Drozd & van Loosbroek (1999) and Geurts (2003) recently introduced the weakstrong distinction into the discussion concerning the acquisition of quantification. They predict that children will start out interpreting all quantifiers as weak ones. Our experiment was set up to test this hypothesis. Using the Truth Value Judgement Task, 39 children (aged between four and seven) and 7 adults were asked to interpret the Dutch quantifier allemaal (‘all’) in pronominal position in an existential sentence, in which allemaal gets a strictly weak reading, or in floated position, in which allemaal gets a strong reading. The strong interpretation of the quantifier is taken as cointersective and the weak one as intersective, following Keenan (2002). Only three children behaved according to the prediction and interpreted allemaal as a weak quantifier when it is presented in a strong quantifier position. The other thirty-six children interpreted the quantifier allemaal as a strong quantifier, even when it occurs in an existential sentence. We’ll argue that, contrary to Drozd & van Loosbroek’s and Geurts’ expectation, these children do not interpret quantifiers as weak, but as strong. They do this even in constructions where the quantifier is obligatorily weak for adults. This can, however, be analyzed within Geurts’ proposal.