In this article, the authors describe how their first-grade class used the book "Inch by Inch" (Lionni 1960)--the story of an inchworm that escapes from a hungry robin by proving he is useful for measuring--as inspiration for a lesson focused on exploring length measurement through examining the meaning of an inch. The authors designed a…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

How better to begin the study of linear equations in an algebra class than to determine what students already know about the subject? A seventh-grade algebra class in a suburban school undertook a project early in the school year that was completed before they began studying linear relations and functions. The project, which might have been…

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…

The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

Researchers of mathematics education have been paying attention to the affective aspect of learning mathematics for more than one decade. Different theoretical frameworks have been suggested to analyze this aspect, where we utilize in the present research the discursive framework of Evans, Morgan and Tsatsaroni. This framework enables to link…

In this study, it was aimed to analyze the structure of prospective middle school mathematics teachers' problems posed with regard to given symbolic representation including addition and subtraction operations with integers. The study conducted with 96 last grade elementary school mathematics teacher candidates studying in Faculty of Education of…

This study investigates representational code-switching (RCS) by considering three high school students' communications in the process of comparing and contrasting pairs of representations (e.g., equation and graph) in the context of rational functions. Supporting this study is research in the realms of students interacting with mathematical…

Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue…

This article offers a description of how empirical experiences through the use of procedural knowledge can serve as the stage for the development of hypothetical concepts using the learning cycle, an inquiry teaching and learning method with a long history in science education. The learning cycle brings a unique epistemology by way of using…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

Spatial abilities are used in many aspects of everyday life, thus developing these abilities should be one of the most important goal of Mathematics Education. These abilities should be developed starting with early school years, thus pre-school and primary school teachers have an important role in setting the foundation of these abilities. A…