This work aims to evaluate the relationship between early numerical competence in kindergarteners and their numerical representations as measured by the number line task (NLT). Thirty-four 5-year-old children participated in the study. Children's early performance on symbolic and non-symbolic numerical tasks was considered to determine which was a…

Too many students are entering post-secondary education lacking foundational mathematics skills that are critical to performance on placement examinations. As a result, students are forced to take remedial courses that are often non-credit bearing and hinder their progress toward graduation. Research suggests that a lack of number sense may…

Mathematics instruction in the United States has historically focused on procedures, facts, and algorithms. Because of that focus, mathematics instruction, in essence, becomes lessons in arithmetic and efficiency. While there are promising changes occurring in mathematics instruction, we still need to help both teachers and students develop a more…

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. Maintenance of mathematical skills is especially important as mathematics has applications in daily life and is directly related to important life…

One pronoun production experiment and one pronoun comprehension experiment were performed to investigate the role of grammatical number information in long-distance anaphora, with referent and pronoun either in adjacent sentences or separated by an intervening sentence. The experiments tested the assumption that the influence of grammatical number…

This paper reports on the development of a Learning Pathway for Number (LPN) with the aim of facilitating the teaching and learning of whole number in the early primary grades (Grades R-4) within the South African educational context. The development of the LPN was based on the Dutch Learning/Teaching Trajectory for Whole Number (Van den…

The gamma function, which has the property to interpolate the factorial whenever the argument is an integer, is a special case (the case "g"?=?2) of the general term of the sequence factorial of "g"-gonal numbers. In relation to this special case, a formula for calculating the general term of the sequence factorial of any…

Little is known about whether and how parents can foster their children's spontaneous focus on number, an unprompted measure of attention to small numbers of objects that predicts later math achievement. In the current study, we asked 54 preschool-aged children and their parents to play together in a children's museum exhibit using either a…

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…

The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

This study explores in-service high school mathematics teachers' conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One 90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on…

This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions--lines or pieces--based on number line models. Findings from three contrasting cases reveal differences in teachers' facilitating and direct guidance…

Crosscutting concepts such as "scale, proportion, and quantity" are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such…

Children demonstrate gaps in the math knowledge that they possess by the time they begin school, and these gaps have been found to predict long-term outcomes not only in math but also in reading. Consequently, it is important to identify what accounts for these early differences and how they can be addressed to ensure that all children enter…