Examination of Mathematical Errors and Mistakes in Calculus Course

Oct 15, 2026

Study investigates mathematical errors and mistakes made by preservice elementary mathematics teachers in a calculus course to clarify where students fail conceptually and procedurally. Qualitative document analysis was conducted using exam materials from 75 preservice teachers from a public university during the 2016–2017 fall term, including interim, practice, and general exams scanned into electronic form. MAXQDA 12 supported content analysis with data coding techniques, concluding that errors included incomplete or incorrect generalization recall, along with other procedural and conceptual mistakes, followed by recommendations grounded in the findings.

LanguageEnglish

CategoryExam

FormatPDF

Pages17

Reading Time43 min

AccessFree to download

Abstract

Introduction

Background of the calculus course

Students’ difficulties with calculus concepts

Methods and data sources

Participants and course context

Exam documents and analysis approach

Findings and implications

Types of errors identified

Recommendations based on results

Examination of Mathematical Errors and Mistakes in Calculus Course Davut KÖĞCE1 Niğde Ömer Halisdemir University Abstract This study was conducted to identify mathematical errors and mistakes made by preservice elementary mathematics teachers in the calculus course. To that end, the document analysis method of qualitative research models was used in the research. The sample of the research included a total of 75 preservice teachers who were attending the Department of Elementary Mathematics Education in the Faculty of Education at a public university and taking the calculus I course during the fall term of 2016-2017 academic year. Accordingly, written documents including the participant preservice teachers’ papers of interim exams, practice exams, and general exams constituted the data source. The exam papers were scanned with a scanner and transformed into the electronic environment. A content analysis was performed with the data by using MAXQDA 12 qualitative data analysis program, and“data coding” of data analysis techniques was utilized. It was concluded that the preservice teachers made procedural and conceptual errors and mistakes, mathematical errors and mistakes such as recalling generalizations incompletely or incorrectly. Some recommendations were made in light of these results. Keywords: Preservice mathematics teachers, Calculus course, Mathematical errors, Mathematical mistakes DOI: 10.29329/epasr.2022.248.15 1Assoc. Prof. Dr., Niğde Ömer Halisdemir University, Faculty of Education, Department of Elemantary Mathematics Education, Niğde, Turkey, ORCID: 0000-0002-3475-2740 [Correspondence](Correspondence: kogced@gmail.com)[: kogced@gmail.com](Correspondence: kogced@gmail.com) Introduction Calculus course that mainly examines the functions by utilizing the disciplines of algebra and geometry is an important subject-matter course given in the departments of mathematics education. Mathematical concepts addressed in the calculus course lay the foundation of advanced mathematics used in the disciplines such as mathematics, sciences, engineering, etc. (Ubuz, 1999) . Proper understanding and interpretation of advanced mathematical concepts depends on the appropriate learning of concepts given in the calculus course (Gökçek & Açıkyıldız, 2016) . In the calculus books, concepts of functions, series, limit, continuity, derivative, and integral are addressed in general (Balcı, 2016; Demir, 2008) . One of the biggest objectives in the calculus course is to examine functions and behaviors of functions. In other words, it is the branch of mathematics engaged in the analysis of functions. Calculus course focuses on examining the image or behavior of a function when its independent variable is infinitesimal or infinitely big. Within this context, students are introduced to the concepts of function, limit and continuity in the first place, and then, several exercises are performed so that they become more competent at operations related to these concepts (Kabaca, 2011) . Next, the concept of derivative, conceptually based on limit and continuity, is taught while emphasis is made on the operation of finding the function which is a derivative of a function in the meantime. Finally, concept of integral, also conceptually based on the concept of limit, is taught. In the teaching of integral, firstly, finding an antiderivative for a function is addressed, and then, it is taught under the title “applications of integral” that the concept of integral means a Riemann sum applied under the operation of limit. In summary, Calculus is an important branch of mathematics that include limit, continuity, derivative, integral of functions, and applications of these concepts (Sofronas et al., 2011) . In Turkey, students meet these concepts addressed in the calculus course in their secondary education years for the first time. Thus, they are key mathematical concepts for students who will choose majors related to sciences and m

FAQs

What is the main purpose of the study?

The study identifies mathematical errors and mistakes made by preservice elementary mathematics teachers in the calculus course.

How were the data and exam materials collected and analyzed?

Written exam documents from interim, practice, and general exams were scanned, converted to electronic form, and analyzed through qualitative content analysis using MAXQDA 12 with data coding techniques.

What types of errors and mistakes were concluded?

The study found both procedural and conceptual errors, including mistakes such as recalling generalizations incompletely or incorrectly, and other mathematical errors and mistakes.

Oct 15, 2026

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