Group work can form a substantial component of degree programme assessments. To satisfy institutional and student expectations, students must often be assigned individual marks for their contributions to the group project, typically by mapping a single holistic group mark to individual marks using peer assessment scores. Since the early 1990s,…

The multiplication principle is a fundamental principle in enumerative combinatorics. It underpins many of the counting formulas students learn, and it provides much-needed justification for why counting works as it does. However, given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we document…

Deep Thought is a logic tutor where students practice constructing deductive logic proofs. Within Deep Thought is a data-driven mastery learning system (DDML), which calculates student proficiency based on rule scores weighted by expert-decided weights in order to assign problem sets of appropriate difficulty. In this study, we designed and tested…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…

A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically, these exams are prepared several days in advance, and generic question scores are used based on rough approximation of the question difficulty and length. For example, for a recent class taught by the author, there were…

This study proposes a computer-assisted system with a design based on Polya's problem-solving model. The system is designed to help average and low-achieving second graders in mathematics with word-based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem-solving procedure into stages and the…

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

High School graduation rates are key indicators of accountability for high schools and school districts in Oregon. Beginning with the 2008-09 school year, the Oregon Department of Education (ODE) implemented the cohort method of calculating graduation rates. The cohort method identifies the year the student entered high school for the first time…

The paper examines how computational thinking can be taught to young children with the use of educational robotics using the kit LEGO WeDo. Computational thinking was measured in terms of four sub-skills, namely, sequencing, correspondence between actions and instructions, debugging, and flow of control. Students were assigned to an experimental…

The fundamentals of computer science are increasingly important to consider as critical educational and occupational competencies, as evidenced by the rapid growth of computing capabilities and the proliferation of the Internet in the 21st century, combined with reimagined national education standards. Despite this technological and social…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

Asteroids are clumps of rock, the sizes of which range from less than a kilometer to a few hundred kilometers in diameter. They are generally found in the unusually large gap between Mars and Jupiter. There are probably more than 40,000 asteroids in this gap called the "asteroid belt." In this paper we describe our efforts in confirming…

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated and theoretically incorrect direct or step-down methods. This article illustrates how Excel's Solver…