Mathematics Module Research Articles

The Influence of Learner Support on Performance in Mathematics’ Modules of Open Distance and e-Learning (ODEL) for in – Service Secondary School Teachers at University of Rwanda, College of Education

The present study argues that there is a great relationship between the learning support and the performance of mathematics of ODeL level one students. The findings of this study were drawn from a large study aimed at examining the influence of learners support on performance in mathematics’ modules of open distance and e-learning (ODeL) for in – service secondary school teachers with a case study of University of Rwanda-College of Education level one mathematics ODeL students 2021-2022. This study investigated the lecturers’ perception towards the learning support; the extent to which ODeL instructional materials contribute to the performance and examination of the relationship between learning support and the performance of mathematics of ODeL students. The study was carried out based on the gap found in literature review where others have been script on ODeL but not on specific topic of mathematics. Through questionnaire, quantitative data were collected from 40 respondents using mixed approach and analyzed using Statistical Package of Social Sciences (SPSS) for descriptive and inferential statistics. The findings revealed that there is a significant relationship between learning support and the performance of mathematics modules. This study, therefore, recommends the provision of ICT tools to ODeL students, put more efforts in using technology as ODeL students, cooperate each other as ODeL students and choose the options related to their background.

Two Pathways into Number Work for Primary Teachers: A Counting Pathway and a Measurement Pathway

Teacher quality in primary schools in South Africa is a serious concern, and how best to prepare teachers in initial teacher education—with regard to mathematics—remains an open and vexing question. There is a confluence of challenges facing the mathematics education community in South Africa: poor conceptual understanding of mathematics amongst teachers; poor attainment in Primary Teacher Education mathematics tests at both first and fourth year levels; and few initial teacher education programmes having evidence of improving knowledge for teaching mathematics. In addition, few lecturers in initial teacher education make explicit the theoretical tenets informing their course design for mathematics. In response to the latter challenge, this paper makes explicit the design choices made in the Emergent Number Sense first year mathematics module in Bachelor of Education degrees, used across six universities in South Africa. It then theorises the choice to commence the B.Ed mathematics programmes with two pathways into number knowledge: (1) a counting pathway, making use of discrete objects or events which can be quantified by counting in ones; and (2) a measurement pathway, making use of continuous extents which can be quantified by introducing a unit of measurement. Each has a distinct metaphor, strategy for the reification of the 10 and supporting representation. This offers the lecturers using the course in their own design trials, and initial teacher educators beyond the Maths4Primary Teachers collective, a conceptual framework for this design choice, which can now be critiqued and further improved.

Modeling and Analysis of Temperature-Dependent Capacity Degradation in Large Format Lithium-Ion Batteries

The large-format lithium-ion batteries, widely used for electric vehicle applications, are generally characterized by spatial non-uniformities in temperature. The presence of thermal gradients and temperature-dependence of cell parameters are responsible for non-uniform degradation within the battery that leads to poor performance of the battery packs and also poses safety risks. In this work, we aim to develop a detailed physics-based simulation framework to model non-uniform, temperature-dependent capacity degradation within these large format batteries based on the classical pseudo two-dimensional (p2D) battery model. The electrochemical model will be coupled with degradation mechanisms to capture solid-electrolyte interface layer growth, reversible lithium plating, structural disintegration, and volume change within the electrodes on the cell level signatures and usable capacity over charge/discharge cycles. The effects of temperature inhomogeneities will be accounted in the multi-cell simulations at different operating temperatures for individual cells with dynamic currents and temperature and concentration dependent battery parameters as the model inputs.Overall, the primary focus of this study is to capture the effect of spatial temperature variation on battery capacity over cycles and help identify an improved design for the battery module. The model is implemented in an efficient equation-based form for the p2D model and degradation mechanisms with dynamic cell inputs using the mathematical modules in the finite element based solver, COMSOL Multiphysics. This approach enables an easier model development and analysis of the detailed physics and allows an easier implementation of any additional side reaction. The relative contributions of various fade modes have also been compared to understand their competitive interplay over cell cycles. The model predictions are validated with the available experimental data and in-house codes for each case. We believe that this simple yet detailed model can be further developed to be computationally feasible for adoption and implementation in a battery thermal management system.

