Sources of confusion are often products of an active mind. Learners typically respond to visual appearance or rush to use recently-met procedures. They can miss meanings that may not be immediately visible.
Multiple purposeful experiences within and outside mathematics help adolescent learners develop their mathematics. Such experiences may often be messy and require extended tasks over a period of time.
Representations are key tools for mathematical learning, particularly the use of linked multiple representations. Often conceptual understanding comes through recognising representations and the connections between them.
Multiplicative reasoning is central to mathematics in all domains, along with other forms of reasoning: deductive (geometry), structural (algebra), statistical, probabilistic, estimating, predicting, hypothesising, axiomatic, and transformational. Multiplicative reasoning is particularly important for the mathematics that is typically studied in late childhood and early adolescence.