(Comprehension: Associate, Discuss, Explain, Translate)
Explain problem-solving strategies, algorithms and heuristics, on pages 267-268. Give an example for each type of strategy. Discuss which one you prefer and why.
8.2 Higher-Level Thinking
(Synthesis and Evaluation: Assess, Analyze, Validate, Specify, Determine, Criticize)
Analyze creativity, critical thinking, and other complex thinking processes that are discussed throughout the chapter and determine unique approaches you would incorporate in your future classroom to foster these skills. Do you think these skills can be learned or these skills are natural gifts? Do you think one skill is more important than the others, why?
8.1
ReplyDeleteThe two types of problem-solving strategies are algorithms and heuristics. Algorithm is the sequence of steps and tasks that guarantees a correct solution if it’s applied correctly. Heuristics are general problem-solving strategies that don’t guarantee a correct solution. Algorithms are often limited to solving well-defined problems, while heuristics can be used to solve ill-defined problems. Both are important to learn as algorithms teach us the basics in each discipline while heuristics give us a general method/structure for solving all types of problems. For example, we can use heuristics to help us identify and break down tasks/goals in a problem, while we might be able to use algorithms to help us tackle the subgoals.
To explain algorithms/heuristics requires the knowledge and comprehension. To answer and justify one’s preference requires evaluation. Overall, this question is mostly a lower-level question that needs a little bit evaluation (higher level).
8.2
Creativity involves new and original behavior that yields a productive and culturally appropriate result. Critical thinking involves evaluation of the accuracy, credibility, and the worth of information using logical reasoning. Creativity favors divergent thinking more, while critical thinking favors convergent thinking more during its process.
To promote creativity in class, I would first promote student mastery of the materials as knowledge promotes creativity. I would ask higher-level questions during class and on projects/homework. I would give enough wait time/planning time for students to think of creative answers and ways to tackle an assignment or project. I would give students the sense of security to take risks by not evaluating their performances all the time and giving them several opportunities for feedback before asking them to turn in a big project. I would show enthusiasm for creative thoughts from students and focus students’ attention on internal rewards.
To promote critical thinking, I would encourage students to question the ideas in the textbooks and show them the proofs for the theorems rather than just giving it to them. I would give them authentic tasks that require math and encourage them to use common sense to evaluate their work.
Both nature and nurture affect creativity and critical thinking. I don’t know which one is more influential as the jury is still out about nature versus nurture in psychology. Genetics affect a person’s intellectual development, which in turn affect his/her ability to learn, be creative, and think critically. Cultural expectations and social institutions such as school (by emphasizing on one right answer can discourage creativity) can also significantly influence one’s creativity and critical thinking.
As far as which skill is more important, I think good critical thinking skills/abilities can take a person very far in life, but probably not make him/her exceptional in any field. Without critical thinking skills, creativity might not be very useful as one might not be able to differentiate between useful and not useful ideas. Creativity, on the other hand, drives innovation and is essential for entrepreneurs to have. However, one can’t make a successful entrepreneur if he/she doesn’t have the critical thinking skills to differentiate between useful inventions and non-useful inventions. But both skills are necessary if one aspires to revolutionize his/her field (sadly, very few people actually do).
This question involves knowledge (recall what creativity and critical thinking skills are), comprehension (understanding the nature of and the strategies to promote creativity and critical thinking in the book), application and synthesis (how to apply the strategies in the chapter to use inside a classroom as a teacher), analysis (recognizing the difference between critical thinking and creativity), and evaluation (comparing the importance of creativity and critical thinking).