Development of Fraction Material Mathematics Module with Realistic Mathematics Education Learning Approach

This research aims to determine the steps of module development and the level of mathematics module fourth grade with realistic mathematics education learning approach quality. This research includes Research and Development (RnD) with the ADDIE development model. The object and subject in this research is the understanding of grade IV faction material in SD Negeri 2 Riau Silip. The instruments used are speech guidelines, expert assessments, and teacher responses, and student responses. The data analysis technique used qualitative and quantitative data. Qualitative data was analyzed from the results of testing the quality and validity of the module. The results of the research contain development steps, namely analysis stages, resistance to pressure, and resistance to development. The results of the assessments of media experts, material experts, learning experts and language experts obtained the following values of 85.3, 90.7, 80, and 80. While the results of the responses of fourth grade teachers and students were 100 and 92.8, the average assessment and expert validation test and the response of class IV teachers and students was 88.13 with the "Very Good" category. Based on the results of the assessments from the experts, the fourth grade teacher's response, and the student's response it was stated that the fourth grade mathematics modui fraction material with a realistic mathematical education learning approach was included in the "Very Good" category so that it was suitable for use in the classroom learning process.

INOVASI SOFTWARE MATEMATIKA LIMIT DAN INTEGRAL BAGI CALON GURU

This community service activity aims to improve the skills of prospective mathematics teachers on limit and integral mathematical software. The activities include training in mathematical software innovation on limit and integral. The training materials include the definition of mathematical software, installation, use of mathematical software in the form of maple math, material delivery, interactive dialogue, presentations, and evaluation. This is an indicator of the successful implementation of community service activities. The results of community service activities are mathematical software innovation modules on limit and integral. The module describes the use of mathematical software on limits and integrals for mathematical calculations and graphs. This community service activity received positive responses, and the results of prospective mathematics teachers’ presentations in applying mathematical software on limits and integrals were very good.

Math-data integrated prediction model for ship maneuvering motion

Highly accurate motion prediction is critical to facilitate safe navigation and autonomous control of a ship. In this paper, a math-data integrated prediction (MDIP) model of ship maneuvering motion is newly developed by combining with mathematical and data-driven modules. The math part is identified by employing variable-order hydrodynamic derivatives which are derived from Taylor expansion. Using extended Kalman filter, an optimal-order mathematical prediction model is obtained. The data-driven part dwells on prediction residuals which are approximated by a least square-support vector machine. Furthermore, integration mechanisms are devised to cohere mathematical and data-driven models as a whole, by deploying summation and neural network approximation, respectively. By comparisons, it is verified that not only order selection but also math-data integration can enhance ship motion prediction accuracy, for which various maneuvering tests are analyzed. The results demonstrate that the proposed MDIP model using math-data integration offers much stronger generalization, thereby paving a new path for ship maneuvering motion prediction.

Improving high school students' performance in basic calculus using the Enhancing Mastery & Expertise in Mathematics supplementary material


 Preparing K-12 students to gear up for higher mathematics and sciences, and to be more mathematically college-ready, teachers were given the essential role in bridging the learning gaps. One way to address this was the utilization of modules. The researcher developed Enhancing Mastery & Expertise in Mathematics (EM&EM) module in Basic Calculus. The objective of this quasi-experimental research was to evaluate the effectiveness of the EM&EM module in improving students' performance about the theorems of differentiation. The experimental and comparison groups comprised forty-six (46) Grade 11 students who used the EM&EM module and the DepEd module, respectively. The instruments used in the study were the pretest, formative tests, and posttest found in the EM&EM module. Mean and standard deviation were used to describe student performance in these assessments. To see if a significant difference existed, the formative test and posttest scores between the two groups were analyzed using an independent t-test, while the pretest and posttest scores within each group were analyzed using a paired sample t-test. The findings showed that the experimental and comparison groups' formative tests and posttest scores did not differ significantly, although the former generally performed better when their mean scores were compared. However, there was a significant difference between the two groups' pretest and posttest scores, and that had a large positive effect on their improvement. Therefore, just like the DepEd module, the EM&EM module was effective in facilitating the learning process. Overall, the EM&EM module significantly and substantially enhanced students' learning of Basic Calculus.

