SPEZIALE, J.

The defendants, Greenwich Education Association and Alan Frey, its president, have appealed from a judgment permanently enjoining arbitration of a grievance instituted by them in connection with a collective bargaining agreement. The defendants claim error in the court's conclusions that: (1) the question of the arbitrability of the grievance was for the court rather than for the arbitrator; and (2) the grievance was not arbitrable under the terms of the collective bargaining agreement.

The facts, briefly stated, are as follows: Alan Frey, as president of the Greenwich Education Association, instituted a grievance relating to an instructional aide at North Street School in Greenwich. The grievance claimed that the aide, being a certified teacher and acting in the capacity of a certified teacher, was not being paid on the teachers' salary schedule contained in the contract between the Greenwich Education Association and the Greenwich board of education, in violation of article II and article IX of the contract. The grievance was processed through the board of education level, demand for arbitration was made, and an arbitration hearing was scheduled. The plaintiff succeeded in obtaining an ex parte temporary injunction to stay the arbitration proceedings until a full hearing could be held. Subsequently, a permanent injunction was issued.

The aide in question, Miss Byam, is a certified physical education teacher. She was hired, however, as an instructional aide at an aide's salary, and the written job description for instructional aide, which she was shown prior to her employment, does not require that an aide be a certified teacher. The focus of the defendants' grievance was that, although Miss Byam had been hired as an aide, the function she actually performed was that of a teacher and required a teaching certificate, which she had; therefore, to pay her less than the amount provided in the salary schedule was a violation of the collective bargaining agreement.

The first issue that we consider is whether the arbitrability of the grievance was a question to be decided by the court or by the arbitrator. The arbitration provision of the agreement provides that if a grievance "is based solely upon an alleged breach of this agreement" the aggrieved person may request in writing that the grievance be submitted to arbitration. This court has long followed the rule that the arbitrability of a dispute is a legal question for the court unless the parties have clearly agreed to submit that question to arbitration. The intention to have arbitrability determined by an arbitrator can be manifested by an express provision or through the use of broad terms to describe the scope of arbitration, such as "all questions in dispute and all claims arising out of" the contract or "any dispute that cannot be adjudicated." Policemen's Firemen's Retirement Board v. Sullivan, 173 Conn. 1, 6, 376 A.2d 399 (1977); Gary Excavating, Inc. v. North Haven, 164 Conn. 119, 122-23, 318 A.2d 84 (1972); College Plaza, Inc. v. Harlaco, Inc., 152 Conn. 707, 707-708, 206 A.2d 832 (1965); Connecticut Union of Telephone Workers, Inc. v. Southern New England Telephone Co., 148 Conn. 192, 196-97, 169 A.2d 646 (1961). The collective bargaining agreement before us contains no express provision, nor is its language sufficiently all-inclusive to warrant the conclusion that the parties intended to have the question of arbitrability submitted to an arbitrator. On the contrary, the agreement makes no mention of who is to determine the question of arbitrability and specifically limits arbitration to "grievance[s] . . . based solely upon an alleged breach of [the] agreement." The trial court correctly concluded that it, not an arbitrator, should decide the question of arbitrability.

As to the ultimate issue, however, the trial court did err in determining that the grievance before it was not arbitrable. At the time this case was decided, there was some ambiguity as to whether this court had adopted the "positive assurance" test of arbitrability, the federal rule set forth by the United States Supreme Court in United Steelworkers of America v. Warrior Gulf Navigation Co., 363 U.S. 574, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960). In fact, the trial court specifically found that this test was not the law in Connecticut, although it also found that even if it were the law, the grievance would still not be arbitrable. It has now been clearly established that the Warrior "positive assurance" test is the law in Connecticut. Policemen's Firemen's Retirement Board v. Sullivan, supra, 7; Board of Police Commissioners v. Maher, 171 Conn. 613, 621, 370 A.2d 1076 (1976). Under the positive assurance test, "judicial inquiry . . . must be strictly confined to the question whether the reluctant party did agree to arbitrate the grievance. . . . An order to arbitrate the particular grievance should not be denied unless it may be said with positive assurance that the arbitration clause is not susceptible of an interpretation that covers the asserted dispute. Doubts should be resolved in favor of coverage." (Emphasis added.) United Steelworkers of America v. Warrior Gulf Navigation Co., supra, 582-83. We hold that the trial court, confronted with the defendants' grievance, could not say with positive assurance that it was not covered by the arbitration provision of the agreement. If Miss Byam were covered by the agreement, then the grievance would clearly be arbitrable. Employees are covered by the agreement only if they are employed in positions requiring teaching, certificates. The trial court concluded that "[t]he position of instructional aide did not require a teaching certificate." This was undoubtedly the basis for its further conclusion that the grievance was not arbitrable, because an employee whose position does not require a certificate is not covered by the agreement and, therefore, not covered by the arbitration provision. It is undisputed that the position of instructional aide, as described in the job description, does not require a teaching certificate. It was the defendants' contention, however, that the job as actually performed by Miss Byam did require one. Thus, the crucial question was clearly one of fact: Did the job as performed require a teaching certificate. Although the court was in a position to determine that the job appeared not to require a certificate, it could only conclude that a certificate was not actually required by hearing evidence and deciding the case on its merits, thus usurping the role of the arbitrator. The court should have denied injunctive relief and allowed the grievance to proceed to arbitration.