The plaintiff, Nancy Madden (Madden), and the defendants, the Contributory Retirement Appeal Board (CRAB) and the Teachers’ Retirement Board (TRB), appeal from a Superior Court judgment regarding the calculation of Madden’s retirement benefits for her service as a public school teacher. We transferred the case to this court on our own motion and affirm the Superior Court judgment.
Teacher retirement benefits are calculated by a formula that multiplies an age factor by the years of service and by the aver*698age salary for the highest three consecutive years of service or the last three years of service whether or not consecutive, whichever is greater. G. L. c. 32, § 5 (2) (a). These appeals raise the question whether, consistent with a retirement system member’s contractual expectation under G. L. c. 32, § 25 (5),2 the TRB can enforce a 1990 regulation to prorate the part-time service of a teacher who joined the retirement system before the regulation’s enactment and became full time after its enactment. This application of the regulation reduces the teacher’s creditable service.3
1. Factual background. The relevant facts are not in dispute. Madden taught special needs students in the Arlington public school system beginning in 1973. She worked as a part-time teacher until September, 1980, when, because of a school closure, she was required to work full time for two years. From September, 1982, until September, 1994, she again taught part time before returning to full-time employment.
Before returning to full-time status in 1994, Madden corresponded with the TRB regarding the retirement benefits consequences of resuming full-time employment. After several communications, the TRB, in February, 1996, informed Madden that because she returned to full-time employment, her entire period of part-time teaching would be prorated under 807 Code Mass. Regs. § 3.04 (2), enacted in 1990. Applying § 3.04 (2) would result in Madden’s receiving credit for fewer years of service and, thus, smaller annual retirement benefits.
Madden appealed the TRB’s decision to CRAB. After a hear*699ing, an administrative magistrate of the Division of Administrative Law Appeals concluded that the TRB properly applied § 3.04 (2) in calculating Madden’s retirement benefits. CRAB adopted the magistrate’s decision, and Madden appealed to the Superior Court under G. L. c. 30A. A Superior Court judge ruled that the TRB could not prorate Madden’s pre-1990 part-time service because it would violate her contractual expectations in the teacher retirement system. The judge held, therefore, that for each year of Madden’s part-time service prior to the promulgation of § 3.04 in 1990, she must be credited with a full year of service. However, because § 3.04 was a proper adjustment to the teacher retirement system, the new regulation could be applied to all part-time work after its promulgation. Thus, the judge allowed the TRB to prorate Madden’s part-time service after 1990.
2. Regulatory background. From 1957 to 1989, the TRB prorated teachers’ part-time service pursuant to the provisions of 807 Code Mass. Regs. § 3.02. That regulation provided that:
“All persons defined as teachers who earn their salary during the school year from September to June, shall, irrespective of the manner in which their salary is paid, be allowed a year’s credit for each full school year of service and one-tenth of a year for each full month of service rendered during a school year.”
In 1989, the Appeals Court interpreted this regulation in a case involving the validity of prorating a teacher’s part-time service. See O’Brien v. Contributory Retirement Appeal Bd., 27 Mass. App. Ct. 1124, 1125 (1989). There, the TRB asserted that it was authorized under § 3.02 to prorate a teacher’s part-time service for purposes of calculating retirement benefits. Id. at 1126. The Appeals Court concluded that § 3.02 did not provide authority to prorate a teacher’s part-time service because “[t]he rule makes no mention of ‘full time’ or ‘part time’ service and it does not draw any distinction between full time teachers and part time teachers.” Id. at 1127. The Appeals Court held that, because a local retirement board may only prorate part-time service pursuant to a rule or regulation, and the regulation purporting to do so did not provide authority to prorate part-time service, the TRB could not prorate part-time service and was therefore required to credit a full year of service for each *700year of part-time work. Id. at 1126, citing Gallagher v. Contributory Retirement Appeal Bd., 4 Mass. App. Ct. 1, 11 (1976).4
Presumably in response to the O’Brien decision, in 1990 the TRB promulgated 807 Code Mass. Regs. § 3.04.5 Section 3.04 explicitly provides for the calculation of part-time service. Section 3.04 (2), which the TRB applied to prorate all Madden’s part-time service, provides that “any part-time employee who becomes full-time shall receive credit for their part-time service on a pro-rated basis as it relates to a full-time position.” 807 Code Mass. Regs. § 3.04 (2).
