Conceptual Difficulties Research Articles

Effective Application of One Minute Paper and Muddiest Point Technique to Enhance Students' Active Engagement: A Case Study

Abstract: Outcome based education involves a student centric approach. Active participation of students in the classroom plays a significant role in the Outcome Based Education model. This paper explains the use of two active learning techniques viz. 1) Muddiest Point Technique 2) One Minute Paper for three courses taught to third year Mechanical Engineering undergraduate program. The Muddiest Point Technique was used for the course Computer Or i e n t e d Nume r i c a l Me t h o d s ( CONM ) by using Padlet as a tool to record the conceptual difficulties. One Minute Paper (OMP) was applied to the two courses, Analysis and Synthesis of Mechanisms (ASM) using traditional One Minute Paper and to another course namely Automation and Control Engineering (ACE) using goggle form. Students' responses to the survey questionnaire showed that implementation of these techniques improved overall understanding of the course content. It gives students a chance to communicate their conceptual difficulties without any hesitation. Keywords : Active learning, Classroom Assessment Techniques (CAT), Covid-19 Pandemic, Hybrid mode, Muddiest Point Technique, One Minute Paper(OMP).

Опыт концептуализации специальных военных операций в современном праве

Special military operations are associated with the establishment of a special legal regime in a certain territory or in relation to certain actions, as well as with the special activities of collective subjects and military officials. Difficulties in international legal and law enforcement conceptualization give rise to various forms of legal understanding of the phenomenon of “special military operation”. The article discusses interrelated conceptual, legal, and institutional issues of special military operations, including the way they apply to Russia’s special military operation (SMO) in Ukraine at different stages of legal regulation. In terms of differentiation of the legal regulation’s object, SMO is already regulated by over 30 federal laws and subsidiary legislation acts, and this list continues to grow. The specifics of the formation of special legislation on SMO that forms a separate subject area of the Russian law is revealed. Specialization of legislation first manifested itself at the level of individual legal norms (such as military award procedures in SMO area) and sub-institutions (such as ensuring monetary and social security of its participants, partial mobilization procedures etc.), with subsequent optimization and integration of legal regulation into single legal institution of SMO. Legal regulation problems in the field of military confrontation in cyber-space and at sea actualized by SMO are also addressed. The authors conclude that some features of social relations to be regulated in the case of SMO require certain legal norms and the method of legal regulation to be revised, as the existing legal mechanisms do not always function effectively.

ОБ ОПРЕДЕЛЕНИИ ДИСЦИПЛИНАРНОГО СТАТУСА ИССЛЕДОВАНИЙ ТУРИЗМА

The article is devoted to one of the most controversial topics in tourism research – whether there is a tourism science. This problem has been in the focus of specialists’ attention for almost half a century. The author traces the discussion history, from the first questions posed to monodisciplinary research and discussion of an interdisciplinary approach, as well as describes the waves of scientific interest caused by the development of the research object – tourism on the one hand, and the processes taking place in science itself on the other hand. The essence of the discussion is presented. The main discussion groups are identified: two polar ones – supporters of the integrated tourism science and their opponents, as well as an intermediate group. Their main arguments are outlined. The purpose of the work is to assess the state of tourism research in Russia and abroad and the prospects for its development. The article analyzes the conceptual and methodological difficulties in understanding tourism. The dominance of multidisciplinarity is shown to be the main obstacle to the elaboration of the general theoretical foundations of tourism development, and the current task of forming an interdisciplinary approach in tourism research is set. The possibilities of scientific integration on the basis of civilizational, humanitarian, and territorial platforms as well as the ‘Sustainable Development’ platform are considered. The importance of integration processes for the development of tourism research is emphasized. In the longer term, a breakthrough in tourism research is associated with overcoming disciplinary restrictions and the transition to non-disciplinarity (transdisciplinarity). Theoretical positions are supported by a large amount of illustrative material. The article is addressed to specialists in various fields of knowledge interested in the problems of the tourism and recreation development, and is designed for a broad discussion of the future research issues in this area.

