The advancement of technology has substantively changed the practices of numerous professions, including teaching. When an instructor first adopts a new technology, established classroom practices are perturbed. These perturbations can have positive and negative, large or small, and long- or short-term effects on instructors' abilities to teach…

We review research literature concerning "number sense" from several related fields. Whereas other authors have pointed to difficulty defining "number sense" or to some degree of inconsistency in the literature, we argue instead that this is a case of polysemy: There are 3 different constructs that go by the same name. In this…

This study examined the pedagogical content knowledge of pre-service preschool teachers on quantity concepts in terms of children's mistakes. A total of 94 pre-service teachers who were attending a teacher training program at a state university, in Turkey, participated this study. 52 of them were second-year, and 42 of them were third-year…

The teacher displayed counting cards that included both dots and numerals in order from one to five, as she counted them with her students. She then turned the cards facedown, keeping them in order, and began an identify-a-hidden-card activity with the class. This class was engaged in the third of three card activities that develop number sense…

Knowledge components (KCs) define the underlying skill model of intelligent educational software, and they are critical to understanding and improving the efficacy of learning technology. In this research, we show how learning curve analysis is used to fit a KC model--one that was created after use of the learning technology--which can then be…

Reasoning about bedrock abstract concepts such as time, number, and valence relies on spatial metaphor and often on multiple spatial metaphors for a single concept. Previous research has documented, for instance, both future-in-front and future-to-right metaphors for time in English speakers. It is often assumed that these metaphors, which appear…

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…

This study reports findings of a systematic replication and as such sought to evaluate effects of an early numeracy curriculum on early number sense attainment for Kindergarten students with autism. Through daily 15-min story-based math lessons with embedded systematic instruction delivered by their classroom teacher, participants learned to…

Math fact fluency involves the quick, accurate retrieval of basic arithmetic combinations and the ability to use this fact knowledge efficiently. Math fact retrieval is typically considered fluent when performed accurately within 2 to 3 seconds, and "efficiency" refers to students' ability to apply fact knowledge to more complex…

Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners' developmental trajectories. Given…

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All…

This article provides a classroom resource for identifying, assessing and promoting one aspect of reasoning--analysing--through the Assessing Mathematical Reasoning Rubric. Practical examples of student work and rubric levels are offered.

The study evaluates the linear number board game "100 House." Taking into account Krajewski's (2003, 2013) development model of mathematical competencies, this game supports the development of mathematical competencies in 6-year-old children. The board game design is based on the American cognitive alignment framework approach and aims…

To understand the concepts or principles in mathematics, children who have a concrete operational stage need physical objects that can bridge abstract concepts in mathematics. This research aims to evaluate the influence of coastal contextual learning media on a child's understanding concept in the material of numbers counting operation. This…

In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…