Mathematical Processes and Perspectives
What to know
Mathematical processes describe how students do mathematics, not just what they compute. Expect questions on problem solving with a model (understand, plan, carry out, check), reasoning and justification, communication, connections within and across mathematics, multiple representations, selecting tools including technology, and attention to precision and structure. Process standards also emphasize analyzing relationships, creating and using representations, and displaying and interpreting data, so link each process to a concrete classroom action.
Traps
Options often confuse explanation with justification: describing steps is not proving why a result holds. 'Using representations' is not merely drawing a picture; the representation must clarify structure or support reasoning. Technology is a tool for exploration and verification, not a substitute for number sense. A correct answer reached by faulty reasoning does not satisfy a justification standard. Watch for problems asking what the teacher should do next, where the best answer targets the underlying reasoning rather than more practice.
Worked example
Two students solve 1/2 ÷ 1/4. One computes 2 by rule; another explains that there are two one-fourths in one-half. The second response better meets communication and reasoning standards because it connects the algorithm to meaning. Rule of thumb: ask 'why is that true?' as often as 'what is the answer?' and require evidence-diagrams, counterexamples, or a general argument.