This is the first in a series of two papers whose goal is to contribute to the debate on a pair of questions: (1) What is the mathematics that we should teach in school? (2) How should we teach it? This paper addresses the first question, and the second paper, to appear in the next issue of ZDM, addresses the second question. The two questions are addressed from a particular theoretical framewo...

This paper examines the impact of a series of design changes to an online mathematics education course in terms of transactional distance between learner and teachers, pre-service education students’ attitudes towards mathematics, and their development of mathematical pedagogical knowledge. Transactional distance theory (TDT) was utilised to investigate and describe the interactions among cours...

aim and background: it has been shown in several studies that, students with mathematics learning disabilities have memory problems. this research compares memory profile of students with and without mathematics learning disabilities. methods and materials: the design of research was cross-sectional with causal-comparative method. the statistical population were 3 rd grade student boys in isfah...

Lakatos (1976) argued that mathematics develops in a much more organic way than its rigid textbook presentation of definition-theorem-proof would suggest. He outlined a heuristic approach which holds that mathematics progresses by a series of primitive conjectures, proofs, counterexamples, proof-generated concepts, modified conjectures and modified proofs. The purpose of this chapter is to appl...

In this final set of notes, we would like to end where we began. In the first set of notes, we mentioned that mathematics could be used to show how CDs and MP3s can reproduce our music well, even though the file sizes of MP3s are relatively small. In this set of notes, we attempt to describe how this is possible. Surprisingly, the exponential function will play a key role. We assume familiarity...

A to the National Museum of American History, “Inspired by the allure of the space age, many Americans of the 1960s took great interest in mathematics and science.” Included among these was Crockett Johnson, a wellknown cartoonist, book illustrator, and children’s author best remembered for his Harold and the Purple Crayon series. From 1965 until his death in 1975, Johnson painted what he descr...

    Nature is characterized by its chaotic behavior. Mathematics is considered one of the appropriate tools to achieve the best definition of possible its chaos variables and process. Classical mathematics deals with the numbers as static and meaningless, but chaos mathematics deals with it as dynamic evolutionary, and value- added. This paper attempts to introduce the transportation problem re...