How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We…

The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in which it is presented in textbooks is surprisingly varied. In this paper, we analyze a number of…

The purpose of this dissertation was to study aspects of how post-secondary students understand combinatorial problems. Within this dissertation, I considered understanding through two different lenses: i) student connections to previous problems; and ii) common combinatorial distinctions such as ordered versus unordered and repetitive versus…

We consider the problem of off-policy policy selection in reinforcement learning: using historical data generated from running one policy to compare two or more policies. We show that approaches based on importance sampling can be "unfair"--they can select the worse of two policies more often than not. We give two examples where the…

This study aims to determine the relationship of junior high school students' spatial and mathematical logical intelligence based on understanding the concepts. Spatial intelligence indicators in this study are reviewed from students' abilities in using images as a tool for solving problems, connecting data with concepts that have been held, and…

Although there is wide rhetoric that programming should be learnt by all as an element of computational thinking (CT), in practice, it is mostly implemented narrowly as an end in itself consisting of routine practice and traditional testing of the ability to code. This paper discusses a way in which programming could be seen through a wider…

Identifying students at risk of failing a course has potential benefits, such as recommending the At-Risk students to various interventions that could improve pass rates. The challenges however, are firstly in measuring how effective these interventions are, i.e. measuring treatment effects, and secondly, to not only predict overall (average)…

Understanding fraction magnitudes is important for achievement and in daily life. However, adults' fraction reasoning sometimes appears to reflect whole number bias and other times reflects accurate reasoning. In the current experiments, we examined how contextual factors and individual differences in executive functioning (Experiment 1),…

The present study attempted to explore the relationship between computational estimation and problem solving in a sample of Year 6 children and adults (N=72). For this purpose, participants were presented with two tasks which asked them to estimate the computational result in eight arithmetic operations (Computational Estimation Task) as well as…

Background: Educational robotics (ER) is increasingly used in classrooms to implement activities aimed at fostering the development of students' computational thinking (CT) skills. Though previous works have proposed different models and frameworks to describe the underlying concepts of CT, very few have discussed how ER activities should be…

Driven by our technologically advanced workplaces and the surge in demand for proficiency in the computing disciplines, it is becoming imperative to provide computational thinking (CT) opportunities to all students. One approach for making computing accessible and relevant to learning and problem-solving in K-12 environments is to integrate it…

The central purpose of the present study is to assess the early numeracy skills of Chilean kindergarten students, taking into consideration the socioeconomic status (SES) of the schools they attend. A sample of 19 urban schools and 498 students were used for the study. "Research Findings": The data analysis showed statistical differences…

The aim of this study is to determine preschool, special education, elementary school teacher and mathematics teachers' views of finger-counting in mathematics teaching. The study was conducted with case study design. The sample of the study consisted of 34 teachers. Data were collected using an 8-item written form, and content analysis was…

Understanding fraction magnitudes is important for achievement and in daily life. However, adults' fraction reasoning sometimes appears to reflect whole number bias and other times reflects accurate reasoning. In the current experiments, we examined how contextual factors and individual differences in executive functioning (Experiment 1),…

This report is based on the discussion that emerged from a convening of a panel of 22 experts in artificial intelligence (AI) and in learning. It introduces three layers that can frame the meaning of AI for educators. First, AI can be seen as "computational intelligence" and capability can be brought to bear on educational challenges as…