How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course?

Czocher, Jennifer A.

doi:10.1016/j.jmathb.2016.10.006

Cited by 54 publications

(34 citation statements)

References 40 publications

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“…Results reported here suggest that students who take Modeling and Analysis, for a semester or two anyway, have the ability to solve differential equations in subsequent courses to a higher degree than those who took Differential Equations. These results are consistent with those reported by Czocher [1], who compared a modeling-based approach to teaching differential equations to an approach focused on their analytical solutions.…”

Section: Discussionsupporting

confidence: 91%

“…The results presented here are more consistent with the study of Czocher [1], who found that students taking a differential equations course taught in a model-driven format outperformed (on common final exam questions) students who took a more traditionally taught course focused on analytical solutions. One way of reconciling all three studies is to conclude that students taking a modeling-based course in differential equations are better able to solve differential equations for a short time but the advantage is not maintained indefinitely.…”

Section: Comparison Of Modeling and Analysis To Differential Equationssupporting

confidence: 89%

“…This raises the question of whether the course should be a mathematics course, an engineering course, or a hybrid. It has been argued [1], with supporting results, that the teaching of differential equations through the modeling of physical and chemical phenomena is effective because it allows students to overcome the cognitive obstacles more easily. On the other hand, it has been reported [2] that there is no difference between students who took a math-based differential equations course and those who took an engineering-based one, in regard to their preparation for differential equations content in a later course.…”

Section: Introductionmentioning

confidence: 94%

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A Course in Differential Equations, Modeling, and Simulation for Engineering Students

Campbell¹,

Smith²,

Calderón³

2019 ASEE Annual Conference &Amp; Exposition Proceedings

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has been on the faculty of the Department of Chemical & Biomedical Engineering at the University of South Florida since 1986. He currently serves as the department undergraduate advisor. Scott was a co-PI on an NSF STEP grant for the reform of the Engineering Calculus sequence at USF. This grant required him to build relationships with engineering faculty of other departments and also faculty from the College of Arts and Sciences. Over the course of this grant, he advised over 500 individual calculus students on their course projects. He was given an Outstanding Advising Award by USF and has been the recipient of numerous teaching awards at the department, college, university (Jerome Krivanek Distinguished Teaching Award) and state (TIP award) levels. Scott is also a co-PI for a Helios-funded Middle School Residency Program for Science and Math (for which he teaches the capstone course) and is on the leadership committee for an NSF IUSE grant to transform STEM Education at USF. His research is in the areas of solution thermodynamics and environmental monitoring and modeling.

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Section: Discussionsupporting

confidence: 91%

Section: Comparison Of Modeling and Analysis To Differential Equationssupporting

confidence: 89%

Section: Introductionmentioning

confidence: 94%

See 1 more Smart Citation

A Course in Differential Equations, Modeling, and Simulation for Engineering Students

Campbell¹,

Smith²,

Calderón³

2019 ASEE Annual Conference &Amp; Exposition Proceedings

View full text Add to dashboard Cite

show abstract

“…However, the application of a mathematical modeling process in mathematical classrooms is a new challenge for primary school [ 6 ], secondary school [ 7 – 9 ] and even higher education students [ 3 , 10 , 11 ], particularly mathematics education program students [ 12 – 14 ]. Previous studies have emphasised that students have difficulty interpreting real contexts into mathematical contexts [ 9 , 15 , 16 ]. For example, in a study conducted by Blomhøj and Kjeldsen [ 10 ], students encountered problems on mathematising the expression ‘proportional to the square of population size’ before finding formula.…”

Section: Introductionmentioning

confidence: 99%

Roles of metacognition and achievement goals in mathematical modeling competency: A structural equation modeling analysis

2018

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This study investigates the relationship between metacognition and achievement goals which may influence mathematical modeling competency in students of mathematics education programs. The current study employs 538 students of mathematics education program; 483 (89.8%) of whom are male and 55 (10.2%) are aged from 18 years old to 22 years old. The study follows a correlational research design to investigate and measure the degree of relationship amongst mathematical modeling competencies, achievement goals and metacognition. Results indicate that achievement goals and metacognition positively influence mathematical modeling competency. Moreover, four metacognition dimensions including awareness, planning, cognitive strategy and self-checking are positive partial mediators because they increase the association between achievement goals and mathematical modeling competency. In conclusion, metacognition and achievement goals positively affect students’ mathematical modeling competency.

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“…The modelling process is initially believed to be difficult (Czocher, 2017;de Oliveira & Barbosa, 2013;Hidayat & Iksan, 2015;Jupri & Drijvers, 2016;Mentzer, Huffman, & Thayer, 2014;Wijaya, Heuvel-panhuizen, Doorman, & Robitzsch, 2014;Yew & Akmar, 2016). In a study conducted by Blomhøj and Kjeldsen in 2013, students encountered problems about mathematising the expression 'proportional to the square of population size' before finding the formula N' = kN 2 .…”

mentioning

confidence: 99%

Does Mastery of Goal Components Mediate the Relationship between Metacognition and Mathematical Modelling Competency?

2018

EDUC SCI-THEOR PRACT

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Prior studies suggested close correlations among metacognition, mastery goal, and mathematical modelling competency. The present study examines the relationship between metacognition and mastery goal that may influence mathematical modelling competency. The current study employs 538 students of a mathematics education program; among these students, 483 (89.8%) are males and 55 (10.2%) are females, aged from 18 to 22 years old. The study follows a correlational research design to investigate and measure the degree of relationship among mathematical modelling competencies, mastery goal, and metacognition. Findings indicate that mastery goal positively affects mathematical modelling competency. SEM analysis indicates significant and positive influence of task-and self-approach goals on mathematical modelling competency, whereas taskavoidance goals are significantly and negatively related to mathematical modelling competency. By contrast, self-avoidance goals did not affect mathematical modelling competency. Task-approach goal is a positive partial mediator, task-avoidance goal is a negative partial mediator, self-approach goal is a positive full mediator, and self-avoidance goal is not a mediator between metacognition and mathematical modelling competency. In conclusion, metacognition positively affects the mathematical modelling competency of students, which is influenced by task-approach, task-avoidance, and self-approach goal but not self-avoidance goal.

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How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course?

Cited by 54 publications

References 40 publications

A Course in Differential Equations, Modeling, and Simulation for Engineering Students

A Course in Differential Equations, Modeling, and Simulation for Engineering Students

Roles of metacognition and achievement goals in mathematical modeling competency: A structural equation modeling analysis

Does Mastery of Goal Components Mediate the Relationship between Metacognition and Mathematical Modelling Competency?

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