Babies and infants love mathematics. Give babies a set of blocks, and they will build and order them, fascinated by the ways the edges line up. Children will look up at the sky and be delighted by the V formations in which birds fly. Count a set of objects with a young child and then move the objects and count them again, and they will be…

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…

Accurate monitoring and control are essential for effective self-regulated learning. These metacognitive abilities may be particularly important for developing math skills, such as when children are deciding whether a math task is difficult or whether they made a mistake on a particular item. The present experiments investigate children's ability…

Research Findings: Teachers and parents often use trade books to introduce or reinforce mathematics concepts. To date, an analysis of the early numeracy content of trade books has not been conducted. Consequently, this study evaluated the properties of numbers and counting within trade books. We coded 160 trade books targeted at establishing early…

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…

Mathematics teachers are frequently looking for real-life applications and meaningful integration of mathematics and other content areas. Many genuinely seek to reach out to students and help them make connections between the often abstract topics taught in school. In this article the author presents ideas on integrating literature and mathematics…

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…

Studies have shown that numerosity-based arithmetic training can promote arithmetic learning in typically developing children as well as children with developmental dyscalculia (DD), but the cognitive mechanism underlying this training effect remains unclear. The main aim of the current study was to examine the role of visual form perception in…

In this article we report on a study of children's attention to numerical content in picture books. Specific research questions are 1) how the content in a designed picture book directs children's attention to numbers, and 2) what kind of numerical reasoning the book reading entails. To answer these questions, we conducted an educational design…

This research investigated students' sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit…

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…

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs' level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex,…