The chairman of the D.C. Council’s education committee said Sunday that he has no plans to launch a full-scale investigation into allegations of widespread cheating on standardized tests in 2008, during the tenure of former Chancellor Michelle Rhee.

Council member David Catania (I-At Large) said that he intends to find out why the scope of a prior cheating investigation was limited to one school, but much of his focus will be on improving the integrity of future tests, which are used to evaluate schools and teachers.

Catania’s statement came three days after the public airing of a 2009 memo indicating that as many as 191 teachers in 70 D.C. public schools may have committed testing infractions in 2008.

The memo, based on an analysis of wrong-to-right erasures on answer sheets, contained no proof of cheating and warned that there wasn’t enough information to draw firm conclusions. But it stoked questions about whether Rhee and other school officials, including current Chancellor Kaya Henderson, were aggressive enough about responding to suspicions of cheating.

Rhee and Henderson both said they did not recall receiving the 2009 memo, and school system officials pointed to multiple investigations — including by local and federal inspectors general — that found no evidence of widespread cheating.

Catania said that in light of the 2009 memo, he is “bewildered by the narrow scope” of a investigation by the D.C. Inspector General, which lasted 17 months and focused only on one school. But he said a full-scale reinvestigation of the five-year-old allegations “would be impractical and would yield little in terms of accountability.”

“Among other things,” he said, “simply identifying and interviewing the hundreds of witnesses would overwhelm the Council’s limited staff and resources.”

It makes more sense to focus on tightening test security and strengthening efforts to identify cheating in the future, the council member said.

Catania introduced a bill earlier this year that would make cheating on standardized tests illegal and would put some test-security protocols into the law. The council will hold a hearing on that bill on Thursday.

The hearing will also include discussion of a report released Friday by the Office of the State Superintendent of Education, which found that teachers in 11 schools cheated on 2012 standardized tests.

The older cheating allegations are also likely to come up.

“I do intend to seek answers regarding the narrow scope of the Inspector General’s investigation in light of the recently released 2009 memo,” Catania said. “I also intend to question DCPS officials about the contents of the 2009 memo.”

This story has been updated.