The mechanisms of dissemination of the counting frames in the teaching of mathematics in Spain during the nineteenth century are studied. José Mariano Vallejo and Pablo Montesino proposed them in order to facilitate an arithmetic initiation based on intuition, following Pestalozzi's proposals. The diffusion channels considered were pedagogical…

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

Drawing on the work of Gattegno, it is suggested that a powerful way of teaching mathematics is to introduce symbols as relationships between visible or tangible resources. The symbols are abstract (formal) from the beginning and yet there are concrete resources to support their use. Drawing on data from a research project in primary schools in…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

In an attempt to further understand connections between children's proficiency and development with single- and multidigit addition, this study investigated the conceptualizations and solution strategies of 26 first-graders presented with several single-digit, multiple addend addition problems. The changes in students' solution strategies over the…

The authors' goal was to evaluate the potential of Math Recovery (MR), a pullout, one-to-one tutoring program that has been designed to increase mathematics achievement among low-performing first graders, thereby closing the school-entry achievement gap and enabling participants to achieve at the level of their higher-performing peers in the…

Past research has documented that the effectiveness of three different math strategies delivered to students via one-on-one instruction (i.e., cover-copy-compare (CCC); e.g., Skinner, Turco, Beatty, & Rasavage, 1989, traditional drill and practice (TDP); e.g., Cybriwsky & Schuster, 1990, and constant time delay (CTD); Kulik, 1994). This study…

Analyzing student work can help teachers improve the teaching and learning of mathematics. Fortunately, the four authors have experienced professional development that supports teachers' professional growth and provides tools to begin the challenge of analyzing student work. However, as they began to assume leadership roles in their schools and…

Technology and mathematics. manipulatives have been brought together in a new format. This joining has resulted in virtual manipulatives that are available on the Internet for students. Virtual manipulatives have been defined as computer based renditions of common mathematics manipulatives and tools. Just as a physical object can be flipped,…

With the introduction of arithmetic as a compulsory part of the elementary school curriculum in late eighteenth- and early nineteenth-century Germany, textbooks and pedagogical methods were wanted. Relying on the traditions of the Rechenbucher and informed by the demand for method found in Wolffian style advanced textbooks, the first generation of…

Much research has pointed to the importance of pretend play as a facilitator of literacy development. However, few studies have investigated the corresponding role of sociodramatic play in mathematical development. This exploratory naturalistic study examined the numerate behaviors that occurred during spontaneous pretend play in a preschool…

This article offers multiplication fact memorization training techniques that have been successfully used with students with learning disabilities in resource room and clinical settings. Techniques include organizing the facts, using finger multiplication, visual mnemonic flashcards, and musical reinforcement. (DB)

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)

The development of the place value system and its universal use demonstrate the elegance and efficiency of mathematics. This paper examines the concept of place value by: (1) presenting the historical development of the concept of place value in the Hindu-Arabic system; (2) considering the evolution of the number zero and its role in place value;…

The article looks at primitive counting techniques and suggests a systematic set of diagnostic activities for teaching young learning disabled children to count. (SBH)