptive approach. Researchers directly measure the mathematical reasoning ability of students in the mathematics education study program. Judging from the research subjects, the population of all 3rd-semester mathematics education students at Bung Hatta University who took geometry courses was 25 students.
 Results: From the analysis results, it was found that the achievement of mathematical reasoning abilities for indicators of students' ability to present mathematical statements orally, in writing, pictures, and diagrams indicated by question number 1 was 74% (Good Category). The indicators of mathematical manipulation ability shown in questions number 2 and 5 are 41% (Category Enough), and 42% (Category Enough). And the indicators of students' ability to conclude, compile evidence, provide comments, or evidence from several solutions shown by questions number 3 and 4 are 67% (Good Category) and 58% (Enough Category).
 Conclusion: The conclusion of this study is to be able to determine the category of mathematical reasoning of the 3rd-semester students of the Bung Hatta University Mathematics Education Study Program.

SZEMERÉDI’S THEOREM: AN EXPLORATION OF IMPURITY, EXPLANATION, AND CONTENT

AbstractIn this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea thatpurityand explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically impure (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I callstructural content(Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5).

Similarity Solution of Stagnation-Point Flow and Heat Transfer of a Micropolar Fluid Towards a Horizontal Permeable Exponentially Elongating Sheet with Radiation, Heat Production/ Immersion

The current study aims to explore stagnation spot flow of a micropolar fluid about a plain linear exponentially expanding penetrable surface in the incidence of radiation and in-house heat production/immersion. Through similarity mapping, the mathematical modeling statements are transformed to ODE’s and numerical results are found by shooting techniques. The impact of varying physical constants on momentum, micro-rotation and temperature is demonstrated through graphs. The computed measures including shear, couple stress, mass transfer and the local surface heat flux with distinct measures of factors involved in this proposed problem are presented through a table.

예비교사들의 무한소, 무한히 큰 수, 극한에 대한 담론 분석

This study investigated seven pre-service teachers’ (who studied analysis) conceptions about infinitesimals, infinite numbers, and explanation methods of limits. Some pre-service teachers thought that infinitesimals and infinite numbers existed. The pre-service teachers who believed that infinitesimals existed explained limits by relying on infinitely small quantities, as did those who believed that infinitesimals did not exist. Some pre-service teachers did not understand the sentences in which quantifiers were used, and they failed to identify statements that contained quantifiers using the Archimedean property of analysis. During interviews, some pre-service teachers demonstrated an intuitive level and did not accept the meta-rules of judging mathematical statements based on axioms and theorems. Their discourse differed from that of analysis in the existence of mathematical objects, endorsed narratives, and meta-rules. This study analyzes the phenomenon of pre-service teachers applying infinitesimals despite having studied standard analysis, focusing on the incommensurability between discourses. This finding can inform teacher education about the curriculum and instruction of analysis.

Language Constraints in Constructing Arguments for Mathematical Proofs

A learning trajectory for constructing mathematical proof has been developed. The trajectory is to provide the students with a step-by-step procedure in constructing arguments for proving mathematical statements. However, in proving activities, the students were found to encounter difficulties in completing a deductive axiomatic argument constituting an accepted mathematical proof. An investigation has been conducted to explore the problems the students experienced in constructing proofs. It was found that they faced language constraints in constructing mathematical arguments. They encountered challenges in how to correctly express the mathematical statements in their constructed proofs.

Метод оценки сложности математических рассуждений в учебных текстах (на примере учебника физики)

The article offers the method for assessing the complexity of mathematical reasoning in various educational texts. It provides for counting the number of mathematical statements (or other elementary judgments) in the conclusions being drawn and taking into account the semantic complexity of the terms denoting the quantities included in the formulas. This allows to calculate the heuristic complexity of the text, depending on the number and complexity of mathematical conclusions, and find the heuristic indicator. To determine the semantic complexity of the entire text and the mathematical reasoning presented in it, a computer is used, which refers to a dictionary-thesaurus – a special file containing terms with an indication of their complexity. This takes into account the volumetric complexity of the formulas, the number of elementary sentences (equations) in mathematical reasoning, as well as the fact that some premises (formulas) are absent, and the pupil must guess before them on his own. Several examples of using the proposed method for analyzing text fragments in physics are considered.