This study elaborates on the pivotal roles of mathematical and statistical models in data-driven predictions in an integrated STEM context using the case of Year 4 students: (?) "a descriptive means" to describe the features of trends and variability of data and (?) "an explanatory means" to explain causal relationships behind…

The mathematics of budgeting and space can lead to a justice-oriented experience for elementary students as they design a proposal for an inclusive playground. The authors' work focused on creating the space for elementary children to see the interconnectedness between mathematics and a community social injustice, lack of inclusive playground…

One of the most vexing challenges facing developmental researchers today is the statistical modeling of two or more behaviors as they unfold jointly over time. Although quantitative methodologists have studied these issues for more than half a century, no widely agreed-upon principled strategy exists to empirically analyze codevelopmental…

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.…

Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the…

There are several conceptualizations of modeling competencies, including among others on the one hand so-called sub-competencies, which are required to progress from one step of a modeling process to the next, and metacognitive individual and group strategies. However, the relationship between metacognitive strategies and modeling sub-competencies…

This research presents the results of the implementation of a model-eliciting activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the…

The purpose of this study was to understand children's operations on fragmenting schemes while they are engaged with three different visual models, including circle, rectangle, and length model. This study was a sequential explanatory mixed method, which included two phases that happened sequentially with the dominant use of the quantitative…

The extent of competition in the market affects the balance of bargaining power of market participants. When price discrimination is low, it increases consumer welfare - that is, if the price does not correspond to the evaluation of each product by the consumer, then discrimination allows for additional consumers to buy the product at a price,…

Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling…

The reality is that textbooks and state standards have more content than can reasonably be covered for proficiency in most classrooms. In years past, this typically meant cutting the last unit or two or moving along regardless of who was keeping up, in many cases resulting in cutting statistics from the curriculum. This article provides five…

In practice, some test items may display misfit at the upper-asymptote of item characteristic curve due to distraction, anxiety, or carelessness by the test takers (i.e., the slipping effect). The conventional item response theory (IRT) models do not take the slipping effect into consideration, which may violate the model fit assumption in IRT.…

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…