This paper presents Programming Adaptive Testing (PAT), a Web-based adaptive testing system for assessing students' programming knowledge. PAT was used in two high school programming classes by 73 students. The question bank of PAT is composed of 443 questions. A question is classified in one out of three difficulty levels. In PAT, the levels of difficulties are adapted to Bloom's taxonomy lower levels, and students are examined in their cognitive domain. This means that PAT has been designed according to pedagogical theories in order to be appropriate for the needs of the course 'Application Development in a Programming Environment'. If a student answers a question correctly, a harder question is presented, otherwise an easier one. Easy questions examine the student's knowledge, while difficult questions examine the student's skills to apply prior knowledge to new problems. A student answers a personalized test composed of 30 questions. PAT classifies a student in one out of three programming skills' levels. It can predict the corresponding classification of students in Greek National Exams. Furthermore, it can be helpful to both students and teachers. A student could discover his or her programming shortcomings. Similarly, a teacher could objectively assess his or her students as well as discover the subjects that need to be repeated.