1
  How Much Did You Get?" The Influence of
Algebraic Knowledge on Computer Science Students

• Yifat Ben-David KolikantDepartment of Science
  TeachingWeizmann Institute of ScienceRehovot
  76100 Israel

2
An Example of a Classroom Situation

•  
• ?The students were asked to solve the following
  problem Develop an algorithm whose input is the
  length and width of a rectangle and whose output
  is its perimeter and area. Implement your
  solution as a Pascal program.
•  
• ? They developed a correct algorithm and
  implemented it as a Pascal program
•  

3
The Beginning of the Confusion

• program Square(input, output)
• var Length, Width, P, S real
• begin
• writeln ('type the length and the width of
  a square')
• readln(Length, Width)
• P 2 ( Length Width )
• S Length Width
• writeln (P, S )
• end.

? Some of them didnt think that the program is
the solution of the problem. They felt there was
not enough data to finish solving the problem !!!
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Confusion..

• ?Then they were asked to verify correctness using
  a trace table for the input 3 4.
• They did it with no difficulties.
• ? Then they were asked to build a trace table for
  the input 6 7. 
• ? Now they were confused !!!

5
They Asked These Questions

• - So, is the first table wrong ???
• - How come the variables have different values
  ???
• - Do we have to write another program to answer
  this exercise ???

6
The Existence of Mental Models

• Intuitively, one would expect that novice
  computer science students would not have a
  pre-existing mental model of an algorithmic
  problem.
• However, I found that students use the mental
  model developped during their study of algebra,
  because of the similarity of the terminology
  (problem, solution, variable, data) and of the
  arithmetical notation.

7
An Example of a Confusing Resemble Algebraic
Problem

• The length of a rectangle is 3 and its width is
  4.
• What is its perimeter and its area ?
• A possible solution process
•  Data is 3 and 4, in variables L and W.
• We should calculate S and   P , using known
  equations.
• P 2(lw) ? 2(34) 14 ,s S lw?34 12 The
  perimeter is 14, the area is 12.

8
Recommendations of Pedagogical Activities for
Novices

• Games that emphasize that an algorithm can be
  executed more than once, each time with a
  different input.
• Running prepared programs to experience the
  perspective of a user, rather than a programmer.
• Group development where one group is the user of
  a program developped by another.