The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…

The equivalence between a statement and its contrapositive is so obvious for an expert that, usually, he does not need any explanation. In this paper, we shall examine the argumentations which students produce in order to justify a statement that, in their opinion, is equivalent to a given statement. We shall observe that the most common…

This paper provides a glimpse into the positive effect on student learning as a result of empowering a classroom teacher of 20 years (Andrea) with subject matter knowledge relevant to developing fraction understanding. Having a facility with fractions is essential for life skills in any society, whether metricated or non-metricated, and yet…

Researches in Mathematics Education about proof by contradiction revealed some difficulties of the students but also that this kind of argumentation comes spontaneously in certain situations. In this paper we shall show some processes that might lead the student to produce a proof by contradiction. In particular, we shall point out a deep link…

The primary purpose of the "2007 Mississippi Mathematics Framework" is to provide a basis for curriculum development for K-12 teachers. The framework provides an outline of what students should learn through competencies and objectives/benchmarks. Suggested teaching strategies and assessments for those strategies are correlated to the…

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

Exponential, and logarithmic functions are pivotal mathematical concepts that play central roles in advanced mathematics. Unfortunately, these are also concepts that give students serious difficulty. This report describe a theory of how students acquire an understanding of these functions by prescribing a set of mental constructions that a student…

This article summarizes research conducted in Gifted Algebra I and Gifted Precalculus classes in a public, suburban high school in spring 2002, which investigated the importance of reading and writing in understanding mathematical principles. The classroom teacher supplemented traditional numerical problem solving with vocabulary quizzes, reading…

The history of education is made up in part of accounts of various subjects which have developed into courses of study. Mathematics of some kind has always been included in such courses. In the American colonies, arithmetic was an important subject for practical reasons. It was needed for trade and commerce. Sailing vessels plying between Europe…

This paper analyzes common practice and the difficulties children encounter and outlines an entre to mathematics learning which may make the child's task easier. (Author)

Students tested on their ability to apply the ratio concept in a simple problem of measurement were retested two years later; one-third showed no change in category. The data were grouped in analogy to the three developmental stages of Piaget. Additional data from a group of eighth graders did not clarify further how students arrive at…

Suggests ways in which the newspaper can be used to teach reading and other language arts skills. Also gives suggestions for its use in other content areas. (VJ)