The new K-12 computing curriculum draft for Taiwan secondary schools was designed to launch in 2018 but the draft only outlined themes and contents for students to learn, without further details on key concepts to be covered in the contents. Therefore, in 2016, a Delphi study was conducted to survey the opinions about what “key learning concepts” should be included for implementation at the secondary level based on the draft. By adopting the Delphi method, different viewpoints from computer scientists and secondary school computing teachers were collected to build consensus of key concepts through a series of convergence. Based on the research results, we found the computer scientists and computing teachers had opposing opinions about whether the secondary school students should learn the advanced concepts. The purpose of this study was to understand the different views on learning concepts of the draft between two groups. The data analyzed in this study were based on the Delphi survey in 2016. This study found computer scientists tended to be more conservative about this issue, therefore they suggested that the advanced and theoretical concepts are not essential at the secondary level, e.g., recursion, searching, sorting, data compression, data conversion, and divide and conquer. This was because the computer scientists considered these concepts as what they had studied in college. Rather, computing teachers knew how to simplify these concepts for teaching at the secondary level. The research findings can serve as useful references for revising and implementing the computing curriculum in the future.