Madden contends she has a contractual right as a member of the teachers’ retirement system that § 3.02, the regulation in effect when she entered the teachers’ retirement system, will be applied to all of her work while she was a member of the teachers’ retirement system. Because in the O’Brien case it was determined that § 3.02 does not permit prorating part-time service, Madden argues that she had an expectation that none of her part-time service would be prorated. CRAB and the TRB contend that Madden did not have a contractual expectation *701when she entered the system that her part-time service would not be prorated and therefore § 3.04 can be applied to prorate all her part-time service. We conclude that only Madden’s post-1990 part-time service may be prorated consistent with her contractual expectations.
3. Prorating part-time service before 1990. The State retirement system creates a contractual relationship between its members and the State. See Opinion of the Justices, 364 Mass. 847, 860 (1973); G. L. c. 32, § 25 (5). There can be no change to the system that deprives members of benefits as long as they have paid the required contributions. In Opinion of the Justices, supra, the Justices explained the meaning of a contractual expectation under G. L. c. 32, § 25 (5): the government may not deprive members of the “core of . . . reasonable expectations” that they had when they entered the retirement system. Id. at 862. See McIntire v. Contributory Retirement Appeal Bd., 417 Mass. 35, 38 (1994). This does not, however, preclude modifications to the retirement scheme, but such modifications must be reasonable and “bear some material relationship to the theory of a pension system and its successful operation.” Opinion of the Justices, supra, quoting Wisley v. San Diego, 188 Cal. App. 2d 482, 485-486 (1961).
Because the TRB maintained a consistent practice prior to 1973 of prorating part-time service, Madden cannot claim that when she entered the teacher retirement system she expected that her part-time service would not be prorated. However, Madden can claim a more general contractual expectation that all retirement regulations in effect when she entered the system would be applied to her in accord with the law. Section 3.02 was the regulation governing the calculation of part-time service when Madden entered the system. Therefore, under G. L. c. 32, § 25 (5), Madden’s contractual expectation is defined by a proper interpretation of that regulation. In 1989, the Appeals Court determined that § 3.02 did not permit the TRB to prorate part-time service. See O’Brien, supra at 1127. Because Madden had an expectation that a lawful interpretation of § 3.02 would apply to her and no other regulation prior to 1990 authorized the TRB to prorate part-time service, Madden is entitled to receive one full year of credit for each year she worked from 1973 until 1990.
CRAB and the TRB contend that Madden cannot base her contractual expectation on the O’Brien decision’s interpretation *702of § 3.02 because that case was decided sixteen years after Madden joined the retirement system. Madden’s contractual expectation is not based on the O’Brien decision; it is based on a proper interpretation of the regulation in effect when she entered the system. A practice which exceeded the TRB’s authority under the promulgated regulations cannot define the scope of a member’s expectations under the regulation and statute. See Boston Retirement Bd. v. McCormick, 345 Mass. 692, 698-699 (1963) (employee can seek remedy despite executing form surrendering rights under the retirement system when retirement board’s action limiting benefits is later determined to exceed board’s statutory authority). Teacher retirement system members are entitled to rely on a properly construed regulation in developing contractual expectations as to their retirement benefits. Thus, Madden had a contractual expectation that the lawful interpretation of § 3.02 as defined by the O’Brien decision would be applied to her.
In addition, CRAB and the TRB argue that prorating Madden’s pre-1990 part-time service does not breach her contractual expectations because Madden knowingly brought herself within the ambit of § 3.04 (2), which allows prorating, by choosing to return to full-time service in 1994. However, Madden was never informed prior to accepting a full-time appointment in 1994 that all her part-time service would be prorated pursuant to § 3.04 (2). Madden first sought guidance from the TRB in November, 1993, and was not notified that the TRB planned to prorate all her part-time service until February, 1996, approximately one and one-half years after Madden resumed full-time teaching. Because the TRB did not inform Madden of its position until 1996, Madden did not resume full-time teaching with the understanding that all her part-time service would be prorated.
4. Prorating part-time service after 1990. Having concluded that Madden’s pre-1990 part-time service cannot be prorated, we now turn to consider whether the TRB can enforce § 3.04 (2) to prorate Madden’s post-1990 part-time service. We must determine whether applying § 3.04 (2) to prorate Madden’s post-1990 service is an impairment of vested contractual rights in violation of G. L. c. 32, § 25 (5), or is a reasonable modification to the teacher retirement system. See Opinion of the Justices, supra at 862. The existence of vested contractual rights “does not preclude reasonable modifications of the pension plan prior to the employees’ retirement. Reasonable modifications *703are often necessary ... to maintain the integrity of the system in order to carry out its beneficent purpose.” Id., quoting Wisley v. San Diego, supra.
