First, try to explore your own understanding of the following:

• The theories that impact your practice
• The educational values you hold
• How your work in schools fits into the larger context of schooling and society
• The historical contexts of your school and schooling and how things got to be the way they are
• The historical contexts of how you arrived at your beliefs about teaching and learning (Kemmis, 1988)

If your general idea for your action research inquiry is the question “How can I improve the integration and transfer of problem-solving skills in mathematics?,” you might think about the following:

• Based on my experience teaching mathematics and my reading of the subject, I have been influenced by Van de Walle’s (2003) theory about teaching and learning mathematics developmentally. In particular, the goal of mathematics is relational understanding, which is the connection between conceptual and procedural knowledge in mathematics. This theory of mathematics directly affects the ways in which I think about teaching mathematics to my students.
• I hold the educational value that children ought to be able to transfer problem-solving skills to other areas of mathematics as well as to life outside of school. That is, I am committed to relevancy of curriculum.
• I believe that mathematical problem solving—and problem solving in general—fits the larger context of schooling and society by providing children with critical lifelong learning skills that can be transferred to all aspects of their life.
• The historical context of mathematics teaching suggests a rote method of memorizing facts and algorithms. Although this approach to teaching mathematics worked for me (as a child and young teacher), it no longer suffices as a teaching method today.
• The historical context of how I came to believe in the importance of changing how I teach mathematics to children has grown out of my own frustration with knowing what to do to solve a problem but not knowing why I need to use a particular approach or algorithm.
• Given this self-reflection on an area of focus related to the integration and transfer of problem-solving skills in mathematics, I can now better understand the problem before I implement an intervention that addresses my concern for how to best teach a relevant problem-solving curriculum.

This is part of the “mind work” or “mental gymnastics” of action research. It is not an activity that will immediately produce new and exciting curricula and/or teaching materials—things that may follow later in the process when you become clearer about an intervention.

Next, try to describe as fully as possible the situation you want to change or improve by focusing on who, what, when, where, and how. Grappling with these questions not only will clarify the focus area for your action research efforts but also will prevent you from moving ahead with an investigation that was too murky to begin with. For example, at this stage, you might answer these questions:

• What evidence do you have that this issue (the problem-solving skills of math students) is a problem?
• Which students are not able to transfer problem-solving skills to other mathematics tasks?
• How is problem solving presently taught?
• How often is problem solving taught?
• What is the ratio of time spent teaching problem solving to time spent teaching other mathematics skills?

Once you’ve adequately described the situation you intend to investigate, try to explain it. Focus on the why. Can you account for the critical factors that have an impact on the general idea? In essence, this is the step in which you develop a hypothesis stating the expected relationships between variables in your study (Elliott, 1991).

In this case, you might hypothesize that students are struggling with the transfer of problem-solving skills to other mathematics tasks because they are not getting enough practice, they lack fundamental basic math skills, or they have not had sufficient opportunity to use math manipulatives. Given these possible explanations for why children have not been successfully transferring problem-solving skills to other areas of mathematics, you might develop the following hypotheses:

• A relationship exists between a mathematics curriculum that emphasizes the children’s ability to know what to do and why to do it and children’s abilities to transfer problem-solving skills.
• A relationship exists between a mathematics curriculum that emphasizes the use of manipulatives (to help children create meaning) and children’s abilities to transfer problem-solving skills.

These reconnaissance activities (self-reflection, description, and explanation) help teacher researchers clarify what they already know about the proposed focus of the study; what they believe to be true about the relationships of the factors, variables, and contexts that make up their work environment; and what they believe can improve the situation. Research in Action Checklist 3–2 summarizes the critical activities for reconnaissance that you should perform at this point in the action research process.