We often associate construction play with toddlers, but we've no reason to think the benefits end when children enter school. As I note in this article, a recent pilot study suggests that first graders who engage in daily construction activities can boost their mathematics ability, spatial reasoning, and executive control.
Moreover, as mentioned above, studies of tweens and adolescents link construction play with superior performance on tests of spatial skills and mathematics (Oostermeijer et al 2014; Richardson et al 2014)
But I think the most compelling evidence comes from everyday experience. We know that people learn from practice, and builders who create small-scale structures must cope with the same physics that constrain the design of bridges and cathedrals.
That's why engineers and scientists build physical models: It helps them test and explore their ideas. If you want to get an intuitive grasp of how the forces of tension and compression work, hands-on experience with construction is invaluable.
So it seems pretty obvious that older kids also benefit from building. The key to keeping them engaged is finding age-appropriate, stimulating materials. LEGOs appeal to many, but my personal favorites are these planks: KEVA Contraptions Plank Set, and KAPLA 200 Blocks Natural Unfinished Wood Pine Planks with Storage Bin and Guide Book. These systems of identical planks have been featured as popular, hands-on exhibits in many science and children's museums. But beware -- building with them requires some dexterity, patience, and good humor. They topple easily, and may not be appropriate for young children who are still developing these skills.