Teaching Problem Solving and Design

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Teaching Problem Solving and Design

• Chris Stephenson
• University of Toronto

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The Goal

• A primary goal of curriculum reform is to create
  classrooms in which students
• are challenged to think critically
• learn how to discover, understand, and analyse
• apply skills and knowledge in new situations

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The Reality

• The majority of teachers pay little attention to
  problem solving in classroom instruction despite
  the fact that
• these skills are documented as essential for
  college and university
• these skills are documented as essential for the
  workplace

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Computer Programming

• Problem solving skills are absolutely key to
  program development.
• The most fundamental obstacles to learning to
  program are related to problem solving.
• BUT!!!
• Most courses still focus on syntax!

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Problem Solving Elements

• Research has identified two basic kinds of
  problems
• transformational problems where a set of
  operators are defined and applied to produce a
  solution
• synthesis problems where known components are
  selected and integrated to achieve a desired goal

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Changing Paradigms

• Programming problems used to be viewed
  exclusively as transformational problems but
  object oriented programming, reusable modules,
  software code libraries, and machine independent
  (portable) code are changing the very nature of
  programming.

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Early Models of Problem Solving

• The first problem solving models broke down into
  two distinct approaches
• the traditional scientific method
• an introspective creative method
• Scientists often report using both methods to
  enable discovery.

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The Scientific Process

• Dewey (1910)
• define the problem
• suggest possible solutions and identify
  alternative
• reason about the solutions and implement
• test and prove

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The Creative Process

• Wallas (1926)
• problem formulation and information gathering
• incubation - allowing the unconscious to work on
  it
• illumination - working to gain insight
• verification - testing for accuracy

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Classroom Model

• Polya (1945 and 1962) was the first to describe
  a problem solving model based on classroom
  experience
• understand the problem
• devise a plan
• carry out plan
• look back

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Polyas Model Part 1

• Understand the problem -
• state the question
• identify the goal
• give knowns, unknows and conditions
• introduce drawings or notations

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Polyas Model Part 2

• Devise a plan -
• outline a potential solution
• look at similar problems
• restate the problem differently
• break it into subproblems

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Polyas Model Part 3

• Carry out plan -
• refine and transform into a solution
• relate tasks to givens and unknowns
• check validity of each step
• define steps in relations to the whole problem

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Polyas Model Part 4

• Look back -
• confirm results and arguments
• assess effectiveness of solution
• assess accuracy of results
• assess usefulness of solution for solving other
  problems

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The Engineering Model

• Etter (1995) presented a model used by students
  to solve engineering problems.
• define the problem - state it clearly
• gather information - describe input and output
• generate and evaluate potential solutions
• refine and implement solutions
• verify and test solution method and result

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Students Need to Know

• What programming is
• The importance of style
• How computers solve problems
• How programmers develop software
• Software development over time

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Programming is...

• Analyzing a problem to be solved.
• Preparing a design for the steps in a set of
  instructions (an algorithm)
• Expressing the algorithm in a language that the
  computer can ultimately execute.
• Providing adequate documentation
• Testing and validating the program
• Maintaining the program over time

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Elements of Style

• Good programming style is the foundation of
  well-designed programs.
• informative headers
• comments and variable descriptions
• useful variable names
• indentation to indicate structure

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How Computers Solve Problems
Memory
Processing
Input
Output
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Software Development
Specification
Analysis
Architecture
Design
Untested Software
Implementation
Testing
Product
The Waterfall Model
Maintenance
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Iterative Model
Release
Marketing
Product
Requirements
(Repeat)
Testing
Analysis
Software
Specification
Implementation
Design
Architecture
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Methodology

• The most common methods used for teaching
  problem solving and critical thinking skills are
• hands-on experience
• real world problems
• cooperative learning

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Problem Solving

• transferable skill
• does not necessarily have to be related to
  computer programming
• large or small problems
• group or individual solutions
• practice makes perfect

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Sample Problem

• Student term marks must be calculated in a
  course.
• The course has 6 assignments and 6 quizzes which
  are done in alternating weeks. The exact number
  of students is unknown.
• The term mark is calculated by
• calculating a quiz mark by dropping the worst
  assignment mark
• calculating an assignment mark by dropping the
  worst assignment mark
• averaging the results quiz and assignment marks
• The program should be able to estimate the term
  mark at any time in the term based on the
  assignments and quizzes to that point

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Options to Solve the Problem

• non computer option
• existing application software
• other generic software such as database or
  spreadsheet
• write a customized program

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Top-Down Design with Stepwise Refinement

• break down the problem into 3-5 simpler problems
• continue the process until the steps are atomic -
  i.e. easy to code
• look for opportunities to reuse code

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Bottom-Up Design

• solve small pieces of the problem
• use the solutions as building blocks to solve the
  bigger problem
• perhaps design the solution Top-Down, but
  implement it Bottom-Up

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Structure Chart
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Flow of Data