The phrase "to teach the controversy" means to present different sides of an argument or debate, even if there is disagreement, in order to encourage critical thinking and discussion about the topic. Full definition
Educational Opportunities for science based curriculum at all levels can be as simple or complex as teaching the controversy of the science: What are the sociological foundations of accepting climate change science. (realclimate.org)
Every generation needs to be taught these controversies anew. (redeeminggod.com)