Many successful teaching and research statements do the same basic three things:
- Describe broad themes or approaches that tie together your research or teaching.
- Narrate specific relevant examples of your achievements related to these themes or approaches that illustrate your experience and qualifications.
- Describe your aspirations and future directions in terms of your research or teaching.
It might help to think of the research and teaching statements in terms of other items in your packet. For example, your writing samples will provide concrete examples of your work as a scholar so don't need to prove this in a research statement. Similarly, your CV will show your publication and teaching record so you don't need to reiterate this either. Instead, provide a high-level overview of your approaches to research or teaching while referring to examples from your experience that help make the case for your excellence in each area.
Statements also provide a space for you to explain what you hope to do in the future. I used my teaching statement to describe examples of graduate and undergraduate classes I could teach that were on the books at the department I was applying to and that I would design from scratch. I used my research statement to explain the areas of research I was hoping to move into in the future.
Your goals with the statement may also be to address potential weaknesses in your application. For example, if you have little teaching experience, your teaching statement is an opportunity to show that you have thought deeply about teaching and that you have gained relevant skills through experience like mentorship that might not show up on your CV.
Specific expectations, in terms of of teaching and research statements, may vary from field to field and even within fields, but you can generally assume that authors have quite a bit of latitude. Look for examples online and, perhaps, more usefully, contact successful recent job market candidates you know to ask their materials.