Mary E. Brenner

Learning by Understanding: The Role of Multiple Representations in Learning Algebra

Prealgebra students learned about functions in a unit that emphasized (a) representing problems in multiple formats, (b) anchoring learning in a meaningful thematic context, and (c) problem-solving processes in cooperative groups. In posttest results, treatment students were more successful in representing and solving a function word problem and were better at problem representation tasks such as translating word problems into tables and graphs than were comparison students. Similar results were found for students who spoke English as a second language.

Performance evaluation for bus transit

Abstract Performance analysis has gained increased attention now that transit organizations are emphasizing efficiency objectives. Debates over both the number of indicators required and their method of selection are reviewed. Research upon which this paper is based uses FY 1980 Section 15 data to first identify and then test a set of performance indicators which are useful for evaluation of fixed route, motor bus transit. Four parallel data sets, based on transformations of the original data, and several exploratory factor analyses were used to detect the underlying structure of the data. Rigorous testing verified that the structure represented the most salient performance dimensions. A small subset of seven performance indicators was identified and tested as representative of these underlying dimensions. These indicators can be used together or individually to assess transit performance for a single system or for cross-sectional comparisons.

Adaptation and Accommodation to Young Children with Disabilities: A Comparison of Korean and Korean American Parents

This article presents a comparative study of the adaptation of Korean and Korean American parents to their children with developmental disabilities. Repeated interviews with 16 mothers in each group were designed to elicit parental descriptions of the major chronological events concerning their child, process of adaptation and accommodation, sources of stress and support, and perceived benefits and contributions to their lives. The interviews were conducted in Korean, transcribed, translated, and analyzed in a structured procedure in keeping with one major tradition of qualitative research. Comparative cross-cultural research allows investigators to see taken-for-granted phenomena that might otherwise go unseen. The study revealed that both Korean and Korean American parents experienced a process of transformation in regard to their beliefs and feelings about their exceptional children. Religion played an important role in this process. Public policy, social services, and available resources were dramatically different in the two nations, and these differences suffused parental accounts of their individual experiences. The similarities and differences between the two groups are presented thematically. The findings are further discussed in relation to major theories about adaptation in families of young children with disabilities.

Meaning and Money.

This paper examines how the inclusion of everyday mathematics into classroom instruction can make mathematics more meaningful to students. The concept of mathematical meaningfulness is reviewed and then compared to the experiences of children learning about money at home and at school. The empirical study used interviews and observations to determine what activities Hawaiian children from preschool through second grade did with money at home, while shopping and during classroom lessons. The interview data are used to show what kinds of knowledge children derived from these experiences at different ages. This everyday knowledge is compared to what children were expected to learn about money in school. The data support the conclusion that certain kinds of differences between everyday and school mathematics can make the inclusion of everyday mathematical topics in classrooms problematic. The paper concludes with a discussion of how everyday mathematics can be more profitably included in the curriculum, with examples from several mathematics programs.

The Multiple Worlds of Successful Cambodian American Students.

Educational policy usually overlooks Cambodian American students as a unique ethnic group, attending instead to the positive statistics that aggregate Asian American students into a single group of successful students. Through ethnographic interviews, this article examines how successful Cambodian American students interpreted values from their multiple worlds in relation to their paths into the university and provides insight into the academically supportive features of their different worlds. Family obligation emerged as a coherent theme that figured prominently in their school experiences. This study complicates the simplistic view of how traditional cultural values influence immigrant ethnic minority school achievement.

Typology for bus transit

Peer groups of similar transit systems are needed for comparative analysis of transit performance and facilitation of econometric analysis. Cluster analysis was used to construct 12 peer groups based upon size, average speed and peak-to-base ratios of urban, fixed-route motor bus transit systems. Analysis of variance, discriminant analysis and a decision tree typology confirmed differences in operating characteristics among the peer groups. The peer groups were also found to be significantly different on seven variables representing the major dimensions of transit performance. Performance profiles are given for each peer group, and suggestions are made for using the peer groups in performance evaluations.

Maternal Stress and Efficacy for Latina Mothers with Infants in Neonatal Intensive Care

This study examined the levels of maternal stress and efficacy for Spanish- and English-speaking Latina mothers whose infants were in neonatal intensive care. Thirty-two Latina mothers participated in the study. Significant group differences were found between Spanish- and English-speaking Latina mothers. More stress was experienced by Spanish- than English-speaking Latina mothers in communicating with NICU staff, in general and learning about infant caregiving tasks, in particular. Maternal efficacy was not related to stress experienced by these mothers in the NICU. Implications for early interventions and future directions for research are discussed for Latina mothers and their newborn infants with special needs.

Prospective Secondary Mathematics Teachers’ Understanding and Cognitive Difficulties in Making Connections among Representations

This study investigates prospective secondary teachers’ cognitive difficulties and mathematical ideas involved in making connections among representations. We implemented a three-week teaching unit to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to formulating connections among representations, in the context of conic curves. Qualitative analysis of data showed that most undergraduate mathematics majors and minors in this study struggled with variation, the Cartesian Connection, and other affiliated ideas such as graph as a locus of points. Furthermore, they were unable to identify basic metric relations encoded in algebraic expressions such as the distance between points, which further compounded their difficulties in making connections among representations. We argue that mathematics teacher education needs more focus on these ideas so that their graduates can successfully teach these big ideas in their future instruction.

Science and Mathematics Teachers Working Toward Equity Through Teacher Research: Tracing Changes Across Their Research Process and Equity Views

We investigated secondary science and mathematics teachers engaged in a two-and-a-half-year professional development effort focused on equity. We examined how teachers conducting research on their own instructional practices—a central learning strategy of the professional development project—informed and/or constrained their views related to three strands of equity: teachers and teaching, students and learning, and students’ families and communities. Data collected included recordings of professional development seminars and school-site meetings, three sets of individual interviews with teacher researchers, and drafts and final products of the classroom research teachers conducted. From our qualitative analyses of data, we found that most teachers addressed at least two of the three equity strands in researching their own practice. We also found that most transformed their understandings of teachers and students as a result of their teacher research process. However, teachers’ views of families and communities changed in less substantive ways. We close with recommendations for other researchers and professional developers intent on supporting science and mathematics teachers in using teacher research to work toward equity.