Strategic choice in mental computation is about choosing what to do and how best to do it.
A student's available knowledge, in conjunction with their goals and beliefs, affects strategic choice in two ways.
Knowledge influences what operations students see as possible.
For example, if a student has little knowledge of multiplication it is unlikely that they will use multiplication to solve a problem in which equal sets are combined. Instead they are likely to resort to counting or addition repeated methods. This might be thought of as 'know to' knowledge.
Knowledge affects how fluently and flexibly the computation is carried out.
For example, students may know that repeated addition can be represented as multiplication. But if they do not know any relevant multiplication facts, they may still add or count to find an answer. This has implications for assessment in that the strategies students choose to use are influenced by access to number-dependent facts. A student might use counting, adding and multiplication strategies when solving equal sets problems.
You can read more in the article From Here to There: The Path to Computational Fluency with Multi-digit Multiplication on the AAMT website.