A glyph--short for hieroglyphic--is a form of picture writing that conveys information. This book uses 10 glyphs to teach math concepts that are linked to the new NCTM Standards. There are four key parts to each glyph: (1) a legend (or survey questions); (2) directions for the teacher that tell students what to draw, color, or write based on…

We compare the activity of young children using a microworld and a JavaScript relational calculator with the literature on children using traditional calculators. We describe how the children constructed different meanings for the equal sign in each setting. It appears that the nature of the meaning constructed is highly dependent on specificities…

The broad goal of this report is to describe a form of knowing and a way of participating in mathematics learning that contribute to and further alternative views of transfer of learning. We selected an episode with an undergraduate student engaged in a number of different tasks involving a physical tool called "water wheel". The embodied…

This study reports the cognitive processing of a Year 8 female student (Kerri) during a test, and during her subsequent homework as she consolidated as part of abstracting; a topic of recent research interest. This case adds to the body of knowledge about how constructing and consolidating can occur simultaneously. The analysis captured the…

This paper adds to the research studies on prospective elementary school teachers' mathematics knowledge with findings on proportional reasoning. In addition to analyzing prospective elementary school teachers' solution strategies for solving a missing value proportion task, it also examines the nature of the drawings and writing they used to…

In this paper we report on a case study of a university student (third year of Mathematics course). She was engaged in proving a statement of elementary number theory. We asked her to write the thoughts that accompanied her solving process. She was collaborative and her protocol is suitable to study the interrelation between affect and cognition.…

As part of a research project on students' understanding of variability in statistics, 272 students, (84 middle school and 188 secondary school, grades 6-12) were surveyed on a series of tasks involving repeated sampling. Students' reasoning on the tasks predominantly fell into three types: additive, proportional, or distributional, depending on…

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…