Mathematical Communication through Written and Oral Expression

In this action research study of my classroom of sixth grade mathematics, I investigated the use of communication of mathematics through both written and oral expression. Giving my students the opportunity to communicate mathematics both in writing and orally helped to deepen the students’ understanding of mathematics. The students’ levels of comprehension were increased when they were presented with a variety of instructional methods. Through discussion and reflection the students were able to find methods that worked best for them and their learning ability. Students’ understanding increased from probing questions that made the students reflect and re-evaluate their solutions. This learning took place when students were made aware of different solutions or ways of doing things from the class discussions that were held. I discovered that when students are challenged to express their thinking both in writing and orally, the students found that they could communicate their thinking in a new way. Some of my students were only comfortable expressing their thoughts in one of the two ways but by the time the project was completed, they all expressed that they enjoyed both ways, and maybe changed the original way they preferred doing mathematics. As a result of this research, I will continue to require students to communicate their thinking and reasoning both in writing and orally.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

Eating And Exercising: Nebraska Adolescents' Attitudes and Behaviors

Prevention Center Papers are occasional publications of the Nebraska Prevention Center for Alcohol and Drug Abuse. Their purpose is to make available information that would not otherwise be easily accessible. This Prevention Center Paper should be considered a working document and does not reflect the official policy or position of the University of Nebraska-Lincoln, The U.S. Centers for Disease Control, the Nebraska Department of Education, or Health Education, Inc. Prevention Center Papers are produced for a limited readership to stimulate discussion and generate a flow of communication between the Prevention Center and those interested in the broad field of disease prevention and health promotion.

Parental Ethnotheories of Child Development: Looking Beyond Independence and Individualism in American Belief Systems

Over the past several decades, the topic of child development in a cultural context has received a great deal of theoretical and empirical investigation. Investigators from the fields of indigenous and cultural psychology have argued that childhood is socially and historically constructed, rather than a universal process with a standard sequence of developmental stages or descriptions. As a result, many psychologists have become doubtful that any stage theory of cognitive or socialemotional development can be found to be valid for all times and places. In placing more theoretical emphasis on contextual processes, they define culture as a complex system of common symbolic action patterns (or scripts) built up through everyday human social interaction by means of which individuals create common meanings and in terms of which they organize experience. Researchers understand culture to be organized and coherent, but not homogenous or static, and realize that the complex dynamic system of culture constantly undergoes transformation as participants (adults and children) negotiate and re-negotiate meanings through social interaction. These negotiations and transactions give rise to unceasing heterogeneity and variability in how different individuals and groups of individuals interpret values and meanings. However, while many psychologists—both inside and outside the fields of indigenous and cultural psychology–are now willing to give up the idea of a universal path of child development and a universal story of parenting, they have not necessarily foreclosed on the possibility of discovering and describing some universal processes that underlie socialization and development-in-context. The roots of such universalities would lie in the biological aspects of child development, in the evolutionary processes of adaptation, and in the unique symbolic and problem-solving capacities of the human organism as a culture-bearing species. For instance, according to functionalist psychological anthropologists, shared (cultural) processes surround the developing child and promote in the long view the survival of families and groups if they are to demonstrate continuity in the face of ecological change and resource competition, (e.g. Edwards & Whiting, 2004; Gallimore, Goldenberg, & Weisner, 1993; LeVine, Dixon, LeVine, Richman, Leiderman, Keefer, & Brazelton, 1994; LeVine, Miller, & West, 1988; Weisner, 1996, 2002; Whiting & Edwards, 1988; Whiting & Whiting, 1980). As LeVine and colleagues (1994) state: A population tends to share an environment, symbol systems for encoding it, and organizations and codes of conduct for adapting to it (emphasis added). It is through the enactment of these population-specific codes of conduct in locally organized practices that human adaptation occurs. Human adaptation, in other words, is largely attributable to the operation of specific social organizations (e.g. families, communities, empires) following culturally prescribed scripts (normative models) in subsistence, reproduction, and other domains [communication and social regulation]. (p. 12) It follows, then, that in seeking to understand child development in a cultural context, psychologists need to support collaborative and interdisciplinary developmental science that crosses international borders. Such research can advance cross-cultural psychology, cultural psychology, and indigenous psychology, understood as three sub-disciplines composed of scientists who frequently communicate and debate with one another and mutually inform one another’s research programs. For example, to turn to parental belief systems, the particular topic of this chapter, it is clear that collaborative international studies are needed to support the goal of crosscultural psychologists for findings that go beyond simply describing cultural differences in parental beliefs. Comparative researchers need to shed light on whether parental beliefs are (or are not) systematically related to differences in child outcomes; and they need meta-analyses and reviews to explore between- and within-culture variations in parental beliefs, with a focus on issues of social change (Saraswathi, 2000). Likewise, collaborative research programs can foster the goals of indigenous psychology and cultural psychology and lay out valid descriptions of individual development in their particular cultural contexts and the processes, principles, and critical concepts needed for defining, analyzing, and predicting outcomes of child development-in-context. The project described in this chapter is based on an approach that integrates elements of comparative methodology to serve the aim of describing particular scenarios of child development in unique contexts. The research team of cultural insiders and outsiders allows for a look at American belief systems based on a dialogue of multiple perspectives.