Correct counting respects the stable order principle whereby the count terms are recited in a fixed order every time. The 4 experiments reported here tested whether precounting infants recognize and prefer correct stable-ordered counting. The authors introduced a novel preference paradigm in which infants could freely press two buttons to activate…

Previous research on students' difficulties in learning chemical equilibrium has shown that students hold misconceptions about this topic, and this often results in unintended learning. However, recent developments in human learning from the behavioural sciences perspective indicate that students' difficulties in learning are much more than…

Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under…

Tractors are used to perform jobs that require different types of agricultural tools to be attached to their rear, to their front, or both. These tools may need to be dragged, towed, or suspended above ground, and sometimes require a power supply; this is usually obtained via a hydraulic system or from the tractor's power take-off system. When…

The purpose of this study was to explore the variations in students' achievement on computational fluency assessments and variations in strategies for solving computation problems. Computational fluency was defined as a student's ability to compute flexibly, accurately, efficiently, and appropriately. Seven- and eight-year-old students completed…

This paper utilizes concept mapping as a tool for conscious and deliberate knowledge building in mathematics and its extension to algorithms. Currently, alleged defects in mathematics education are obvious: instead of conceptual elaboration, everyday praxis relies on routine computations that are likely to lead into alienated concepts with weak…

The aim of this simulation study, determine the relationship between true latent scores and estimated latent scores by including various control variables and different statistical models. The study also aimed to compare the statistical models and determine the effects of different distribution types, response formats and sample sizes on latent…

Contextualization is a method used for mathematics curriculum design within lesson plans and as a pedagogical practice in face-to-face classes. Many researchers are studying the effects of using contextualization in the teaching and the learning process for mathematics (Bottge & Cho, 2013; Perin, 2011; Young, Hodge, Edwards, & Leising,…

Recent policies and initiatives emphasized the importance of helping all students acquire Computer Science (CS) knowledge and develop Computational Thinking (CT). This study investigated the impact of a school-university partnership model on school students' CT development in the context of an after-school program. This study also examined the…

Measuring computational fluency, an aspect of procedural fluency, is complex. Many attempts to measure this construct have emphasised accuracy and efficiency at the expense of flexibility and appropriate strategy choice. Efforts to account for these latter constructs through assessing children's computational reasoning using structured interviews…

In the lead article, Davenport, Davison, Liou, & Love demonstrate the relationship among homogeneity, internal consistency, and coefficient alpha, and also distinguish among them. These distinctions are important because too often coefficient alpha--a reliability coefficient--is interpreted as an index of homogeneity or internal consistency.…

The present article provides a synthesis of the conceptual and statistical issues involved in using multisite randomized trials to learn about and from a distribution of heterogeneous program impacts across individuals and/or program sites. Learning "about" such a distribution involves estimating its mean value, detecting and quantifying…

The objective of this work is to present a spreadsheet tool that illustrates an ideal case of dynamic matrix control (DMC) calculations. The ideal case presented in this work is a hypothetical single- input-single-output DMC control system for setpoint tracking, in the absence of disturbance and mismatch between the measured and predicted process…

Automatic short answer grading (ASAG) is the task of assessing short natural language responses to objective questions using computational methods. The active research in this field has increased enormously of late with over 80 papers fitting a definition of ASAG. However, the past efforts have generally been ad-hoc and non-comparable until…

Recent work has demonstrated that how we process the relative order--ordinality--of numbers may be key to understanding how we represent numbers symbolically, and has proven to be a robust predictor of more sophisticated math skills in both children and adults. However, it remains unclear whether numerical ordinality is primarily a by-product of…