James Hiebert’s research while affiliated with University of Delaware and other places

We propose a model for investigating the quality of mathematics teaching using learning opportunities as an alternative dependent variable to student learning outcomes. We define learning opportunities as opportunities intended by the teacher and engaged by students. We use a general learning goal—conceptual understanding—to show that sufficient empirical evidence exists to identify features of learning opportunities that reliably connect with commonly desired learning outcomes. If accepted, our model would allow teaching researchers to reallocate scarce resources to study, in more detail, the nature of teaching that yields learning opportunities with desired features engaged by students. We believe the model could clarify the criteria for justifying appropriate dependent variable selection in research designs, grant proposals, and manuscript drafts.

In this chapter we propose a way to create theories of teaching that are useful for teachers as well as researchers. Key to our proposal is a new model of teaching that treats sustained learning opportunities (SLOs) as a mediating construct that lies between teaching, on the one hand, and learning, on the other. SLOs become the proximal goal of classroom teaching. Rather than making instructional decisions based on desired learning outcomes, teachers could focus on the kinds of SLOs students need. Because learning research has established reliable links between specific types of learning opportunities and specific learning outcomes, theories of teaching no longer must connect teaching directly with learning. Instead, theories of teaching can become theories of creating SLOs linked to the outcomes teachers want their students to achieve. After presenting our rationale for moving from theories of teaching to theories of creating SLOs, we describe the benefits of such theories for researchers and teachers, explain the work needed to build such theories, and describe the conditions under which this work could be conducted. We conclude by peering into the future and acknowledging the challenges researchers would face as they develop these theories.

The chapter brings together the individual chapter perspectives on theorizing teaching and thus initiating exchanges among the authors on outstanding issues and discrepancies to provide insights for how research on teaching may move forward. The Delphi study conducted for this aim was based on summaries of the answers of all individual chapters on three questions; authors were asked to rate and comment on each other’s ideas. Comparing ratings and comments exposed the variability in the contributors’ perspectives on (a) the existence, degree of development, and grain size of theories of teaching (first question), (b) the attributes of theories of teaching (second question), and (c) the process of developing theories of teaching (third question). We identify general trends with respect to these issues, leaving a more in-depth discussion for the next chapter.

If you have carefully worked through the ideas in the previous chapters, the many questions researchers often ask about what methods to use boil down to one central question: How can I best test my hypotheses? The answers to questions such as “Should I do an ethnography or an experiment?” and “Should I use qualitative data or quantitative data?” are quite clear if you make explicit predictions for what you will find and fully develop rationales for why you made these predictions. Then you need only worry about how to find out in what ways your predictions are right in what ways they are wrong. There is a lot to know about different research designs and methods because these provide the tools you can use to test your hypotheses. But as you learn these details, keep in mind they are means to an end, not an end in themselves.

Every researcher wants their study to matter—to make a positive difference for their professional communities. To ensure your study matters, you can formulate clear hypotheses and choose methods that will test them well, as described in Chaps. 1, 2, 3 and 4. You can go further, however, by considering some of the terms commonly used to describe the importance of studies, terms like significance, contributions, and implications. As you clarify for yourself the meanings of these terms, you learn that whether your study matters depends on how convincingly you can argue for its importance. Perhaps most surprising is that convincing others of its importance rests with the case you make before the data are ever gathered. The importance of your hypotheses should be apparent before you test them. Are your predictions about things the profession cares about? Can you make them with a striking degree of precision? Are the rationales that support them compelling? You are answering the “So what?” question as you formulate hypotheses and design tests of them. This means you can control the answer. You do not need to cross your fingers and hope as you collect data.

Theoretical frameworks can be confounding. They are supposed to be very important, but it is not always clear what they are or why you need them. Using ideas from Chaps. 1 and 2 , we describe them as local theories that are custom-designed for your study. Although they might use parts of larger well-known theories, they are created by individual researchers for particular studies. They are developed through the cyclic process of creating more precise and meaningful hypotheses. Building directly on constructs from the previous chapters, you can think of theoretical frameworks as equivalent to the most compelling, complete rationales you can develop for the predictions you make. Theoretical frameworks are important because they do lots of work for you. They incorporate the literature into your rationale, they explain why your study matters, they suggest how you can best test your predictions, and they help you interpret what you find. Your theoretical framework creates an essential coherence for your study and for the paper you are writing to report the study.

spiepr Abs1 Every day people do research as they gather information to learn about something of interest. In the scientific world, however, research means something different than simply gathering information. Scientific research is characterized by its careful planning and observing, by its relentless efforts to understand and explain, and by its commitment to learn from everyone else seriously engaged in research. We call this kind of research scientific inquiry and define it as “formulating, testing, and revising hypotheses.” By “hypotheses” we do not mean the hypotheses you encounter in statistics courses. We mean predictions about what you expect to find and rationales for why you made these predictions. Throughout this and the remaining chapters we make clear that the process of scientific inquiry applies to all kinds of research studies and data, both qualitative and quantitative.

Building on the ideas in Chap. 1, we describe formulating, testing, and revising hypotheses as a continuing cycle of clarifying what you want to study, making predictions about what you might find together with developing your reasons for these predictions, imagining tests of these predictions, revising your predictions and rationales, and so on. Many resources feed this process, including reading what others have found about similar phenomena, talking with colleagues, conducting pilot studies, and writing drafts as you revise your thinking. Although you might think you cannot predict what you will find, it is always possible—with enough reading and conversations and pilot studies—to make some good guesses. And, once you guess what you will find and write out the reasons for these guesses you are on your way to scientific inquiry. As you refine your hypotheses, you can assess their research importance by asking how connected they are to problems your research community really wants to solve.

We investigated how the time elementary preservice teachers (PSTs) spent studying certain mathematics topics during teacher education coursework was related to performance on teaching-related tasks administered after graduation. In two studies, participants completed tasks assessing their specialized content knowledge (SCK) for teaching 12 mathematical topics addressed to varying degrees in the preparation program. We found that instructional time was positively associated with SCK demonstrated both immediately postgraduation and 2 years later. Several possible confounding factors were assessed; one, entering PSTs’ average SCK for topics, appeared to influence the relationship. Accounting for professional learning postgraduation, such as attending professional development, did not change the underlying relationship. Considering these findings, we identify policy implications for the mathematics curriculum of PST education.