The paper highlights early steps in the development of the school system and its progression with a focus on the Vologda governorate in 1725-1917. Speaking of the materials, this part reviews the works on the history of pedagogy published in the pre-revolutionary period, as well as modern Russian scholarly literature. Research problems were…

The sixth in a series of six guidebooks on minimum course content for second-year algebra, this booklet presents an introduction to sequences, series, permutation, combinations, and probability. Included are arithmetic and geometric progressions and problems solved by counting and factorials. Overall course goals are specified, a course outline is…

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

This chapter considers psychological and neuroscience research on how people understand the integers, and how educators can foster this understanding. The core proposal is that new, abstract mathematical concepts are built upon known, concrete mathematical concepts. For the integers, the relevant foundation is the natural numbers, which are…

We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical…

Background: The purpose of the current cross-sectional study was to examine the developmental progression in working memory (WM) between the ages of 9 and 16 years in a large sample of children with mild to borderline intellectual disabilities (MBID). Baddeley's influential WM model was used as a theoretical framework. Furthermore, the…

The relative contribution of students' capability to perceive structural versus surface similarity on their motivation transfer was studied. It was hypothesized that surface similarity would lead to greater transfer of self-efficacy among tasks due to its readily perceptible nature. More specifically, it was hypothesized that the perception of…

This study examined auditive and visual working memory and metacognitive knowledge in 92 gifted children (aged between eight and twelve), utilising a pre-test-training-post-test design, known as the cognitive training design. This approach was used to examine the working memory and metacognitive knowledge of gifted children concerning the…

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, as well as regular features presenting book and software reviews and math problems. The first of two issues of volume 14…

It is important for students to develop a relational understanding of the equal sign, but students often have simultaneous operational and relational conceptions (i.e., SOR conceptions). This case study carefully explored how a student's conception of the equal sign changed during a classroom teaching experiment and analyzed the possibilities and…

At an unrivaled and enduring pace, computing has transformed the world, resulting in demand for a universal fourth foundation beyond reading, writing, and arithmetic: computational thinking (CT). Despite increasingly widespread acceptance of CT as a crucial competency for all, transforming education systems accordingly has proven complex. The…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…