Discriminant Analysis. Two classification problems Discrimination Cluster.
Classification of Introductory-Level Physics Problems
Transcript of Classification of Introductory-Level Physics Problems
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Pedagogy in Introductory Physics: Working Toward a “Taxonomical”
Classification of Introductory-Level Physics Problems
Jeff Schueler
Phys 486
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Motivation
• Recent Physics Education Research (PER) has made progress in adopting important findings from expert-novice and cognitive science research
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Motivation
• Recent Physics Education Research (PER) has made progress in adopting important findings from expert-novice and cognitive science research – Findings show that asking students to solve high-level thinking
problems can help them attain a more “expert-like” status as a problem solver
– As a result, physics problem developers have begun to move down this route
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Motivation
• Recent Physics Education Research (PER) has made progress in adopting important findings from expert-novice and cognitive science research – Findings show that asking students to solve high-level thinking
problems can help them attain a more “expert-like” status as a problem solver
– As a result, physics problem developers have begun to move down this route
What does expert-like mean?
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Motivation
• Recent Physics Education Research (PER) has made progress in adopting important findings from expert-novice and cognitive science research – Findings show that asking students to solve high-level thinking
problems can help them attain a more “expert-like” status as a problem solver
– As a result, physics problem developers have begun to move down this route
• In order to successfully use these problems, an understanding of the relationship between the problems themselves and the cognitive processes involved in the problems needs to be established
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GOAL
To come up with an adaptation of a taxonomy (an orderly classification
of items according to their presumed natural relationship) of educational
objectives specifically for physics problem solving
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GOAL
Answer the following questions: •Can physics problems be categorized according to cognitive processes and knowledge domains? •Is there any relationship between physics problems, knowledge domains, and cognitive processes? •Are there relevant cognitive processes that are not activated by existing physics problems?
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GOAL
Answer the following questions: •Can physics problems be categorized according to cognitive processes and knowledge domains? •Is there any relationship between physics problems, knowledge domains, and cognitive processes? •Are there relevant cognitive processes that are not activated by existing physics problems?
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GOAL
• Choose an already existing taxonomy of educational objectives that satisfy the following criteria: 1. Addresses problem solving
2. Involves not only knowledge domains, but also cognitive processes that have been identified by PER as relevant for problem solving in physics
3. Makes a clear distinction between the knowledge involved in problem solving.
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NTEO
• Choose an already existing taxonomy of educational objectives that satisfy the following criteria: 1. Addresses problem solving
2. Involves not only knowledge domains, but also cognitive processes that have been identified by PER as relevant for problem solving in physics
3. Makes a clear distinction between the knowledge involved in problem solving.
• Only one existing TEO (called the New Taxonomy of Educational Objectives) met each of the criteria, so it was adopted.
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NTEO
• A two-dimensional framework: – Three systems of thinking (self, metacognitive, and cognitive)
– Three domains of knowledge (information, mental procedures, and psychomotor procedures)
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NTEO
• A two-dimensional framework: – Three systems of thinking (self, metacognitive, and cognitive)
– Three domains of knowledge (information, mental procedures, and psychomotor procedures)
• Actions of the systems upon the knowledge domains are driven by 6 levels arranged in hierarchical order: Level 6: Self-system
Level 5: Metacognitive system
Level 4: Knowledge utilization
Level 3: Analysis
Level 2: Comprehension
Level 1: Retrieval
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Self
Metacognitive
Cognitive
Information
Mental Procedures
Psychomotor Procedures
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NTEO
• A two-dimensional framework: – Three systems of thinking (self, metacognitive, and cognitive)
– Three domains of knowledge (information, mental procedures, and psychomotor procedures)
• Actions of the systems upon the knowledge domains are driven by 6 levels arranged in hierarchical order: Level 6: Self-system
Level 5: Metacognitive system
Level 4: Knowledge utilization
Level 3: Analysis
Level 2: Comprehension
Level 1: Retrieval
Focus on these levels, as they are the cognitive levels!
