This paper reports on a two-part investigation into how students think about and use summation (sigma) notation. During an instructional design experiment, two participating students struggled with this notation, but also reasoned about it in creative ways. This motivated a follow-up study in which we administered a free-response three-item survey…

The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don't make any…

We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students' errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

This study aims to evaluate cognitive conflict in constructing mathematical concepts, based on thinking errors. The data were collected through observations of words or sentences, leading to the derivation of qualitative outputs. Furthermore, the results showed that the two selected subjects experienced cognitive conflicts regarding thinking…

The teacher must, first of all, have a good knowledge of mathematics to detect the errors in the student's mathematical knowledge and to identify the general situation in the classroom. This depends on the mathematical knowledge gained in the teacher training schools. General mathematics topics occupying an important place in the departments of…

Many mathematics education researchers agree that students struggle to understand the key concepts in linear algebra courses. The purpose of this study was to examine in-service teachers' errors and misconceptions in the area of linear combinations. The participants were 73 Zimbabwean mathematics teachers who were enrolled in an in-service…

Many countries do not include the normal distribution concept in their middle school mathematics curriculum, but on the grounds that middle school mathematics teachers need to know more than just mathematics, researchers argue that preservice teachers (PTs) ought to have knowledge and skills in this area. This study was aimed to investigate PTs'…

Laplace transform (LT) is an essential mathematical tool for solving linear ordinary differential equations (ODE) with boundary values, by transforming differential equation into algebraic equations which are easier to manipulate. In this article, we analyse the errors students make and misconceptions they have in solving linear ODE using LT…

The study of the variational behavior of functions constitutes an important element in the understanding of the change of phenomena in real life. His understanding is an essential axis in the mathematical training of university students, especially those who pursue engineering careers. This article presents the results of a study whose objective…

Teaching at the Right Level (TaRL) is an emerging and widely implemented remedial educational approach that is currently being piloted in many countries. Morocco has been experimenting with this approach since the 2022-2023 school year. This study aims to assess the effectiveness of using the TARL approach as a remedial model in addressing…

The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven…

This qualitative case study aimed to investigate prospective middle school mathematics teachers' instructional responses based on the students' correct and incorrect functional thinking within the context of pattern generalization. The data were collected from thirty-two prospective teachers through a written task and semi-structured interviews…

This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined…

This research aimed to determine the difficulties that the students experience in inequality solutions that contain inequality in general and rational (proportional) expressions, and to solve these difficulties with an activity. Totally 108 students, who were enrolled in the Department of Mathematics and Science Education, consisted respectively…