After 35 years of working for the school system, my Superintendent told me I would not be rehired next year. I have never been late for work,

I am surprised that your employment is at will, as I would have expected it to be subject to the hiring and firing provisions of a collective bargaining agreement.  As an at will employee, your employment can be terminated for any reason not prohibited by statute.  If you believe that termination of your employment resulted from discrimination based on a statutorily prohibited reason (e.g. race, religion, age, etc.) you may have a claim.  Even if not, however, unless you are being offered something for resigning, I don't see why you would, unless you think it will look better to a subsequent employer than being fired.