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John P. Rice, the manager of blended learning for the 46,000-student District of Columbia schools, wants every elementary school in his district using ST Math.

But he鈥檚 stopped short of centrally mandating that principals adopt the program, instead going with an opt-in model鈥攁nd regular doses of friendly encouragement.

鈥淚f I had told all 70 schools three years ago they had to do it, I have no idea where we would be now,鈥� Mr. Rice said. 鈥淭his way, schools are banging on my door to get [ST Math.] It will probably happen in every school soon, but it won鈥檛 be forced.鈥�

During the 2012-13 school year, as part of a larger effort to change mathematics instruction to better reflect the goals of the Common Core State Standards, the district adopted the software. ST Math鈥檚 developers, the mind Research Institute, lined up corporate partners to help cover the hefty initial sign-up cost: $34,000 for schools with fewer than 350 students and $48,000 for schools with 350 students or more.

Thirty-one of the city鈥檚 70 elementary schools opted to use the software that school year.

But just 11 of those schools met the mind Research Institute鈥檚 criteria for 鈥渇ull implementation": 85 percent of students getting at least halfway through the syllabus.

One major obstacle: balancing the student-computing time needed to use ST Math effectively with the demands of three other blended-learning math-software programs the central office had also recommended.

鈥淚t was definitely a function of overload,鈥� Mr. Rice said. 鈥淪ome schools just had a hard time being able to regularly get [students] in the computer lab.鈥�

Such challenges are fairly common with district-level blended-learning-software adoptions, said Steven M. Ross, a Johns Hopkins senior research scientist.

But in a study released in 2014, Mr. Ross and colleagues found that most district superintendents, chief academic officers, technology directors, and other high-level officials still preferred centralized procurement of instructional software.

That was particularly true when it came to buying software sought for core instruction, as opposed to a supplemental or enrichment tools.

鈥淭he bigger the product gets, the more value there is to [purchasing] being centralized,鈥� Mr. Ross said.

One reason: Large urban districts in particular have very high student-mobility rates, and it can create problems when students are expected to start with a brand-new curriculum and software if they switch schools midyear.

Hybrid Option Favored

Like Steven Hodas, a practitioner-in-residence at the Center on Reinventing Public Education, Mr. Ross favors 鈥渉ybrid鈥� procurement approaches in which district central offices play important, but limited, roles in selecting blended-learning software.

The District of Columbia system has increasingly moved in that direction.

The elementary schools that fully implemented ST Math in 2012-13 saw significant gains: The proportion of students scoring 鈥減roficient鈥� or 鈥渁dvanced鈥� on standardized tests rose 19 percentage points, compared with 5-percentage point growth for non-ST Math schools.

Those results鈥攁nd some creative professional development (and marketing) by the district鈥攈ave helped encourage other schools already using ST Math to go all in on the program, and helped persuade schools that did not opt to use the software to reconsider.

In February of this year, for example, Mr. Rice arranged for J.C. Nalle Elementary, one of the schools that embraced the new software most fully, to host an ST Math open house for teachers and leaders from other schools.

Kim S. Burke, Nalle鈥檚 eighth-year principal, said she appreciated the balance of autonomy and guidance that the district had given her in implementing the new blended-learning model.

鈥淧rincipals don鈥檛 always have all the latest cutting-edge information,鈥� Ms. Burke said. 鈥淚t鈥檚 really helpful when you have a technology office trying to stay on top of those things and saying, 鈥榊ou might want to consider this'鈥攕o long as you鈥檙e not forced鈥� to adopt software that isn鈥檛 a fit for your school.