Analysis of Students’ Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform

Msomi, A. M.; Bansilal, Sarah

doi:10.29333/iejme/11474

Cited by 8 publications

(11 citation statements)

References 25 publications

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“…The participants' written and interview responses were analysed, using the analytical framework described below, which distinguished between three types of errors: conceptual, procedural, and foundation /technical errors. Some aspects of this framework have been used in Mutambara and Bansilal (2021), which focused on errors in linear combinations and spanning as well as Msomi and Bansilal (2022), which analysed errors in the area of Laplace transform.…”

Section: Methodsmentioning

confidence: 99%

“…Foundational errors are those, which occur because of poor background knowledge such as when a student incorrectly applies or misinterprets a previously learnt procedure or concept that is being applied in the new concept incorrectly (Msomi & Bansilal, 2022;Mutambara & Bansilal, 2021). According to Kiat (2005) technical errors are due to due to carelessness while carrying out a suitable procedure.…”

Section: Foundational or Technical Errorsmentioning

confidence: 99%

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Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Mutambara¹,

Bansilal²

2022

INT ELECT J MATH ED

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The aim of this paper is to identify errors and misconceptions that student demonstrated when learning linear independence and linear dependence concepts. A case study is presented involving 73 in-service mathematics teachers at a university in Zimbabwe who were studying for a Bachelor of Science Education Honors Degree in mathematics. Data was generated from a content analysis of the written responses of the participants to two items from a structured activity sheet. Follow up interviews with five participants were used to gain a better understanding of their misconceptions. The study found that the participants had different kinds of misconceptions leading to errors which could be described as procedural, conceptual, and foundational respectively and the distribution of the errors differed across the two problems. For question 1 which was set within the vector space M2×2, students found it harder to move past the first few two steps of formulating the general vector equation and doing scalar multiplication; those who passed those two steps were mostly able to get to a correct solution. For question 2 which was set within ℝ 3 most students went past the first two steps formulating the general vector equation and converting that to an augmented matrix but then made many foundational errors, most of which were related to misinterpretations of the solutions to the system of equations.

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Section: Methodsmentioning

confidence: 99%

Section: Foundational or Technical Errorsmentioning

confidence: 99%

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Mutambara¹,

Bansilal²

2022

INT ELECT J MATH ED

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“…In terms of the constructivist perspectives of learning, errors and misconceptions are naturally formed as part of the process of learning, and teachers should try to learn more about these so that they can better support their learners [19][20][21][22]. As learners construct new knowledge, they do this based on what they know already and understand or do not understand yet.…”

Section: Errors and Misconceptions As Part Of The Learning Processmentioning

confidence: 99%

Using the Van Hiele Theory to Explain Pre-Service Teachers’ Understanding of Similarity in Euclidean Geometry

Mbatha,

Bansilal

2023

Education Sciences

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Helping learners to develop a solid grasp of geometric concepts poses a challenge for teachers. Therefore, it is important that teachers have a sound understanding of the geometry they teach. The aim of this qualitative study was to explore pre-service teachers’ (PST’s) understanding of the concept of similarity in Euclidean geometry and to use van Hiele’s theory to explain misconceptions evidenced by the PSTs. Data in this study were collected from 34 first-year PSTs studying for a Bachelor of Education degree in high school mathematics. The authors analysed the written responses to a 13-item worksheet and also conducted interviews with seven of the participants. The analysis of the data was guided by van Hiele’s theory which was used to identify misconceptions amongst PST’s who had not yet developed the appropriate reasoning skills linked to particular van Hiele levels of geometric thought. It was found that these students used reasoning that is characteristic of the elementary levels to make judgments. Many PST’s faced challenges with similarity notation and the process of proving the similarity between two figures. This study recommends that PST’s should be given more opportunities to connect visual and analytic representations of similarity.

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“…According to Herholdt and Sapire (2014), slips are random deviations in declarative knowledge which do not indicate systematic misconceptions. An error occurs when a student believes a false concept as a true concept (Msomi & Bansisal 2022). For example, in school mathematics, it is often the case that learners misconstrue the concept of the difference of two squares as follows: x 2 -y 2 = (x -y) 2 .…”

Section: Introductionmentioning

confidence: 99%

Mitigating errors and misconceptions among Grade 11 learners in algebra through error analysis

Ndemo

Ndemo²

2023

African Journal of Teacher Education and Development

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Background: A good command of algebra concepts is vital for proficiency and success in higher mathematics and related disciplines. However, students are beset by conceptual challenges which require consistent attention because errors and misconceptions hinder learning and understanding.Aim: With the aim of mitigating the problem of errors and misconceptions in school mathematics learning, a qualitative descriptive-interpretative research study was conducted.Setting: The study involved 30 ordinary-level learners purposively sampled from one rural boarding high school in Zimbabwe.Methods: Focus group discussions in which learners scrutinised illustrative sketches of erroneous worked examples were used as means to raise informants’ awareness of common errors and misconceptions in school algebra. Task-based interviews were used to elicit data in the form of participants’ written responses to tasks involving school algebra concepts. Content analysis informed by Biggs and Collis’ model and Kiat’s taxonomy of errors was applied to the textual data.Results: With respect to basic ideas in algebra such as notions of coefficients, operators and variables and simplifying algebraic fractions, Grade 11 learners reached the extra-extended and relational levels of the SOLO model and solutions were free from conceptual and procedural areas. With regard to solving quadratic equations, lower levels of the SOLO model manifested with solution attempts marred with conceptual errors.Conclusion: It can be concluded that error analysis has a potential to mitigate the problem of errors and misconception among Grade 11 learners depending on the nature of content involved.Contribution: These findings have important implications for mathematics education and research in school algebra in the sense that it has contributed to efforts intended to find strategies that can provide solutions to the persistent problem of errors and misconceptions in mathematics education.

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Analysis of Students’ Errors and Misconceptions in Solving Linear Ordinary Differential Equations Using the Method of Laplace Transform

Cited by 8 publications

References 25 publications

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence

Using the Van Hiele Theory to Explain Pre-Service Teachers’ Understanding of Similarity in Euclidean Geometry

Mitigating errors and misconceptions among Grade 11 learners in algebra through error analysis

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