Because of the Appeals Court’s decision in O’Brien, teachers who, prior to 1990, worked most of their career part-time and then worked their last three years full time (mixed service teachers) received the same level of retirement benefits as a teacher who worked exclusively full time even though the mixed-service teacher worked less time and contributed less to the retirement system. This disparity occurred because the mixed-service teachers, for purposes of the teacher retirement benefits formula, were credited a full year for each of their part-time years of service and a full-time salary based on their last three years of service.6
In 1990, the TRB addressed this disparity by promulgating § 3.04 which, inter alia, permitted prorating the part-time service of any teacher who changed status from part time to full time after the regulation went into effect. We have recognized that “paying excessive benefits to some claimants puts a strain on the system in making the payments due to others.” Massachusetts Teachers Ass’n v. Teachers’ Retirement Bd., 383 Mass. 345, 348-349 (1981). The TRB’s attempt at correcting the disparity certainly “bear[s] some material relationship to the theory of a pension system and its successful operation” by assuring that members receive a proportional share of retirement benefits and, thus, can be prospectively enforced without upsetting the contractual expectation of retirement system members. Opinion of the Justices, supra at 862. Therefore, the TRB can, *704consistent with Madden’s contractual expectations, prorate her part-time service worked after the promulgation of § 3.04.
Judgment affirmed.
General Laws c. 32, § 25 (5), provides:
“The provisions of sections one to twenty-eight, inclusive, and of corresponding provisions of earlier laws shall be deemed to establish and to have established membership in the retirement system as a contractual relationship under which members who are or may be retired for superannuation are entitled to contractual rights and benefits, and no amendments or alterations shall be made that will deprive any such member or any group of such members of their pension rights or benefits provided for thereunder, if such member or members have paid the stipulated contributions specified in said sections or corresponding provisions of earlier laws.”
Prorating the years of service of a part-time teacher means that the teacher will be credited with only the portion of the year worked. For example, a teacher who worked a full year of half-time service will receive one-half year of credited service for the purpose of calculating teacher retirement benefits. See note 6, infra.
In O’Brien v. Contributory Retirement Appeal Bd., 27 Mass. App. Ct. 1124 (1989), the plaintiff worked her entire seventeen year career part time. Her salary was one-half the salary of a full-time teacher. Her retirement benefits should have been one-half as great as an otherwise similarly situated full-time teacher. However, pursuant to § 3.02, the TRB prorated her years of service which resulted in her receiving retirement benefits one-quarter as great as a full-time teacher. This occurred because the plaintiff’s salary was already one-half as great as a full-time teacher’s salary. By reducing her years of service, the TRB prorated the calculation of her teacher retirement benefits twice which resulted in a disproportionately low amount. The Appeals Court noted that “[s]uch a result is indeed arbitrary and unreasonable.” Id. at 1127 n.3.
Title 807 Code Mass. Regs. § 3.04 (1993) provides:
“(1) Any part-time employee who qualifies for membership, shall receive one year of creditable service provided they work the hours required by their position and provided their entire service is on a part-time position.
“(2) Subject to verification as specified by the agency any part-time employee who becomes full-time shall receive credit for their part-time service on a pro-rated basis as it relates to a full-time position.
“(3) Subject to verification as specified by the agency any full-time employee who becomes part-time shall receive credit for their part-time service on a pro-rated basis as it relates to a full-time position.”
To illustrate the disparity, we offer the following hypothetical. Teacher A, a sixty-four year old teacher, worked twenty years exclusively full-time and the last and highest three years of her salary averaged $50,000. Under the teacher retirement benefits formula, Teacher A would receive $24,000 annually. (Age Factor [.024] multiplied by Years of Service [20] and by Salary [50,000] 24,000.) Teacher B, a sixty-four year old mixed service teacher worked twenty years. She worked the first seventeen years half-time and the last three years full time. Her last and highest three years of salary averaged $50,000. Under the teacher retirement benefits formula, she also would receive $24,000 annually. (Age Factor [.024] multiplied by Years of Service [20] and by Salary [50,000] $24,000.) Thus, even though Teacher B worked fewer hours for the first seventeen years of her career and contributed less to the retirement system than Teacher A, Teacher B would receive the same retirement benefits as Teacher A.