Relators-appellees (“relators”) are twenty-two school bus drivers and mechanics who were employed by respondent-appellant and cross-appellee, Springfield Local School District Board of Education, three of whom are also cross-appellants. Relators’ bargaining representative, Local 530 of the Ohio Association of Public School Employees/AESCME-AEL-CIO, entered into a collective bargaining agreement with the board that was effective, according to its terms, from September 1,1990, through 11:59 p.m. on August 31,1993.
In early 1993, the board notified the union that it was considering subcontracting its school busing services to a private company that is a division of Laidlaw Transit, Inc. (“Laidlaw”). Despite the board and union’s negotiations for a new collective bargaining agreement, no new agreement was reached by the August 31 expiration date of the existing agreement.
On September 13, 1993, the board adopted a resolution authorizing the superintendent of the school district to enter into a transportation contract with Laidlaw and abolishing the classifications of bus driver and mechanic. On September 14, union members went on strike. On September 17, most of the relators ended their strike and notified the superintendent that they wanted to have their continuing and other contracts honored by the board and that they wished to go back to work as school bus drivers employed by the board.
Also on September 17, 1993, relators filed a complaint in the Court of Appeals for Summit County. In their complaint, as subsequently amended, relators *559requested a writ of mandamus to compel the board to reinstate them to their positions as bus drivers with the board, award them back pay and benefits for the time they had been excluded from employment, order the board to recognize and honor relators’ continuing and limited contracts, prevent the board from taking any further action under the Laidlaw contract, and declare all prior actions concerning the Laidlaw contract to be void. Relators went back to work driving buses and performing their regular duties.
On October 11,1993, the board executed a transportation contract with Laidlaw in which Laidlaw agreed to provide bus drivers for transporting students for the school district and further agreed to offer existing drivers employment and recognize their accumulated seniority and benefits. In accordance with its previous resolution, the board abolished its positions of bus driver and mechanic, and relators were deemed to be employees of Laidlaw.
On January 19, 1994, the court of appeals denied the writ and dismissed the case. On appeal, we reversed the judgment of the court of appeals and remanded the cause for further proceedings. State ex rel. Boggs v. Springfield Local School Dist. Bd. of Edn. (1995), 72 Ohio St.3d 94, 647 N.E.2d 788 (“Boggs I”). We held that the court of appeals erred in dismissing the case based on materials filed by the board that were extrinsic to the complaint. Id. at 97, 647 N.E.2d at 791-792.
On remand, the court of appeals granted summary judgment in favor of the board and again denied the writ of mandamus.
On appeal, we found that relators “are entitled to a writ of mandamus.” State ex rel. Boggs v. Springfield Local School Dist. Bd. of Edn. (1998), 82 Ohio St.3d 222, 225, 694 N.E.2d 1346, 1349 (“Boggs II”). We held, “Where a collective bargaining contract executed pursuant to R.C. Chapter 4117 includes an express termination date, the agreement may be deemed to continue by implied mutual assent after that date only until such time as either party to the agreement acts in a manner inconsistent with the inference that both parties wish to be governed by the contract.” Id. at syllabus. When relators returned to work and indicated their intent to be governed by statutory law rather than the expired collective bargaining agreement, their rights were governed by R.C. 3319.081. Id. at 226, 694 N.E.2d at 1349. We thus concluded that relators “have a clear legal right to recognition of their rights to continued employment pursuant to R.C. 3319.081.” Id. at 227, 694 N.E.2d at 1350.
Based on the foregoing, we reversed the judgment of the court of appeals and remanded the cause “for application of this decision to each of the relators, including award of back pay to be calculated in accord with established principles.” Id. at 227, 694 N.E.2d at 1350.
*560On remand, the treasurer of the local school district learned that all but twelve of the relators from Boggs II had retired. By letter dated March 24, 1999, the treasurer sent letters to the remaining relators specifying that they were being reinstated as board employees pursuant to Boggs II. The treasurer advised relators that they must either report to the superintendent on April 12, 1999, to receive job assignments, resign from their employment with the board, or face termination proceedings if they did neither. In a separate letter, Laidlaw demanded that relators either resign their public employment with the board and continue their employment with Laidlaw or resign from their employment with Laidlaw.
In response to the letters, eight of the remaining twelve relators submitted their resignations from public employment with the board. The board accepted these resignations on May 11, 1999. The other four relators, Kimberly Brannon, Delores Halman, Mary Coomer, and Carol Gresens, who had not resigned from employment with the board, reported for work at the bus garage to drive their assigned routes. But Laidlaw informed these four relators that they would no longer drive school buses and that they had to report to the superintendent. The superintendent told them that the board was “no longer in the transportation business” and that these four relators would not be allowed to drive buses.
