In a collaborative project, two mathematics education professors, a third-grade teacher, and her students collected information from the students as they thought through how to ask, collect, and then answer their own data-driven questions. Findings indicated the students exhibited a growing understanding, sophistication, and comfort with the use…

Describes a long term teaching experiment carried out with students from grades 9 and 10. Aims at clarifying the role of the Cabri environment in teaching-learning processes. Analysis of protocols shows the possible evolution of a justification into a proof but at the same time indicates that this evolution is not expected to be simple and…

"Options". "Opinions". "Challenges". These are the key words used by a group of gifted 3rd- and 4th-grade students when asked what they want out of math. Although not surprised by the desire for challenges, most of the author's colleagues are intrigued by the students' wishes for options and opinions in math. After…

This paper has arisen as a result of teaching Models in Biology to undergraduates of Bioengineering at the Gediminas Technical University of Vilnius. The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous…

The argument examined in this paper is that music--when approached through making and responding to coherent musical structures, facilitated by multiple, intuitively accessible representations--can become a learning context in which basic mathematical ideas can be elicited and perceived as relevant and important. Students' inquiry into the bases…

Elementary education students enrolled in an experimental mathematics course participated in this study. The course is taught using a social constructivist approach and is designed to improve students' mathematical problem-solving ability and deepen their understanding of mathematics. The research question for the present study is as follows: In…

In this study we investigated relationships between convergent and divergent thinking with an emphasis on fluency, originality, flexibility and elaboration in the mathematical domain. A related purpose was to examine relationships between problem types in mathematical tasks. The math section of a performance-based assessment was used to assess 857…

As school curricula undergo changes in both content and pedagogy, pressure is placed on teacher preparation programs and undergraduate mathematics departments to model learning environments in mathematics appropriate for education students. Yet the reality of many post-secondary mathematics courses includes traditional style classes containing a…

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university.…

In this article we analyze the dialogic learning of one pair of students in order to investigate how these students cope with a collaborative learning situation in the classroom. Our aim is to substantiate the claims that not only are young students (8 year olds) capable of solving mathematical problems collaboratively, but that they also take an…

Developed by the ABCs of Construction National Workplace Literacy Project, these curriculum materials for the occupational area of pipefitting contain a lesson that deals with reading charts and graphs. The lesson consists of an objective, instruction, and seven exercises. Three types of problems are provided in each exercise: "try…

This paper examines a range of studies done on the "Geometric Supposer" software and its use since the mid-1980s. It describes how the "Geometric Supposer" is a response to the call for reform by the mathematics community to create classroom environments that allow students to construct their own knowledge. This approach to…

The third volume of this proceedings contains more of the research reports begun in Volume 2. Papers include: (1) "A Semiotic Model for Analyzing the Relationships between Thought, Language and Context in Mathematics Education" (Juan D. Godino and Angel M. Recio); (2) "Conceptions as Articulated in Different Microworlds Exploring…

This two-volume document provides the proceedings of a conference on the psychology of mathematics education. Plenary session themes were "Diversity and Equity," (with papers by Gilah Leder; Walter Secada; and Ubiratan D'Ambrosio), "Teacher Education," (with a paper by Thomas Cooney), and "Technology" (with papers by…

Examines an intervention study of 23 students in an elementary teacher education program to determine the effects of three nontraditional mathematics courses on the teacher candidates' conceptual understanding of mathematics and the learning of mathematics. Results indicate that the intervention produced significant changes in prospective…