Teacher Leadership: Emergent Leadership in a Complex System Functioning as a Professional Learning Community

The extent to which organizational, social, cultural, and leadership contexts within schools support or impede the complexity of emergent leadership as it relates to professional learning communities was investigated in this study. Through in-depth interviews exploring ways in which teacher leadership manifests itself, the ability of teachers to understand their own leadership capacity, and how their emergent leadership influences others, data from this study reshape the notion that schools do not need to reform, but need to transform from traditional schools of teaching into contemporary schools of learning, providing the type of professional knowledge needed to foster 21st century skills for students. Data were collected through one-on-one semi-structured interviews conducted With fourteen teachers from four schools designated as the highest and lowest Title I and Non-Title I schools in a large urban district based on state wide achievement scores. These interview data were analyzed to develop five thematic constructs with sixteen themes. Thematic constructs were also developed to address the four context factors that may support or impede emergent teacher leadership. The findings suggested that teacher leadership has the ability to develop through the process of collaboration which is socially constructed in the context of professional learning communities. Findings further reveal that deep considerations for the ramifications of working within such a complex system as a learning community be made. These considerations include understanding that teacher leadership leads to a shift in decision making from a hierarchical to democratic model, that collaboration builds organizational intelligence, that struggling students are motivators for reflective professional discourse, and that influential peers set the model for this type of intuitive teacher leadership. Implications for further practice and directions for future research are also discussed

Analogy and mathematical reasoning : a survey

We survey the literature of Artificial Intelligence, and other related work, pertaining to the modelling of mathematical reasoning and its relationship with the use of analogy. In particular, we discuss the contribution of Lenat's program AM to models of mathematical discovery and concept-formation. We consider the use of similarity measures to structure a knowledge space and their role in concept acquisition

A Dialectic Approach to Problem-Solving

International audienceWe analyze the dynamics of problem-solving in a framework which captures two key features of that activity. The first feature is that problem-solving is a social game where a number of problem-solvers interact, rely on other agents to tackle parts of a problem, and regularly communicate the outcomes of their investigations. The second feature is that problem-solving requires a careful control over the set of hypotheses that might be needed at various stages of the investigation for the problem to be solved; more particularly, that any incorrect hypothesis be eventually refuted in the face of some evidence: all agents can expect such evidence to be brought to their knowledge whenever it holds. Our presentation uses a very general form of logic programs, viewed as sets of rules that can be activated and fire, depending on what a problem-solver is willing to explore, what a problem-solver is willing to hypothesize, and what a problem-solver knows about the problem to be solved in the form of data or background knowledge. Our framework supports two fundamental aspects of problem-solving. The first aspect is that no matter how the work is being distributed amongst agents, exactly the same knowledge is guaranteed to be discovered eventually. The second aspect is that any group of agents (with at one end, one agent being in charge of all rules and at another end, one agent being in charge of one and only one rule) might need to sometimes put forward some hypotheses to allow for the discovery of a particular piece of knowledge in finite time