In this article, the author takes up the special trinomial (1 + x + x[squared])[superscript n] and shows that the coefficients of its expansion are entries of a Pascal-like triangle. He also shows how to calculate these entries recursively and explicitly. This article could be used in the classroom for enrichment. (Contains 1 table.)

The study focused on the development of the concept of fractions in a group of 11- and 12-year-old students who were deaf or hard of hearing. The approach implemented in the study relied extensively on the use of games with very little formal instruction. It emphasized the development of appropriate language to facilitate an understanding of the…

Although some bright students in primary school are able to organise numerical data into classes, most attend to the characteristics of individuals rather than the group, and "see the trees rather than the forest". How can teachers in upper primary and early high school teach students to organise large sets of data with widely varying…

This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers.

Child-staff ratios are an important quality indicator. They are often collected by observing one randomly selected classroom several times during a 2-h period on a single day. However, it is unclear whether these measures represent the ratios that children actually experience during most of their time in care. This study compared ratio data…

It is over 25 years since Wood, Bruner and Ross (1976, "Journal of Child Psychology and Psychiatry," 17, 89-100) introduced the idea of "scaffolding" to represent the way children's learning can be supported. Despite problems, this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing…

This article describes surprising misconceptions revealed by a fifth-grade student during a series of interviews about probability.

When teachers learn to take time to understand how students are thinking about mathematics, they will be better able to develop students' mathematical understanding. Teachers must become investigators--of mathematics and of student thinking--in their own classrooms. When teachers explore mathematics, analyze student thinking, and write cases from…

The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…

A conceptually sound, research-based method is presented to make sense of students' thinking about length. It is suggested that the levels of framework is an important tool for improving instruction and formative assessment as well as effectively diagnosing and remediating students' difficulties in learning about length. Some of the measurement…

Laura Ingalls Wilder's purpose in writing the "Little House" books for children illustrate the day-to-day experiences of a girl, and her stories provide glimpses into a young mind's conceptualization of aspects of living that are mathematical in nature, such as geometric and quantitative conceptions, logical reasoning and communication, and…

The effects of feedback to assist elementary school students classified as either normally achieving (NA) or with a mathematics learning disability (MLD) in acquiring the fact series of 0 to 9 for the operations of addition, subtraction, multiplication, and division were examined in Study 1. The acquisition of each fact series was facilitated by…

This paper presents a goal-based scenario approach to teaching introductory database concepts to undergraduates using two different scaffolding methods. One method, termed "worked-out examples," attempts to reduce extraneous cognitive load by requiring students to complete increasingly complex missing parts of worked out examples. The other…

This article describes how the design of digital learning objects can spark professional learning. The challenge was to build learning objects that would help experienced special education teachers, who had been teaching in math classes, to demonstrate their proficiency in middle and secondary school mathematics on the PRAXIS examination. While…

This paper is an analysis of published research on computer-assisted instruction (CAI) for mathematics involving students with learning disabilities. A systematic search of the literature on computer-assisted instructional interventions for students with learning disabilities yielded 25 studies that met the criteria for inclusion in this analysis.…