High school students in Oklahoma would be asked to identify “discrepancies” in the 2020 election as part of U.S. history classes, according to new social studies standards recently approved by the Oklahoma Board of Education.

The proposed standards seem to echo President Trump’s false claims about his 2020 defeat. They ask students to examine factors such as “the sudden halting of ballot-counting in select cities in key battleground states” and “the security risks of mail-in balloting.”

They now head to the state’s Republican-controlled Legislature, which could take up the issue before its term ends in late May, or punt the issue to the governor’s desk.

The standards, supported by the state’s hard-charging Republican superintendent, have already received pushback, including from Gov. Kevin Stitt, also a Republican, whose office characterized the changes as a “distraction.” A spokeswoman said the governor had not yet seen the standards in full and it was not clear if he would support them.

The additions related to the 2020 election are among several changes that injected a strong conservative viewpoint to the state’s portrayal of modern American politics and Mr. Trump.

Mr. Trump repeatedly denied the results of the 2020 election, a view that has been widely embraced by some Republicans, despite a lack of evidence.

An earlier version of the new standards — which were released for public comment in December — simply asked students to examine “issues related to the election of 2020 and its outcome.” The new changes were made after the public comment period and quietly approved by the Board of Education last month. They were first reported by NonDoc, a nonprofit news outlet in Oklahoma.

The state superintendent, Ryan Walters, said that the standards were not meant to “support or negate a specific outcome” and that “a well-rounded student should be able to make their own conclusions using publicly available data and details.”

In a statement, he said, “We believe in giving the next generation the ability to think for themselves rather than accepting radical positions on the election outcome as it is reported by the media.”

Mr. Walters, a former history teacher and Trump ally, has emerged as a combative culture warrior in education and national politics. His push to put Bibles in every Oklahoma classroom is being battled in court, and he was briefly floated as a candidate for U.S. secretary of education, before Mr. Trump nominated the former pro-wrestling executive Linda McMahon.

But within his own state, Mr. Walters has clashed with members of his party, including Governor Stitt, who was once an ally. Most recently, the two went head-to-head over Mr. Walters’s plan to collect the citizenship status of public school children, which Governor Stitt vowed to fight.

Amid his feud with Mr. Walters, and after new national test scores showed Oklahoma remaining near the bottom in reading and math, Mr. Stitt last month replaced half of the state’s Board of Education. The board is made up of five governor appointees and Mr. Walters, who was elected. At least one of the new members said he had not been informed of the changes to the social studies standards, which were approved two weeks after the new members joined.

A spokeswoman for the governor, Abegail Cave, said the governor’s priority was transforming Oklahoma into “the best state for education.”

“He thinks a lot of what has happened over the past few months and past few years has been more of a distraction,” Ms. Cave said. The new social studies standards, she said, “follow the pattern of being a distraction.”

Standards for academic subject areas are rewritten every six years in Oklahoma under state law. They include lengthy outlines on what public schools are expected to teach and what students should know at different grade levels.

For example, U.S. history students in Oklahoma learn about the civil rights movement, including key court cases, tactics such as the Montgomery bus boycott and violent responses to the movement, including the Birmingham church bombing and the assassination of the Rev. Dr. Martin Luther King Jr.

The changes centered on more recent history. In examining significant events during Mr. Trump’s first term, an earlier version of the standards had asked students to “explain the responses to and impact of the death of George Floyd, including the Black Lives Matter movement.”

In the latest version, that standard was removed.

Another change involved the origin of the Covid-19 pandemic. Students would be asked to identify the source of the pandemic as coming from a Chinese lab. That theory has long been hotly debated, but is embraced by Republicans and increasingly favored by C.I.A. officials.

The earlier version was less pointed: “Evaluate federal and private response to the Covid epidemic, as well as its lasting impact on global health and American society.”

Mr. Walters said the various changes “give students the best opportunity to learn about history without leftist activists indoctrinating kids.”

His office did not respond to questions about why the edits were made after the period of public review.

State Representative John Waldron, a former social studies teacher who is now vice chair of the House Democratic caucus, said he would oppose the changes and accused Mr. Walters of subverting the typical process to insert his own political beliefs.

“The state superintendent campaigned to end indoctrination in our schools, but what he is doing instead with these new standards is promoting his own brand of indoctrination,” Mr. Waldron said in an interview.

The edits also made more subtle changes to a unit on “the challenges and accomplishments” of Joseph R. Biden Jr.’s administration.

They removed bullet points on the country’s economic recovery in the aftermath of the pandemic and on a signature $1 trillion infrastructure bill.

Remaining were bullet points on the “the United States-Mexico border crisis” and Mr. Biden’s foreign policies on issues like the Russian invasion of Ukraine and the Israel-Hamas war.