Enhancing teacher creativity in digitalizing math-literacy modules through technological pedagogical content knowledge training

Mathematical literacy is one of the abilities that must be mastered by teachers. To increase teachers' creative competence, digital modules oriented towards mathematical literacy are supported by Technological Pedagogical and Content Knowledge (TPACK) training. This study aims to evaluate the validity and practicality of digital modules oriented towards mathematical literacy. This study uses the design research method with the Plomp model, which consists of three stages: preliminary research, the prototype stage, and the evaluation stage. The instruments used were validation sheets for material experts and media experts, as well as student and teacher response questionnaires to see the effectiveness and practicality of the digital modules that had been developed. The results of the study show that digital modules oriented towards mathematical literacy using TPACK training have been successfully carried out. Based on the results of the analysis, effectiveness, and practicality, the feasibility of the module is 87.65%, which is in the very good category. Therefore, it can be concluded that the developed mathematical literacy-oriented digital modules have valid, practical, and effective qualities to enhance teacher creativity.

Social Arithmetics Module Based on Islamic Values and Realistic Mathematics Education to Improve Students’ Problem-Solving Skills

Mathematics learning must be made more exciting and meaningful to overcome the perception that mathematics is a tricky subject. Students must be facilitated to build their knowledge through mathematics learning linked to realistic problems and integrated with Islamic values so that they can solve relevant daily problems. This research aims to develop a Social Arithmetic module based on Islamic values ​​and Realistic Mathematics Education (RME) to help junior high school students improve their problem-solving skills. This research uses R&D with the ADDIE development model. The development of the mathematics module consists of three stages, namely the preliminary, development, and evaluation stages. The resulting module prototype has been assessed as valid by material and media experts. Meanwhile, based on student and teacher responses to the questionnaire, the module was proven suitable for use in mathematics learning. In addition, the results of the paired t-test stated that the module was effective in improving students' problem-solving skills. Therefore, this research concluded that the Social Arithmetics module based on Islamic values ​​and RME that were developed has met the valid and practical criteria and has proven effective in improving the problem-solving abilities of seventh-grade junior high school students.

Pengembangan Modul Program Linear Berbasis Konstruktivisme untuk Siswa Prakerin

Mathematics modules should have self-instructional, self-contained, stand-alone, adaptive, and user-friendly characteristics and be able to describe students' knowledge construction processes in studying teaching materials through modules. This development research adopts the ADDIE theory. The resulting product is a constructivism-based mathematics module for internship students. The validation results of material and design experts stated that the resulting product was excellent. Data were also obtained from small and large group instrument questionnaires and the results of assignments and linear program formative tests. The results of the XI Marketing 1 class module assignment with 35 students for the KKM 70 mathematics subject are completeness of 74.3%; unfinished 25.9%. Formative test results for class XI Marketing 1 Linear Program with 35 KKM 70 students in the learning process using the module obtained an average value of 72.43; complete 77.1%; incomplete 22.9%. Formative test results for class XI Marketing 2 with a total of 35 students in the KKM 70 learning process using textbooks obtained an average score of 60 with 54.3% complete and 44.7% incomplete. Learning using the Constructivism-Based Linear Programming module is more effective and can form student independence.

Development of Problem-Based Learning Mathematical Module with STEM Approach to Improve Problem-Solving Ability and Self Efficacy

The aim of this research was to produce problem-based learning mathematical modules with STEM approach with a valid, practical and effective in improving problem-solving ability and self efficacy. This study used a Research and Development (RnD) with a 4-D development model. The 4-D development process stage consists of Define, Design, Develop, and Disseminate. This research did not reach the disseminate stage due to time constraints. Based on the results of the research, it was found that the problem-based learning mathematical modules with STEM approach that was developed met the criteria, namely, (1) validity with a percentage of 88% with very valid criteria, (2) practicality with a percentage of 91.5% with very strong criteria. practical, (3) effective in increasing problem-solving ability with an n-gain result of 0.64 with medium criteria, (4) effective in increasing self-efficacy with an n-gain result of 0.575 with medium criteria.

