MINNEAPOLIS — Minnesota students in grades three through eight showed big improvements in standardized test scores in math this year and held steady in reading, but math scores for students in 11th grade declined with well fewer than half meeting state proficiency standards.

The Department of Education reported Wednesday that overall, almost two-thirds of students were proficient in math and three-quarters of all students proficient in reading in tests taken earlier this year. Both numbers are improvements over 2011 scores. Non-white students also showed mostly improved scores in both math and reading, but they continued to score lower in most math and reading testing measures than did their white counterparts.

“Minnesota continues to be near the bottom in terms of eliminating the racial achievement gap, and we don’t like that position,” said Brenda Cassellius, the state’s education commissioner.

White students exceeded the proficiency of the overall student population in both math and reading scores, while American Indian, Asian, Hispanic and black students all lagged behind to varying degrees.

The Minnesota Comprehensive Assessment tests help determine whether students graduate from high school, and determine areas of priority in state education policy. The test scores had previously helped identify underperforming schools that were subject to sanctions under the federal No Child Left Behind law, but Minnesota was granted a waiver earlier this year to opt out of those requirements.

Math scores for students in grades three through eight rebounded in 2012, after taking a big dive in 2011. State education officials attributed last year’s dip to a new math test, given for the first time in 2011, including the requirement that all eighth graders be proficient in algebra.

In 2012, 61.3 of students overall tested proficient in math. That’s up from 56 percent in 2011, which was a nearly 10 percent drop from 2010.

But third- through eighth-grade students were given a break on the math test this year that they won’t get next year: They were allowed to take the test up to three times, then pick their best score to file with the state. In 2013, students will get to take up to two practice math tests — but a final test administered in March is the only one that will be scored by the state.

That’s necessary to meet requirements of the federal waiver from No Child Left Behind, said Minnesota Department of Education spokeswoman Charlene Briner.

Cassellius said the improvement in math scores reflected that students were starting to respond to the more rigorous expectations in math that were first announced in 2007.

Among 11th grade students, math scores — which reached a four-year high of 48 percent in 2011 — fell back to 41.8 percent in 2012. Cassellius said she believed it was because those students pre-dated teaching of the more rigorous math standards, and she predicted the number would rise again in the coming years. In 2014, the state is replacing its 11th grade math test with an updated version meant to more closely reflect the tougher expectations in math.

Overall reading proficiency rose to 75.3 of students in 2012, up from 61.3 percent in 2011. Students in grades three through eight, and grade 10, increased their proficiency nearly across the board — only fifth grade students dropped slightly, from 78.9 percent proficient in 2011 to 78 percent in 2012.

While non-white students generally improved in both reading and math scores, they continued to trail both white students and the overall student population. While 61.3 percent of students overall were math proficient, among American Indians that number was 38.5 percent; Asian students, 59.4 percent; Hispanic students, 38.2 percent; and black students, 32.6 percent. All four of those groups trailed in reading scores, too.

Cassellius said that finding ways to shrink the racial achievement gap remained a main priority of her boss, Gov. Mark Dayton. She said efforts to address it include trying to direct more resources to early childhood education programs and all-day kindergarten followed by a sharper focus on ensuring literacy among all students by third grade.

“We want to put the pedal to the metal, accelerate the growth faster and help them catch up to their peers,” Cassellius said.