ОСОБЕННОСТИ ЛИНГВОДИДАКТИЧЕСКОГО ПОДХОДА К РАБОТЕ С ТЕКСТОМ ПРИ ОБУЧЕНИИ РУССКОМУ ЯЗЫКУ ИНОФОНОВ - БУДУЩИХ ЮРИСТОВ-МЕЖДУНАРОДНИКОВ

The article presents a functional and communicative model of working with professional text in the process of assimilating and producing a language thesaurus of international legal topics in Russian in a foreign audience at an advanced stage of training. The purpose of the study is to develop an integrated methodically grounded approach to the process of teaching the language of a specialty, in our case – the language of a future specialist in the field of international law and international relations. The research is based on an interdisciplinary approach to the studied problematics, since the formation of professional competencies among foreigners occurs in Russian, which is a means of obtaining a specialty. The general scientific methods of cognition used in this study include observation and analysis of the text and linguistic material, an experiment to test the developed methodology, and analysis of the results obtained. The article substantiates an integrated approach to the study of professionally oriented text, describes the grammatical, lexical and conceptual difficulties characteristic of professional non-adapted texts and hindering their production by foreign students. The selected lexical material, on the basis of which the analysis of the integrated approach was carried out, was not previously included in such studies. In the conclusion of the article, the results of the experimental final testing of students are given, indicating the productivity of the described complex methodological training model.

Геоинформационное моделирование индекса человеческого развития стран ОЭСР и их регионов

The article is devoted to the development of the Human development Index (HDI) in the framework of inter-territorial comparisons of the countries of the Organization for Economic Cooperation and Development (OECD) and their regions. The processes of creating a basic cartographic basis for conducting geoinformation modeling of the human development index at the country and regional levels at the same time are considered. New features of the mathematical-cartographic modeling apparatus are revealed, the main conceptual difficulties of developing the thematic content of such modeling are described. Based on the analysis of the international and Russian versions of the human development index, the concept of thematic content of this index is proposed to ensure inter-territorial comparisons. Within the framework of geoinformation modeling, the results were obtained from the standpoint of general ideas about the differentiation of territories according to the values of the human development index. An approach to the integration of evaluation and typological models is proposed, which allowed not only to consider the typology of territories according to the degree of intensity of the values of the human development index indicators, but also to consider them in conjunction with the entire variety of index values within this type, which made it possible to give a comprehensive characteristic of the territory. The analysis made it possible to consider the territory from the standpoint of public health, the effectiveness of the system of secondary specialized and higher education, as well as to assess the size of the territory’s economy in relation to the population. On the basis of this, a number of the main problems of the territories were identified from the standpoint of the components of the human development index and a number of recommendations were given to those making managerial decisions within the framework of national and regional policy.

NewBee: Context-Free Grammar (CFG) of a New Programming Language for Novice Programmers

Learning programming and using programming languages are the essential aspects of computer science education. Students use programming languages to write their programs. These computer programs (students or practitioners written) make computers artificially intelligent and perform the tasks needed by the users. Without these programs, the computer may be visioned as a pointless machine. As the premise of writing programs is situated with specific programming languages, enormous efforts have been made to develop and create programming languages. However, each programming language is domain-specific and has its nuances, syntax and semantics, with specific pros and cons. These language-specific details, including syntax and semantics, are significant hurdles for novice programmers. Also, the instructors of introductory programming courses find these language specificities as the biggest hurdle in students learning, where more focus is on syntax than logic development and actual implementation of the program. Considering the conceptual difficulty of programming languages and novice students’ struggles with the language syntax, this paper describes the design and development of a Context-Free Grammar (CFG) of a programming language for the novice, newcomers and students who do not have computer science as their major. Due to its syntax proximity to daily conversations, this paper hypothesizes that this language will be easy to use and understand by novice programmers. This paper systematically designed the language by identifying themes from various existing programming languages (e.g., C, Python). Additionally, this paper surveyed computer science experts from industry and academia, where experts self-reported their satisfaction with the newly designed language. The results indicate that 93% of the experts reported satisfaction with the NewBee for novice, newcomer and non-Computer Science (CS) major students.

