This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

Research on number sense presents contradictory arguments and results regarding the effects of context-based tasks and activities on students' number sense. The aim of this study was to examine fourth-grade elementary school students' number sense as they solve context-based (CB) and non-context-based (NCB) items. A survey design was employed and…

This paper provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how…

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high…

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…

Being able to effectively interpret students' thinking and respond effectively in the moment are important skills that preservice teachers (PSTs) need to learn. This study zooms in on 14 PSTs' planning, teaching, and reflections involved in number string lessons, and investigates to what extent PSTs anticipate their students' strategies and…

"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…

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…

This paper analyses the strategies used by pre-service primary school teachers for solving simple addition problems involving negative numbers. The findings reveal six different strategies that depend on the difficulty of the problem and, in particular, on the unknown quantity. We note that students use negative numbers in those problems they find…

The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…

Although students' invented strategies typically prove to be effective in the improvement of students' mathematical understanding, little is known about how preservice teachers interpret and respond to student-invented strategies on whole number multiplication. This study investigated the nature of 25 preservice teachers' interpretations of and…

Number and operations serve as the "cornerstone" of the K-12 mathematics curriculum in many countries. Solving problems in the mathematical domains of algebra, geometry, measurement, and statistics is often closely connected to student knowledge of number and operation (Griffin, 2005). Although considerable knowledge exists regarding the…

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use…

Explores students' abilities in mental computation, finds out the strategies they use most naturally, and develops a theoretical framework by giving 60 children a questionnaire and interviewing them on a series of arithmetic operations to be solved by mental computation. Generates a classification of children's strategies. Contains 31 references.…

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…