Concepts, Categories & Problem Solving
How does the mind simplify a complicated world without oversimplifying it too much?
Retrieval Warm-Up
Without notes, write one idea you already know that might connect to Concepts, Categories & Problem Solving. Then write one question the lesson should help you answer.
Essential Question
How does the mind simplify a complicated world without oversimplifying it too much?
Learning Objectives
- Explain concepts and categories as tools for organizing information.
- Distinguish a prototype from a rigid category boundary.
- Compare algorithms and heuristics.
- Explain fixation, mental set, subgoals, and insight.
- Evaluate how problem representation can change difficulty.
cognition
Vocabulary in Context
cognition · concept · category · prototype · algorithm · heuristic · fixation · mental set · insight · subgoal
Substantial Core Reading
Categories make thinking efficient, but a useful category is not a perfect boundary. Problem solving depends on how a task is represented, what prior strategies are available, and whether the thinker can revise an ineffective approach.
Worked Example / Synthesis
A student repeatedly applies a familiar formula to a novel problem and fails. The difficulty may reflect mental set rather than lack of ability. Re-representing the problem visually or breaking it into subgoals can expose a better path.
Psychological Scientist's Desk
Evaluate: “If you are smart enough, every problem should have an obvious solution.”
Students identify the roles of prior knowledge, strategy, fixation, representation, time, and feedback.
Data Lens
Compare fictional completion time and accuracy under trial-and-error, explicit-subgoal, and familiar-method-only conditions. State the pattern and one limitation.
Claims Laboratory
Calibrate this claim: “One observation about Concepts, Categories & Problem Solving tells us everything important about a person.”
Guided Investigation
Problem Representation Lab: solve or inspect the same underlying problem in numerical, verbal, and visual formats. Compare which representation makes the structure easiest to see and why.
Independent Assignment
Write a short problem-solving protocol: define the goal, identify constraints, generate subgoals, test a strategy, monitor results, and revise if needed.
Research Notebook Checkpoint
Does the semester question contain a category, construct, or judgment that needs a clearer definition? Refine it and identify possible boundary cases.
Academic Journal Reflection
When can a familiar strategy help problem solving, and when can it become a trap?