The best replacement for problem solving is decision making.

The best alternatives to problem solving are rated as following:
★★★★★  decision making
★★★  critical thinking
★★  problem-solving
★★  research
★  problem solving
★  troubleshooting
★  scientific method
  community policing
  nursing process
  conflict resolution
  analytical skills
  appreciative inquiry
  problem spotting
  solving problem
  root cause analysis
  transformative mediation
  problem posing
  rational decision making
  metacognition
  problem finding
  word problems
  case study

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Speaking about problem solving, one probably shouldn't forget about linear functions.

Other search terms related to problem solving and their ratings are:
★★★★★ linear functions
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problem solving
decision making
critical thinking