This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities--especially the ones that involve Bayes' rule--with…

Thematic analysis is frequently used to analyse qualitative data in psychology, healthcare, social research and beyond. An important stage in planning a study is determining how large a sample size may be required, however current guidelines for thematic analysis are varied, ranging from around 2 to over 400 and it is unclear how to choose a value…

Two problems at two different abstraction levels of computational biology are studied. At the molecular level, efficient pattern matching algorithms in DNA sequences are presented. For gene order data, an efficient data structure is presented capable of storing all gene re-orderings in a systematic manner. A common characteristic of presented…

Within the past few years there has been an increasing emphasis on making computer science (CS) more accessible for all K-12 students. In 2013 there were 12 states that allowed CS courses to count towards high school graduation, and in 2018 that number had grown to 35 states plus the District of Columbia (Code.org, 2018). Due to the increasing…

The self-teaching hypothesis describes how children progress toward skilled sight-word reading. It proposes that children do this via phonological recoding with assistance from contextual cues, to identify the target pronunciation for a novel letter string, and in so doing create an opportunity to self-teach new orthographic knowledge. We present…

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions--"tolerance for ambiguity," "persistence," and "collaboration"--and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices…

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 third-grade students on a measure…

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…

This study compared five common multilevel software packages via Monte Carlo simulation: HLM 7, M"plus" 7.4, R (lme4 V1.1-12), Stata 14.1, and SAS 9.4 to determine how the programs differ in estimation accuracy and speed, as well as convergence, when modeling multiple randomly varying slopes of different magnitudes. Simulated data…

This article investigates the effect of kinesthetic educational game on students' mental computation speed. A Solomon four-group design was used to avoid the influence of pretest-posttest design. In order to determine which grade is appropriate for this game, a pilot study was conducted with 30 students. As for the main study, 123 students…

This paper explores Computational Thinking (CT) through the experiences and interactions of sixth-grade students as they were engaging in a science lesson utilizing robotics. This robotics unit institutes the shifting from traditional to engaging hands-on activities coupled with CT skills that are exciting, intriguing, and inviting to students.…

This comparative research study examined Grade Five Malaysian Aboriginal pupils' mathematical performance on 30 computation and 20 word problem items in the academic Malay language and community "Temiar" language. The items were constructed in the Malay language before adapting and audio recording into the "Temiar" language…

The aim of this study was to examine the effect of interdisciplinary activities organised online within the scope of an eTwinning project carried out with gifted students on the students' technology awareness and computational thinking (CT). However the research was not funded by eTwinning. The study was carried out through web-based tools for a…