carol zander university of washington, bothell presents recursion

Carol ZanderUniversity of Washington, Bothell

presents

Recursion

Background

• Virtues of active learningo Human Tableau (Angelo & Cross), students act

out key ideaso Kinesthetic Learning (Begel, Garcia, Wolfman),

physically engaging exercises o Active & Cooperative Learning (McConnell),

face-to-face interaction and group process

Background

• Colleague was teaching recursion in a CS2-like course

• Allowed me to present a problem, solve it, and have the students simulate the run-time stack

The set-up

Problem

• Evaluate a prefix expressiono valid expressiono single digit operandso operators: + - * /

• Worked with/ * + 9 3 – 4 2 + 5 1

which is (9+3)*(4-2)/(5+1)

Programint evaluate(index in array) { char symbol = expr[++index];

if (symbol is a an operand) return symbol as a digit;

// symbol is an operator + int leftOperand = evaluate(index); int rightOperand = evaluate(index); switch (symbol) { case ‘+’: return leftOperand + rightOperand; case ‘-’: return leftOperand – rightOperand; case ‘*’: return leftOperand * rightOperand; case ‘/’: return leftOperand / rightOperand; default: break; }}

The execution

Run-time stack

Each student got an index card with one symbol from the prefix expression on it

They were to use the board for the rest of the memory of the activation record

3

+

Run-time stack

• Idea was that they would form a human run-time stack

• Move around

• Pop off stack

• Push onto stack

The result

Anticipated an ah-ha moment . . .

Instead it was an uh-oh moment

Actual results were absolute, glorious, complete cluelessness!

They had no idea what was going on

The following is a dramatization of the actual event. No students were actually clueless in the making of this presentation.

Such a shame that it was such a dismal failure because ...

It seemed like agood ideaat the time

Lessons Learned

Not a complete failure

Besides learning to never try that active learning exercise ...

Recursion is very complex for students. They must fully understand problem-solving recursively first.

Executing recursive functions is so different from solving them ...

Is it a chicken-and-egg problem?

Perhaps a simple, linear recursive problem in class ...

Give the prefix problem for homework. Have them draw an execution tree. Good idea??