Journal Article

  • Understanding how science students respond to anomalous data is essential to understanding knowledge acquisition in science classrooms. This article presents a detailed analysis of the ways in which scientists and science students respond to such data. We postulate that there are seven distinct forms of response to anomalous data, only one of which is to accept the data and change theories. The other six responses involve discounting the data in various ways in order to protect the preinstructional theory. We analyze the factors that influence which of these seven forms of response a scientist or student will choose, giving special attention to the factors that make theory change more likely. Finally, we discuss the implications of our framework for science instruction.

  • The transition from student to expert professional can be accelerated when a trajectory for change is plotted and made visible to learners. Trajectories or paths toward expertise are domain specific and must first be documented and then used within instructional contexts to promote knowledge transitions. This article describes how models of expertise can serve to help students attain higher levels of competence.

  • We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as pedagogical implications of constructivism. In response, we advance a theoretical reformulation of telling as the set of teaching actions that serve the function of stimulating students' mathematical thoughts via the introduction of new ideas into a classroom conversation. We reformulate telling in three ways: (a) in terms of the function (which involves attention to the teacher's intention, the nature of the teaching action, and the students' interpretations of the action) rather than the form of teachers' communicative acts; (b) in terms of the conceptual rather than procedural content of the new information; and (c) in terms of its relationship to other actions rather than as an isolated action. This reformulation resolves some of the concerns with teaching as telling and helps establish the legitimacy of providing new information within a constructivist perspective on learning.

  • Presents requisites for and characteristics of reform, identifies sources of problems teachers face when implementing change, and gives tips for success.

  • This paper addresses issues linking research into the classroom teaching and learning of mathematics with the growth of knowledge in mathematics teaching, developments in the practice of teaching and the enhanced learning of mathematics by students in classrooms. A basic premise is that research promotes development. The paper considers both insider andoutsider research and co-learning between teachers and educators in promoting classroom inquiry. Through a consideration of elements of theory such as knowledge and inquiry in teaching and of learning as knowledge growth through research/inquiry leading to enhancement of students' learning of mathematics, a framework is suggested. Its purposes include analysis of a research project's contribution to teaching development and conceptualization of research which has teaching development as one of its aims. Use of the framework is exemplified through its application to reports of three mathematics education research projects in the public domain. A brief afterword links the framework to concepts in activity theory.

  • This paper analyzes the tension between the traditional foundation of efficacy in teaching mathematics and current reform efforts in mathematics education. Drawing substantially on their experiences in learning mathematics, many teachers are disposed to teach mathematics by "telling": by stating facts and demonstrating procedures to their students. Clear and accurate telling provides a foundation for teachers' sense of efficacy--the belief that they can affect student learning--because the direct demonstration of mathematics is taken to be necessary for student learning. A strong sense of efficacy supports teachers' efforts to face difficult challenges and persist in the face of adversity. But current reforms that de-emphasize telling and focus on enabling students' mathematical activity undermine this basis of efficacy. For the current reform to generate deep and lasting changes, teachers must find new foundations for building durable efficacy beliefs that are consistent with reform-based teaching practices. Although productive new "moorings" for efficacy exist, research has not examined how practicing teachers' sense of efficacy shifts as they attempt to align their practice with reform principles. Suggestions for research to chart the development of, and change in, mathematics teachers' sense of efficacy are presented.

  • A dataset concerning the relationship between respiratory function (measured by forced expiratory volume, FEV) and smoking provides a powerful tool for investigating a wide variety of statistical matters. This paper gives a brief description of the problem, the data, and several issues and analyses suggested by the problem of quantifying the relationship between FEV and smoking.

  • Defines constructivist learning environments and explains why the idea is worthy of study. Discussion includes the different assumptions underlying common metaphors for instruction, the idea of learning environments, the outcomes of learning environments, and the components or functions that make up learning environments.

  • This paper describes a model for generating andaccumulating knowledge for both teaching andteacher education. The model is applied firstto prepare prospective teachers to learn toteach mathematics when they enter theclassroom. The concept of treating lessons asexperiments is used to explicate theintentional, rigorous, and systematic processof learning to teach through studying one's ownpractice. The concept of planning teachingexperiences so that others can learn fromone's experience is used to put into practicethe notion of contributing to a sharedprofessional knowledge base for teachingmathematics. The same model is then applied tothe work of improving teacher preparationprograms in mathematics. Parallels are drawnbetween the concepts emphasized for prospectiveteachers and those that are employed byinstructors who study and improve teacherpreparation experiences. In this way, parallelsalso are seen in the processes used to generatean accumulating knowledge base for teaching andfor teacher education.

  • We are now conducting an extensive study, funded by the National Science Foundation, to investigate the parameters, capabilities and distinctiveness of design experiments. The goal of the project is to explicate a design experiment methodology that advances the overall goal of understanding and improving teaching and learning. This task will consume the three years of the grant (and likely will extend beyond it, in practice). The goal is to study the nature of how innovations in the sciences, their computational infrastructure, and their implementations in education should be constructed - so as to be educative to scholars and practitioners.

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