The Effectiveness of Hybrid Learning in Improving of Teacher-Student Relationship in Terms of Learning Motivation

The Advanced Mathematical Thinking (AMT) ability is one of the prioritized mathematical abilities needed to be developed in learning mathematics during tertiary education. The present study sought to test the effectiveness of hybrid learning in improving students' advanced mathematical thinking. The research used a quasi-experimental design with a non-equivalent control group design. The subject of this study was students of a mathematics education study program at a university in Bandung who attended lecture for the multi-variable in a calculus course. The sampling technique used was purposive sampling. Of the many variable calculus classes consisting of 2 classes, one class was chosen as the experiment group and the other class as the control group. The sample consists of 40 people for each group. Data analysis used the MANOVA test with normality and homogeneity tests as a prerequisite test. The results showed a difference in AMT's significance between the hybrid learning and conventional groups, where hybrid learning had a higher AMT. Other than that, there is a difference in the significance of AMT between the high motivation group and the low motivation group, where high motivation has a higher AMT, and there is an interaction of learning models and motivational factors to increase AMT. Doi: 10.28991/esj-2021-01288 Full Text: PDF

Mathematical Modelling from the Instrumentation of Improper Integrals

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

Missouri Mathematics Project (MMP) Model: Encouraging the Enhancement of Reasoning Ability and the Advanced Mathematical Thinking (AMT)

This article was written aiming to look at the application of the model Missouri Mathematics Project (MMP) in enhancing reasoning ability and the Advanced Mathematical Thinking (AMT) of students. This research is an experimental study with a quantitative approach and Randomized Pretest-Posttest Control Group Design research design. The sample in this study were students of class XI.1 who became an experimental class by giving treatment in the form of learning model Missouri Mathematics Project (MMP) and class XI.2 students as a control class by giving treatment using conventional learning. The instruments in this study were tests in the form of pretest and posttest which were used to see the improvement of reasoning ability and the Advanced Mathematical Thinking (AMT) of students. Based on the results of the study it can be concluded that the model Missouri Mathematics Project (MMP) can improve students' reasoning abilities and the Advanced Mathematical Thinking (AMT). For reasoning ability, the average N-gain of the experimental class is 0.76 while the N-gain for the control class is 0.13, while for Advanced Mathematical Thinking (AMT) the average N-gain of the experimental class is 0.66 while the N-gain for the control class is 0.49.

Advanced Mathematic Thinking Ability Based on The Level of Student's Self-Trust in Learning Mathematic Discrete

<p class="BodyAbstract">Mathematical thinking and self-confidence are indispensable aspects of learning mathematics and are influential in solving mathematical problems. In higher education mathematics learning, advanced mathematical thinking skills are required (Advance Mathematical Thinking. Advanced mathematical thinking processes include: 1) mathematical representation, 2) mathematical abstraction, 3) connecting mathematical representation and abstraction, 4) creative thinking, and 5) mathematical proof. Discrete mathematics is one of the courses in mathematics education FKIP UNS. The problems in Discrete Mathematics courses are usually presented in the form of contextual problems. Students often experience difficulties in making mathematical expressions and mathematical abstractions from these contextual problems. In addition, students also experience difficulties in bookkeeping. Most students often prove by using examples of some real problems. Even though proof in mathematics can be obtained by deductive thinking processes or inductive thinking processes, the truth is that mathematics cannot only come from the general assumption of inductive thinking. Based on this, a qualitative descriptive study was carried out which aims to determine the advanced mathematical thinking skills based on the level of student self-confidence. Research with the research subjects of FKIP UNS Mathematics Education Students in Discrete Mathematics learning for the 2019/2020 school year gave general results that the student's ability in advanced mathematical thinking was strongly influenced by the level of student confidence in learning. The higher the student's self-confidence level, the better the student's advanced mathematical thinking ability, so that high self-confidence has a great chance of being successful in solving math problems.</p>

Uma proposta de articulação entre teoria e prática no estudo da integral definida

ResumoEste trabalho é um recorte de uma tese de doutorado, em desenvolvimento, cujo objetivo é de desenvolver uma alternativa pedagógica e tecnologógica, que contemple aspectos do Pensamento Matemático Avançado, bem como, aplicações, aprimoramento do conhecimento e do significado da Integral Definida, em contextos intramatemáticos e extramatemáticos, em cursos de Matemática. Neste recorte, apresentamos o percurso de nossa investigação, abordando, inicialmente, os aspectos relacionados às dificuldades na aprendizagem do Cálculo Integral, em particular, da Integral Definida. Ainda, destacamos que a exploração de aplicações desse conteúdo, em distintas áreas, é considerada como uma possibilidade para o seu ensino e para sua aprendizagem. Aspectos teóricos, metodológicos e tecnológicos são apresentados, como orientadores do planejamento da estratégia pedagógica. É destacado um exemplo de aplicação teórico-prática, na perspectiva de melhorias na qualidade do ensino e da aprendizagem desse tópico. Palavras-chave: Integral Definida; Conexões Intramatemáticas; Conexões Extramatemáticas; Educação Matemática no Ensino Superior.AbstractThis work is an doctoral thesis excerpt, under development, whose objective is to construct a pedagogical and technological alternative that contemplates Advanced Mathematical Thinking aspects and applications, improvement of knowledge and the meaning of the Definite Integral, in intramathematical and extramathematical contexts, inside the mathematical programs. In this excerpt, it is presented the research way, initially approaching the aspects related to the learning disabilities in Integral Calculus, particularly Definite Integral. Still, it is emphasized that the exploitation of applications of this content, in different areas, is considered as a possibility for its teaching and learning. Theoretical, methodological and technological aspects are presented as guide of pedagogical strategy planning. An example of theoretical-practical application is highlighted, with a view to improving the quality of teaching and learning on this topic.Keywords: Definite Integral; Intramathematics Connections; Extramathematcal Connections; Mathematics Learning in Higher Education.

Eksplorasi berpikir kreatif melalui discovery learning Bruner

Creative thinking is an essential component of advanced mathematical thinking. The components of creative thinking are lateral thinking (creating one’s own and non-routine ways), divergent thinking (using a variety of ways), and convergent-integrative thinking (using patterns in other situations). One way to develop creative thinking is learning with Bruner’s discovery learning model, namely learning with an enactive, iconic, and symbolic stage. Learning activities with Bruner’s discovery learning on the material of the two-variable linear equation system (SPLDV) to explore creative thinking are: 1) preliminary activities: goals and perceptions, 2) core activities include: the enactive stage, which is giving contextual problems to be solved themselves of students to explore lateral thinking, the iconic stage, which is writing solutions and presentations to explore divergent thinking, and the symbolic stage, which is the elaboration of the results of the previous stages to be brought to the mathematical process in the form of modeling and elimination and substitution methods to explore lateral thinking, divergent thinking, and convergent thinking integrative, and 3) closing activities: feedback and conclusions.

Advanced Mathematical Thinking dalam Pembelajaran Matematika Tingkat Lanjut

Students' Advanced Mathematical Thinking in advanced mathematics courses were still relatively low. This happens because the lecturer did not provide opportunities for students to be able to construct their own mathematical concepts and students were still weak in mastering concepts in prerequisite courses. The lecturer is expected to provide opportunities for students to be active in learning and be able to construct their own advanced mathematical concepts through the implementation of innovative learning based on constructivism to improve students' Advanced Mathematical Thinking in advanced mathematics courses. The purpose of this literature study is to find out more about advanced mathematical thinking and its components (representation, abstraction, creative thinking, and proof) in advanced mathematics learning and how to develop it.