Analysis of longitudinal recordings of children's spontaneous speech can illuminate both the format of children's (and adults') grammatical knowledge, and the process by which that knowledge is acquired. Snyder & Stromswold (1997) applied this methodology to the acquisition of English argument structure (datives, causatives, verb-particle constructions), and found that acquisition is (i) incrementally additive (over time, the child's repertoire of grammatical structures is monotonically increasing), and (ii) parametric (multiple structures can be added in a single step). Likewise, Sugisaki & Snyder (2006) examined prepositional questions in children's English and Spanish, and found evidence that acquisition is also (iii) deterministic (no backtracking). Models of grammar and acquisition compatible with (i-iii) are discussed in light of evidence from Snyder's (2001) Compounding Parameter: treelets and the Structural Trigger Learning algorithm (Fodor 1998), cues (Lightfoot 1999, 2006), and learning paths (Dresher 1999).