New Directions in Elementary Differential Equations

Boyce, William E.

doi:10.1080/07468342.1994.11973640

Cited by 8 publications

(13 citation statements)

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“…Due to the importance of DEs, the topic has attracted many researchers, and the literature shows that a number of researches (e.g. Artigue, 1989;Blanchard, 1994;Boyce, 1994;Chau & Pluvinage, 1999;Kallaher, 1999;Habre, 2000;Rasmussen, 2001;Kwon et al, 2003;Saglam, 2004;Arslan, 2005;Raychaudhuri, 2008) and projects (Consortium for Ordinary Differential Equations Experiments in Harvey Mudd College; The Boston University Ordinary Differential Equations Project) have been carried out on the teaching of DEs. Nevertheless, most of these studies are about new approaches to teaching DEs and several researchers have pointed out a shortage of studies on students' understanding of DEs (Kwon, 2002;Habre, 2003;Rowland & Jovanoski, 2004;Raychaudhuri, 2008).…”

Section: Introductionmentioning

confidence: 99%

Traditional instruction of differential equations and conceptual learning

Arslan

2010

Teaching Mathematics and its Applications

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Procedural and conceptual learning are two types of learning, related to two types of knowledge, which are often referred to in mathematics education. Procedural learning involves only memorizing operations with no understanding of underlying meanings. Conceptual learning involves understanding and interpreting concepts and the relations between concepts. The relationship between these learning types has been discussed for a long time. For some researchers, procedural knowledge forms the basis for conceptual knowledge, while for others the relationship is reversed. The aims of the study reported here were first to explore the nature of students' learning in traditional differential equations (DEs) courses and second to clarify the relationship between procedural and conceptual learning. To address these aims an achievement test with 13 open-ended questions, probing procedural and conceptual learning with regard to DEs, was administered to 77 candidate mathematics teachers, enrolled in a traditional DEs course. The analysis of students' responses to the test items showed that 85% of candidate teachers gave correct responses on procedural questions whilst only 30% of them gave correct responses to the conceptual questions. These findings suggest that the candidate teachers' learning was primarily procedural in the context of traditional instruction and content and that this did not lead them to develop the conceptual knowledge needed to interpret new situations properly and to produce new ideas beyond the ones they had memorized. In addition, based upon the student levels in both procedural and conceptual learning, it was concluded that conceptual learning supports and generates procedural learning but procedural learning does not support conceptual learning.

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Section: Introductionmentioning

confidence: 99%

Traditional instruction of differential equations and conceptual learning

Arslan

2010

Teaching Mathematics and its Applications

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“…Because, in a traditional differential equation environment, Selahattin (2010b) reported that nature of students' learning is procedural and is restricted to mastering and applying a few algebraic techniques. M Artigue, (1989) supported these results in a sense, so as to learner do not have understanding of differential equation concept (Boyce, 1994;Rasmussen, 2001). Literature also shows that usually deprived academic achievement results in calculus are caused by lack of conceptual understanding and inadequacy of teacher's content knowledge (Makgakga & Makwakwa, 2016;Muzangwa & Chifamba, 2012).…”

Section: Resultsmentioning

confidence: 98%

An Evolving Research to Tackle Teaching and Learning Challenges during Differential Equations Course: A Combination of Non-routine Problems and Teacher Training

Bibi

Ahmad

Shahid

et al. 2019

Int Elect J Math Ed

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Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with differentiation and integration is only introduced first time at the 12th year of study or at pre-university level, and the students have no previous knowledge and understandings of this topic. Therefore, the aim of current study is to determine whether teaching and learning of DEs is a challenging task and also, to find out the ways these challenges can be tackled to develop a better understanding for differential equations problem solving. Results showed that teaching and learning of differential equation is not only a difficult part of the mathematics as compared to algebra, trigonometry but also demand high level of conceptual understanding and special efforts for solving differential equation problem. Addition of non-routine problems has been found major factor to enhance teaching and learning. Teacher should also be properly equipped and trained, so that they may educate both routine and nonroutine differential equation problem.

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“…It is invariably part of the first or second-year curriculum at any university of science and technology. According to Boyce (1994), the topic of differential equations has traditionally been taught as a pure analytical course. Several types of differential equations are presented along with the analytical method of obtaining their solution.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…However, in the last decades the focus of teaching differential equations has gradually shifted to a contextualized, problem-based approach. More emphasis is placed on the modelling process, on the applications of differential equations in real life, on graphical methods to research differential equations and on numerical methods to solve differential equations by computer (Boyce, 1994).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Changing students’ beliefs about the relevance of mathematics in an advanced secondary mathematics class

Gijsbers

Smits

Pepin

2019

International Journal of Mathematical Education in Science and

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This study shows that using authentic contexts for learning differential equations in a differentiation-by-interest setting can enhance students' beliefs about the relevance of mathematics. The students in this study were studying advanced mathematics (wiskunde D) at upper secondary school in the Netherlands. These students are often not aware of the relevance of the mathematics they have to learn in school. More insights into the application of mathematics in other sciences can be beneficial for these students in terms of preparation for their future study and career. A course differentiating by student interest with new context-rich curriculum materials was developed in order to enhance students' beliefs about the relevance of mathematics. The intervention aimed at teaching differential equations through guided small-group tasks in scientific, medical or economical contexts. The results show that students' beliefs about the relevance of mathematics improved, and they appreciated experiencing how the mathematics was applied in real-life situations.

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New Directions in Elementary Differential Equations

Cited by 8 publications

References 0 publications

Traditional instruction of differential equations and conceptual learning

Traditional instruction of differential equations and conceptual learning

An Evolving Research to Tackle Teaching and Learning Challenges during Differential Equations Course: A Combination of Non-routine Problems and Teacher Training

Changing students’ beliefs about the relevance of mathematics in an advanced secondary mathematics class

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