This paper presents the design and development of a rubric for assessing mathematical modelling for mathematical modelling tasks at the secondary level. A rubric was crafted based on the mathematical modelling competencies synthesised by the researchers identified from four sources. The rubric was fine-tuned following an interview with three…

When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi-parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two-parameter sensitivity analysis…

By means of three case studies, we will present two mathematical modelling activities that are suitable for students enrolled in senior high school and the first year of mathematics at university level. The activities have been designed to enrich the learning process and promote the formation of vital modelling skills. In case studies one and two,…

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation.…

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However,…

Energy Conservation Theory of Second Language Acquisition (ECT-L2A) (Han, Bao, & Wiita, 2017b), an interdisciplinary theory juxtaposing a physics perspective and an applied linguistics perspective, conceptualizes individuals' ultimate attainment as a function of dynamic transformation of endogenous and exogenous energies throughout the…

The purpose of this study is to identify primary school students' thinking processes within the mathematical modeling process and the challenges they encounter, if any. This is a basic qualitative research study conducted in a primary school in the city of Kütahya in the academic year of 2015-2016. The study group of the research was composed of…

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…

The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

The present article considers a fundamental question in evaluation research: "By how much do program effects vary across sites?" The article first presents a theoretical model of cross-site impact variation and a related estimation model with a random treatment coefficient and fixed site-specific intercepts. This approach eliminates…

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

Psychological models of temporal discounting have now successfully displaced classical economic theory due to the simple fact that many common behavior patterns, such as impulsivity, were unexplainable with classic models. However, the now dominant hyperbolic model of discounting is itself becoming increasingly strained. Numerous factors have…

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…