Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

It is evident that more qualitative research on Advanced Placement [AP] classrooms for students from marginalized backgrounds is needed to uncover how AP practices and pedagogies might better serve students who had been historically excluded from the AP Program. I asked my former calculus students (32 total - 22 participated) from my last three…

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in…

This paper describes an activity using a dog treat ball to introduce systems of first-order differential equations. Beads are placed in the first of two hemispherical chambers of a food-dispensing dog toy. As the ball is turned, students track the number of beads in the first chamber, the second chamber, and the exterior of the ball. Students…

This study describes the metacognition profile of female and male mathematics' education students in understanding the concept of integral calculus in the category of classifying and summarizing. This research method was an explorative method with the qualitative approach. The subjects of this study were mathematics education students at the…

We share our experience and lessons learned from using Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) modeling scenarios in our Differential Equations I class at Middle Tennessee State University. Specific projects with Python codes are presented. Discussions are brought forth on how to…

This study was designed to micro-analyze the role of the design of interactive diagrams in learning-teaching the concept of the indefinite integral. The presented case study focuses on the engagement of one pair of 17-year-old students with an interactive diagram for graphically learning-teaching the indefinite integral concept. The authors…

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

The current paper aims to identify the mathematical connections activated by 10 Mexican high school students while solving mathematical tasks that involve the exponential and logarithmic function. We used the Expanded Mathematical Connections Model (EMCM) and the OntoSemiotic Approach of Cognition and Mathematical Instruction (OSA) as theoretical…

This study investigates the impact of implementing integral calculus lectures which were originally very suitable in face-to-face delivery, but during the Covid-19 pandemic situation, these were delivered online through e-learning. This research analyzes the correlation between self-efficacy, creativity perception, and productive disposition…

In this paper we present the results of a survey of research studies on the learning of multivariable calculus in a wide geographic spectrum. The goal of this study is to describe what research results tell us about students' learning of calculus of two-variable functions, and how they inform its teaching. In spite of the diversity of cultures and…

This article describes a partially flipped course design for Calculus II which has been implemented by a varied instructional team at a medium-sized public engineering university (Colorado School of Mines (Mines)) over a period of three years. We have identified three main factors which have contributed to the success of the implementation: (1)…

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.

We expand on prior qualitative research about mathematics identity development using data from a large national US survey of 10,437 students in 336 college calculus classes. Multinomial logistic regression models find that a stronger mathematics identity predicts higher student interest in pursuing certain STEM careers when compared with non-STEM…

What if your students could access "any" resource during a test? How would they react? How would "you" react? This paper presents some results from a trial of allowing students access to notes, calculators, and any device connected to the internet, which occurred during a midterm in a second-year ordinary differential equations…