We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of…

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

Two lessons introducing probability taught by an expert and a nonexpert sixth-grade teacher were analyzed for the quality of teaching. The expert teacher more consistently explicated the relationship between formal symbols and the given mathematical tasks. Other differences concerned the handling of student contributions. (40 references) (MKR)

Observations and interviews with (n=16) undergraduate mathematics and mathematics education majors learning to do formal mathematical proofs found three major sources of students' difficulties: concept understanding, mathematical language and notation, and getting started on a proof. (25 references) (MKR)

Describes observations, written samples, and interviews of (n=24) high school teachers learning concepts of group, subgroup, coset, normality, and quotient group in an Abstract Algebra course. General observations are made about the role of errors and misconceptions in light of an action-process-schema framework. (32 references) (MKR)

Describes the development, refinement, and validation of a framework for nurturing and assessing multidigit number sense in young children. Major constructs incorporated were counting, partitioning, grouping, and number relationships. The framework was validated through case studies of six first-grade children. (30 references) (MKR)

Asserts that college students lack understanding of the concept of function. Based on an epistemological theory, offers an instructional treatment using computers that presents a process concept of function and results in substantial improvements in student understanding for many students. (29 references) (MDH)