Jennifer Lopez and Ben Affleck are doing their best when it comes to their kids … TMZ has learned they walked into a school together despite their divorce in full swing.

Sources with direct knowledge tell TMZ … the exes were seen making their way to the back-to-school night Tuesday at an L.A. area school where they each have kids that attend. Our sources tell us the exes were totally cool with each other and very cordial.

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But don’t get it twisted — our sources are adamant they’re not rekindling anything — they’re still getting divorced.

We’re told they’re a couple who still care for each other … they’re wrapped up in a years-long love affair.

But their kids are the real focus. Just last week, the two, along with their respective children, were spotted at The Beverly Hills Hotel, where witnesses saw them kissing and holding hands during the lunch.

We broke the story — Jen pulled the plug on the marriage last month.

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We’re glad to see they’re back on speaking terms, which is a step up from last month when our sources said they weren’t talking at all.