
388 So.2d 1261 (1980)
Mary Kathryn FOX, f/k/a Mary Kathryn Haislett, Appellant,
v.
Benton Myron HAISLETT, Appellee.
No. 79-1731.
District Court of Appeal of Florida, Second District.
September 17, 1980.
Rehearing Denied October 20, 1980.
*1263 Paul H. Amundsen and Susan E. Trench of Peeples, Earl, Smith, Moore & Blank, P.A., Miami, for appellant.
Thomas E. Reynolds and Edward D. Foreman, St. Petersburg, for appellee.
DANAHY, Judge.
Both the mother and the father are unhappy with, and challenge on this appeal, a post-judgment ordered entered by the trial judge concerning the extent of the father's obligation to pay the tuition and fees at a private school in which the parties' minor child is currently enrolled. We agree with the mother that the trial judge improperly modified the provisions in the final judgment of dissolution of marriage requiring the father to pay such expenses, and we reverse.
The marriage of the parties was dissolved by a final judgment entered on October 8, 1971. That final judgment incorporated an agreement between the parties which provided that the father would pay $250.00 per month as child support for the parties' one minor child, a daughter. Custody of the daughter was given to the mother. The dispute in this case concerns the following paragraph of the agreement:
13. PRIVATE EDUCATION FOR CHILD: The parties hereto desire that the child of the parties shall receive a private education in private schools in the State of Florida or other states where the child might reside. The [father] agrees that he shall pay all fees and tuitions necessary to maintain said child in the private education and which is contemplated to begin with kindergarten of this year.
The minor child, Kelly, attended a private school during kindergarten and the first, second and third grades. The father paid the tuition during these years, which was approximately $350.00 for the year of kindergarten and $1,000 for each of the first, second and third grades.
Kelly then moved with her mother to Gainesville and was enrolled in a private school there for the fourth grade. The father paid the tuition and fees for that year, which were approximately $1,000.00. After the fourth grade, however, Kelly's mother transferred her to a public school in Gainesville because she believed that the private school was not much better than the public school. Kelly attended public school in Gainesville for the following two years.
When Kelly was about to enter the seventh grade, she and her mother moved to Miami. There Kelly attended a public school during the fall semester of her seventh grade. The mother testified that during this semester, Kelly's grades dropped from A's and B's to C's and D's, and there were drastic changes in her social behavior. *1264 For these reasons, the mother decided to enroll Kelly in a private school for the spring semester of seventh grade, and notified the father of this decision. The mother testified that she shopped around for a suitable private school and found that many would not accept the child due to religious affiliation or lack of space. She finally selected the Carrollton School, where the tuition is in excess of $2,300.00 per year. That amount is less than the tuition at some private schools investigated by the mother and higher than that at some other schools.
When the mother demanded that the father pay the tuition at the Carrollton School, he refused to do so. The mother then initiated these proceedings by filing a motion asking that the father be held in contempt of court for his failure to abide by the provisions in the final judgment regarding Kelly's private education.
The father's response asserted three defenses: (1) that the mother was estopped to assert or enforce the provisions of the final judgment regarding Kelly's private education because she had agreed to a modification of those provisions; (2) that the parties had agreed that Kelly's education would be pursued in public rather than in private schools and this agreement modified the provisions of the final judgment by relieving the father of any further obligation to pay the expenses of a private education; and (3) that the tuition and fees at the Carrollton School were unreasonable, excessive, and beyond the intent of the parties when they originally agreed that the father would pay the costs of a private education for Kelly.
