The volume of data that can be captured and stored from students' everyday interactions with digital environments allows for the creation of models of student knowledge, skills, and attributes unobtrusively. However, models and techniques for transforming these data into information that is useful for educators have not been established. This…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

In order to increase students' awareness for and comfort with mathematical modeling of biological processes, and increase their understanding of diffusion, the following lab was developed for use in 100-level, majors/non-majors biology and neuroscience courses. The activity begins with generation of a data set that uses coin-flips to replicate…

Unexpected outcomes can reflect noise in the environment or a change in the current rules. We should ignore noise but shift strategy after rule changes. How we learn to do this is unclear, but one possibility is that it relies on learning to learn in uncertain environments. We propose that acquisition of latent task structure during learning to…

Randomized experiments are considered the gold standard for causal inference because they can provide unbiased estimates of treatment effects for the experimental participants. However, researchers and policymakers are often interested in using a specific experiment to inform decisions about other target populations. In education research,…

Biomodeling is the study of the structures and behaviors of interacting biological entities such as molecules, cells, or organisms. While physical and chemical processes give rise to various spatial and temporal structures, even the simplest biological phenomenon is infinitely more complex (Kling 2004). Over the past decade, much of biomodeling…

The relevance of this problem is related to the urgent need to explain peculiarities of anticipation and probabilistic forecasting in adolescence. It has revealed a contradiction: on the one hand, the problem of anticipation in ontogenesis is well developed, and, on the other hand, there remain understudied mechanisms of anticipation in…

We address the problem of selecting the best of a set of units based on a criterion variable, when its value is recorded for every unit subject to estimation, measurement, or another source of error. The solution is constructed in a decision-theoretical framework, incorporating the consequences (ramifications) of the various kinds of error that…

When calculating class rank, high schools often give additional weight to grades earned in College Board Advanced Placement (AP) courses as an incentive for students to take hard courses. This paper examines changes in student course-taking behavior after an increase in AP grade weights at Texas high schools. We find that raising the magnitude of…

An experiential education program was designed to target risk perceptions and preventative measures that make people feel comfortable in human-coyote interactions. The research was conducted in a Canadian national park where a coyote caused a human fatality in 2009. Based on previous research, we explored the effects of an experience-based coyote…

A mysterious conflict of solutions emerged when a group of tenth- and eleventh-grade students were studying a seemingly ordinary problem on combination and probability. By investigating the mysterious "conflicts" caused by multiple randomization procedures, students will gain a deeper understanding of what it means to perform a task…

Among the wide range of factors related to the acquisition of statistical knowledge, competence in basic mathematics, including basic probability, has received much attention. In this study, a mediation model was estimated to derive the total, direct, and indirect effects of mathematical competence on statistics achievement taking into account…

This work studied the entrepreneurial aspirations of 3,987 adolescents regarding self-employment and the influence of gender, age, nationality, type of school, location of the school, educational level and performance. The Logit model is used to analyze the data. The results indicate that the pupils' aspirations to be self-employed increase in the…

Syundz (c. 314-237 BC), born in China during the Warring States Period, was a realist philosopher who contributed to the Hundred Schools of Thought, a period of cultural and philosophical development that flourished from the 6th century to 221 BC. Syundz commented on many ideas, particularly those of Confucius and Mencius, and a collection of…

The lexical restructuring model (LRM) is a theory that attempts to explain the developmental origins of phonological awareness (PA). According to the LRM, various characteristics of words should be related to the extent to which words are segmentally represented in the lexicon. Segmental representations of words allow children to access the parts…