Glen Cove Superintendent Dr. Joseph Laria said that the accusations, "if true, represent a grave disservice to the children, families and community."
As many as 18 teachers are being investigated at Landing Elementary and Margaret A. Connolly Elementary.
At Landing Elementary Friday morning, parents dropping off their kids were astonished at the apparent testing scandal in their midst.
"They're in a tremendous amount of trouble and deserve every penalty they get," said one parent.
The Glen Cove school district has revealed it's been quietly investigating allegations that teachers coached students while they took state standardized tests for English and math in the spring of 2012.
Laria said no criminal misconduct was suspected and no charges were pending against any teachers or administrators.
The probe is looking at "protocols and practices applied during the administration" of exams last spring.
The statement, posted on the district's website, referred to "coaching" of students during the English Language Arts and math tests in grades 3 through 5 at two schools.
A spokesman for the state education department says the agency is monitoring the situation.
Officials point out that during the period in which the alleged cheating took place, test scores went down in the schools.
"The teachers are under pressure from up above for performance because their jobs may be on the line based on the scores," said education activist Zefi Christopoulos.
A school spokeswoman says that while some scores did go up in that testing cycle, many more dropped.
Here is the full text of Dr. Laria's statement:
"It is with great disappointment that the Glen Cove City School District must report allegations of testing administration irregularities. These allegations, if true, represent a grave disservice to the children, families and community of Glen Cove.
"The allegations relate to 'coaching' of students during the administration of NYS grades 3, 4 and 5 ELA and Math assessments in spring of 2012 conducted at Connolly and Landing Elementary Schools.
"Upon the advice of counsel, the Board of Education retained outside counsel to conduct an investigation that consisted of interviews with staff members, students (with parent permission) and building administrators regarding protocols and practices applied during the administration of this exam. In addition, the New York State Education Department was made aware of this investigation in accordance with SED requirements.The district launched this proactive and necessary investigation in November 2012 after allegations were brought to the district's attention. There is no reason to believe that there is any criminal misconduct and there are currently no pending district charges against any teachers or administrators."
(The Assocated Press contributed to this report)