Engaging non-mathematics students in mathematics learning through collaborative teaching

Abstract Mathematics is a common component of many science and social science degrees, but frequently not considered a prerequisite for their study. This can lead to some students studying mathematics components at undergraduate level with little or no previous mathematical learning and varying levels of motivation, or desire, to study mathematics. This situation has consequences for student experience and teaching practice, including the potential for lower levels of student engagement, higher levels of student anxiety and lack of student motivation for studying a subject that is not what they chose as their degree subject. This paper details an intervention designed to address issues experienced in the teaching of mathematics to undergraduate students, with varying motivation for the study of mathematics and high levels of mathematics anxiety, in their first year of study in a department of Earth Sciences at a UK university. The intervention provided a bespoke mathematics module, designed and taught collaboratively by a teaching specialist in mathematics and a subject specialist in Earth Sciences. The mathematics specialist was able to provide extensive experience in teaching students from widening participation backgrounds and those with mathematics anxiety, making the content more accessible to the students, particularly those with mathematics anxiety. The Earth Sciences specialist was able to contextualize the mathematics content, showing students how the content was applicable to the rest of the degree and helping locate the mathematical content within the broader scope of the discipline. Previous approaches to this module were taught either solely by an Earth Sciences specialist or solely by a mathematics specialist. Compared with those approaches the collaborative teaching intervention improved student attainment by 10% in the average module mark and moved the module from having the lowest student satisfaction scores in the department to the highest. This innovation also benefited both teachers with respect to professional development, which is discussed in the paper.

Development of grubi mathematics module to improve the ability to calculate the addition and subtraction of small numbers in grade 2 elementary students

The study aims to know the feasibility, effectiveness, and response of the grubi math module to increase the ability to calculate numbers and decrease numbers in second-grade students. Research and development (R&D) using the ADDIE model. The research subject consists of validator experts in materials and media, 24 students in the 2nd grade. Data collection instruments include expert validation sheets, pretest-posttest are essay questions, and student responses. Research obtained (1) the worthiness assessment of the module from materials expert 92.5% and media expert 96.7% with both "very good" criteria, (2) the effectiveness of modules with one group pretest-posttest design to achieve a lower average pretest value (91.38) means that learning students experience an increase, (3) the module gains responses from students with percentage of 89.30% with the "very good" criteria. Through these data it is shown that the grubi math module is worthy of being used as a teaching material in the elementary school on the basis of valiance and from experts, the effectiveness and response of students in the development of the grubi math module to increase the ability to calculate numbers and deformity. As for second-grade teachers who perform math studies on similar materials to use the grubi math module.

Improving multimodal passenger transportation technology under the wartime conditions in Ukraine

Abstract. Problem. Ukraine has a rather complex transport network, so the mismatch between the work of carriers when transferring from one mode of transport to another can create a large number of inconveniences for passengers. Issuance of various travel documents, the complexity of processing luggage and its movement between vehicles, a more thorough check of documents and luggage by employees of law enforcement agencies at border crossings and transfer points lead to an increase in travel time. On the other hand, ensuring the demand for some main directions of transportation can only be through the use of several modes of transport, so there is a need to improve the existing logistics technology for multimodal passenger transportation.
 Goal. The goal of this publication is to improve the technology of multimodal passenger transportation under martial law Methodology. Analytical research methods were used to form the relationship between the train delay at the border station and the number of passengers in it. Mathematical modulation methods were used in the formation of a new agreed schedule for the arrival of international passenger trains at the Kyiv-Passenger transport hub. Results. The research has shown that even under the current wartime conditions, it is possible to improve the operation of various types of passenger transport and the consistency of their traffic schedules to better meet the needs and quality of passenger transportation. The authors of the article analyzed the state and causes of delays in passenger trains at the Mostyska-2 border crossing, through which the largest railway passenger flows between Ukraine and the EU countries currently follow. Based on the analysis, the dependence of the train delay time at the border station on the number of passengers in the train was revealed, and in order to reduce the duration of these delays, it was proposed to improve the existing technology for calculating the travel time of a passenger train by introducing and using value F, corresponding to the train delay time at the border station per passenger. Originality. It is suggested to improve the model for organizing the interaction of different types of transport in the transport interchange Kyiv-passenger hub, by introducing a new value φ based on the dependence of the train delay time at the border station on the number of passengers transported in it, taking into account the specifics of the introduction of martial law in Ukraine. Practical value. The introduction and integration of the proposed technology into the existing mathematical models for the formation of a rationally coordinated schedule of multimodal passenger transportation will significantly reduce the waiting time for passengers at transfer points, rationalize the capacity and population of the rolling stock and increase the financial profit for carriers, it can also be used for the development of the system, information technologies and the use of a "single ticket".