On April 13, 1999, the board authorized the new position of “General Public Employee” and assigned relators Brannon, Coomer, Halman, and Gresens to the position. In this new position, these relators were required to report to the superintendent and the business manager to receive specific job assignments. The new position further specified a one-hundred-eighty-six-day work schedule.
Before April 12, 1999, as bus drivers employed by Laidlaw, the cross-appellants, Brannon, Coomer, and Halman, worked six hours per day and were paid at hourly rates of $13.61, $13.61, and $13.87, respectively. Effective April 12, 1999, they worked as aides and custodians for four hours per day at reduced hourly rates: Brannon ($13.03), Coomer ($13.03), and Halman ($13.06).
On July 21,1999, the court of appeals accepted the following stipulations by the parties:
“a. [The board] will allow those relators, who have not retired, but have submitted their resignations prior to May 4, 1999, to retract those resignations.
“b. [The board] will offer relators, who have not retired or who have withdrawn their resignations, continuing contracts.
“c. Relators make no claims of injury other than economic damages.
“d. Relators have suffered no economic damages prior to April 12, 1999; therefore, no calculation of such prior damages is necessary on remand. Economic damages, if any, shall begin to run from April 12,1999.”
*561In their brief on remand, relators sought an order compelling the board to recognize their rights to continued employment as bus drivers and to pay relators Brannon, Coomer, and Halman back pay and lost benefits from April 12, 1999. The board countered that only relators Brannon, Coomer, and Halman had a continuing interest in this case and that they had been properly reassigned as general public employees by the superintendent.
In November 2000, the court of appeals held that under Boggs II, relators were entitled to reinstatement to their positions as bus drivers, and the court ordered the board “to offer each relator who has not retired reinstatement to the position of bus driver.” The court of appeals further held that the relators who were reassigned to the position of general public employee had not established their entitlement to lost wages and benefits.
This cause is now before the court upon the board’s appeal and relators’ cross-appeal.
In its appeal, the board asserts that the court of appeals erred in granting a writ of mandamus reinstating relators to the specific position of bus driver. The board claims that the court of appeals exceeded its authority on remand and that the superintendent of the school district acted within his authority under R.C. 3319.01 in reassigning relators to the new position of general public employee.
The board’s contentions are meritless. In Boggs II, we held that relators were entitled to a writ of mandamus, and we never specified that relators were not entitled to the specific relief they had requested, which included compelling their reinstatement to their positions as bus drivers employed by the board, awarding them back pay and benefits for the time they had been excluded from employment, and declaring the board’s actions concerning the Laidlaw contract to be void.
We now clarify that under Boggs II, relators are entitled to the relief they requested. As we recently observed, our holding in Boggs II recognized that “nothing in R.C. 3319.081 or any other statutory provision authorizes layoffs of nonteaching local school district personnel” and “[therefore, in the absence of a collective bargaining agreement, R.C. 3319.081 prohibits a school district’s board of education from abolishing positions and laying off nonteaching personnel.” State ex rel. Ohio Assn. of Pub. School Emp./AFSCME, Local 4, AFL-CIO v. Batavia Local School Dist. Bd. of Edn. (2000), 89 Ohio St.3d 191, 195, 729 N.E.2d 743, 747. Under these circumstances, the board was not authorized to lay off relators by abolishing their positions “while, in effect, retaining the same positions and hiring nonpublic employees to fill them.” Id. The board’s contracting out of these jobs to Laidlaw was consequently invalid and relators were not properly terminated from their continuing contract status. See, e.g., State ex rel. Fenton v. Dept. of Human Serv. (1993), 87 Ohio App.3d 284, 288, 622 N.E.2d 18, *56221, where the appellate court rejected a contention that reinstatement of public employees to their former positions was impossible where positions were abolished, holding that a layoff of the employees was void.
In addition, the board’s attempts on remand to coerce relators into choosing between employment with the board and with Laidlaw under its contract defies the spirit of our holding in Boggs II. Because the board’s attempted abrogation of their positions was ineffective, relators were entitled to recognition as bus drivers who are continuing-contract employees of the board.
Moreover, the board could not rely on the superintendent’s authority under R.C. 3319.01 to reassign relators to a new classification of general public employee. Where a superintendent retains the right to assign nonteaching employees, the superintendent is not authorized to modify a written contract. See, generally, Buchter, Hastings, Sheeran & Stype, Ohio School Law (2000) 161, Section T 7.13; Miner v. Lake Local School Dist. Bd. of Edn. (June 18, 1984), Stark App. No. CA-6322, unreported, at 3, 1984 WL 4930 (“R.C. 3319.01 gives the superintendent of a school district the express authority to assign non-teaching employees to appropriate positions. However, there is no statutory authority for the superintendent to unilaterally modify a written agreement.”)1 Relators had continuing contracts as bus drivers and their salary notices specified their employment as bus drivers.
