The implication is free inquiry, but teaching the controversy is really a poorly defined slogan, which usually implies imagined division among evolutionists that suggests creationism and/or intelligent design are competitive alternatives.
The real controversy is the reliability of science and of the interpreters of the Bible as guides to the understanding of nature. I wonder how long I would be permitted to stay in a classroom if I taught the “real controversy.” The Bible insists that the earth is flat while science argues that the world is roughly spherical. Galileo was sent to purgatory based on a Scripture that insisted in its day that the earth revolved around the sun.
Science looks at accumulated sediments and sets earth’s age in billions of years, while the “begats” produce an age of 6,000 years. Those controversies would need to be taught. Science proposed the germ theory of disease as an alternative to the demon “theory.” Scientists synthesize biological chemicals forbidden by “the breath of God” dogmatists.
Perhaps we should put a hold on surgeries while we reconstruct the antivivisectionist tenants of faith. Would teaching the controversy include the hundreds of religion-based creation myths or only the twin versions of “truth” from Genesis? The implication is that science is abandoning its own tenant of objectivity by not teaching all possible explanations for a phenomenon.
If all scientific understanding is coded in the Bible, then it is well-disguised and even as dedicated and insightful a seeker as Newton failed to find answers there. Small consolation to the small-town public school science teacher attempting to teach the rudiments of scientific method and theories instead finding him(her)self run out of town for lacking the sophistry of the seminary that is necessary to present the Bible as a credible scientific text. Modern attempts to assert the preeminence of biblical text over scientific scholarship present a worldview fully as incredulous as the assertion of Tertullian. This early scholar argued “We have no need for curiosity since Jesus Christ, nor for inquiry since the Gospel.” Modern disciples of Tertullian have the church and access to the Internet to attempt to hammer the “square peg of science” into the “round hole of the Bible.”
Science is a limited area of knowledge constrained by a rigid set of premises that has been amazingly successful. It has earned the right to a classroom.