A great number of teachers in the United States have found themselves wrestling with an internal conflict between their teaching beliefs and a need to revert back to traditional modes of teaching in order to have their students demonstrate proficiency on high-stakes tests. While they want to include more non-traditional methods in their repertoire of teaching strategies, they fear that in implementing these methodologies their students will not be prepared for success on standardized testing. This paper examines why teachers experience this conflict, even when they have a commitment to non-traditional teaching strategies. Additionally, the data that is presented will demonstrate that students can and do develop computational skill, a necessity for achievement on standardized tests, in a learning environment that fosters inquiry, discovery and problem-solving.