Class 3 weekly assessments are open-book now, so he's stopped revising anything

Our son's school has changed its weekly class 3 assessments to open-book this term. The circular says the aim is to test understanding rather than memory, and I can see the sense in that. What I have observed so far, which is only three weeks, is that he no longer looks at anything before an assessment. His reasoning is that the book will be there. His scores have not dropped, so I cannot say it is a problem yet. It may simply be that the early chapters are easy. My partner, who teaches, thinks I should leave it alone. I am less sure. Has anyone's child had open-book assessments at this age, and did the lack of revision catch up with them later?