Each education provider under this chapter and the department of corrections shall negotiate and execute a written contract for each school year or such longer period as may be agreed to that delineates the manner in which their respective duties and authority will be cooperatively performed and exercised, and any disputes and grievances resolved through mediation, and if necessary, arbitration. Any such contract may provide for the performance of duties by an education provider in addition to those set forth in this chapter, including duties imposed upon the department of corrections and its agents under RCW 28A.193.050 if supplemental funding provided by the department of corrections is available to fully pay the direct and indirect costs of these additional duties.