In the present paper I look at Edmond Halley's reconstruction of Book VIII of Apollonius's "Conic" as an example of a second-order historical text. Such texts constitute a particular class of original works whose distinction is that they present mathematicians of the past engaging with texts from their own past, as we do when…

Reading and math proficiency are assumed to be crucial for the development of other academic skills. Further, different studies found reading and math development to be related. We contribute to the literature by looking at the relationship between reading and math using continuous time models. In contrast to previous studies, this allows us to…

Coefficient alpha reliability persists as the most common reliability coefficient reported in research. The assumptions for its use are, however, not well-understood. The current paper challenges the commonly used expressions of coefficient alpha and argues that while these expressions are correct when estimating reliability for summed scores,…

Mathematical modelling is endorsed as both a means and an end to learning mathematics. Despite its utility and inclusion as a curricular objective, one of many questions remaining about learners' modelling regards how modelers choose relevant situational attributes and express mathematical relationships in terms of them. Research on quantitative…

The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

The literature on proof by contradiction (PBC) is nearly unanimous in claiming that this proof technique is "more difficult" for students than direct proof, and offers multiple hypotheses as to why this might be the case. To examine this claim and to evaluate some of the hypotheses, we analyzed student work on proof construction problems…

This descriptive research aimed to know students' problem-solving ability in arithmetic operations on algebra forms through an Indonesian realistic mathematics education, namely Pendidikan Matematika Realistik Indonesia (PMRI), approach in secondary school number 17 Palembang. The learning process, material, and assessment used were principles and…

This research project explores the interconnections between three constructs: joy, play, and learning. The research specifically focuses on children's ideas and experiences of joy, play, and learning at a public Montessori School in the United States of America and in the context of engaging with selected math games. The games used are…

The purpose of this investigation was to explore the effects of stereotype threat on women's construction of gender and mathematical identities, and to examine how these various cognitive negotiations may affect their mathematical reasoning on challenging definite integral applications. This was a qualitative study that primarily utilized the…

Singapore students have consistently demonstrated outstanding levels of performance in mathematics and problem solving captured in international assessments. However, these stellar results stand in contrast to Singapore's real-world problem-solving capacities, evidenced by her diffident innovation levels and a limited talent pool with…

For many years, multiple representations have played a major role in the teaching and learning of mathematics (NCTM, 2014). The present study defined and investigated a particular phenomenon called representational conflict, which can arise when students simultaneously use multiple representations on the same mathematical task. Representational…

An elementary method to calculate the area, centroid and volume of rotation of the Koch curve is presented. Classroom extensions are provided to allow students to investigate the method used.

Wireless sensor networks (WSN) are an ad hoc network consisting of miniaturized autonomous sensors that communicate with each other over a radio link. In this paper, the authors' contribution is a cross-layer approach. To achieve this approach, the authors proposed in the first part an improvement of LEACH algorithm named WEIGHTED_LEACH. This…

This article describes the background of Fibonacci and his numeral system and how he made arithmetic easier. It includes ways students can learn about Fibonacci sequences and the Fibonacci spiral.

In the third of a series, the author describes how symmetrical quintic functions can be expressed in three equivalent formats--like other symmetrical functions. Quadratic functions have a line of symmetry through their vertex and cubic functions have 1800 rotational symmetry around their point of inflection. However, polynomial functions of degree…