Analogies Are Like Bowling Balls, or Why Analogies

166 Pages·2006·0.74 MB·English

Analogies Are Like Bowling Balls, or Why Analogies
to English Need Some Explanation to Help Students
Learn Scheme
Clint Eric Ryan
Electrical Engineering and Computer Sciences
University of California at Berkeley
Technical Report No. UCB/EECS-2006-75
http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-75.html
May 22, 2006
Copyright © 2006, by the author(s).
All rights reserved.

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Analogies Are Like Bowling Balls,
or
Why Analogies to English Need Some Explanation to Help Students Learn
Scheme
by
Clint Eric Ryan
B.S. (University of Arkansas at Fayetteville) 2000
A thesis submitted in partial satisfaction
of the requirements for the degree of
Master of Science
in
Computer Science
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Senior Lecturer Michael Clancy, Chair
Lecturer Brian Harvey
Professor Marcia Linn
Spring 2006
The thesis of Clint Eric Ryan is approved:
Chair Date
Date
Date
University of California, Berkeley
Spring 2006
Analogies Are Like Bowling Balls,
or
Why Analogies to English Need Some Explanation to Help Students Learn Scheme
Copyright (cid:13)c 2006
by
Clint Eric Ryan
i
To my wife
Clarissa
to whom I dedicate pretty much everything.
ii
Contents
Contents ii
List of Figures v
List of Tables vii
Acknowledgments ix
1 Introduction 1
1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Words and Sentences in CS 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Classroom Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Goals and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Theory 10
2.1 Misconceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Analogy, Similarity, and Structure Mapping . . . . . . . . . . . . . . . . . . 21
3 Materials and Methods 26
3.1 Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Differences Among Semesters . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Interviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Interview Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
iii
3.5 Scoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.6 Possible Treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 Results 66
4.1 One-Word Sentences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Empty Words and Sentences . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Essential Elements of English and Scheme Sentences . . . . . . . . . . . . . 92
4.4 What Students Did Not Say About English, Scheme, and Collections . . . . 94
4.5 Comparison of Sentences and Lists . . . . . . . . . . . . . . . . . . . . . . . 95
4.6 Other Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Discussion 99
5.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.2 Sources of Mistakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3 Success or Failure of Treatments . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4 Limitations and Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6 Conclusions and Future Work 111
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 Implications for Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
References 121
Bibliography 126
A Interview Questions 127
A.1 Spring A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.2 Summer A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.3 Fall A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.4 Spring B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
B Changes in the Curriculum 142
B.1 Additions to Summer A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
iv
B.2 Additions to Fall A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.3 Additions to Spring B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
C A Quick Introduction to Scheme 148
C.1 Scheme Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
C.2 Working with Words and Sentences . . . . . . . . . . . . . . . . . . . . . . . 150
C.3 Working with Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
C.4 More Advanced Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
v
List of Figures
2.1 Incorrect Logo and Correct BASIC for the Same Problem . . . . . . . . . . 11
3.1 An Analogy for Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Comparing English and Scheme . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Comparing English and Scheme, Revised . . . . . . . . . . . . . . . . . . . . 37
3.4 WebScheme Activity on Empty Words and Sentences . . . . . . . . . . . . . 38
3.5 Defining Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.6 Question O5, negate-all . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.7 Question O6, divide-by-largest Main Handout . . . . . . . . . . . . . . . 47
3.8 Question O6, divide-by-largest Test Cases Handout . . . . . . . . . . . . 48
3.9 Question O6, divide-by-largest Code Handout . . . . . . . . . . . . . . . 48
3.10 Question E5, number-spell . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.11 Question E6, sum-of-square-roots . . . . . . . . . . . . . . . . . . . . . . 53
4.1 Questions O1–O4, butfirst and butlast of One-Word Sentences . . . . . 66
4.2 Question O5, negate-all . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Summary of Question O6, divide-by-largest . . . . . . . . . . . . . . . . 75
4.4 Questions E1 and E2, Creating Empty Sentences . . . . . . . . . . . . . . . 81
4.5 Questions E3 and E4, empty words and sentences . . . . . . . . . . . . . . . 84
4.6 Question E6, Empty Words as Errors. . . . . . . . . . . . . . . . . . . . . . 90
4.7 Question E7, Placing an Empty Word in a Sentence . . . . . . . . . . . . . 91
4.8 Questions P1 and P2, Essential Elements of Sentences . . . . . . . . . . . . 92
5.1 Warning from Exploring Computer Science with Scheme . . . . . . . . . . . 103