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NTEO
Schematic diagram of the levels of model behavior used in NTEO.
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Classification of Physics Problems in TIPP
• Two criteria:
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Classification of Physics Problems in TIPP
• Two criteria:
1. Type of knowledge in a problem
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Classification of Physics Problems in TIPP
• Two criteria:
1. Type of knowledge in a problem
2. Highest complex cognitive process necessary for solving it
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Level 1: Retrieval
Information:
(1a). Recalling and recognizing of
physics information.
Mental Procedures:
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Level 1: Retrieval
Information:
(1a). Recalling and recognizing of
physics information.
Mental Procedures: (1a). Recalling and recognizing of physics mental procedures.
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Level 1: Retrieval
Information:
(1a). Recalling and recognizing of
physics information.
Mental Procedures: (1a). Recalling and recognizing of physics mental procedures. (1b). Executing physics mental procedures.
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Level 2: Comprehension
Information:
(2a). Integrating
Mental Procedures: (2a). Integrating
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Level 2: Comprehension
Information:
(2a). Integrating
(2b). Symbolizing
Mental Procedures: (2a). Integrating (2b). Symbolizing
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Example
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Classification of Physics Problems in TIPP
This problem would be classified as:
(I:2, MP:1)
Highest cognitive process with regards to information (I) is symbolizing (level 2)
Highest cognitive process with regards to mental procedures (MP) is executing (level 1) 1/31/2013 24
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(I:2, MP:1)
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Level 3: Analysis
Information: (3a) Matching
Mental Procedures: (3a) Matching
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Level 3: Analysis
Information: (3a) Matching
(3b) Classifying
Mental Procedures: (3a) Matching (3b) Classifying
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Level 3: Analysis
Information: (3a) Matching
(3b) Classifying
(3c) Analyzing errors
Mental Procedures: (3a) Matching (3b) Classifying (3c) Analyzing errors
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Level 3: Analysis
Information: (3a) Matching
(3b) Classifying
(3c) Analyzing errors
(3d) Generalizing
Mental Procedures: (3a) Matching (3b) Classifying (3c) Analyzing errors (3d) Generalizing
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Level 3: Analysis
Information: (3a) Matching
(3b) Classifying
(3c) Analyzing errors
(3d) Generalizing
(3e) Specifying
Mental Procedures: (3a) Matching (3b) Classifying (3c) Analyzing errors (3d) Generalizing (3e) Specifying
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Example 2
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(I:3, MP:3)
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Level 4: Knowledge Utilization
Information: (4a) Decision making
Mental Procedures: (4a) Decision making
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Level 4: Knowledge Utilization
Information: (4a) Decision making
(4b) Overcoming obstacles
Mental Procedures: (4a) Decision making (4b) Overcoming obstacles
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Level 4: Knowledge Utilization
Information: (4a) Decision making
(4b) Overcoming obstacles
(4c) Experimenting/Investigating
Mental Procedures: (4a) Decision making (4b) Overcoming obstacles (4c) Experimenting/Investigating
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Assessment
• Can physics problems be categorized according to cognitive processes and knowledge domains?
• Is there any relationship between physics problems, knowledge domains, and cognitive processes?
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Concluding Remarks
• Reliability of rating problems – Among professors and graduate students who have administered the
TIPP, the inter-rater coefficient of assessing reliability of rating the problems was > 0.7, provided a clear statement of assumptions in the problem.
– Problems without a clear statement of assumptions had a kappa coefficient of < .5, likely due to different professors assuming different difficulty levels in the problems
• Rich database of problems allowing instructors to freely choose problems based off of the shift in thinking they want their students to achieve.
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References
• http://prst-per.aps.org/abstract/PRSTPER/v9/i1/e010103
• http://arxiv.org/ftp/physics/papers/0508/0508131.pdf
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Questions?
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