Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating…

This article describes a unique supplementary program that teaches early childhood mathematics (Pre-K to Grade 2), through a series of six problem-solving adventure stories. The mathematics concepts are taught to the children through the medium of oral storytelling sagas in an integrated approach that addresses language arts as well as early…

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…

This article reports work to assist learners in acquiring insights into certain grammatical and lexical areas of English by drawing on their awareness of fairly elementary mathematical concepts--and shows how often English structures can behave in ways parallel to numbers. For learners with an appropriate background and learning style, it is…

Offering mathematics majors the opportunity to engage in current, real-world applications can be an important enhancement to their undergraduate course curriculum. Instead of focusing on the traditional topic areas in pure and/or applied mathematics, one may structure a seminar course for senior mathematics majors by concentrating on a specific…

This paper reflects on the use of didactic material in mathematics classes. It focuses on the mathematical activities of students and the didactical activities of teachers. Its point of departure is a critique of technical-managerial approaches to teaching, learning, and innovation. Based on this critique, fundamental tensions between the…

The focus is on the metacognitive awareness of ten high-achieving high school pupils in mathematics in Denmark and England and their understanding of their cognitive learning processes and strategies. Mainly unstructured focus group interviews investigate how they explain that they learn a mathematical concept that is new to them. I develop the…

Development in the ability of 11-year-olds to solve numerical problems of addition, multiplication, and proportion was analysed by means of three Rasch models of change. The students, who had participated in a New Zealand numeracy project in 2002, comprised two groups that differed in socio-economic status: 1,274 students came from low…

The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical…

This paper reports the results of a study of primary school mathematics teaching in northern Botswana in order to highlight the strategies teachers use in bi/multilingual classrooms. Questionnaire and interview data collection procedures were used. The findings, which are based on responses of randomly selected primary school teachers, confirmed…

Evaluating the statistical process is considered a higher order skill and has received little emphasis in instruction. This study analyses thirty 15-year-old students' responses to two statistics assessment tasks, which required evaluation of a statistical investigation. The SOLO taxonomy is used as a framework to develop a hierarchy of responses.…

Discussions of quantitative literacy have become increasingly important, and statistics educators are well aware of the link between statistics education and quantitative literacy. Both the statistics education and quantitative literacy movements have emphasized the importance of students practicing skills in multiple contexts--a goal also…

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its…

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level…

Mathematics majors' study of abstract algebra should provide these students with opportunities to connect what they are learning to their prior experiences with algebra in high school. This paper illustrates how such connections can be used to motivate the notion of binary operation and the axioms for a group.