Numeracy is a key competency for living in our modern knowledge society. Therefore, it is essential to support numerical learning from basic to more advanced competency levels. From educational psychology it is known that learning is most effective when the respective content is neither too easy nor too demanding in relation to learners'…

The article reviews the development of mathematics error analysis as a means of diagnosing students' cognitive reasoning. Errors specific to addition, subtraction, multiplication, and division are described, and suggestions for remediation are provided. (CL)

The purpose of this study was to describe and compare kindergarten and first-grade children's performance on addition and subtraction problems presented in two contexts: verbal (in which problem data were linked to physical referents such as objects or people and their actions), and abstract (in which no such links to physical situations…

Most of the research on mathematical and scientific thinking has been concerned with uncovering knowledge structures and reasoning processes in people of different levels of competence. How these structures and processes are acquired has only recently become a major concern. Thus, some of the major research on mathematical and scientific thinking…

Over a 10-month period, normal children showed an increased reliance on memory retrieval and a decreased reliance on counting when they solved addition problems. There was an increase in speed of counting and of retrieving addition facts from long-term memory. Children with a mathematical learning disability showed no change in problem-solving…