An Integrated RME and PIL Mathematics Module for Technical Vocational High School Learning: A Need Analysis

Text-based learning resources play an essential role in supporting students’ mathematics learning. However, there are still limited studies about developing mathematics modules as one of text-based learning resources for Technical Vocational High School (TVHS) students. Therefore, this study investigates the need to develop an integrated Realistic Mathematics Education (RME) and Project-based Inquiry Learning (PIL) mathematics module for TVHS learning. This study is a descriptive survey involving 66 tenth grade TVHS students and 21 TVHS mathematics teachers in a sub-urban area of Central Java, Indonesia. Moreover, it also involves ten mathematics lecturers who teach “teaching mathematics for secondary school learning” courses from public and private universities in Indonesia. The data collection was conducted using printed questionnaires (for students) and online questionnaires (for teachers and lecturers). The data was summarized and analyzed descriptively. Based on the data analysis, it can be concluded that there are still limited realistic problems in Indonesian mathematics textbooks for TVHS students. Therefore, developing an integrated RME and PIL mathematics module is necessary. The characteristics of the integrated RME and PIL mathematics module are: (1) The module’s content should be presented in Bahasa Indonesia, providing realistic contexts by the area of expertise of the TVHS students and contexts across fields; (2) The learning activities should be carried out in groups, inside classrooms, involves creating projects not only by the area of expertise of the TVHS students, and the project results are displayed directly in an exhibition gallery; (3) The learning media can use both manual and Information and Communication Technology (ICT)-based tools; (4) The assessment can be conducted in both written and authentic assessments.

PENGEMBANGAN MODUL MATEMATIKA BERBASIS DISCOVERY LEARNING MATERI STATISTIKA UNTUK PENINGKATAN LITERASI NUMERASI SISWA SMP NEGERI 1 SEKAMPUNG

The research conducted is in the form of development research which aims to produce a mathematical module based on discovery learning statistics material to improve students numeracy literacy that is valid and practical. This study aims to determine the quality of the product developed through validity tests by validators and practicality by students. The research method used in development research is the ADDIE model with steps; (Analyze, Design, Develop, Implement, and Evaluate). The product trial was carried out at SMP Negeri 1 Sekampung with a small group trial of 10 students to determine the practicality of the developed module. Based on the results of the study, the quality of the resulting product based on the module's validity met the valid criteria with a percentage of 77.43% obtained from the material and design aspects. The results of practicality were obtained from the results of the student response questionnaire with a percentage of 90.77% which was included in the very practical category. The conclusion of this study is that the mathematical module based on discovery learning statistics material for increasing student numeracy literacy that was developed is valid and practical to use in learning. Before using the module, it is better to explain the instructions for using the module first.

Factors that influence student engagement with technology-enhanced resources for formative assessments in first-year undergraduate mathematics

Even prior to COVID-19, there had been an increase in the use of technology in undergraduate mathematics education to support the development of mathematical understanding and skill, and to enhance the student learning environment. Technology-enhanced resources can be used to provide formative assessment which can help students identify gaps in their knowledge and point towards appropriate action. In this paper, we report on the evaluations of a number of technology-enhanced resources that used formative assessment techniques and were provided for students attending non-specialist first-year undergraduate mathematics modules in Ireland. Analysis of the evaluations and consultation with literature identified 12 decisive factors that encourage students’ successful engagement with the resources, covering aspects such as the educational context, affordances and types of technology, technological communication and formative assessment. These factors constitute important knowledge for practitioners as they can use them in the planning, design, and development of technology-enhanced resources for use in their modules. The measures observed during the evaluations indicated both positive and negative engagement providing a link between observations and resultant student engagement, which was found lacking in previous studies on student engagement.

