Theoretical and Methodological Proposal on the Development of Critical Thinking through Mathematical Modeling in the Training of Engineers

Gutiérrez, Jaqueline Acebo; Gallegos, Ruth Rodríguez

doi:10.1145/3362789.3362828

Cited by 7 publications

(12 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Therefore, teachers need to introduce modeling in math learning, especially in differential equation courses. Previous research has shown that mathematical modeling can help develop competencies in different math classes [11].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Students' Mathematical Critical Thinking Ability in Solving The Application of First-Order Differential Equations

Nurrahmah¹,

Waluya²,

Asih³

et al. 2021

Proceedings of the 1st International Seminar on Teacher Training and Education, ISTED 2021, 17-18 July 2021, Purwokerto, Indone

View full text Add to dashboard Cite

Many mathematical problems of natural symptoms whose mathematical models can be formulated in the form of differential equations. Because the problem is complex, students need to develop their thinking skills, one of which is critical thinking. This study aims to describe students' mathematical critical thinking ability in solving the problem of the application of first-order differential equations. The method used in this study is descriptive qualitative. The subject of this study was a 6th-semester student of Indraprasta PGRI Indraprastha, with as many as three people. The selection of subjects is donetopicsosive sampling, based on the results of pretests. The instruments used are critical thinking skills tests (pretest and posttest questions), interview guidelines, and researchers. Data analysis techniques are carried out through data reduction, presentation of data, and verification. The results showed that there were student's critical thinking ability in solving problems of applying first-order differential equations, especially in subjects with high (L6) and moderate pretest (M9) results that met all indicators. However, issues with low pretest results (L2), from the three questions given, could only work on one question and did not fulfill the critical thinking indicators in the other two questions.

show abstract

Section: Discussionmentioning

confidence: 99%

“…This needs to be done to reassure students that mathematical modeling often leads to differential equations, and differential equations are part of problem investigations in various other areas. Because real-life problems are complex, students must develop their thinking skills [11]; one of them is thinking critically.…”

Section: Introductionmentioning

confidence: 99%

Students' Mathematical Critical Thinking Ability in Solving The Application of First-Order Differential Equations

Nurrahmah¹,

Waluya²,

Asih³

et al. 2021

Proceedings of the 1st International Seminar on Teacher Training and Education, ISTED 2021, 17-18 July 2021, Purwokerto, Indone

View full text Add to dashboard Cite

show abstract

“…The importance of mathematical training in engineering education and the relevance of its strengthening in some cases are shown in [16,17,18,19,20]. [21] carried out a theoretical and methodological study on the critical thinking THE METHOD OF A CONTINUOUS CONTROL-ASSESSMENT ACTIVITY "Consistency" ("testing through the whole course")…”

Section: Content Of the Decision Support System On The Example Of Matmentioning

confidence: 99%

A System for Supporting the Adoption of Pedagogical Decisions based on an Assessment of Ownership of Strategies

et al. 2020

View full text Add to dashboard Cite

Large-scale changes associated with the digitalization of all industries require from the student to have both knowledge proficiency in the subject field and the formation of critical thinking, the ability to apply and update their knowledge, and the ability to apply knowledge to solve professional problems. Of particular importance in the learning process is the formation of a student’s system of goals, mastery of basic activity strategies. This requires flexible control mechanisms and monitoring to obtain a large amount of information about the current level of potential development of the student. The analysis shows the relevance of developing systems for supporting the adoption of pedagogical decisions in the context of mass education, based on a multi-aspect assessment of the results. The paper describes the author’s theory of adequacy based on the fact that the quality indicator of a model can be obtained by comparing the estimated model with a model accepted as a reference model. The mathematical basis is a clear definition of strategies, their analysis and improvement based on the algebraic approach, the application of which is reflected in the formation of three components: a system of basic elements; systems of standard transformations and standard combinations of elements; an approximation mechanism designed to represent the strategy as the result of applying standard transformations and typical combinations of basic elements. It is substantiated that the results for automated (automatic) decision-making can be obtained on the basis of continuous control and evaluation activities organized according to the developed methodology. The content of the decision-making system is described on the example of a mathematics course.

show abstract

“…Instructors have introduced engineering tasks in calculus classes as a way to increase students' problem solving skills [17] and improve critical thinking [2] . When students engage in mathematical modeling in the engineering curriculum, it is often in the form of simulation [5] .…”

Section: Literature Reviewmentioning

confidence: 99%

“…Both the Common Core State Standards for Mathematics (CCSSM) and the Next Generation Science Standards (NGSS) emphasize the importance of mathematical modeling [1] . Mathematical modeling in the classroom helps to develop the critical thinking and math skills required for engineering [2] . It allows students to "revise their preconceptions and… understand the underlying principle[s] of mathematics" [8] and integrate topics similar to professionals in the field [1] .…”

Section: Introductionmentioning

confidence: 99%

Student Perception of Mathematical Modeling Before and After Completing a Two Joint Robot Computer Simulation Task

Johnston

Salzman

2020 ASEE Virtual Annual Conference Content Access Proceedings

View full text Add to dashboard Cite

Engineers frequently utilize computer simulation as part of their design processes to model and understand the behavior of complex systems. Simulation is also an important tool for developing students' understanding of modeling and strengthening their intuition for problem solving in complex domains. This project uses a two-joint robot arm problem and accompanying computer simulation to demonstrate to AP BC Calculus students how and why we would use calculus concepts simultaneously in Cartesian and polar coordinate systems. We developed the simulation in a way that allows students to experience mathematical modeling in an applications-based engineering context. A small cohort of students in AP BC Calculus completed an open-response survey of their perceptions on mathematical modeling before and after completing our simulation. Analyzing these data using direct content analysis showed that students seemed to increase their understanding of mathematical modeling as an iterative process, although some students narrowed their description to focus on computer simulation. This study supports the role of simulation in developing students' understanding of mathematical modeling and developing specific content knowledge, and how engineering can provide a valuable context for the application of mathematical modeling.

show abstract

Theoretical and Methodological Proposal on the Development of Critical Thinking through Mathematical Modeling in the Training of Engineers

Cited by 7 publications

References 22 publications

Students' Mathematical Critical Thinking Ability in Solving The Application of First-Order Differential Equations

Students' Mathematical Critical Thinking Ability in Solving The Application of First-Order Differential Equations

A System for Supporting the Adoption of Pedagogical Decisions based on an Assessment of Ownership of Strategies

Student Perception of Mathematical Modeling Before and After Completing a Two Joint Robot Computer Simulation Task

Contact Info

Product

Resources

About