Assessment items are commonly field tested prior to operational use to observe statistical item properties such as difficulty. Item parameter estimates from field testing may be used to assign scores via pre-equating or computer adaptive designs. This study examined differences between item difficulty estimates based on field test and operational…

Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x)…

This randomized control treatment study investigated the role of generative paraphrasing interventions on word problem-solving (WPS) accuracy in English language learners (ELL) who were at risk for math difficulties (MD). One hundred and forty-two third-grade monolingual and English language learners were randomly assigned to either an untreated…

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

Students have intuitive notions of the meaning of variability; some may see variability as how values in a set vary from each other. This article provides a measure of variability that is based on that conception. We introduce this new measure and a method for calculating it. Finally, we prove that this measure is equivalent to the population…

This paper revisits the use of effect sizes in the analysis of experimental and similar results, and reminds readers of the relative advantages of the mean absolute deviation as a measure of variation, as opposed to the more complex standard deviation. The mean absolute deviation is easier to use and understand, and more tolerant of extreme…

There are two main lines of research in estimating classification accuracy (CA) and classification consistency (CC) under Item Response Theory (IRT). The R package cacIRT provides computer implementations of both approaches in an accessible and unified framework. Even with available implementations, there remains decisions a researcher faces when…

Estimation is useful in situations where an exact answer is not as important as a quick answer that is good enough. A web-based adaptive system for practicing estimates is currently being developed. We propose a simple model for estimating student's latent skill of estimation. This model combines a continuous measure of correctness and response…

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Technology and smart devices have become ubiquitous staples in every aspect of human life. Given the rise of computation in everyday life, introducing technology to early childhood students requires exposure to logical thinking and problem-solving skills through programming approaches or computational thinking. This research addresses an inquiry…

Technology is becoming more integral across professional fields and within our daily lives, especially since the onset of the pandemic. As such, opportunities to learn computational thinking are important to all students--not only the ones who will eventually study computer science or enter the information technology industry. However, large…

This article describes the analysis of regression-discontinuity designs (RDDs) using the R packages rdd, rdrobust, and rddtools. We discuss similarities and differences between these packages and provide directions on how to use them effectively. We use real data from the Carolina Abecedarian Project to show how an analysis of an RDD can be…

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the…

The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than…

Mangarevan traditionally contained two numeration systems: a general one, which was highly regular, decimal, and extraordinarily extensive; and a specific one, which was restricted to specific objects, based on diverging counting units, and interspersed with binary steps. While most of these characteristics are shared by numeration systems in…