The metaphors that students form and encounter have been shown to exert a powerful influence on how they think about mathematics. In this paper, we explore the linguistic metaphors about learning and doing mathematics that were prevalent in 11 advanced mathematics lectures. We present four metaphor clusters that were common in the corpus that we…

Internal and external assessment instruments, such as the Vanuatu Standard Test of Achievements (VANSTA) and the Pacific Island Literacy and Numeracy Assessment (PILNA), reveal that mathematics achievements in the Republic of Vanuatu remain below the minimum standard. This study drew on the constructivist grounded theory approach to explore…

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

This study uses a new communicational lens that conceptualizes the activity of learning mathematics as interplay between mathematizing and identifying in order to study how the emotional, social, and cognitive aspects of learning mathematics interact with one another. The proposed framework is used to analyze the case of Idit, a girl who started…

A mathematician who has been teaching for 58 years discusses 3 types of knowledge that are subjects for teaching or learning (what, how, and why) and why teaching must include problem solving or the use of the Socratic, Moore, or discovery method. (MKR)

Describes computation of a continued radical to approximate the golden ratio and presents two well-known geometric interpretations of it. Uses guided-discovery to investigate different repeated radicals to see what values they approximate, the golden-rectangle interpretation of these continued radicals, and the golden-section interpretation. (KHR)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

Presents seven scenes showing everyday classroom situations that give students the options of applying their own problem-solving strategies to solve everyday problems of life and enable them to experience mathematical power coming from self-initiated insights into mathematical concepts. (MDH)

The author analyzes his 11-year-old daughter's investigation of patterns in multiplication. In an investigation initiated herself, Becca generates hypotheses, discovers patterns, asks questions, and discards procedures that do not produce desired results. Providing a classroom environment that values questioning is a key recommendation. (MLN)

THE OBJECTIVE OF THIS RESEARCH WAS TO EXTEND, ELABORATE, AND IMPROVE THE SET-FUNCTION LANGUAGE (SFL). THE SFL IS A NEW SCIENTIFIC LANGUAGE FOR FORMULATING RESEARCH QUESTIONS ON MEANINGFUL LEARNING, FRAMED IN TERMS OF THE MATHEMATICAL NOTIONS OF SETS AND FUNCTIONS. IN THE FIRST PAPER, THE SFL IS DESCRIBED. ITS RELATION TO THE STIMULUS RESPONSE…

This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In…