The Virtue Ethics Anthropological Turn: Reactualization of Aristotle's Ethics in the Second Half of the 20th Century

The article examines the specifics of the virtue ethics as an anthropological turn in the moral philosophy of the 20th century based on Aristotle's ethics ideas. The article sets a goal to show the specificity of borrowing these ideas determined the virtue ethics thematic development direction in conceptualizing the moral assessment of human activity, but it also became the cause of the main conceptual difficulty (problematization of human nature), it has not been overcome. The article provides an analytical review of the main works of the most significant representatives of the virtue ethics, reconstructs the approaches developed in the works to the conceptualization of moral evaluation of human activity and establishes the role of Aristotle's ideas in the approaches. It is shown the appeal to Aristotle's philosophy primarily occurs when developing a method for determining the moral content of an action in a specific situation, where the application of a universal rule should be supplemented by many conditions of this situation, as well as when trying to return the motive and personal qualities to the description of the conditions. The latter also entails the conceptualization of personal qualities as a moral state of a person, correlated with his development (in possibility — by nature, in reality — in interaction with other people). It is concluded that the virtue ethics borrowed Aristotle's ideas in fragments and without a deep analysis of his philosophy. As a result, the problem of conceptualizing human nature was not solved, which would allow us to come to moral assessments of an act without appeal to a transcendental legislator or abstraction of duty. The achievements of ethics of virtue show: 1) it is impossible to selectively return individual concepts from the past to moral philosophy, but a comprehensive description of the phenomenon of morality in human activity is necessary, 2) the return of old concepts also brings back old problems of former moral theories (in the case of virtue, this is the problem of making a choice and forming a disposition).

Let’s draw molecules: Students’ sequential drawing processes of resonance structures in organic chemistry

Drawing is a fundamental skill in science, technology, engineering, and mathematics (STEM) disciplines to express one’s reasoning and externalize mental models in problem-solving. Although research has highlighted the effectiveness of drawing as a learning strategy and the importance of drawing accuracy for learning success, little is known about learners’ actual drawing process. However, especially in organic chemistry, the investigation of drawing processes is of great importance as generating different representations, such as structural formulas, is inherent to problem-solving in this visual-laden discipline. Resonance structures, for example, are often used to estimate reactive sites in a molecule and to propose reaction pathways. However, this type of representation places a high cognitive demand on learners, which, besides conceptual difficulties, leads to drawing difficulties. To support learners in drawing and using resonance structures in problem-solving, it is necessary to characterize how they generate their drawings. To this end, a qualitative, exploratory study has been conducted to investigate undergraduate students’ (N = 20) drawing processes of resonance structures while solving an organic case comparison task. Using eye-tracking, the characteristics regarding the construction of productive and unproductive drawings became visible. Results indicate that unproductive drawings often stem from integrating and connecting unrelated information during the drawing process. Further, the results show that the productivity of a drawing depends on learners’ flexibility in information selection. Implications for supporting learners’ drawing process and using eye-tracking for characterizing drawing processes in other STEM disciplines are discussed.

