Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

An Exploratory Analysis of John Dewey's Writings: Implications for School Leaders

The purpose of this study was to synthesize the operational definition of education through an exploratory analysis of John Dewey’s writings. Dewey’s definition of education changed from 1938 to 1896. Findings suggest that schools promote more social and emotional learning through instructional activities such as service-learning.

Goma curriculum, a character education paradigm: Composing a text for shaping classroom character culture

The written text, and approaches to reading it, serves well as an analogy for the classroom space as a "text" that teachers are able to compose; and students are able to read, interpret meaning(s) of, and make responses to and about (Rosenblatt, 1988). Researchers point to ways in which the classroom can be conceptualized as a text to be evoked, experienced, and read (Freire & Macedo, 1987; Powell, 2009; Rosenblatt, 1988; Spears-Bunton & Powell, 2009).^ The present study analyzed secondary data including: 10 transcripts of teacher talks and six self-reports retrieved from the program evaluation archives of DOR Foundation. The data described six teachers' classroom experiences subsequent to professional development centered on Goma character education curriculum that was used during a summer youth program located in South Georgia. Goma, an acronym that stands for Goal, Objective, Method, and Attitude, is a character education paradigm derived from The Inclusive Community Building Ellison Model, the theoretical framework used for this study. The Model identifies conflict resolution as one of its five foci (Hunt, Howard, & Rice, 1998). Hunt (2006) conceived Goma as part of a 7-Step unitary process, also named the 7-Step pathway, to demonstrate how conflict resolution is accomplished within a variety of contexts.^ Analysis of the data involved: (a) a priori coding of teacher talks transcripts using the components of the Goma 7-Step pathway as coding categories, (b) emergent coding of teacher talks transcripts for the types of experiences teachers evidenced, and (c) emergent coding of teachers' self-reports for categories of teachers' instructional activities. Results of the study showed positive influence of Goma curriculum on participating teachers and their instructional practices. Teachers were shown to have had cognitive, instructional, emotional, and social experiences that were most evident when they reported changes in their attitudes toward their students, themselves, and their instructional practices. The present study provided implications for classroom teachers wherein all aspects of teachers' instructional practices can be guided by principles of positive character; and can be used to help compose the kinds of "texts" that may likely contribute to a classroom character culture.^

Factors affecting the alignment of *grades and reading scores for third-grade students on the Florida Comprehensive Assessment Test

The purpose of this study was to aid in understanding the relationship between current Reading report card grading practices and standards-based state standardized testing results in Reading and factors associated with the alignment of this relationship. Report card and Florida Comprehensive Assessment Test (FLAT) data for 2004 were collected for 1064 third grade students in nine schools of one feeder pattern in Florida's Miami-Dade County Public Schools. A Third Grade Teacher Questionnaire was administered to 48 Reading teachers. The questionnaire contained items relating to teachers' education, teaching experience, grading practices, and beliefs about the FCAT, instructional Reading activities, methods, and materials. ^ Findings of this study support a strong relationship between report card grades and FCAT Reading achievement levels. However, individual school correlational analysis showed significant differences among schools' alignment measures. Higher teacher alignment between grades and FCAT levels was associated with teachers spending more time on individualized methods of Reading instruction and to teachers feeling there was not enough time to teach and help individual students. Lower teacher alignment of grades and achievement levels was associated with teachers taking homework into account in the final Reading grade. Teacher alignment of grades and achievement levels was not associated with teacher beliefs concerning the FCAT, instructional activities in Reading and Language Arts, the Reading program used, the model of delivery of the Reading program, instruction or type of instructional planning done by the teachers. ^ This study highlights the need for further investigations related to determining additional teacher factors that may affect the alignment relationship between report card grades and standards-based state standardized testing results. ^

Goma Curriculum, A Character Education Paradigm: Composing a Text for Shaping Classroom Character Culture

The written text, and approaches to reading it, serves well as an analogy for the classroom space as a “text” that teachers are able to compose; and students are able to read, interpret meaning(s) of, and make responses to and about (Rosenblatt, 1988). Researchers point to ways in which the classroom can be conceptualized as a text to be evoked, experienced, and read (Freire & Macedo, 1987; Powell, 2009; Rosenblatt, 1988; Spears-Bunton & Powell, 2009). The present study analyzed secondary data including: 10 transcripts of teacher talks and six self-reports retrieved from the program evaluation archives of DOR Foundation. The data described six teachers’ classroom experiences subsequent to professional development centered on Goma character education curriculum that was used during a summer youth program located in South Georgia. Goma, an acronym that stands for Goal, Objective, Method, and Attitude, is a character education paradigm derived from The Inclusive Community Building Ellison Model, the theoretical framework used for this study. The Model identifies conflict resolution as one of its five foci (Hunt, Howard, & Rice, 1998). Hunt (2006) conceived Goma as part of a 7-Step unitary process, also named the 7-Step pathway, to demonstrate how conflict resolution is accomplished within a variety of contexts. Analysis of the data involved: (a) a priori coding of teacher talks transcripts using the components of the Goma 7-Step pathway as coding categories, (b) emergent coding of teacher talks transcripts for the types of experiences teachers evidenced, and (c) emergent coding of teachers’ self-reports for categories of teachers’ instructional activities. Results of the study showed positive influence of Goma curriculum on participating teachers and their instructional practices. Teachers were shown to have had cognitive, instructional, emotional, and social experiences that were most evident when they reported changes in their attitudes toward their students, themselves, and their instructional practices. The present study provided implications for classroom teachers wherein all aspects of teachers’ instructional practices can be guided by principles of positive character; and can be used to help compose the kinds of “texts” that may likely contribute to a classroom character culture.