The drag effect on a falling ball caused by air is a conventional subject in the most well-known textbooks of classical mechanics and fluid dynamics. Further, there are some papers that employ video analysis to track objects movements in the air making it possible to obtain position data as a function of time and its graphs. However, none of them…

We report the results of a study on informal covariate statistical reasoning conducted with 22 students (aged 16 and 18 years). We designed and implemented a task in a digital technology environment to introduce the line of best fit. The task design having elements that foresee misconceptions reported in the literature, and by focusing on four…

Temporality-driven covariate classification had limited impact on: the specification of directed acyclic graphs (DAGs) by 85 novice analysts (medical undergraduates); or the risk of bias in DAG-informed multivariable models designed to generate causal inference from observational data. Only 71 students (83.5%) managed to complete the…

Curriculum prerequisite networks have a central role in shaping the course of university programs. The analysis of prerequisite networks has attracted a lot of research interest recently since designing an appropriate network is of great importance both academically and economically. It determines the learning goals of the program and also has a…

Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense…

For several years, I taught a general education course on the Manhattan Project for students majoring in the arts and humanities who needed a physical science credit as a condition of their graduation requirements. As might be imagined, the challenge in teaching this course was to find a balance between quantitative and qualitative content. A…

The literature emphasizes the interest and need to learn the concept of continuity with understanding, although this meaning it is not consensual nor specified how it may emerge and be developed in the learning process. In this paper we report the results of a study aiming to analyse Brazilian preservice mathematics teachers' understanding of the…

Access to knowledge has never been easier in the internet age, and so it is important that students develop skills to discriminate undependable information from reliably investigated research. We have created an exercise that teaches good research practice by exploring the history, ethics, and design of clinical trials. Students apply their…

Mathematics teachers' ability to translate and make connections between representations of functions requires investigation. Consequently, this qualitative case study article focuses on pre-service mathematics teachers' nature of understanding of the tangent function; a function bearing unique characteristics compared with the sine and cosine…

Students' solutions of enumerative combinatorial problems may be assessed along two main dimensions: the correctness of the solution and the method of enumeration. This study looks at the second dimension with reference to the Cartesian product of two sets, and at the 'odometer' combinatorial strategy defined by English (1991). Since we are not…

One of the characteristics of the twenty-first century is the increase in the information sources available to designers to make their design decisions. However, current verbal protocol analysis methods and theoretical frameworks do not explain how internal and external information sources contribute to novice designers' moment-to-moment thought…

Researchers have identified students' difficulties reasoning about inverse functions. Through our review of this literature, three meanings stand out: a formal, 'undoing', and quantitative meaning. Using these meanings as a guide, we analyzed student work collected from a lesson on the topic of inverse functions taught by an experienced high…

Deeper learning (DL) is firmly rooted in learning science and computer science. However, a dearth of review studies has probed its trajectory in DL in foreign languages (DLFL). Utilizing SSCI from the Web of Science Core Collection, we employ Citespace and Vosviewer to analyze the scientific knowledge graph of DLFL literature. Our analysis…

Quantitative reasoning plays a crucial role in students' and teachers' successful modeling activities. In a semester-long teaching experiment with an undergraduate student, we explore how her conception of a graph plays a role in her ability to quantify and maintain quantitative structures. We characterize here Lydia's conception of a graph as one…

This manuscript proposes the use of the "I notice, I wonder" routine in college mathematics classrooms to address issues of diversity, equity, and inclusion. Examples are given of prompts that incorporate meaningful conversations about real-world issues affecting our students or about issues of inclusion, access, and representation in…