ПЕДАГОГІЧНІ УМОВИ ОРГАНІЗАЦІЇ ІНФОРМАЦІЙНОКОНСУЛЬТАТИВНОГО СЕРЕДОВИЩА ЗАКЛАДУ ОСВІТИ: ІННОВАЦІЙНІ ПІДХОДИ ТА ВЕКТОРИ РОЗВИТКУ

The article fixes the fact that in view of the emphasis on the independent acquisition of knowledge by students, the consulting and corrective components of the pedagogues’ professional activity are strengthened. They have to carry it out in the institution’s information educational space and for this purpose possess by modern ICT and tools, both in the field of basic and related educational subjects. The aims of the article are to substantiate the pedagogical terms for the organization of an informational and consultative environment and to highlight the requirements for its productive functioning both for those seeking education and for the pedagogical staff, which will ultimately ensure high quality of educational services. Such methods as analysis, generalization, systematization, extrapolation and SWOT analysis were used to study indicators of the functioning of the informational and consultative environment of vocational education institutions in Ukraine; as well as modelling and substantiating the pedagogical terms for its optimal organization. A study of the state of the issues of the organization of the information and consultative environment in educational institutions in Ukraine has been carried out according to the functional-structural criterion. It covers such indicators characteristic of the subjects of the environment (internal and external) as immersiveness, presence, interactivity, saturation, structuredness, openness, scalability and adaptability. A SWOT analysis has been carried out, which made it possible to identify the advantages and risks, strengths and weaknesses that take place in the organization of the information and consultative environment of vocational education institutions. The conceptual, substantive, organizational and technical-technological difficulties in the organization of the informational and consulting environment of the educational institution have been clarified and summarized. The organizational, technical, methodical and resource conditions that collectively contribute to the organization of the informational and consultative environment of the educational institution have been identified and described. It has been substantiated that the combination of the above-mentioned factors makes it possible to formulate a set of necessary and sufficient pedagogical terms. Among them: the readiness of pedagogical staff and students for consultative activities with the use of modern ICT; resource provision of advisory activities focused on the content of professional education; implementation of multi-channel and multi-disciplinary online counselling, which realizes the functions of the educational institution information environment; creative and developmental subject-subject interaction via ICT and tools, which initiates methodological reflection of pedagogues and students in consultative activities. It was concluded that the creation of the specified pedagogical terms will enable the functioning of all components of the educational institution’s information and consultative environment in the best relationship, will ensure the creation of an atmosphere of fruitful cooperation, productive learning, effective management of the study process, as well as the provision of quality educational services. Prospects for further research are defined in the creation of a methodology for the organization of informational and consultative environments in a professional education institution and its empirical verification.

What is life? Active particles tools towards behavioral dynamics in social-biology and economics.

This review paper is devoted to study the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on the challenging perspective of developing a mathematical theory for living systems including mutations and selection. The quest starts with the identification of a number of common complexity features of living systems. Then, mathematical structures are derived to include these features, while mathematical models are derived by inserting in the structures models of individual based interactions. Three applications are examined by active particles methods, i.e., models of SARS2-CoV-2 pandemics, models of idiosyncratic learning in open markets and of the dynamics of prices accounting for human behaviors. A critical study, which pervades the whole paper, shows that also economics can be viewed as a behavioral science thus accounting for specific aspects typical of living systems.

Jurisdictional Conflict Between the World Trade Organization and Regional Trade Agreements: Res Judicata Revisited

This article discusses the long-standing issue of jurisdictional conflict in World Trade Organisation (WTO) jurisprudence, which has, in the recent decades, been exacerbated by the proliferation of Regional Trade Agreements (RTAs). An examination of WTO jurisprudence reveals that jurisdictional conflict stems from the lack of choice of forum clauses in WTO-covered agreements, and the lack of a hierarchy of sources in international law. While there exists legal basis for the application of general principles of international law such as res judicata, a careful analysis demonstrates that there is conceptual difficulty applying the doctrine in the context of WTO disputes. To remedy this, the article argues that the WTO Dispute Settlement Understanding (DSU) could be amended to allow for the operation of res judicata. WTO, res judicata, jurisdiction conflict, regional trade agreements, general principles of law, Dispute Settlement Understanding

Analysis of students difficulties in mathematics problem-solving ability on number pattern material

This research aims to analyze and describe students' difficulties in solving mathematical problem-solving abilities on number pattern material. The research method is qualitative research, with the research subjects being grade eight students in one of the schools in the city of Semarang in the academic year 2022/2023. The research instrument was in the form of a mathematical problem-solving ability test and interviews. The mathematical problem-solving ability test indicator uses the indicators proposed by NCTM, with the stages of problem-solving according to Polya. The results showed that students with the concept difficulty type could only understand the problem. The student with the principal difficulty type could carry out the strategy planning stage. Finally, the students with the conceptual difficulty type have been able to implement the stage of planning strategies in solving mathematical problems.

