In an ethnomathematics-based program there exists the need for teachers to identify pedagogical actions in the form of teaching-learning practices. In this theoretical paper we outline a curriculum proposal based on D'Ambrosio's "Trivium," composed of "literacy," "matheracy," and "technoracy." The Trivium…

Mathematics is a fundamental part of human knowledge and one of the central planks of the modern technological revolution. But in our enthusiasm to promote its benefits too rarely do we stop to question our intended aims of teaching mathematics and the outcomes of learning mathematics in school. In this paper the standard aims of school…

We analyse students' answers to a set of tasks designed to gain information about their ability to reason proportionally. These tasks have been particularly designed to control for false positive, i.e. that students arrive at the correct answer for the wrong reasons, an effect we actually observe with respect to students' ability to reason…

In an environment of rapid and unpredictable change determined and directed by technologies that are constantly changing, the assumption that being technologically literate is the key to being a sustained, contributing life-long learner is well founded. However, technological literacy is seldom referred to or considered in academic arguments as a…

Human culture relies on extensive use of social transmission, which must be integrated with independently acquired (i.e. asocial) information for effective decision-making. Formal evolutionary theory predicts that natural selection should favor adaptive learning strategies, including a bias to copy when uncertain, and a bias to disproportionately…

A cognitive schema is a mechanism which allows an individual to organize her/his experiences in such a way that a new similar experience can easily be recognised and dealt with successfully. Well-structured schemas provide for the knowledge base for subsequent mathematical activities. A new experience can be assimilated into a previously existing…

A student realizes that a point particle that is able to rise at a given point P[subscript 0] at height H when launched vertically from the origin O of a Cartesian plane at a fixed initial speed V[subscript 0] cannot reach, by means of a direct shot from a small spring cannon, a point P positioned at the same height H and distance d from…

Background: Problem posing, the generation of questions by learners, has been shown to be an effective instructional strategy for teaching-learning of complex materials in domains such as mathematics. In this paper, we demonstrate the potential of problem posing in two dimensions. Firstly, we present how problem posing can result in unfolding of…

Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to mathematical concepts and enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements…

This study begins with the belief that the ways in which teachers see and attend to educational encounters matter for their actions in classrooms. Using microethnography as a framework, this dissertation explores the relationship between teacher candidate attention, problem formulation, and action. Through analysis of the M.Ed. inquiry reports of…

Many problems related to synthesis with intelligent tutoring may be phrased as program synthesis problems using AI-style search and formal reasoning techniques. The _x000C_first two results in this dissertation focus on problem synthesis as an aspect of intelligent tutoring systems applied to STEM-based education frameworks, specifically high…

The absence of unified and inclusive special education service delivery models represents a longstanding challenge to the education of students with the full range of disabilities in inclusive schools and classrooms. An exemplar model is offered for elementary schools within a multi-tiered system of support (MTSS) framework. To establish its…

Mathematical problem solving is one of the most valuable aspects of mathematics education and the most difficult for elementary school students. Cognitive and metacognitive difficulties in this area cause students to develop negative attitudes and emotions as affective reactions, hampering their efforts and achievements. These metacognitive and…

Based on L. S. Vygotsky's sociocultural theory, previous scaffolding studies have examined some factors associated with adjustment of parental support during collaborative problem solving. However, a factor that remains unexplored in the literature is the potential relationship between parental empathy and parental support in collaborative problem…

How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set (e.g., translations and dilations). However, invariance over…