This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…

Teacher perception is one of the most important factors determining classroom teaching practices. Multiple representations are used extensively in mathematics classrooms, especially in developing conceptual understanding. The data in this study, which aims to compare Turkish and US middle school mathematics teachers' perceptions of multiple…

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…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…

The ability to think analytically is vital in today's world. In an era defined by rapid technological advancements, economic globalization and societal complexities, analytical thinking skills are paramount to career success. Analytical thinking has been conceptualized and defined in a variety of ways, reflecting its multifaceted nature and the…

Solving problems involving absolute value is one of the hardest topics for students learning in elementary algebra course. This is an important topic in student's mathematics life since absolute value functions are important example of a function which is continuous on the real line but not differentiable at the origin. A deep understanding of…

The aim of this research was to study and investigate first year university calculus students' misconceptions about how to use the definition of limit to find the first derivative of functions and then remediate these misconceptions by using APOS theory (Action, Process, Object, and Schema). Students (n = 82 female and male) were selected based on…

The transition to tertiary mathematics requires students to use definitions of mathematical objects instead of intuitions. However, routines of defining and of proving with definitions are difficult to engage in, as they are not familiar to students who come from secondary school mathematics. Defining is highly complex because of its underlying…

As the global economy transforms into a knowledge-based society with an enhanced focus on information and innovation, success will depend on the ability of global citizens to work effectively with knowledge and technology (Drucker, 1993; Sawyer, 2006; Schwab, 2017). Working effectively with knowledge and technology requires thinking critically and…

Choosing the right word to express meaning can be a challenge for English language learners (ELLs) in both English as second language and English as a foreign language settings, persisting through all proficiency levels in productive language use for several reasons. In order to make correct word choices, ELLs must master the various aspects of a…

Several studies related to mathematical proof have been done by many researchers on high-level materials, but not yet examined on the material of transformation geometry. The aim of this research is identification learning obstacles pre-service teachers on transformation geometry. This study is qualitative research; data were collected from…

Purpose: The main goal of this article is to learning define and justify group problem solving as an approach to citizenship education. It is demonstrated that the choice of theoretical framework of democracy has consequences for the chosen learning goals, educational approach and learning activities. The framework used here is an epistemic theory…

In an environment of rapid and unpredictable change determined and directed by technologies that are constantly changing, the assumption that being technologically literate is the key to being a sustained, contributing life-long learner is well founded. However, technological literacy is seldom referred to or considered in academic arguments as a…

Purpose: While the number of entrepreneurship education programmes offered around the world is on the rise, research into the assessment of entrepreneurship education programmes is still lacking. The purpose of this paper is to take the stance that entrepreneurship education has to focus on a set of transversal competences aimed at teaching…