All primary school children in England are required to write computer programs and learn about computational thinking. There are moves in other countries to this effect such as the U.S. K-12 Computer Science Framework (CSF) for development. Debates on how to program and what constitutes computational thinking are ongoing. Here we report on a study…

Computational Thinking has been described as an essential skill which everyone should learn and can therefore include in their skill set. Seymour Papert (Papert, 1980) is credited as concretising Computational Thinking in 1980 but Jeanette Wing (Wing, 2006) popularised the term in 2006 and brought it to the international community's attention.…

While much research has focused on understanding the process by which young children learn to count, little work has explored the effects of direct instruction on this process. In the current study, we explored the impacts of training children in an explicit counting procedure on two distinct cardinality tasks. Two- to 5-year-old children first…

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

Wollack, Cohen, and Eckerly suggested the "erasure detection index" (EDI) to detect fraudulent erasures for individual examinees. Wollack and Eckerly extended the EDI to detect fraudulent erasures at the group level. The EDI at the group level was found to be slightly conservative. This article suggests two modifications of the EDI for…

This study aims to design a mechanism with which the density of any solid or liquid can be determined without measuring its mass and volume in order to help students comprehend the concept of density more easily. The "solidensimeter" comprises of two scaled and nested glass containers (graduated cylinder or beaker) and sufficient water.…

We present a theoretical approach to the problem of the transition from Calculus to Analysis within the undergraduate mathematics curriculum. First, we formulate this problem using the anthropological theory of the didactic, in particular the notion of praxeology, along with a possible solution related to Klein's "Plan B": here,…

The purpose of the present study is to examine content knowledge (CK) and pedagogical content knowledge (PCK) of Greek teachers in number sense and specifically in mental calculations with rational numbers (fractions, decimals and percentages). Examined within the framework of CK were the type of strategies employed by teachers and the extent of…

Data from student learning provide learning curves that, ideally, demonstrate improvement in student performance over time. Existing data mining methods can leverage these data to characterize and improve the domain models that support a learning environment, and these methods have been validated both with already-collected data, and in…

Recent research indicates that using multimodal learning experiences can be effective in teaching mathematics. Using a social semiotic lens within a participationist framework, this paper reports on a professional learning collaboration with a primary school teacher designed to explore the use of metaphors and modalities in mathematics…

Cardinal number acquisition plays an important role in children?s sense of number. Various investigations have revealed the influence of cultural variables on cardinal number acquisition. In this research, we investigated Turkish children?s acquisition of cardinal numbers. Quantitative research method was used. The participants were 100 preschool…

Educational robotics are increasingly appearing in educational settings, being considered a useful supporting tool for the development of cognitive skills, including Computational Thinking (CT), for students of all ages. Meanwhile, there is an overwhelming argument that CT will be a fundamental skill needed for all individuals by the middle of the…

How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…

The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal…

North Korea's development of nuclear weapons and, more recently, intercontinental ballistic missiles (ICBMs) has added a grave threat to world order. The threat presented by these weapons depends critically on missile range, i.e., the ability to reach North America or Europe while carrying a nuclear warhead. Using the limited information available…