MADISON — Students who received vouchers to attend private or religious schools in Milwaukee performed worse on statewide reading and math tests than their counterparts in public schools, according to test scores released Tuesday that could play an integral role in whether the program expands statewide.

The results, released by the Wisconsin Department of Public Instruction, show that while scores statewide are improving, voucher students are nowhere near their public school counterparts — even in the Milwaukee public schools they left.

Currently, only low-income students in Milwaukee can receive a voucher from the state. Gov. Scott Walker wants to expand the program to all of Milwaukee County and phase out the low-income qualifying ceiling. Some Republican lawmakers are talking about making the program statewide, arguing the option should be available for students unhappy in public schools.

But the scores may make it harder for supporters to make their case.

The results throw into question Walker’s proposal to expand the program at the same time he wants to cut public school aid by more than $800 million, State Superintendent Tony Evers said.

The test results show that for all grades, 34.4 percent of voucher students were proficient or advanced in math compared to Milwaukee public schools’ 47.8 percent average and the 43.9 percent average for low-income Milwaukee public schools students. Statewide, 77.2 percent of public school students scored proficient or advanced in math.

On reading scores, 55.2 percent of voucher students were advanced or proficient compared with 59 percent of Milwaukee public school students. Among Milwaukee’s low-income public school students, 55.3 percent proficient or advanced. Overall, 83 percent of public school students in Wisconsin hit those marks.

Private and religious schools that accept voucher students receive $6,442 from the state for each pupil. With about 21,000 students currently enrolled, the program has cost about $130 million in taxpayer money this year

The governor, who wants to eliminate the program’s 22,500-student cap, has not proposed reducing the subsidy. His fellow Republicans also are pushing a plan that would change the way charter schools are created in Wisconsin, a move that critics said would take even more money and students away from public schools.

Over the past six years, scores on the Wisconsin Knowledge and Concepts Examinations have increased overall and the achievement gap between white students and minorities has narrowed. The tests are given each year in the fall.

For all students, reading scores improved from nearly 73 percent in 2005 proficient or advanced to 77.2 percent in 2010. In math, scores improved from nearly 82 percent at those two highest levels to 83 percent.

The gaps between white students and blacks, Hispanics, Asians and American Indians narrowed over that time, though none of those groups scored as high as whites.

For example, 46 percent of black students got the highest math scores in the latest tests compared with nearly 84 percent of white students. On reading, 60 percent of black students were at the top level compared with more than 88 percent of whites.

Evers, the state superintendent, said the results show that while progress has been made, it must be accelerated through investing in public education.

More than 40 percent of students who took the tests come from families with incomes low enough to qualify for free or reduced-price lunch. The numbers are much higher for minority groups: 80 percent of black students, 77 percent of Hispanics, 67 percent of American Indians and 53 percent of Asian students are considered low-income.

The Wisconsin Knowledge and Concepts Examinations tests, which began in 1992, were given to 430,000 students in third through eighth grade and 10th grade last fall. The test initially was required under state law, but beginning in 2002 was used to comply with the federal No Child Left Behind to determine whether schools are progressing as required.

Voucher students took the tests for the first time this year, as required under a law change approved by Democrats when they controlled the Legislature. That included about 10,600 students.

Walker has proposed doing away with that requirement and instead allowing voucher students to use any nationally normed test to measure a student achievement, a move that would not allow for direct comparisons with public school students’ scores.

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