This continues through levels of Counting Strategies, Derived Combinations, and beyond. The result
of this phase is an explicit cognitive model of students’ learning of mathematics in the target domain,
including knowledge structures, the development of these structures, including mechanisms or processes
related to this development, and LT that specify hypothetical routes that children might take in learning the
targeted mathematics competencies (space constraints prohibit full description—see Clements, Sarama,
& DiBiase, 2004).