Manipulatives have been found to be effective in increasing mathematics achievement when they are put to good use (Canny, 1984; Clements & Battista, 1990; Clements, 1999; Sowell, 1989; Suydam, 1984), but their use in mathematics instruction is not clear and it is often debated to be effective (Ball, 1992; McNeil & Jarvin, 2007). The…

This study was designed to examine the effect of academic advisor type on retention of first-year, full-time, four-year degree-seeking students at a mid-size research university in the western U.S., while controlling for several predictor variables identified in contemporary and seminal literature as having a potential impact on student retention.…

Qualitative classroom data from video recordings and students' written work can play important roles in improving mathematics instruction. In order to take full advantage of these data sources, it is helpful to have a strong analytic lens to orient one's reflections on the data. One promising analytic lens is the National Research Council's five…

Quartiles are usually introduced early, often in primary school together with box-and-whisker plots. Various methods are used, and in lack of explanation in many textbooks at elementary level, this leads to unnecessary confusion. We discuss some elementary methods that are consistent with the most common definition and are also easy to understand.

Data from published studies is used to recover information about the sample mean self-reported number of times cheated by college students. The sample means were estimated by fitting distributions to the reported data. The few estimated sample means thus recovered were roughly 2 or less.

Like scientists, children seek ways to explain causal systems in the world. But are children scientists in the strict Bayesian tradition of maximizing posterior probability? Or do they attend to other explanatory considerations, as laypeople and scientists--such as Einstein--do? Four experiments support the latter possibility. In particular, we…

Purpose: Childhood stuttering is common but is often outgrown. Children whose stuttering persists experience significant life impacts, calling for a better understanding of what factors may underlie eventual recovery. In previous research, language ability has been shown to differentiate children who stutter (CWS) from children who do not stutter,…

Using a panel data set of scientists in the US, we examine the hypothesis that workers in jobs poorly matched to their education are more likely to retire. In pooled estimates, we confirm that the mismatched are more likely to retire and that among retirees, the mismatched retire at younger ages. Hazard function estimates also support the…

The aim of the study was to explore teacher-child interaction in 24 whole-class read-aloud sessions in Chilean kindergarten classrooms serving children from low socioeconomic backgrounds. Fifteen sessions focused on story meaning, and nine focused on language coding/decoding. We coded teacher and child turns for their function (i.e., teacher…

It is well known that students of inferential statistics find the hypothetical, probabilistic reasoning used in hypothesis tests difficult to understand. Consequently, they will also have difficulties in understanding "p"-values. It is not unusual for these students to hold misconceptions about "p"-values that are difficult to…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood based statistics may be useful for testing latent variable distribution fit. We develop Satorra-Bentler type…

Fisher randomization tests for Neyman's null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using the F statistic to conduct such a test are examined both theoretically and computationally, and it is argued…

Feeding disorders exhibited by children with developmental disabilities, which include limiting food intake or refusing to consume solid foods, often result in poor health consequences. Interventions for feeding disorders vary in terms of their acceptability to children with disabilities and their families. One specific procedure, the…

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…