Scientific knowledge is empirically based, which is to say it is based on observations. Likewise, a scientific approach to problem solving will be empirical and communicated in such a way that others can understand the entire thought processes, research applied and procedures employed.
An empirical system for scientific problem solving is often called a scientific method. While there is no one scientific method or single prescribed set of procedures for doing science, it is advantageous to employ a rationale process that is reproducible and encourages imaginative inquiry. In a position statement by the National Science Teachers Association (NSTA), the NSTA recognizes that
“Although no single universal step-by-step scientific method captures the complexity of doing science, a number of shared values and perspectives characterize a scientific approach to understanding nature. Among these are a demand for naturalistic explanations supported by empirical evidence that are, at least in principle, testable against the natural world. Other shared elements include observations, rational argument, inference, skepticism, peer review and replicability of work.” http://www.nsta.org/about/positions/natureofscience.aspx
Following is a common example of a scientific method for problem solving.
Step 1: Identify the Problem (also called the question) that is to be explored or resolved.
Questions can come from: Observations in nature or other aspects of the world around us; Questions from previous learning; Imagination.
Step 2: Research the Problem. Study information about the question to better educate yourself in your search for a resolution. Research can be from: Books and Journals; Interviews; Previous Experiments; Prior Knowledge; Further Observations; Building Models
Step 3: Hypothesis: Predict a testable solution to the problem. Predictions based on models are also called hypotheses because they are testable and relate directly to the original question.
Step 4: Test the Hypothesis: This is often accomplished with some form of an experiment, further exploring of models, or conducting more extensive research. During this stage of the process observations are recorded as raw data. Provide complete disclosure of the variables, controls and other procedures used.
Step 5: Analysis: Make sense of the data. Organize the data into charts, graphs, figures or other illustrations wherever possible and provide discussion of the analysis.
Step 6: Conclusions: A conclusion relates the analysis to the original question in a clear and concise manner.