In this article, I describe the processes involved in designing and carrying out a case study project. The case study focuses on a science teacher, Donald, who was undertaking an inquiry-based curriculum change to an advanced chemistry course in a specialized science, technology, engineering, and mathematics school. I describe the groundwork…

Graduate students initiating qualitative research, like any inquiry, must hone and refine what they will study--the purpose of the research. Without clarity in the research purpose, the study's design will not likely unfold in a systematic way. However, narrowing one's research focus, such that methods follow research question, is much easier said…

This chapter describes how the mean of fractal processes does not exist and is not a meaningful measure of some data. It discusses how important it is to stay open to the possibility that sometimes analytic techniques fail to satisfy some assumptions on which the mean is based. (KHR)

This chapter discusses the way that mathematics curricula are developed in the United States. It suggests that curriculum development in mathematics education makes little progress because it fails to adhere to scientific methodology. Weaknesses in the current development process, how such development can become scientific, how curriculum…

This chapter discusses three different approaches for the use of the history of mathematics and science in educational research. These approaches require increasing levels of scholarly engagement with historical materials and offer correspondingly increased levels of insight. Each of the three techniques includes brief examples of historical…

This chapter presents the shift in perspectives about schooling embodied in the National Council of Teachers of Mathematics' (NCTM) Standards-based reform movement, describes the impact of these shifts on the types of questions that need to be answered, and defines the ways in which scholarly evidence needs to be developed. Issues of concern…

This chapter describes the corruption of research design and explains why and how a computer-based curriculum innovation project was transformed from a quasi-experimental design to a comparative case study. The first section introduces the Systems Thinking and Curriculum Innovation Network (STACI) that examined the impact of technology on teaching…

This chapter presents some ways to reorganize science and mathematics education guided by a wisely chosen, strategic, and secure research base. Needs for systemic reform, educational equity and quality as complementary goals, and urgent and strategic investment in research are discussed. Targets for new research and development are also identified…

This chapter describes a research design model that utilizes both theory and common, core classroom conditions in order to create and investigate new instructional strategies. Transformative and conjecture-driven teaching experiments are introduced which were developed to change and reform current teaching practice. It is suggested that such a…

This chapter describes a study adopting the findings from an investigation of the cognitive processing and knowledge requirements of individuals taking the Graduate Record Examination Quantitative (GRE-Q) Test. The study investigates subgroup differences such as major field of study, gender, and racial-ethnic backgrounds of students taking the…

This chapter focuses on a particular type of classroom teaching experiment that is conducted in collaboration with a practicing teacher. The first section discusses the theoretical orientation that underpins this methodology and outlines the types of problems that are addressed in the course of a classroom teaching experiment. The three central…

This handbook brings together important mathematics education research that makes a difference in both theory and practice, research that anticipates problems and necessary knowledge before they become impediments to progress, interprets future-oriented problems into researchable issues, presents the implications of research and theory development…