This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

The purpose of this paper is twofold: On the one hand, this work frames a variety of considerations on cognitive processes underlying mathematical concept construction in two research strands, namely an actions-first strand and an objects-first strand, that mainly shapes past and current approaches on abstraction in learning mathematics. This…

Many adolescent learners have difficulty understanding the relevance of mathematics for their lives. This problem is particularly pernicious among Black and Latino adolescents who often face cultural stigma that can affect their perceived value of mathematics. The present study used concurrent nested mixed methods to explore this issue in 419…

Student explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 4th-grade students at-risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of students'…

This paper is an attempt to reconstruct how C.V. Raman, a peripheral scientist in the early 20th century colonial India, managed to develop a research programme in physical optics from his remote colonial location. His attempts at self-training and self-education eventually led him to the discovery of the Raman Effect and to the Nobel Prize in…

Conventions play an important communicative role in mathematics. Likely due to the complex relationship between conventions and school mathematics, few education researchers have questioned or investigated the consequences of instruction and curricula that primarily, if not unquestionably, maintain conventions. Drawing on Piagetian notions of…

Background: A fundamental aim of standardized educational assessment is to achieve reliable discrimination between students differing in the knowledge, skills and abilities assessed. However, questions of the purity with which these tests index students' genuine abilities have arisen. Specifically, literacy and numeracy assessments may also engage…

Understanding complex systems requires reasoning about causal relationships that behave or appear to behave probabilistically. Features such as distributed agency, large spatial scales, and time delays obscure co-variation relationships and complex interactions can result in non-deterministic relationships between causes and effects that are best…

"The Most Reasonable Answer" is an innovative and comprehensive guide to engaging students in inquiry dialogue--a type of talk used in text-based classroom discussions. During inquiry dialogue, students collectively search for the most reasonable answers to big, controversial questions, and, as a result, enhance their argumentation…

In our work in environmental education (EE) as part of formal schooling we partnered with local schools to explore the practice of embedding, or integrating EE within formal school curriculum using inquiry-based pedagogies. In this paper we report on and discuss our growing understanding of the practice of pedagogical documentation and the…

Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with…

"Making" represents an increasingly popular label for describing a form of engineering design. While making is growing in popularity, there are still open questions about the strategies that students are using in these activities. Assessing and improving learning in making/ engineering design contexts require that we have a better…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

This year marks the 25th anniversary of the publication of a "National Statement on Mathematics for Australian Schools", which was the first curriculum statement this country had including "Chance and Data" as a significant component. It is hence an opportune time to survey the history of the related statistics education…