Set Theory, Dynamism, and the Event: Reinjecting Time into the Foundations of Mathematics

This article concentrates on exploring the relevance of the postmodernist concept of the event to mathematical philosophy and the foundations of mathematics. In both the scientific and philosophical study of nature, and particularly event ontology, we find that space and dynamism are fundamental. However, whether based on set theory or category theory, modern mathematics faces conceptual and philosophical difficulties when the temporal is intentionally invoked as a key aspect of that intrinsic dynamism so characteristic of mathematical being, physical becoming, process, and thought. We present a multidisciplinary investigation targeting a diverse audience including mathematicians, scientists, and philosophers who are interested in exploring alternative modes of doing mathematics or using mathematics to approach nature. Our aim is to understand both the formal character and the philosophy of time as realized through a radical mode of thinking that goes beyond the spatial in mathematics. In particular, we suggest the need to transcend the purely geometrical view altogether in future foundational research in both mathematics and mathematical philosophy. We reexamine these issues at a fundamental and comprehensive level, where a detailed exposition and critique of both modern set theories and theories of space is outlined, with emphasis on how the philosophy of Idealism has been permeating much of old and new mathematics. Furthermore, toward the end of the article, we explore some possible constructive directions in mathematical ontology by providing new proposals on how to develop a fragment of mathematics for the description of dynamic events.

Prospective teachers’ conceptual understanding of the polarization of light

It is seen that the polarization of light, which has a wide applications in daily life and modern techniques, is not understood. A detailed investigation of prospective teachers’ conceptual understandings and misconceptions on the polarization of light can be a guide for both teaching the subject and revealing students’ conceptual understanding of electromagnetic waves. This study aims to determine prospective teachers’ conceptual understanding of the polarization of light. Using qualitative research methods, it was realised with the participation of 20 prospective teachers. Participants were asked five open-ended questions to determine their conceptual understanding of the polarization of light. These open-ended questions include polarization explanations and drawings. After first coding, eleven of them were interviewed. Findings indicate that participants have incorrect or insufficient conceptual understanding of the polarization of light. Participants’ explanations and drawings showed that prospective teachers thought of polarization as losing magnetic field, propagating in a single direction, and collecting beams of light. Based on the results obtained in the study, it is believed that prospective teachers’ conceptual difficulties about the polarization of light stem from not having completely understood the electromagnetic structure of light and the function of polaroids. Based on the results, explaining the limitations of each light model, using three-dimensional simulations, and inquiry-based teaching are suggested.

Empirical adaptationism revisited: is it testable and is it worth testing?

Empirical adaptationism is often said to be an empirical claim about nature, which concerns the overall relative causal importance of natural selection in evolution compared with other evolutionary factors. Philosophers and biologists who have tried to clarify the meaning of empirical adaptationism usually share, explicitly or implicitly, two assumptions: (1) Empirical adaptationism is an empirical claim that is scientifically testable; (2) testing empirical adaptationism is scientifically valuable. In this article, I challenge these two assumptions and argue that both are unwarranted given how empirical adaptationism is currently formulated. I identify a series of conceptual and methodological difficulties that makes testing empirical adaptationism in a biologically non-arbitrary way virtually impossible. Moreover, I show that those in favor of testing empirical adaptationism have yet to demonstrate the distinctive value and necessity of conducing such a test. My analysis of the case of empirical adaptationism also provides reasons for scientists to reconsider the value and necessity of engaging in scientific debates involving the notion of overall relative causal importance.

