Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov's work is often cited as a source of impressive demonstration of young…

George Spencer-Brown's Laws of Forms was first published in 1969. In the fifty years since its publication, it has influenced mathematicians, scientists, philosophers, and sociologists. Its influence on mathematics education has been negligible. In this paper, I present a brief introduction to the theory and its philosophical underpinnings. And I…

This paper constructs an overview of the historical development of the International Journal for Technology in Mathematics Education (IJTME) during the period 2004- 2018. The titles of the published papers in this period are examined, focusing on what technological tools were studied, and what theoretical ideas were used to study the teaching and…

In this paper, we identify, from historical vantage points, the following six purposes of school algebra: (a) algebra as a body of knowledge essential to higher mathematical and scientific studies, (b) algebra as generalised arithmetic, (c) algebra as a prerequisite for entry to higher studies, (d) algebra as offering a language and set of…

There is a long-standing tradition in mathematics education to look to history to inform instruction. An historical analysis of the genesis of a mathematical idea offers insight into: (i) the contexts that give rise to a need for a mathematical construct; (ii) the ways in which available tools might shape the development of that mathematical idea;…

From the early nineties, most reformed curricula at upper secondary level choose to give functions a major position and a priority over rational expressions and equations of traditional algebra. The goal of this paper is to introduce key challenges resulting from this choice and to discuss the contribution that software environments associating…

Education researchers are increasingly working in practice-based partnerships in order to direct their research efforts toward important problems of practice. We argue for the creation of an infrastructure to support routine and sustained interaction among researchers, practitioners, and designers in order to make partnership efforts more…

This report provides information on Austin Independent School District's bilingual and English as a Second Language programs implemented in 2016-2017, summarizing the numbers of students served, and students' language acquisition and academic performance.

The integration of digital technology confronts teachers, educators and researchers with many questions. What is the potential of ICT for learning and teaching, and which factors are decisive in making it work in the mathematics classroom? To investigate these questions, six cases from leading studies in the field are described, and decisive…

In this paper I consider the problem of designing strategies for teacher education programs that may promote an aware style of teaching. Among the various elements to be considered I focus on the need to address prospective teachers' belief that they must reproduce the style of mathematics teaching seen in their school days. Towards this aim, I…

Block scheduling has grown rapidly in recent years. In North Carolina, 77 schools started block scheduling in 1995-96, bringing the total number of blocked schools in the state to 207. A previous evaluation compared 1995 End-of-Course (EOC) Test scores for block-scheduled (blocked) and nonblocked schools. This report presents results of the…

Virtually every public issue depends on data, projections, inferences, and systemic thinking. Besides basic mathematics skills, numeracy (quantitative literacy) encompasses estimating tolerances and errors, constructing complex computer simulations, using flowcharts, drawing inferences, and calculating in three dimensions. The narrow…

It is feasible for school districts to develop and use subject area tests as reliable as those previously available only from commercial publishers. Three projects in local item development in a large school district are described. The first involved only Algebra 1. The second involved life science and career education at the elementary level; and…

Results from North Carolina's End-of-Course Testing Program in 1989-90 are presented. Participation, student characteristics, and achievement are summarized, largely in table form, for the following subject areas: (1) Algebra I, (2) Geometry, (3) Algebra II, (4) Biology, (5) Chemistry, (6) Physics, (7) U.S. History, and (8) English I. Background…

This report describes participation, student characteristics, and achievement for 10 high school courses assessed by the North Carolina End-of-Course Testing Program in 1990-91. Subject areas are: (1) Algebra I; (2) Geometry; (3) Algebra II; (4) Economic, Legal, and Political Systems in Action (ELP); (5) U.S. History; (6) English I; (7) Physical…