Educators often argue that mathematics should be taught so that the students in the course are actually "doing mathematics." Is there a consensus among mathematicians and mathematics educators as to the meaning of "doing mathematics?" In an effort to answer this question, we administered a survey to hundreds of university-level…

What if Stephen Douglas instead of Abraham Lincoln had won the U.S. presidential election of 1860? What if John F. Kennedy had not carried some of the eight states he won by 2 percentage points or fewer in 1960? What if six hundred more people in Florida had voted for Al Gore in 2000? And what if, in that same year, the U.S. House of…

This article describes Realistic Mathematics Education (RME), a design theory for mathematics education proposed by Hans Freudenthal and developed over 40 years of developmental research at the Freudenthal Institute for Science and Mathematics Education in the Netherlands. Activities from a unit to develop student understanding of logarithms are…

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions…

This article describes a set of learning activities that use algebraic problems and written student work to help preservice and in-service teachers understand students' algebraic thinking. (Contains 4 figures.)

The first volume of the 31st annual proceedings of the International Group for the Psychology of Mathematics Education conference presents plenary lectures; research forums; discussion groups; working sessions; short oral communications; and posters from the meeting. Plenary lecture papers include: (1) On Humanistic Mathematics Education: A…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…