Relationship between programming concepts underlying programming skills

We investigated the relationship between programming skills and that of programming concepts in the introductory programming course in this paper. We introduced Modification and Programming skills from other existing skills. From the results of the midterm and final exams of our course, we got the scores in the skills, and from them we estimated the ability in concepts. By correlation, contingency, and covariance of the result of examinations, we found out that Modification and Programming are different from Tracing. We found things about concepts too, that some concepts are local while others are global, that their thinkings sometimes conflict, that the conditional statement is difficult than the loop, that the nested one is significantly difficult than the not nested one, and that understanding the concept of a structure is crucial for understanding the conditional structure and nested loop. We also found that the skills get more separated according to the development of abilities of students.