Students’ common mistakes in basic differentiation topics

Othman, Zarith Sofiah; Khalid, Ahmad Khudzairi; Mahat, Aishah

doi:10.1063/1.5041709

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…Similarly, Luneta and Makonye (2010) asserted that "students' performance in calculus is undermined by weak, basic algebraic skills of factorization, handling operations in directed numbers, solving equations, and poor understanding of indices" (p. 167). Again, Othman et al (2018) found that students made mistakes in basic differentiation formulas due to insufficient mathematical knowledge and being overly focused on specific mathematical rules.…”

Section: What Are the Causes Of Students' Mistakes In Calculus?mentioning

confidence: 99%

“…Research suggests that, in general, students find calculus a difficult subject (Bressoud, 2021;Sofronas et al, 2011), and they commit errors and hold misconceptions in both the procedural and conceptual domains of knowledge (Othman et al, 2018). Yet research also suggests that conceptual knowledge may facilitate acquisition of procedural skills (Chappell & Killpatrick, 2003).…”

Section: Why Problem-based Learning (Pbl) Is Useful In Calculusmentioning

confidence: 99%

“…However, to acquire procedural fluency in the application of a formula, students need exposure to additional exercises that allow the development of these skills. Without such exposure, students are likely to make mistakes such as those that Othman et al (2018) observed, e.g., forgetting to reduce the exponent by one and incorrectly using the Power Rule even after they simplify expressions. In addition, specifically targeted patterns of variation under separation help the learner ease the cognitive load associated with learning new skills .…”

Section: Step 6: Apply the Concept Of The Formula In Various Contextsmentioning

confidence: 99%

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A Unique Experience Learning Calculus: Integrating Variation Theory with Problem-Based Learning

Pogorelova

2023

Journal of Research in Science, Mathematics and Technology Education

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The paper proposes a pedagogical approach to teaching and learning calculus differentiation formulas that synthesizes the principles of variation theory (VT) and bianshi in a problem-based learning (PBL) format. Unlike traditional approaches that view formulas procedurally, the paper adapts Steinbring’s (1989) distinction between “concept” and “symbol,” abstracting differentiation calculus formulas as “concept” (i.e., the meaning of the formula) and “symbol” (i.e., procedural knowledge about how to apply the formula). The paper then aligns this distinction with VT and bianshi pedagogies. While VT emphasizes more static elements of conceptual knowledge (e.g., highlighting the contrast between conceptual and non-conceptual features of the object of learning), bianshi broadens the concept of variation, offering more dynamic principles of variation through procedural variation (e.g., via the process of problem solving) (Gu et al., 2004). Combining VT and bianshi into a single pedagogical application yields an eight-step approach to teaching and learning calculus differentiation formulas.

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Section: What Are the Causes Of Students' Mistakes In Calculus?mentioning

confidence: 99%

Section: Why Problem-based Learning (Pbl) Is Useful In Calculusmentioning

confidence: 99%

Section: Step 6: Apply the Concept Of The Formula In Various Contextsmentioning

confidence: 99%

See 1 more Smart Citation

A Unique Experience Learning Calculus: Integrating Variation Theory with Problem-Based Learning

Pogorelova

2023

Journal of Research in Science, Mathematics and Technology Education

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“…Kesalahan ini disebabkan oleh kurangnya pemahaman mahasiswa tentang konsep turunan fungsi. Hal ini dinyatakan juga oleh (Othman et al, 2018) yaitu mahasiswa sulit menyelesaikan permasalahan turunan fungsi, bahkan sering melakukan kesalahan dalam konsep turunan sederhana.…”

Section: Tahap Evaluation (Evaluasi)unclassified

Pengembangan E-module Materi Persamaan Nirlanjar dengan Pendekatan Konstruktivisme Berbantuan Microsoft Excel

Fitriasari

Ningsih

2021

Universitas Jambi

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Penelitian ini bertujuan untuk menghasilkan e-module materi Persamaan Nirlanjar dengan pendekatan konstruktivisme berbantuan Microsoft Excel yang valid dan praktis bagi mahasiswa. Penelitian ini merupakan penelitian pengembangan menggunakan model pengembangan ADDIE (Analysis, Design, Development, Implementation, and Evaluation). Subjek penelitian ini adalah 12 orang mahasiswa semester 6 Program Studi Pendidikan Matematika Universitas PGRI Palembang Tahun Akademik 2019/2020. Data dalam penelitian ini dikumpulkan melalui angket, dokumentasi dan wawancara. Data dalam penelitian ini dianalisis secara deskriptif kualitatif dan kuantitatif. Hasil penelitian ini adalah produk e-module materi Persamaan Nirlanjar yang dikembangkan dengan pendekatan konstruktivisme berbantuan Microsoft Excel valid dan praktis bagi mahasiswa. Validitas e-module dilihat dari hasil penilaian para pakar terhadap materi dan media yang digunakan dalam e-module. Skor validitas e-module secara keseluruhan adalah 83,5%. Kepraktisan e-module dilihat dari hasil respon mahasiswa yang menggunakan e-module dalam pembelajaran materi Persamaan Nirlanjar. Hasil respon mahasiswa adalah 90,16% dengan kategori kepraktisan sangat baik. Berdasarkan hasil dan analisis data dapat disimpulkan bahwa e-module yang dikembangkan valid dan praktis sehingga dapat digunakan dalam pembelajaran Persamaan Nirlanjar.

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“…Based on research findings from Mohd Fauzi et al (2021) found that among the factors that cause student failure in answering test questions is that students do not understand the requirements of the question and are not able to translate the question in the form of calculations and students who are weak in the basic concepts of mathematics have affected the answers given in the solution of differentiation topics. Taken together, Othman et al (2018) revealed that students' errors and misunderstandings in differentiation were caused by a lack of fundamental mathematical knowledge. Furthermore, it was discovered that students frequently did not make full use of their previous learning but instead relied on memorizing strategies to study, which contradicts 21st-century learning approaches.…”

Section: Introductionmentioning

confidence: 96%

Analysis of Course Learning Outcomes: Student Errors in The Calculus Subject among Engineering Students

Alias,

Abu Mansor,

Mahlan

et al. 2023

IJARBSS

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Calculus is an important subject in engineering that requires a high level of mastery of basic mathematics. However, since the last phase of the Covid 19 pandemic, most students have not really mastered the basics of mathematics as well. The weakness of students in mastering the theory and basic concepts of mathematics is one of the causes of this problem. This will affect the examination results obtained once they are at the IPTA level. Therefore, this study was conducted to find out whether the evaluation of Course Learning Outcomes (CLO) for the subject of Calculus can be achieved or not. This evaluation is based on students' mistakes in answering the basic mathematic questions related to the topic of differentiation and integration. A total of 30 students in Bachelor's Degree in Engineering were involved in this study. Errors from student answers are seen. This study found that the percentage of students error related to the basics of calculus and the students achievement in the assessment test given are in a moderate level and need to be improved. Therefore, the findings from this study are very useful for lecturers in improving their teaching and learning techniques, especially in the lecture room.

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Students’ common mistakes in basic differentiation topics

Cited by 6 publications

References 11 publications

A Unique Experience Learning Calculus: Integrating Variation Theory with Problem-Based Learning

A Unique Experience Learning Calculus: Integrating Variation Theory with Problem-Based Learning

Pengembangan E-module Materi Persamaan Nirlanjar dengan Pendekatan Konstruktivisme Berbantuan Microsoft Excel

Analysis of Course Learning Outcomes: Student Errors in The Calculus Subject among Engineering Students

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