Mary Mueller

Expanding Participation in Problem Solving in a Diverse Middle School Mathematics Classroom.

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications, developing and implementing problem-solving heuristics and strategies, and understanding and evaluating the solutions of others. We then delineate what aspects of our environment encouraged the students to take part in these activities, particularly emphasising the proactive role of the teacher, the tasks the students completed, and the social norms of our after-school sessions. Finally, we discuss the relationship between our study and the literature on equity research in mathematics education.

Learning to Reason in an Informal Math After-School Program

This research was conducted during an after-school partnership between a University and school district in an economically depressed, urban area. The school population consists of 99% African American and Latino students. During an the informal after-school math program, a group of 24 6th-grade students from a low socioeconomic community worked collaboratively on open-ended problems involving fractions. The students, in their problem solving discussions, coconstructed arguments and provided justifications for their solutions. In the process, they questioned, corrected, and built on each other’s ideas. This paper describes the types of student reasoning that emerged in the process of justifying solutions to the problems posed. It illustrates how the students’ arguments developed over time. The findings of this study indicate that, within an environment that invites exploration and collaboration, students can be engaged in defending their reasoning in both their small groups and within the larger community. In the process of justifying, they naturally build arguments that take the form of proof.

Lesson Study in a Professional Development School.

For the past six years, the Cranford Public School District and Seton Hall University in northern New Jersey, USA have been Professional Development School partners. As a result of this partnership, experienced teachers have systematically mentored pre-service candidates in university field experiences. The Japanese practice of Lesson Study was used as a vehicle for reflection and collaboration in a graduate program for experienced teachers and then during the field experiences of elementary pre-service interns and it is this initiative we describe here. As part of the partnership, graduate classes are regularly offered on-site at a local school to a cohort group of teachers. An Advanced Teaching Strategies class used models of teaching (Joyce et al., 2004) combined with the Lesson Study process to develop lessons in the current curriculum that students found challenging. Teachers used concept attainment, concept formation and inquiry models with suggested formats from Japanese teachers for planning and debriefing Lesson Study groups (available at http://www.teacherscollege.edu/lessonstudy). Teachers co-planned lessons, designed informal observation forms to collect data on each other’s classes, and observed colleagues teach. Groups met, discussed student reaction in the lesson and made revisions which they then tried out in a subsequent lesson. Teachers audio-taped and took notes of their planning and debriefing sessions. Other information teachers consulted to analyze lessons were the content of planning discussions, observations, videotaped lessons, and debriefing sessions. Based on these various sources, teacher teams developed reports describing the evolution of their lessons. In year 2, elementary teachers from this graduate course shared their newly acquired skills in Lesson Study with university interns. An on-site elementary math methods course was designed so that interns and teachers could have an opportunity

Creating Home-School Partnerships: Examining Urban and Suburban Teachers' Practices, Challenges, and Educational Needs.

This study examines suburban and urban teachers’ family involvement practices, challenges they face in involving families, and their educational needs. A questionnaire was administered to 89 teachers. Data were coded using a constant comparative analysis. Codes were analyzed to determine the number of teachers whose responses fell into each category and by comparing suburban and urban teachers’ responses. Results of this study suggest that although urban and suburban teachers share some similarities in terms of their practices, challenges, and needs, a number of differences were evident. Overall, suburban teachers’ responses were more detailed and included specific strategies. We also found that urban teachers’ interests in further education did not necessarily align with the areas in which they reported challenges.