This paper presents the findings of a study involving 16 undergraduate students enrolled in a basic financial mathematics course. The study aimed to examine the nature of the students' problem-posing and problem-solving products and processes, as well as the interactions between the two. The findings revealed that the majority of the posed…

Cutting-edge technology enhances the teaching-learning process, with Multimedia-Based Instruction (MMBI) emerging as a powerful tool to achieve educational goals. MMBI creates visually engaging, resource-rich materials that support students in understanding abstract mathematical concepts, boosting interest and curiosity. According to Mayer (2001),…

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

Using Balacheff's (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set…

This article presents a set of "work-sharing routines," which teachers can use to broaden their repertoire of using student work, with an eye toward cultivating students' belonging. The authors define work-sharing as using actual mathematical student work, ideally from students in the class, to facilitate learning. Although there are…

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…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

In this paper, we report the analysis of thought processes used by Pre-Service Teachers' (PSTs') through clinical interviews as they solved an algebra task involving a linear pattern. The PST's were asked about a mathematical model they had constructed to describe a pattern problem. Our analysis suggests that conflict factors arise due to…

Incorporating open-ended real-world tasks enhances students' access to mathematical and real-life knowledge and maximizes learning experiences. This article examines how a secondary mathematics teacher used an open-ended problem on distributing pay raises to teach mathematical concepts and fairness to students. The teacher's actions exemplify…

The empirical data in this study are from a series of two lessons on measurement implemented in seven classes with 119 six-year-old students in Sweden. Both problem solving and problem posing were shown to be important in early mathematics when students in this study worked on one problem-solving task and one problem-posing task on measurement. As…

The purpose of this study was to investigate university students' conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem…

In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…

This dissertation examines the development of combinatorial reasoning in high school students through an in-depth analysis of a problem-solving session involving the Pizza Problem. The study, part of the long-term Rutgers-Kenilworth longitudinal research project, focuses on four 11th-grade students as they explore and connect concepts related to…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…