This conclusion comports with our duty to construe statutes to avoid unreasonable or absurd results. R.C. 1.47(C); State ex rel. Besser v. Ohio State Univ. (2000), 87 Ohio St.3d 535, 540, 721 N.E.2d 1044, 1049. The board should not be able to rely on the superintendent’s statutory authority to reassign employees in order to salvage its illegal layoff of relators and concomitant privatization of school bus services.
Furthermore, despite the superintendent and the board’s claims that it was no longer in the transportation business, this is also not a case where busing services were no longer necessary in the school district. See Ferdinand v. Hamilton Local Bd. of Edn. (1984), 17 Ohio App.3d 165, 169-170, 17 OBR 296, 301, 478 N.E.2d 835, 840-841, distinguishing State ex rel. Cutler v. Pike Cty. Joint Area Vocational School Dist. (1983), 6 Ohio St.3d 138, 6 OBR 195, 451 N.E.2d 800.
*563Based on the foregoing, relators are entitled to reinstatement by the board to continuing-contract status as bus drivers. The court of appeals did not err in holding that under Boggs II, they were so entitled.
Relators’ Cross-Appeal: Offer of Reinstatement
In their cross-appeal, relators Brannon, Coomer, and Halman initially assert that the court of appeals erred in ordering the board to offer each relator who had not retired reinstatement to the position of bus driver rather than reinstating them. Their claim has merit.
In Boggs II, we held that relators “have a clear legal right to recognition of their rights to continued employment pursuant to R.C. 3319.081.” Boggs II, 82 Ohio St.3d at 227, 694 N.E.2d at 1350. In fact, as noted previously, the court of appeals acknowledged this by stating in its opinion, “Because the Supreme Court remanded this case for application of its decision that a writ should be granted, this Court must grant Relators the mandamus relief they requested: reinstatement to their positions as bus drivers.” (Emphasis added.) The court of appeals also lacked authority to disregard our mandate. State ex rel. Sharif v. McDonnell (2001), 91 Ohio St.3d 46, 47, 741 N.E.2d 127, 129; State ex rel. Crandall, Pheils & Wisniewski v. DeCessna (1995), 73 Ohio St.3d 180, 184, 652 N.E.2d 742, 745.
Therefore, we reverse that portion of the court of appeals’ judgment ordering that the board offer relators who have not retired reinstatement as bus drivers for the board and order the board to reinstate those relators to the bus driver positions with the board.
Relators’ Cross-Appeal: Lost Wages and Benefits
Relators Brannon, Coomer, and Halman next assert that the court of appeals erred in denying their requests for back pay and lost School Employees Retirement System (“SERS”) benefits.
A wrongfully excluded public employee may obtain back pay and related benefits in a mandamus action following reinstatement or, in some cases, may obtain reinstatement and back pay and related benefits in the same mandamus action. See State ex rel. Schneider v. N. Olmsted City School Dist. Bd. of Edn. (1992), 65 Ohio St.3d 348, 350, 603 N.E.2d 1024, 1025, and cases cited therein. In order to be entitled to back pay and related benefits, the wrongfully excluded public employee must establish the amount recoverable with certainty. Monaghan v. Richley (1972), 32 Ohio St.2d 190, 61 O.O.2d 425, 291 N.E.2d 462, syllabus; State ex rel. Baran v. Fuerst (1992), 65 Ohio St.3d 413, 415, 604 N.E.2d 750, 752. This “certainty” generally refers to a specific monetary value as well as the quality of proof required. See State ex rel. Hamlin v. Collins (1984), 9 Ohio St.3d 117, 120, 9 OBR 342, 345, 459 N.E.2d 520, 524.
*564Relators Brannon, Coomer, and Halman first contend that the court of appeals erred in not applying the hourly rates they were paid by Laidlaw in determining their request for back pay and benefits. The parties stipulated that these relators do not claim back pay and related benefits for the period before April 12, 1999, when they were employed at the higher rates paid by Laidlaw. They claim that on and after April 12,1999, when they earned approximately thirteen dollars per hour in their new positions as general public employees, they were entitled to earn the hourly rates that they had been paid by Laidlaw.
Relators’ contention is meritless. The amount recoverable by a public employee entitled to reinstatement is that amount which “the employee would have received had he not been wrongfully dismissed, reduced by the amount he earned, or in the exercise of due diligence could have earned in appropriate employment, during the discharge period.” Id. at 118, 9 OBR at 343, 459 N.E.2d at 522. The board paid relators Brannon, Coomer, and Halman as nonteaching public employees more than what it had paid them when they were wrongfully discharged in 1993.
