**FEATURES** |

Explicating the Teacher's Perspective From the Researchers' Perspectives: Generating Accounts of Mathematics Teachers' Practice
*Martin A. Simon, Ron Tzur* In this article we articulate a methodology for studying mathematics teacher development in the context of reform. The generation of accounts of teachers' practice, an adaptation of the case study, provides an approach to understanding teachers' current practice and to viewing their current practice in the context of development toward envisioned reforms. The methodology is an alternative both to studies that focus on teachers' deficits and to teachers' own accounts of their practice. Conceptual frameworks developed within the mathematics education research community are applied to the task of investigating the nature of practice developed by teachers in transition. We characterize this methodology as explicating the teacher's perspective from the researchers' perspectives. |

Upper Elementary School Pupils' Difficulties in Modeling and Solving Nonstandard Additive Word Problems Involving Ordinal Numbers
*Lieven Verschaffel, Erik De Corte, Heidi Vierstraete* Our goal in this study was to collect in a systematic way empirical data about the scope and the nature of upper elementary school pupils' difficulties with modeling and solving nonroutine additive word problems. We focused only on problems in which straightforward addition or subtraction of the 2 given numbers yields either 1 more or 1 less than the correct answer. A paper-and-pencil test containing several of these nonroutine items was administered to a large group of 5th and 6th graders, who had great difficulties in solving these problems, with various shortcomings underlying these difficulties. Many errors resulted from the superficial, stereotyped approach of adding or subtracting the 2 given numbers without considering the appropriateness of that action in relation to the problem context. Other errors, however, seem to have different origins, such as misconceptions about numbers and arithmetic operations. |

Opportunities to Learn Fractions in Elementary Mathematics Classrooms
*Maryl Gearhart, Geoffrey B. Saxe, Michael Seltzer, Jonah Schlackman, Cynthia Carter Ching, Na'ilah Nasir, Randy Fall, Tom Bennet, Steven Rhine, Tine F. Sloan* In this study we addressed 2 questions: (a) How can we document opportunities to learn aligned with the NCTM Standards? (b) How can we support elementary teachers' efforts to provide such opportunities? We conducted a study of the effect of curriculum (problem solving vs. skills) and professional development (subject-matter focused vs. collegial support) on practices and learning. From analyses of videotapes and field notes, we created 3 scales for estimating students' opportunities to learn. Analyses of fractions instruction in 21 elementary classrooms provided evidence of the technical quality of the indicators and indicated that support for teachers' knowledge may be required for a problem-solving curriculum to be beneficial. |

Reflective Thinking Among Preservice Elementary Mathematics Teachers
*Denise S. Mewborn* Four preservice elementary teachers were studied during a field-based mathematics methods course. The purpose of the study was to investigate the elements of mathematics teaching and learning the preservice teachers found problematic and how they resolved those problems. Data were collected in the form of individual interviews, group discussions, and individual journals. The preservice teachers exhibited concerns about the classroom context, pedagogy of mathematics, children's mathematical thinking, and, to a lesser extent, the mathematics content. The data indicate a relationship between the preservice teachers' locus of authority and the reflective quality of their thinking. |

The Fennema-Sherman Mathematics as a Male Domain Scale Reexamined
*Helen J. Forgasz, Gilah C. Leder, Paul L. Garnder* The Fennema-Sherman
Mathematics Attitude Scales (MAS) have been used extensively in research on
gender differences in mathematics learning outcomes. The MAS comprise 9
scales measuring attitudes related to mathematics learning, including
Mathematics as a Male Domain. The construct "mathematics as a male
domain" remains a critical variable in explorations of the continued
disadvantage experienced by females in the field of mathematics. We present
recent research evidence that indicates that several items in the Mathematics
as a Male Domain scale of the MAS may no longer be valid. In light of this
evidence, it is appropriate to consider revisions to the scale to ensure that
it continues to measure accurately its originally operationalized construct. |

Curricular Influences on the Motivational Beliefs and Practice of Two Middle School Mathematics Teachers: A Follow-Up Study
*James A. Middleton* In this study I
examine the structures of 2 teachers' beliefs about what makes mathematics
intrinsically motivating and provide instances of the representations of
their beliefs at 2 times: before the introduction of middle school
mathematics curricula organized around the tenets of Realistic Mathematics
Education and after 1 year of implementing a pilot program.
Personal-constructs analyses are paired with observations of teachers'
classrooms and their beliefs and perceptions as reported in semistructured
interviews. Results indicate that the teachers became more attuned to the
conceptual complexity and challenge of mathematics activities and placed less
emphasis on task ease over their year of involvement in the pilot program.
Results are discussed in relation to "job-embedded learning," a
form of staff development that fosters teachers' development of meaning with
regard to reforms, and how such learning enables shifts in teacher beliefs
and practice. |