RASCH MODELLING TO EVALUATE REASONING DIFFICULTIES, CHANGES OF RESPONSES, AND ITEM MISCONCEPTION PATTERN OF HYDROLYSIS

This study evaluates the difficulties in concept reasoning, changes in response patterns, and item misconception hydrolysis patterns using Rasch modeling. Data were collected through the development of 30 distractor-based diagnostic test items, measuring ten levels of conceptual reasoning ability in three types of salt hydrolysis compounds: 〖〖Na〗_5 P〗_3 O_10, NaOCl and 〖〖(NH〗_4)〗_2 〖SO〗_4. These 30 written test items were completed by 849 students in Gorontalo, Indonesia. The findings show empirical evidence of the reliability and validity of the measurement. Further analysis found that the students’ reasoning difficulty levels of the concept of saline solutions were varied; the calculation of saline solution’s pH level is the most difficult construct to reason. In particular items, changes in response patterns were found; the misconception curve showed a declining trend and disappeared along with the increase of comprehension along the spectrum of students’ abilities. The item misconceptions pattern was found repeatedly in similar items. This finding strengthens the conclusion that resistant misconceptions potentially tend to cause students' conceptual reasoning difficulties and are difficult to diagnose in conventional ways. This study contributes to developing ways of diagnosing resistant misconceptions and being a reference for teachers and researchers in evaluating students' chemical conceptual reasoning difficulties based on Rasch modeling. Keywords: reasoning difficulties, hydrolysis, misconception, Rasch model.

SENIOR HIGH SCHOOL STUDENTS’ DIFFICULTIES IN LEARNING HYBRIDISATION IN CHEMISTRY

The concept of hybridisation is one of the most difficult concepts for chemistry students to grasp at all levels of learning. Research showed the students conceptual difficulty ranged from their lack of the pre-requisite knowledge for grasping the topic hybridisation to chemical bond formation and orientations of atomic orbitals. This study investigated the difficulties Senior High School Students face in learning hybridisation. The study adopted a mixed-method approach using the sequential exploratory design. Purposive sampling was used to select six schools that offer elective chemistry subject. Simple random sampling was then used to select 120 Senior High School form 1 students to take part in the study. Convenient sampling was used to interview 24 students from the sample. Hybridisation Achievement Test (HAT) and Semi-structured interviews were self-constructed and used to collect data. Descriptive statistics and Content analysis were used to analyse the data. Results showed that, majority of students had difficulties in explaining the concept of hybrid orbitals, writing the electron configuration of 6C, explaining the effect of hybridisation on formation of chemical bonds in 6C, and type of hybridisation and shapes of compounds such as NH3, OF2, BCl3, CO2, SiO2, C2H2, BeF¬2 and C2H4. The study also showed that students had difficulties in explaining and demonstrating the formation of C = C double bond in ethene and other compounds. Equally students were challenged in demonstrating the differences between the formation of sigma and pi bonds in compounds. Students had difficulties in using electron orbital diagrams to explain the shape of CO2 as linear. The study concluded that Senior High School form 1 chemistry students in the Upper West Region of Ghana lacked the most basic and fundamental concept of hybridisation. Teachers need to use conceptual change instructional approaches to teach hybridisation in order to foster students’ understanding and reduce misconceptions. Keywords: atomic orbitals; hybrid orbitals; hybridisation; mixed- method approach; sigma and pi-bonds;

Development and Validation of a Four-Tier Test for the Assessment of Secondary School Students' Conceptual Understanding of Amino Acids, Proteins, and Enzymes.