Relators were not entitled to the higher rates paid by the private entity because, as the court of appeals determined, “[t]he fact that the private entity gave Relators certain raises over the years did not give them any right to earn those same wages with Respondent.” In other words, the fact that Laidlaw paid relators higher hourly rates does not establish with the requisite certainty that had the board not wrongfully discharged relators in 1993, they would have received the same hourly rates from the board as Laidlaw paid them. Cf. State ex rel. Brettrager v. Newburgh Hts. (2000), 89 Ohio St.3d 272, 275, 730 N.E.2d 981, 983 (“Brettrager could not establish with the requisite certainty the monetary amount of the purported full-time compensation to which he claimed entitlement because the village ordinance conditioned pay raises on evaluations and recommendations”). Instead, as the court of appeals observed, relators Brannon, Coomer, and Halman were at best entitled to the hourly rates paid them by the board as general public employees, which was higher than the rates it paid them when they wrongfully discharged relators as bus drivers in 1993.
Relators Brannon, Coomer, and Halman next contend that they are entitled to back pay for the two hours per day that they lost when the board employed them as general public employees beginning April 12, 1999. When these relators were wrongfully discharged, they worked six hours per day, but as of April 12, 1999, their hours were reduced to four hours per day. The court of appeals recognized that these relators “should have been paid for a six-hour day each school day.” Nevertheless, the court of appeals refused to compensate these relators for their lost work hours because relators did not provide the court “with a school calendar or other means by which to determine the number of work days.”
*565The court of appeals erred in so holding. Relators did present evidence of a 1998-1999 one-hundred-eighty-six-day school calendar for board employees with continuing contracts working four or six hours per day.
The amount of back pay to which relators Brannon, Coomer, and Halman are entitled was established with the requisite certainty. Although certainty is generally established by a specific monetary amount, Hamlin, 9 Ohio St.3d at 120, 9 OBR at 345, 459 N.E.2d at 524, a definitive dollar figure is not available for wrongfully discharged employees who have not yet been reinstated because the damages continue to accrue until that time. In these cases, the necessary certainty requires only a readily ascertainable dollar figure upon reinstatement. Here, these relators have sufficiently proved their back pay: the hourly rate at which the board currently pays them times the two additional hours they would have worked each day had they not been wrongfully discharged as bus drivers times the number of work days from April 12, 1999, until their reinstatement.
The court of appeals erred in failing to award back pay to relators Brannon, Coomer, and Halman in this amount.
Finally, relators Brannon, Coomer, and Halman assert that the court of appeals erred by not ordering the board to pay its SERS contributions for them after April 12, 1999. Relators established that the rate of the board’s SERS contribution was fourteen percent of each of their salaries. See, also, R.C. 3309.49. The board has never disputed this percentage figure. Therefore, the court of appeals’ conclusion that relators “did not present any evidence as to how their statutory benefits are calculated” is meritless.
Moreover, the SERS benefits were established with the requisite certainty because the gross wages to which the percentage applies and to which these relators are entitled will also be readily ascertainable upon their reinstatement as bus drivers by the board.
Conclusion
For the foregoing reasons, we reverse the judgment of the court of appeals insofar as it ordered the board to offer to reinstate those relators who have not retired to the position of bus driver rather than ordering the board to reinstate them. The judgment is also reversed to the extent that the court failed to order back pay and benefits to relators Brannon, Coomer, and Halman for the reduced work hours and lost SERS contributions they have incurred and will continue to incur until they are reinstated as bus drivers employed by the board. We hereby order the board to reinstate those relators who have not retired and to award back pay and benefits to relators Brannon, Coomer, and Halman for the reduced work hours and lost SERS contributions they have incurred and will continue to *566incur until their reinstatement as bus drivers employed by the board. In all other respects, the judgment of the court of appeals is affirmed.
Buckley, King & Bluso, James E. Melle and Scott F. Sturges, for appellees and cross-appellants. Johnson & Angelo, James A. Budzik and Jeffrey C. Miller, for appellant and cross-appellee.Judgment affirmed in part, reversed in part and unit granted.
Moyer, C.J., Douglas, Resnick, F.E. Sweeney, Pfeifer and Lundberg Stratton, JJ., concur. Cook, J., not participating.. Cf., also, Baker & Carey, Baker’s Ohio School Law (2000) 334, Section 7.18, in which the authors suggest that school boards that wish to authorize superintendents to assign teachers to other positions should note specific assignments in board minutes or on contract documents, and that express language should be included in documents indicating that the teacher is subject to reassignment by the superintendent. No such express language is evident in the relevant documents here.