Nearly half of all students in the Lawrence school district either already have or soon will be taking a new assessment test, one devised by the district to help guide math instruction.

The new 25-question test is being administered in third through eighth grades, part of a year of “field testing” for the new assessment that is designed to establish benchmarks that, in turn, will be expected to help determine how effectively the district’s math curriculum is connecting with students.

The district already has two other assessments:

• State assessments, which measure whether a student has learned what the state says the student should.

• Measures of Academic Progress (MAP) tests, which assess what a student knows, what a student has the potential to know and — as the student takes subsequent tests — how much growth the student is experiencing through knowledge.

The district’s new tests, known as “benchmark assessments,” will fall somewhere in between, by gauging students’ learning in relation to where teachers are in their course instruction. Math assessments are being developed this year, with plans for reading and other subjects to be added later.

“We’re not having these just to have a district assessment,” said Terry McEwen, the district’s division director for assessment, research, grants and school improvement. “And it’s not some attempt to find out if (one teacher’s class) is doing better than another. It is to find out, in a common way, if we have a gap in the curriculum.”

An example, McEwen said: Say the new assessment revealed that third-graders, as a whole, had fared relatively poorly on a question or questions involving addition or subtraction with money. Teachers and administrators then could compare notes — based on a known, common set of questions — and devise changes in the way the subject is taught, or when it is taught, to improve desired results.

“It’s ways for us to make adjustments, both at the district level and at the teacher level,” McEwen said.

McEwen’s comments came Monday night, after he had briefed members of the Lawrence school board about the district’s ongoing assessment program.

Randy Masten, who earlier in the meeting had expressed concerns regarding the costs of administering multiple state assessments, expressed worry after the meeting that a new assessment — even one with only 25 questions — could end up costing the district plenty.

Data is useless unless it can be analyzed, he said, and analysis takes time, energy and money.

“My fear is that we will reach a point where we’re overtesting and underteaching,” Masten said.