A new national survey found that a slight majority of parents —51 percent—responding last week said they were “not concerned at all” or “not too concerned” about the negative impact that the coronavirus pandemic might have on their children’s education.

However, the survey from Gallup released Wednesday also found that the share of parents who say they’re not too concerned about the virus’ negative impact has dropped by several percentage points since just over two weeks ago. The share of those who were “somewhat concerned” or “very concerned” also rose over the same time period.

In addition, the poll finds that the share of parents who said their children’s school is providing an online learning program grew from roughly two-thirds to more than eight in 10 over the same time period.

Two important caveats: The ability to access the internet is crucial for the survey respondents. And the poll has a relatively significant margin of error.

The coronavirus pandemic has forced the vast majority of schools nationwide to close for several weeks; several states and U.S. territories have closed their schools’ doors for the rest of the 2019-20 academic year. At the same time, states and districts have rushed to get remote learning sessions up and running, with varying success.

The Gallup survey indicates that those remote learning plans have become reality for a growing number of students, although they obviously haven’t put many parents’ concerns to rest when it comes to the long-term future of their children’s education,

To gauge parents’ level of concern about the coronavirus’ negative affects on their children’s education, Gallup polled parents in four separate time increments beginning on March 23-25 about their sentiments on the coronavirus and education.

The survey results relied on 621 adult members of the Gallup Panel—a representative sample of adults nationwide—who have at least one child in kindergarten through 12th grade. The margin of error is plus or minus eight percentage points, and the survey was taken online.

However, keep this in mind: Although the survey is weighted for demographics, the Gallup write-up of the findings also says, “Since it is an online survey, the data do not represent the experiences of parents who do not have internet access, either generally or specifically during the COVID-19 crisis.”

The digital divide has been one of the defining features of the coronavirus crisis, as various leaders and groups have sounded the alarm over the large share of students who do not have reliable internet access at home and are therefore are at a disadvantaged when schools provide remote learning. Some districts have also struggled to come up with the resources to provide reliable remote learning options. Efforts are under way in Washington to remedy some of these disparities, but it’s unclear if or to what extent they’ll succeed.

In an interview, Megan Brenan, a Gallup research consultant who analyzed the survey results, said the fact that those surveyed have internet access might be a factor in the findings; those who can afford the internet needed to participate in the survey might in general be less concerned about their children’s schools closing their doors. But she said she was still “surprised” in general at the share of parents who didn’t express much or any concern.

Want to see those survey results broken down by partisan affiliation? You’ll see a major disparity in levels of concern between Democrats and Republicans:

Disparities in access to the internet and other areas played a definitive role in the survey’s other main finding: the share of parents who say their child’s school is providing “online distance learning.” The huge push to get instruction online seems to have had an appreciable impact on this front.

A significant share of parents in the Gallup survey were still selecting instructional materials on their own in the most recent survey period, although it was down from the percentage of parents reporting they were doing so on March 23-25.

Brenan wrote in an analysis of the poll findings that, “Parents with an annual household income of at least $90,000 are more likely than those with a household income of less than $90,000 to say their child is receiving online distance learning from their school.”