Orna Muller Tel-Aviv University, Israel
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Transcript of Orna Muller Tel-Aviv University, Israel
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Orna Muller Tel-Aviv University, Israel
ICER - Seattle, Oct 1-2, 2005
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Focus of research:Algorithmic Problem-Solving
What is the impact of patterns’
incorporation in instruction
on the development of
Problem-Solving skills?
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Cognitive Theories
Pedagogical Implications
In Practice :Pattern-Oriented-Instruction (POI)
POI Evaluation :Research Methodology
Data AnalysisPreliminary observations
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Schema Theory and problem-solving
Our knowledge is organized in Cognitive Schemas, stored in memory.
Cognitive Schema – The abstraction of similar experiences.
In problem solving: A schema consists of a solution plan & related information - where and how to use it.
Links between pattern’s components form a chunk.
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Schemas and problem-solving (Cont.)
Solving a problem requires access and retrieval of relevant schema(s).
Schema’s connectivity improves accessibility.
Chunks retrieval reduces Cognitive Load and helps coping with complex situations.
Schema model explains Novice-Expert differences in problem solving.
(Marshall, 1995; Paas et al., 2003; Rumelhart, 1989; Sweller, 1988)
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Analogical Reasoning
A major problem-solving strategy:
Using a familiar situation to make
sense of a novel one.
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Analogical Reasoning phases:
1. Identifying relevant schemas in memory;
2. Mapping similarities between the current problem and a schema (or previous example);
3. Making inferences;
4. Adapting the schema to fit the new problem. (Gentner & Holyoak, 1997)
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Don’t know how to get started,
Don’t see resemblance between problems,
Mislead by surface features in a problem’s statement,
Cumbersome, inefficient solutions.
Students difficulties in Analogical Reasoning
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Pattern-Oriented Instruction (POI)
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Why patterns?
Reuse of algorithmic & design
solutions to similar problems at
various situations is a central theme in
CS, and the major driving force
behind the definition of patterns.
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Classify problems by goal (rather then by programming constructs);
Building blocks of algorithm development;
Encapsulate “algorithmic ideas”;
Several patterns may be combined at different manners to form a solution.
Algorithmic Patterns – Solutions to recurring alg. problems
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Counting
Conditional accumulation
Extreme value computation
Search for an element in a sequence
Do all elements satisfy a condition?
Integer to digits decomposition. (~ 30 patterns )
Algorithmic Patterns - examples
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Name: Maximum Value
Initial state: collection of values.
Goal: maximal value in the collection
Algorithm:
Initialize Max to First_value
While there are more items do
Assign next element to Next_Element
If Next_Element > Max then
Assign Next_Element to Max
Remarks: Highlights concerning the pattern, its use and related patterns.
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Utilizing Algorithmic Patterns in a problem solution
An algorithmic solution consists of:• Search pattern,• Do all elements satisfy a
condition?• Adjacent elements traversal.
Given a matrix of integer values,
Check the existence of a row, whose elements form an increasingly ordered sequence.
7 3 11 2 0
1 6 3 4 1
3 5 6 9 15
10 4 2 7 3
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Pattern-Oriented-Instruction Guidelines
Shifting emphasis from programming to problem-solving;
Organizing problems around types of algorithmic tasks (and not around programming features);
Illuminating various aspects of a pattern and its use; Discussing links between patterns, distinguish between similar patterns.
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A pattern
Representative, typical uses
A pattern
A Name, Definition
Common misuses
Comparing alternative solutions
Interweaving other patterns
Special cases/ contexts
Pattern modifications (new patterns)
Connecting pattern’s various aspects
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POI Guidelines (Cont.)
Elaborating on the idea behind a solution (“Algorithmic idea”);
Gradual increasing of difficulty level - Criteria involve pattern-related considerations.
Abstracting a pattern from various examples.
Integration with programming instruction – in a spiral way: patterns are revisited when adding a new programming feature;
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“Hard Copy” Patterns
Cognitive Schemas(knowledge construction)
assimilation
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What is “pattern assimilation”?
• Noticing similarities,
• Abstracting commonalities,
• Recognizing patterns’ applicability,
• Awareness of common mistakes,
• Correct modifications,
• Efficiency considerations,
• Identifying patterns in a given solution,
• Distinguishing between similar patterns.
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Evaluating the effectiveness of
Pattern Oriented Instruction on
algorithmic problem-solving skills
Research Goal
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Research Methodology
Comparison research; A field setting;
Experimental and two control groups.
Research sample:
High-school students (~100 each group), 20 teachers (classes) in 15 schools,
180 hours CS1 course.
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Research Groups
Experimental Group
Control Group AControl Group B
•Algorithmic- Patterns study materials,
• POI approach
•Same problems -
organized by programming constructs,
• No pattern definitions
(No intervention)
Written Questionnaire
Categorization Assignment – an interview
Observations
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Instruction materials development, Teacher workshops, Two-years pilot of POI, Patterns’ materials revised, Pilot comparison test, Main data collection;
Data analysis – in progress.
Research Stages
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Research Tools Questionnaire - algorithmic problems
Categorization Assignment - interviews
Additional data collection:
o Teachers’ interviews; Class observations;
o Teachers’ POI workshops;
o Teachers’ instruction materials: exams, lab assignments, websites;
o Students’ notebooks.
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Categorization Assignment
Assignment description:
Categorize eight algorithmic problems
according to criteria chosen by the student.
•Semi-structured individual interview – thinking aloud; • ~ 35 minutes;•Probing student’s reasoning, plans for solutions, clarifications, reflection on performance,…
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Categorization Assignment’s Goals
Get insight of student’s early stage of problem analysis:
– Employing analogical reasoning;
– Grasping the essence of a problem;
– Formulation of an idea for a solution;
– Making links to other problems;
Seeking POI impact.
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Data Analysis - Preliminary Observations
Teachers: Powerful instructional tool for- Reviewing a large variety of examples, Evaluating & composing assignments.
Students: Exchange of ideas in POI group is more precise, abstract and fluent.
Better awareness of solution’s efficiency, more than one solution are compared.
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Preliminary Observations (cont.)
More elegant solutions.
Better recognition of differences between similar problems.
Faster characterization of a problem.
Common distraction by surface similarities but shorter recovery time by POI.
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Preliminary Observations (cont.)
Better realization of sub-tasks composition.
High correlation between quality of categorization and performance in written questionnaire.
Preference of pattern’s names which are closer to programmed implementation.
Patterns are retrieved from memory; Retrieval from hard-copy materials is rare!
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Thank You