Republican Gov. Susana Martinez remains optimistic that lawmakers will approve a centerpiece of her school improvement plan before time runs out in the legislative session this week.

The House is expected to debate a proposal Tuesday that will require school districts to hold back third-graders who can’t read proficiently, rather than promoting them to the next class.

The focus is on the third grade because educational researchers say students who can’t read by then are likely to struggle in later grades and will be at a high risk of dropping out of school.

Under current law, parents can overrule a school that wants to hold back failing students, sending children to the next grade regardless of whether they are academically ready. However, the legislation will eliminate the parental veto when students reach the third grade, ending a practice known as “social promotion.”

Martinez contends the legislation is critical to improving student achievement. About 47 percent of New Mexico’s third graders were not reading at their grade level last year, according to state testing, and 53 percent of fourth graders weren’t proficient in reading.

The legislative session ends Thursday.

If the House approves the governor’s proposal, it goes to the Senate, which approved a nearly identical measure Monday along with a competing proposal backed by many Democrats but opposed by Martinez. Both chambers must approve the same bill before it clears the Legislature and heads to the governor for her signature.

“There is still enough time for us to make sure that we get the right reading initiatives pushed forward so that our kids can read in order to succeed,” Martinez told reporters Tuesday.

If the legislation is enacted, schools must notify parents if students are struggling with reading in kindergarten through grade three. Starting in 2012-2013, schools also must provide intensive instruction to improve the child’s reading skills. There’s $8 million in next year’s proposed budget for reading programs and services in early grades.

Opponents of the legislation say the focus should be on programs to help struggling students because some children can be harmed and suffer a loss of self-esteem if they are held back in a grade.

The governor is modeling her education initiative after Florida, which a decade ago implemented a policy of holding back third graders who can’t read proficiently.

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