Of the following ideas, identify which one would be the most important for a new teacher to know: Knowledge of the major paradigms, knowledge of the major concepts, Historical and cultural, or pedagogical knowledge?
This is a great question. Unfortunately, it forces a false choice as to all three concepts are important for a teacher to understand as they enter the profession. At the same time, I am not sure any teacher who is entering the profession is able to "know" any of the three domains. They can have engaged in study in each of the domains, and it is hopeful that they have done so. The entry of a new teacher into the profession requires that they have as much knowledge as possible in the three domains mentioned as well as others such as classroom management skills and foundational elements of special education and differentiated instruction.
Knowledge of the major paradigms is essential for teachers to understand how students learn. The more a teacher entering the profession understands these, the better the chance they can recognize nuanced learning approaches of students and tailor make approaches to maximize their ability to learn. Pedagogical knowledge is essential because it guides the core vision of the teacher, enabling them to understand their function in the classroom and how this is to be maximized. Knowledge of historical, cultural, and content concepts is essential for teachers to possess as it makes them more effective in the classroom setting in teaching their students.
I am not sure a choice can be made because the three domains are essential. At the same time, I am not sure that any teacher "knows" all elements about the domains. The ongoing professional reflection intrinsic to teaching demands that teachers gain more knowledge and understanding in domains such as these in their first year or their twentieth year. It is in this regard where I think that the question facilitates great thought and introspective analysis, but to make a choice of one concept at the cost of others reduces the effectiveness of a new teacher.
My answer is to say that one is missing--the knowledge of students. Having experience with all kinds and levels of students is helpful, far beyond the student teaching experience. Volunteer in a homeless shelter and look at how many students there are. Volunteer in a summer reading program and see how some students struggle with the most basic skill. Visit programs for daycare and look at how young ones are cared for when they enter the building. Volunteer for a summer school program for middle school and learn the children's characteristics. Volunteer in a GED program for young adults or a GED program for adults and find out what they are going through or how they got there. In the jail system, the one most common answer for why a student dropped out is "Nobody cared" or "They were glad to get rid of me". Find out why. Listen to them talk about themselves and their obstacles to learning. In this day and age, teachers need to get beyond the school learning and find out about the people they will be teaching. Some of that knowledge is shocking, and helps teachers understand their classrooms better.