Learning about probability can pose difficulties for students at all levels. Performing probability experiments using games can encourage students to develop understandings of probability grounded in real events. In this reflective paper, we explore the thinking of a group of students and teachers as they reasoned about experimental and…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Greater understanding can increase our knowledge and intervention effectiveness for activity participation problems of children with disabilities. We examined participation difficulties of children with autism spectrum disorders (ASD) and intellectual disabilities (ID) in the 2011 Survey of Pathway to Diagnosis and Services. We utilized propensity…

How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the…

This paper describes the development and efficacy of an online tool for assessing the numeracy of undergraduate students. The tool was designed to be easy to administer, provide immediate feedback to students on whether they had the required level of numeracy, and to be consistent with other measures of adult numeracy. When used with students…

Pedagogical Content Knowledge (PCK) is a powerful construct for examining the complexity of teacher knowledge. Together with teachers' moment-by-moment choices of action, it provides insight into teachers' knowledge and its influence on student learning. This paper investigates the PCK experienced by a senior secondary mathematics class during a…

Having the ability to make informed decisions about health, financial investments, and even the weather are all important to our everyday lives. However, most people receive no formal education on how to read and understand data presented in formats such as data tables and graphs. Research within the field of statistical reasoning demonstrates a…

Purpose: In healthy speakers, the more frequent and probable a word is in its context, the shorter the word tends to be. This study investigated whether these probabilistic effects were similarly sized for speakers with dysarthria of different severities. Method: Fifty-six speakers of New Zealand English (42 speakers with dysarthria and 14 healthy…

The purpose of this study is to investigate the effect of probability teaching with the argumentation approach on the academic achievement of pre-service mathematics teachers and the permanence of probability knowledge. Quantitative research method was adopted in the study and quasi-experimental design was used. The study group consisted of 44…

Reflective thinking, problem solving and probabilistic thinking are important processes in mathematics education and considered to what extent those processes can be carried out by elementary school students is essential. The study is conducted with 188 eighth grade students. As a result, no significant difference is observed in reflective…

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…

Evolutionary theory explains a wide range of biological phenomena. Proper understanding of evolutionary mechanisms such as natural selection is therefore an essential goal for biology education. Unfortunately, natural selection has time and again proven difficult to teach and learn, and students' resulting understanding is often characterized by…

Knowledge of probability is perceived as valuable in the 21st century. This knowledge enables people to understand and make informed decisions relating to uncertain events that occur in real life. Hence, many educational authorities have considered the inclusion of the teaching of probability important in their school curricula. This study…

Immediacy is one of the necessary criteria to show strong evidence of treatment effect in single case experimental designs (SCEDs). With the exception of Natesan and Hedges (2017) no inferential statistical tool has been used to demonstrate or quantify it until now. We investigate and quantify immediacy by treating the change-points between the…

A number of studies report that frequency is a poor predictor of acceptability, in particular at the lower end of the frequency spectrum. Because acceptability judgments provide a substantial part of the empirical foundation of dominant linguistic traditions, understanding how acceptability relates to frequency, one of the most robust predictors…