Dean Jones says, "We don't allow students to serve as graders per university policy. So that option is 'out.'
However, you are certainly free to use multiple-choice exams as you prefer. Instructors have the academic freedom to determine instructional and assessment methods. Tell you what: I will note that you expressly prefer that option in your contract so that no future administrative body criticizes you for that choice. Given the large class sizes and that you are offering the classes five days a week, your request seems reasonable. Yes, you will be helping us out -- I think we can help you out in this way.
Was there anything else we needed to discuss?"
Your response: