Table 2.

Patterns of misunderstandings and methods of changing materials (assume H₂SO₄ appears in the original problem)

Target of learning	Pattern of misunderstanding	Example	Changing materials
Applying conditions (e.g., x ∈ acid)	Applying conditions understood by learners who are narrower than the correct one.	If x ∈ H2SO4	H2SO4 → HCl
	Applying conditions understood by learners who are broader than the correct one.	If x ∈ electrolyte	H2SO4 → NaCl
Hierarchy of material classes	In learners’ understanding, a material belongs to a class, although, it does not in fact, belong.	NaCl ∈ acid	H2SO4 → NaCl
	In learners’ understanding, a material does not belong to a class, although it does, in fact, belong.	HCl ∉ acid	H2SO4 → HCl