High

Tasks can be vehicles for productive mathematical discussions. How to support such discourse in collaborative digital environments is the focus of our theorization and empirical examination of task design that emerges from a larger research project. We present our task design principles that developed through an iterative research design for a project that involves secondary teachers in online courses to learn discursively dynamic geometry by collaborating on construction and problem-solving tasks in a cyber learning environment. In this study, we discuss a task and the collaborative work of a team of teachers to illustrate relationships between the task design and productive mathematical discourse. Implications suggest further investigations into interactions between characteristics of task design and learners mathematical activity.

To contribute to understanding how teachers can develop geometrical understanding, we report on the discursive development of teachers’ geometrical reasoning through instrument appropriation while collaborating in an online dynamic geometry environment (DGE). Using the theory of instrument-mediated activity, we analysis the discourse and DGE actions of a group of middle and high school mathematics teachers who participated in a semester-long, professional development course. Working in small teams, they collaborated to solve geometric problems. Our results show that as teachers appropriate DGE artifacts and transform its components into instruments, they develop their geometrical knowledge and reasoning in dynamic geometry. Our study contributes to a broad understanding of how teachers develop mathematical knowledge for teaching.

Rich tasks can be vehicles for productive mathematical discussions. How to support such discourse in collaborative digital environments is the focus of our theorization and empirical examination of task design that emerges from a larger research project. We present the theoretical foundations of our task design principles that developed through an iterative research design for a project that involves secondary teachers in online courses to learn discursively dynamic geometry by collaborating on construction and problem-solving tasks in a cyberlearning environment. In this study, we discuss a task and the collaborative work of a team of teachers to illustrate relationships between the task design, productive mathematical discourse, and the development of new mathematics knowledge for the teachers. Implications of this work suggest further investigations into interactions between characteristics of task design and learners mathematical activity.

We report on a case study that seeks to understand how teachers’ pedagogical interventions influence students’ instrumentation and mathematical reasoning in a collaborative, dynamic geometry environment. A high school teacher engaged a class of students in the Virtual Math Teams with GeoGebra environment (VMTwG) to solve geometrical tasks. The VMTwG allows users to share both GeoGebra and chat windows to engage in joint problem solving. Our analysis of the teacher’s implementation and students’ interactions in VMTwG shows that his instrumental orchestration (Trouche, 2004, 2005) supported students’ instrumentation (Rabardel & Beguin, 2005) and shaped their movement between empirical explorations and deductive justifications. This study contributes to understanding the interplay between a teacher’s instrumental orchestration and students’ instrumentation and movement towards more deductive justifications.

Modeling and argumentation are two important scientific practices students need to develop throughout school years. In this paper, we investigated how middle and high school students (N=512) construct a scientific argument based on evidence from computational models with which they simulated climate change. We designed scientific argumentation tasks with three increasingly complex dynamic climate models. Each scientific argumentation task consisted of four parts: multiple-choice claim, open ended explanation, five-point Likert scale uncertainty rating, and open-ended uncertainty rationale.
We coded 1,294 scientific arguments in terms of a claim’s consistency with current scientific consensus, whether explanations were model based or knowledge based and categorized the sources of uncertainty (personal vs. scientific). We used chi-square and ANOVA tests to identify significant patterns. Results indicate that (1) a majority of students incorporated models as evidence to support their claims, (2) most students used model output results shown on graphs to confirm their claim rather than to explain simulated molecular processes, (3) students’ dependence on model results and their uncertainty rating diminished as the dynamic climate models became more and more complex, (4) some students’ misconceptions interfered with observing and interpreting model results or simulated processes, and (5) students’ uncertainty sources reflected more frequently on their assessment of personal knowledge or abilities related to the tasks than on their critical examination of scientific evidence resulting from models. These findings have implications for teaching and research related to the integration of scientific argumentation and modeling practices to address complex Earth systems.

Though addressing sources of uncertainty is an important part of doing science, it has largely been neglected in assessing students' scientific argumentation. In this study, we initially defined a scientific argumentation construct in four structural elements consisting of claim, justification, uncertainty qualifier, and uncertainty rationale. We consulted literature to characterize and score different levels of student performances on each of these four argumentation elements. We designed a test comprised of nine scientific argumentation tasks addressing climate change, the search for life in space, and fresh water availability and administered it to 473 students from 9 high schools in the United States. After testing the local dependence and unidimensionality assumptions, we found that the uncertainty qualifier element was not aligned with the other three. After removing items related to uncertainty qualifier, we applied a Rasch analysis based on a Partial Credit Model. Results indicate that (1) claim, justification, and uncertainty rationale items form a unidimensional scale, (2) justification and uncertainty rationale items contribute the most on the unidimensional scientific argumentation scale as they cover much wider ranges of the scale than claim items, (3) average item difficulties increase in the order of claim, justification, and uncertainty rationale, (4) students' elaboration of uncertainty exhibits dual characteristics: self-assessment of their own knowledge and ability versus scientific assessment of conceptual and empirical errors embedded in investigations, and (5) students who can make warrants between theory and evidence are more likely to think about uncertainty from scientific sources than those who cannot. We identified limitations of this study in terms of science topic coverage and sample selection and made suggestions on how these limitations might have affected results and interpretations.

This qualitative study examined how and why research experiences for teachers (RETs) influenced middle and high school science teachers’ beliefs, attitudes, and values about teaching science as inquiry. Changes teachers reported after participating in the RET ranged from modifying a few lessons (belief change) to a comprehensive revision of what and how they taught to better reflect inquiry (attitude change). Some teachers who described comprehensively changing their instruction also described implementing actions meant to change science education within their respective schools, not just their own classrooms (value change). We present how and why teachers went about changes in their practices in relation to the researcher-created teacher inquiry beliefs system spectrum (TIBSS). The TIBSS conceptualizes the range of changes observed in participating teachers. We also describe the features of the RET and external factors, such as personal experiences and school contexts, that teachers cited as influential to these changes.

This report summarizes the 2013, 2014, and 2015 findings from a longitudinal survey of district professional development coordinators across the state of Florida. The results are presented with six sections: 1) District policy and practice, 2) Leadership, 3) Funding, 4) Lesson study schedule, 5) Professional development programs, and 6) Sustaining lesson study.

The state of Florida has taken an unprecedented approach to teacher professional development in its Race to the Top
(RTTT) Program application by proposing to promote an international innovation that originates in Japan, “lesson study,” as
a statewide teacher professional development model. Since winning the US$700 million RTTT funding in 2010, the Florida
Department of Education and districts have been promoting lesson study as one of the statewide vehicles to implement
the state standards aligned with the Common Core State Standards. This study analyzed the state and districts’ approaches
to promote lesson study using policy documents, statewide district survey data, and interviews. We found that a majority
of districts mandated lesson study implementation without securing or spending sufficient funding. In addition, the existing organizational structures and routines for professional development pose a major challenge in capacity building of district leaders and teachers to engage in lesson study.