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- Higher cognitive skills taught in math include problem solving, reasoning, logic, and communicating math knowledge.
- The National Council for Teachers of Mathematics developed five standards related to processing in math.
- Effective instruction must depend on students' ability to use knowledge and generalize that knowledge into alternative situations.
- Problem solving depends on four factors: tasks, characteristics of the problem solver, processing behaviors, and the environment.
- Two theories that describe problem solving are between concept systems and modeling processes.
- Memory, language, a lack of strategies, and an inability to distinguish needed from unneeded information prevent students from problem solving.
- Open- and closed-ended problem solving differ significantly in final student outcomes. Open-ended problem solving focuses on the process while closed problem solving focuses on the final answer.
- Computers can facilitate the increase of logic, reasoning, and problem solving skills through non-verbal understanding of relationships.
- Problem solving situations created with hypermedia allows teachers to integrate open-ended problem solving by creating a range of paths that ultimately lead students to problem answers.
- Strategies allow students to create a plan for solving math problems.
- Types of strategies include: self-instruction, mediated/assisted performance, and direct instruction.
- Diagramming may be an effective type of strategy that facilitates problem solving.
- One program, Inspiration, is particularly useful for helping students create math related concept maps.
- Programming continues to be one method for teaching students higher level math skills.
- Logo or Turtle Math allows students to create their own work while problem solving the needs and logic of the computer.
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