Previous studies noted the scantiness of diagnostic instruments for the assessment of students’ understanding of fundamental biochemistry concepts. Consequently, within this study, a four-tier test for the examination of secondary school students’ conceptual understanding of amino acids, proteins, and enzymes has been developed. Items in the test consist of the answer tier, the reason tier, and a confidence rating for each of these tiers. Following the three-phase development process, the final version of the test, comprising eight items, was administered to 123 students in the main study. The internal consistency of both cognitive scores and confidence ratings proved to be adequate (Cronbach’s alpha values were 0.76 and 0.87, respectively) and the test–retest reliability was also satisfactory (Pearson’s r value was 0.74 for the cognitive scores and 0.88 for the confidence ratings). If the correct responses to both the answer and the reason tier of items are considered, the mean score on the test was 3 out of 8 (38%). The students were more confident when producing the correct compared to the wrong answers but, overall, their confidence was not high (3.65 out of 6). Furthermore, the confidence in the incorrect answers that were provided (3.52 out of 6) indicates the presence of alternative conceptions. Such results show that the content regarding amino acids, proteins, and enzymes is conceptually challenging for the students. Therefore, the test can help secondary school teachers to uncover the students’ conceptual difficulties related to this content and develop effective strategies for their remediation and prevention.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11165-022-10075-5.

Brief Historical Review about Magnetism: From the Ancient Greeks up the Beginning of the XXth Century

Magnetism is omnipresent in multiple natural and constructed phenomena we interact with daily. However, few students knew about the different explanations advanced relative to this mysterious magnetic force imperceptible by our senses before the advent of the discovery of the atomic and molecular aspects of matter. Unfortunately, the concepts associated with the study of magnetism presented in many textbooks do not consider the conceptual difficulties encountered by scientists and the false theories developed and abandoned following new experiments and theories. Towards the end of the 18th century, with the developments of classical physics, among others in mechanics, electrostatic, electricity, and measuring instruments, scientists pierced the secret of the magnet stone and the compass used in navigation for several centuries BC. On the other hand, the progress made in studying matter at the atomic scale at the beginning of the 20th century made it possible to explore the phenomenon of magnetism in greater depth and give it a quantum interpretation. It is impossible to present all the conceptual complexity concerning the development of magnetism in a few pages. Thus, we will limit to synthesizing the most discoveries related to magnetism from the ancient time, five centuries before Jesus Christ, to the beginning of the 20th century. Thus, we will mainly focus on the erroneous theories developed throughout history by renowned scientists and the conceptual difficulties related to the study of magnetism.

ANALYZING STUDENTS MATHEMATICS LEARNING DIFFICULTIES IN THE MATTERIALS OF LINEAR EQUATION SYSTEM WITH TWO VARIABLES IN GRADE VIII OF SMP MUHAMMADIYAH 1 PRAMBANAN SLEMAN REGENCY IN THE ACADEMIC YEAR OF 2018/2019

Mathematics learning difficulties are commonly faced by the students of SMP Muhammadiyah 1 Prambanan in the Materials of Linear Equation System with Two Variables. This study aims to determine the students’ mathematics learning difficulties in the Materials of Linear Equation System with Two Variables (SPLDV) in SMP Muhammadiyah 1 Prambanan seen from the factual, conceptual, and procedural difficulties. The research sucject were grade VIII C students of SMP Muhammadiyah 1 Prambanan in the academic year of 2018/2019. The object of this research is the difficulties of learning mathematics in the Materials of Linear Equation System with Two Variables. The data were collected through test, interview guidelines, and image recording. The data were analyzed using Miles and Hubberman model steps which include (1) data reduction (2) data display (3) verification. The results showed that the students found difficulties in learning the Materials of Linear Equation System with Two Variables (SPLDV), with the average score for factual difficulties were 52%, conceptual difficulties 63%, and procedural difficulties 64%. Students experience factual difficulties due to lack of understanding of the problems so they cannot change into mathematical sentences. Whereas students who experience conceptual difficulties because they cannot use the rules equate one variable coefficient. As for procedural difficulties because students do not write the steps to work correctly, so the results are less precise.