The trial judge heard the testimony of both parties, which revealed their disagreement on the question whether Kelly should receive a private education at this point in her schooling. The father, who has remarried and has another daughter in school (public), has changed his mind on the benefits of a private education and expressed the belief that Kelly would be better off in a public school. After considering all the evidence presented, the trial judge entered the order from which this appeal is taken. That order first recited that the mother's motion for contempt was denied. It then recited that the father's petition for modification of the final judgment was denied, although the father had filed no such petition. The order then recited the following:
ORDERED AND ADJUDGED that the [father] shall not be responsible for any of the educational expenses of the minor child in the Carrollton School which she is presently enrolled for the current semester which began January 1, 1979, as said enrollment was accomplished by the wife over the objection of [the father] after an extended period of public education of said minor child. It is further
ORDERED AND ADJUDGED that [the father] shall be responsible for tuition and fees of the minor child of the parties beginning with the school year which commences in the fall of 1979. The obligation of the [father] for tuition and fees shall in no event exceed the tuition and fees at the school in Gainesville, Florida, where said child was previously enrolled and where said child was enrolled at the time of entry of the Property Settlement Agreement by the parties, and which fees were therefore within the contemplation of the parties at the time they entered into the Property Settlement Agreement in this cause.
The trial judge no doubt selected a means of resolving in some fair manner the dispute between the mother and father concerning the expenses of Kelly's private education, but in so doing he neglected to apply the correct rules of law. Those rules take into consideration the interests of the minor child and her rights under the provisions of the final judgment.
At the threshold, we reject the father's argument that the provisions in the final judgment concerning Kelly's private education do not fall into the category of "child support" and thus are not governed by the rules of law pertaining to the enforcement and modification of child support provisions. A parent's obligation to his minor child includes the obligation to provide for the child's education. Finn v. Finn, 312 So.2d 726 *1265 (Fla. 1975). Therefore, provisions for education are a proper element in an allowance for the benefit of a minor child in a final judgment of dissolution of marriage. Rouse v. Rouse, 313 So.2d 458 (Fla. 3d DCA 1975); Annot., 56 A.L.R.2d 1207 (1957). In our view, the issues in this case clearly involve a matter of child support.
The first rule which the trial judge should have recognized is that he has no authority to cancel or reduce a past-due installment of child support. Pottinger v. Pottinger, 133 Fla. 442, 182 So. 762 (1938); Petrucci v. Petrucci, 252 So.2d 867 (Fla. 3d DCA 1971). Modification of child support provisions may not be retrospective in application. Therefore, the trial judge erred in relieving the father of any obligation to pay those educational expenses at the Carrollton School already incurred by reason of Kelly's enrollment in that school.
We recognize the rule that matters of avoidance, such as estoppel, are a valid defense in an action to enforce past-due installments of child support. Teta v. Teta, 297 So.2d 642 (Fla. 1st DCA 1974); Hurst v. Hampton, 274 So.2d 891 (Fla. 4th DCA 1973). Additionally, in extraordinary or compelling circumstances, a court may decline to enforce such a past-due obligation. Pottinger v. Pottinger, supra; Smithwick v. Smithwick, 343 So.2d 945 (Fla. 3d DCA 1977); Warrick v. Hender, 198 So.2d 348 (Fla. 4th DCA 1967). In this case, however, we find no evidence supporting the father's claim of estoppel, nor do we find any evidence of extraordinary or compelling circumstances.
This does not mean, however, that the trial judge abused his discretion in denying the mother's motion to hold the father in contempt. The imposition of contempt as a sanction against a party defaulting in the payment of child support is a discretionary matter, not a matter of right. The trial judge may apply equitable considerations and those considerations in this case support the trial judge's decision not to impose the extreme sanction of contempt. Pottinger v. Pottinger, supra; Warrick v. Hender, supra; Boyle v. Boyle, 194 So.2d 64 (Fla. 3d DCA 1967).
Insofar as the trial judge's decision limiting the father's obligation for future educational expenses is concerned, it was erroneous insofar as it purported to modify the educational expense provisions of the final judgment. In the first place, a trial judge is without authority to modify child support provisions where no pleading is filed directed to modification. Cortina v. Cortina, 98 So.2d 334 (Fla. 1957); Smithwick v. Smithwick, supra. The father filed no petition herein or other pleading which might be construed as a request for modification.
