Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…

In studies over recent years, there has been an increasing interest in teachers' predicting middle school students' thinking processes. However, as far as we are aware, there are no studies examining students' thinking in terms of mathematical thinking components. This study primarily aimed to determine the mathematical thinking of middle school…

Computational thinking and activity are vital aspects of what it means to conduct scientific and mathematical work. In light of this, some propose that students' mathematical education should include an integration of computing into their mathematical experiences, giving students opportunities to engage with computational tools as they reason…

This study examined the engagement of preservice elementary teachers (PSTs) with mathematics tasks that were open in various ways and to varying extents. In K-12 settings, practitioners who have implemented recently popular open tasks report increased engagement and from a wider variety of students. While these anecdotal reports and related…

Professional noticing of children's mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169-202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children's mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics…

This paper presents Big Ideas of Measurement as a framework of students' thinking about measurement. Drawing from research-based evidence, the framework is a collection of key concepts that students must develop for a robust understanding of measurement and, as such, are key aspects of students' thinking teachers should learn to notice. In a case…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

The use of tasks to promote mathematical reasoning (MR) in teaching practice is essential to meet curricular goals. However, that practice is often a huge challenge for teachers, and particularly for prospective teachers and thus it is essential to highlight it as a goal for initial teacher education. This study focuses on preservice mathematics…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage's formal operational stage. Teachers, especially those working with secondary school…

The objective of this research is to study the "Scratch" programming language as a didactic tool to teach functions. The introduction of didactic tools allowing comprehension in simple and attractive ways is required. Given the traditional teaching/learning system, it is necessary to organize participatory and collaborative dynamic…

This paper presents research that exists at the crossroad of scholarly practice and scholarly inquiry. We outline the process in the design, enactment, and empirical examination of an elementary methods course activity, Exploring and Supporting Student Thinking (ESST), which engaged 18 elementary prospective teachers (PTs) in two sessions of…

The ability to think critically and mathematically is strongly needed so that the students are able to face the challenges of 4.0 industrial revolution. By thinking critically, they are expected to be more adaptive in finding solutions to each problem. This study aims to identify the students' mathematical critical thinking skills in solving…