Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

This paper discusses the results of a three-year mixed methods study into the effectiveness of a mathematics education unit. This was written for both pre-service primary education students and re-training in-service teachers, to prepare them for the teaching of pre-algebra and early algebra. The unit was taught rom 2013 to 2015 inclusively in a…

Many developmental mathematics programs emphasize computational fluency with the assumption that this is a necessary contributor to student success in general studies mathematics. In an effort to determine which skills are most essential, scores on a computational fluency test were correlated with student success in general studies mathematics at…

Although teachers' professional knowledge and instructional beliefs are known to have a variety of subcomponents, research on the structure and interrelations of these subcomponents is relatively scarce. This article presents some findings of a preliminary, quantitative empirical study examining the relationships between mathematics teachers'…

This study aimed to present part of a mathematics programme for preschool age, to examine its efficiency in improving children's mathematical abilities in the area of number, and to investigate its suitability for Saudi practice. Pre- and post-tests, using TEMA-2 for one experimental and two control groups were conducted and quantitatively…

This study concerns pupils' experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils' understanding of operations such as "b/c of a" in lessons where the teachers were aware of some pupils' difficulties beforehand and what needed special attention.…

This paper considers the responses of 26 teachers to items exploring their pedagogical content knowledge (PCK) about the concept of average. The items explored teachers' knowledge of average, their planning of a unit on average, and their understanding of students as learners in devising remediation for two student responses to a problem. Results…

This article reviews the nature of learning difficulties in mathematics and, in particular, the nature and prevalence of dyscalculia, a condition that affects the acquisition of arithmetical skills. The evidence reviewed suggests that younger children (under the age of 10) often display a combination of problems, including minor physical…

The ability and to make good estimates is essential, as is the ability to assess the reasonableness of estimates. These abilities are becoming increasingly important as digital technologies transform the ways in which people work. To estimate is to provide an approximation to a problem that is mathematical in nature, and the ability to estimate is…

This study examined US undergraduate students' intent to study abroad upon college entry and their actual participation in study abroad during their undergraduate years, correlating the college outcomes of three cohorts to identify trends. The findings show that study abroad intent and participation are interrelated and shaped by an array of…

Although elementary number theory topics are closely linked to foundational topics in number and operations and are prevalent in elementary and middle grades mathematics curricula, little is currently known about how students and teachers make sense of them. This study investigated pre-service elementary teachers' developing understanding of…

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

Proportional reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop proportional reasoning naturally. Research suggests that many students do not apply proportional methods appropriately and that they often erroneously…

This paper reports on one phase of a long-term project investigating mathematical content knowledge of pre-service teachers. A cohort of second year PSTs conducted a diagnostic assessment and a series of associated tutoring sessions with a primary aged child. The focus here is on the PSTs' ability to make appropriate task choices following the…

This article reports on the mathematical competency of students entering third-level education in the University of Limerick (UL). Data from diagnostic testing, gathered on 5,949 students between the years 1998 and 2008, are used to demonstrate the changes in competency levels of students entering UL. There has been a significant decline in the…