Vision-language models count exactly on small sets but drift to estimation on larger ones, a pattern reminiscent of children before they master counting. Children overcome the barrier by epistemic actions: pointing at each item while reciting number words, moving counted items aside, partitioning the array. We give VLMs the same actions using a training‑free agent loop on ordinary image tools that lack visual intelligence. Our central claim concerns measurement rather than intervention: a model that counts by marking leaves a normally hidden serial procedure on the image, and developmental counting principles turn those marks into an interpretable audit of serial visual reasoning. Each tag is classified against point‑level ground truth as hit, duplicate, phantom, or omitted, the answer is checked against the number of tags, and order irrelevance is tested by forcing opposite traversal orders.
Across nine models, 682 images, and seven harness conditions we find that (i) the exact‑counting range is a model‑specific signature, with R80 spanning from three to 150 dots, nearly two orders of magnitude; (ii) as an intervention the finger mostly fails: tags help only four models on small‑count photographs, mislead imprecise pointers, and rarely outperform a verbal routine or a blind point list—what the loop provides is an auditable trace, not higher accuracy; (iii) as a measurement it succeeds: a tag‑perturbation probe shows precise pointers read their answers from the tags, pointing precision predicts which models benefit, dense scenes fail by omission, and models rarely revise after seeing their own tags; (iv) capacities dissociate: models follow an instructed traversal order yet often change their answer when the order reverses, and children’s regular‑over‑scattered advantage appears only under the routine and survives lattices that defeat a rows‑times‑columns shortcut.
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