Journal Article

  • This article gives an example of how student-conducted experiments can enhance a course in the design of experiments. We focus on a project whose aim is to find a good mixture of water, soap and glycerin for making soap bubbles. This project is relatively straightforward to implement and understand. At its most basic level the project introduces students to mixture experiments and general issues in experimental design such as choosing and measuring an appropriate response, selecting a design, the effect of using repeats versus replicates, model building, making predictions, etc. To accommodate more advanced students, the project can be easily enhanced to draw on various areas of statistics, such as generalized linear models, robust design, and optimal design. Therefore it is ideal for a graduate level course as it encourages students to look beyond the basics presented in class.

  • We next reexamine the content of questions posed in the previous section. The first question in example 1 is stated in a closed form. At the outset it has the potential to determine the number of people who claim understanding of a piece of mathematics. The same is true for the first question in example 2, stated in closed form. The contrasting questions in each example, however, ask students to analyze and evaluate various methods.

  • Constructivist theory has been prominent in recent research on mathematics learning and has provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes in mathematics teaching, it offers no particular vision of how mathematics should be taught; models of teaching based on constructivism are needed. Data are presented from a whole-class, constructivist teaching experiement in which problems of teaching practice require the teacher/researcher to explore the pedagogical implications of his theoretical (constructivist) perspectives. The analysis of the data led to the development of a model of teacher decision making with respect to mathematical tasks. Central to this model is the creative tension between the teacher's goals with regard to student learning and his responsibility to be sensitive and responsive to the mathematical thinking of the students.

  • To improve classroom teaching in a steady, lasting way, the teaching profession needs a knowledge base that grows and improves. In spite of the continuing efforts of researchers, archived research knowledge has had little effect on the improvement of practice in the average classroom. We explore the possibility of building a useful knowledge base for teaching by beginning with practitioners' knowledge. We outline key features of this knowledge and identify the requirements for this knowledge to be transformed into a professional knowledge base for teaching. By reviewing educational history, we offer an incomplete explanation for why the United States has no countrywide system that meets these requirements. We conclude by wondering if U.S. researchers and teachers can make different choices in the future to enable a system for building and sustaining a professional knowledge base for teaching.

  • Inspired by the seminal work of Ann Brown, Allan Collins, Roy Pea, and Jan Hawkins, a growing number of researchers have begun to adopt the metaphors and methods of the design and engineering fields. This special issue highlights the work of some of these active reserachers and provides a number of commentaries on it.

  • The authors argue that design-based research, which blends empirical educational research with the theory-driven design of learning environments, is an important methodology for understanding how, when, and why educational innovations work in practice. Design-based researchers' innovations embody specific theoretical claims about teaching and learning, and help us understand the relationships among educational theory, designed artifact, and practice. Design is central in efforts to foster learning, create usable knowledge, and advance theories of learning and teaching in complex settings. Design-based research also may contribute to the growth of human capacity for subsequent educational reform.

  • In this article, the authors first indicate the range of purposes and the variety of settings in which design experiments have been conducted and then delineate five crosscutting features that collectively differentiate design experiments from other methodologies. Design experiments have both a pragmatic bent--"engineering" particular forms of learning--and a theoretical orientation--developing domain-specific theories by systematically studying those forms of learning and the means of supporting them. The authors clarify what is involved in preparing for and carrying out a design experiment, and in conducting a retrospective analysis of the extensive, longitudinal data sets generated during an experiment. Logistical issues, issues of measure, the importance of working through the data systematically, and the need to be explicit about the criteria for making inferences are discussed.

  • Limitations with current approaches to the investigation of the transfer of learning in design experiments constrain the type of information that is available to researchers as they make design decisions. This article addresses these limitations by presenting a reconceptualization of transfer, called actor-oriented transfer, which emerged from design experiment work. The merits of this alternative model are considered in terms of the information it provides to design experimenters.

  • In this article, a general model is proposed for design research in education that grows out of the author's research and work in related design fields. The model emphasizes the stage sensitivity of (a) research questions, (b) data and methods, and (c) the need for researchers to design artifacts, processes, and analyses at earlier stages in their research that can then be profitably used (perhaps by different researchers) in later stages.

  • This article focuses on a form of instructional design that is deemed fitting for reform<br>mathematics education. Reform mathematics education requires instruction that<br>helps students in developing their current ways of reasoning into more sophisticated<br>ways of mathematical reasoning. This implies that there has to be ample room for<br>teachers to adjust their instruction to the students' thinking. But, the point of departure<br>is that if justice is to be done to the input of the students and their ideas built on, a<br>well-founded plan is needed. Design research on an instructional sequence on addition<br>and subtraction up to 100 is taken as an instance to elucidate how the theory for<br>realistic mathematics education (RME) can be used to develop a local instruction theory<br>that can function as such a plan. Instead of offering an instructional sequence that<br>"works," the objective of design research is to offer teachers an empirically grounded<br>theory on how a certain set of instructional activities can work. The example of addition<br>and subtraction up to 100 is used to clarify howa local instruction theory informs<br>teachers about learning goals, instructional activities, student thinking and learning,<br>and the role of tools and imagery.

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