In this article, we use a simple lattice model to illustrate the concepts of entropy, free energy, and thermodynamic equilibrium from a microscopic perspective. These physical concepts are based on elementary knowledge of discrete probability distribution and weighted average. Calculations about this model involve basic algebra and counting, which…

Automatic answer assessment systems typically apply semantic similarity methods where student responses are compared with some reference answers in order to access their correctness. But student responses in dialogue based tutoring systems are often grammatically and semantically incomplete and additional information (e.g., dialogue history) is…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Using a data set that augments a student survey with administrative data from the Iowa State University Office of Financial Aid, the authors posed two questions: Do students know whether they have student loans? Do students know how much they owe on outstanding student loans? We used logistic and ordered logit regressions to answer these…

Probability knowledge and skills are needed in science and in making daily decisions that are sometimes made under uncertain conditions. Hence, there is the need to ensure that the pre-service teachers of our children are well prepared to teach probability. Pre-service teachers' conceptions of probability are identified, and ways of helping them…

Student modeling is a widely used approach to make inference about a student's attributes like knowledge, learning, etc. If we wish to use these models to analyze and better understand student learning there are two problems. First, a model's ability to predict student performance is at best weakly related to the accuracy of any one of its…

DECIDE is a teacher-friendly, integrated approach designed to stimulate learning by allowing students to make decisions about situations they face in their lives while using scientific weather principles. This learning unit integrates weather science, decision theory, mathematics, statistics, geography, and reading in a context of decision…