Furthermore, a fundamental prerequisite to modification of child support payments is a showing of a substantial change of circumstances, including financial circumstances, of one or both parties. Burdack v. Burdack, 371 So.2d 528 (Fla. 2d DCA 1979). The party seeking modification has the burden of showing such a change in circumstances. No such showing was made in this case. On the contrary, the father relies on the argument that modification was accomplished by an agreement of the parties that Kelly should receive a public rather than a private education; therefore, the father argues, the trial judge erred in requiring him to pay tuition in any amount for Kelly.
Our initial reaction is to question the validity of an agreement such as that which the father alleges was reached in this case.[1] The third district court of appeal has indicated that parents may validly agree to reduce or eliminate child support previously ordered. Wiener v. Wiener, 343 So.2d 1319 (Fla. 3d DCA 1977). On the other hand, the first district court of appeal has emphatically rejected that proposition. In Armour v. Allen, 377 So.2d 798 (Fla. 1st DCA 1979), the court said:

*1266 [T]he existence of an agreement . . purporting to relieve the husband of child support payments, may be a relevant factor going to the willfulness of the husband's failure to pay, but does not affect the obligation of child support as such. The law is clear that the parents may not contract away the rights of their child for support. Neither may the mother waive the child's right to support by acquiescing in the father's non-payment of support. Child support is a right which belongs to the child. It is not a requirement imposed by one parent on the other; rather it is a dual obligation imposed on the parents by the State.
The fourth district court of appeal has stated a similar view. Lang v. Lang, 252 So.2d 809 (Fla. 4th DCA 1971). That court had previously expressed these thoughts, with which we are inclined to agree:
The power of the parties to modify by agreement or for one party to waive or otherwise be deprived of the provisions of child support in a divorce decree is subject always to the supervision and scrutiny of the court and will be given sanction and recognition only if the best interests of the child or children are fully served. An agreement, either express or implied, which purports to relieve a father of his duty to support a minor child entirely and permanently offends against public policy and is void. However, the mother and father may as between themselves validly agree, expressly or impliedly, that one rather than the other shall provide or procure the proper support if the best interests of the child are served thereby. (emphasis added)
Warrick v. Hender, supra, at page 351.
But in this case we need not address the question whether post-judgment modification of child support by agreement is valid and effective, because we find a total lack of proof establishing an agreement between the parties to modify the educational provisions in the final judgment as contended by the father. Therefore, we reject the father's argument that the trial judge should have relieved him entirely of any obligation to pay the expenses of a private education for Kelly.
The father is quite correct, however, in his contention that the provision in the final judgment for payment of the tuition and fees for private education should not be interpreted as unlimited and require him to pay tuition and fees at a private school no matter how outrageously expensive the school might be. We agree with the proposition that a provision requiring a father to pay tuition, with no limitation expressed, should be construed to require the payment of tuition in a reasonable amount. Norrell v. Norrell, 236 Ga. 797, 225 S.E.2d 305 (1976). We disapprove of the trial judge's determination that the tuition at the last private school attended by Kelly in Gainesville measures the extent of the father's obligation because those fees were within the contemplation of the parties at the time they entered into the agreement which was incorporated in the final judgment. There is no support in the record for such a determination.
We reverse and remand with directions that the trial judge determine whether the tuition and fees at the Carrollton School, where Kelly is presently enrolled, are reasonable in amount and, if not, what amount of tuition and fees would be reasonable for Kelly to receive an acceptable private education in Miami. After making that determination, as to which he may receive additional evidence, the trial judge shall enter an appropriate order limiting the father's obligation to that amount of tuition and fees found to be reasonable, subject to modification upon a showing of a substantial change in the circumstances upon which the trial judge based his determination of reasonableness.
REVERSED AND REMANDED WITH DIRECTIONS.
HOBSON, Acting C.J., and RYDER, J., concur.
NOTES
[1]  Cases dealing with the validity and effect of agreements between former spouses relieving the father from further payment of child support provided in an earlier decree are collected in an annotation at 57 A.L.R.2d 1139 (1958).