Development of Problem Based Mathematics Module (Calculating Professional Zakat) to Improve Student's Mathematic Problem Solving

This study aims to determine: (1) the effectiveness of the problem-based math module of zakat to improve students’ mathematical problem solving skills in MA. The private Darul Mursyidi Sialogo Islamic Boarding School; (2) to determine the improvement of students’ mathematical problem solving abilities by using the problem-based math module of zakat. This research is a development research using 4-D development developed by Thiagarajan. The stages are define (define), design (design), develop (development) and disseminate (spread). Research on the development of the problembased math module of zakat at the disseminate stage was carried out in a limited manner in schools which were the research subjects. The subjects in this study were students of class XI MA. Private Darul Mursyidi Sialogo Islamic Boarding School. From the results of the development test: (1) the problem-based zakat math module meets the validity criteria with a valid predicate, (2) the practical problem-based zakat math module based on the revision of the expert team and the results of interviews, and (3) the problem-based zakat math module is effectively used based on the results of the observation of the ideal time percentage achievement, the results of the test of mathematical problem solving abilities meet classical completeness, namely 80% of the test subjects, and (4) an increase in students’ mathematical problem solving abilities using modules from test I to trial II and fulfill classical completeness.
 Keywords: Zakat; mathematics module; problem solving

Pengembangan Modul Matematika sebagai Penunjang Pembelajaran secara Online untuk Siswa SMK yang Melaksanakan Prakerin (Praktek Kerja Industri)

This study aims to produce a Mathematics Module to Support Online Learning for Vocational High School Students Carrying Out Internships (Industrial Work Practice). This research is development research, with the research design used is Research and Development (R&D) with the ADDIE model (Analyze, Design, Development, Implementation, Evaluation) which consists of five stages, namely the analysis stage, design stage, development stage, implementation stage and evaluation stage. The subjects of this study were 20-30 students of class XI Automotive Light Vehicle Engineering at Setih Setio 1 Muara Bungo Vocational School. The procedure for this research was preliminary research, designing modules, preparing instruments, expert tests, individual tests, and student tests. The feasibility of this product is seen from the results of expert validation by achieving the appropriate criteria for the module. Research results based on the assessment of material experts in the very feasible category, and the media expert's assessment in the very feasible category, the assessment of students on small-scale tests and large-scale tests gave an average percentage of positive responses. Based on the assessment of material experts, media experts, design experts, student responses, it can be concluded that the mathematics module with statistics material is appropriate for use as a support for SMK students who carry out Internship (Industrial Work Practice).

DEVELOPMENT OF THE OPPORTUNITY MODULE TO IMPROVE HIGH SCHOOL LEVEL UNDERSTANDING ABILITY OF MATHEMATICAL CONCEPTS

This research aims to improve the module which refer to the developing of understanding the mathematics concept. The teaching material of this lesson sets is opportunity material. The procedure of module development that used in this research is 4D development module (Define, Design, Develop, Disseminste). The instrument that used in this research to measure the validity of module, responsive students’ of question are to measure the practicality of module, and the sheet of pretest-posttest validity to measure the effectivity of mathematics module. Based on the validity test, the result of this research should that opportunity module was valid with the percentage of validity level was 96,83%. The result of practicality for the tes in limited group was 3.47 with the percentage 83,4% was categorized very practical. The result of the effectivevess test in limited group with the acquisition of values was 80% in effective categori, and the result of of test in controlled class with the axquisition values was 85,3% in effective category. The students’ ability in understanding the mathematics concept increased to 0,79 in bigh category. This result showed that the develompment of the module was valid, practical and effective and able to improve the stundents’ ability in understanding the mathematics concept. This module suggested to be used to improve the students’ ablitiy in understanding mathematics concept in opportunity material