The linguistic and structural properties of two major physics textbooks are compared. The structure of each textbook is measured and differences in the amount of space, words, and mathematics devoted to different parts of the text are reported.
The linguistic richness of each text and each textual part is measured using LEX. The readability of each textbook is characterized using standard readability formulas. A new readability formula that corrects for mathematics is proposed.
The evolution of one of the textbooks over a fifteen year (four versions of the text) time span is also investigated. The reading difficulty of the textbook increased by approximately one-half a grade level over fifteen years. The lexical richness of the textbook also increased over the same period.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

 to quantitatively analyze the evolution of specific textbook features from an early edition to a more recent edition
 to study the similarities and differences of textbooks published at approximately the same time by different publishers
 to compare the linguistic properties of different texts
 to develop a mathematical readability formula to complement textual readability formulae already developed
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Only the chapters pertaining to Newton’s Laws as they apply to forces were studied.
These chapters relate to the Newtonian Force Concep measured by the Force Concept Inventory
David Hestenes, The Physics Teacher (1992)
 Chapters 1-6 in Fundamentals of Physics
 Chapters 1-5 in University Physics
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

 Selection based on popularity of text – top two bestselling calculus-based physics textbooks on Amazon.com © at inception of project
 Fundamentals of Physics 3 rd Edition
Halliday Resnick – published 1988
 Fundamentals of Physics 7 th Edition
Halliday Resnick Walker – published 2004
 University Physics 11 th Edition
Young Freedman – published 2003
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

 software was created to analyze features in a text passage
(occurrences, area, sentences, mathematical difficulty, etc.)
 textbook pages were converted to TeX format to be compatible with software
 tags were added to text as required by LEX software and counting software
 a twelve – point validation procedure was developed to check for any errors in the text files and software
 method resulted in high statistics study
(50,000 words – 1,000 equations – 60,000 cm 2 of page area)
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

 a text with mostly common words is easier to read than a text composed of mostly rare words
 lexical richness is characterized by a LEX value developed by
Donald Hayes
 possible LEX values range from -123 to +85
 LEX value of 0.0, (the LEX value of common newspapers) is consistent since the year 1600
 texts with higher LEX values are more difficult to read than texts with lower LEX values
 common words include the 10,000 most common words in the English language – other words are considered rare
 if a rare word is used more than 6 times in a text, the word is no longer considered rare
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Text Source
Nature—main research articles
Popular Science Articles
Newspapers
National Geographic – articles
New Yorker - articles
Fundamentals of Physics 7 th Edition
University Physics 11 th Edition
Fundamentals of Physics 3 rd Edition
Sports Illustrated – articles
TV – primetime shows
Dairy farmer talking to cows
APS Meeting – April 2008 – St. Louis, Missouri
LEX Score
34.7
4.6
0.0
-0.6
-3.9
-3.91
-5.11
-6.2
-10.3
-36.4
-56.0
Jennifer Campbell

APS Meeting – April 2008 – St. Louis, Missouri
Donald Hayes, Nature (1992)
Jennifer Campbell

Fundamentals of Physics 3 rd
-6.2
Edition
Chapter Text Examples Review
-6.84
-6.39
4.29
Fundamentals of Physics 7 th Edition
-3.91
Chapter Text Examples Review
-4.48
-5.09
9.02
University Physics 11 th
-5.11
Edition
Chapter Text Examples Review
-4.22
-6.22
6.18
APS Meeting – April 2008 – St. Louis, Missouri
Technical terms such as vector, gravity, and inertia were discarded because they occurred frequently. This accounts for the low LEX score of the texts.
The review sections have a large amount of technical terms in a small amount of text. This accounts for the high LEX value of these sections.
The error of the LEX value is
0.63.
Jennifer Campbell

The textbook pages were subdivided into three basic types of blocks:
 text – includes all text found in chapter text, examples, and text specific sections
 figures – includes all figures, tables, and their captions
 blank space – includes white space inside text and margin – does not include page borders
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

The page was also subdivided into sub-blocks that were identified by the authors:
 Chapter Text – text that is part of the main exposition, not part of one of the blocks below
 Examples
 End of Chapter Questions and Problems
 and Other –
Fundamentals of Physics 3 rd Edition: Hints and Review sections
Fundamentals of Physics 7 th Edition: Checkpoints and Review sections
University Physics 11 th Edition: Test Your Understanding,
Problem Solving Strategies, and Review sections
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

A comparison of the allocation of page area to the text blocks, figure blocks, and blank area.
Fundamentals of
Physics 3 rd Edition
4%
19%
77%
Fundamentals of
Physics 7 th Edition
12%
7%
81%
University Physics
11 th Edition
10%
17%
73%
Text Figures Blank Space
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

University Physics
11 th Edition
Fundamentals of
Physics 7 th Edition
Fundamentals of
Physics 3 rd Edition
0 20000
Text
Figures
Blank Space
Fundamentals of
Physics 3 [cm 2 ]
36575.36
9258.33
Fundamentals of
Physics 7 [cm 2 ]
University Physics 11
[cm 2 ]
47352.22
57521.18
7293.642
13006.5
2003.8
4104.92
7708.288
APS Meeting – April 2008 – St. Louis, Missouri
40000 cm 2
60000 80000
Text Figures Blank Space
Jennifer Campbell

40%
30%
20%
10%
0%
Chapter Text Examples Problems
Fundamentals of Physics 3rd Edition
Fundamentals of Physics 7th Edition
University Physics 11th Edition
Other
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

To study the mathematical presentation of the text, a measure of the density of the mathematics was developed. Mathematic expressions were converted to simple English sentences.
For example:
3x + 2y = 10 would read
“three multiply x add two multiply y equals ten”
The number of words in the expression is a measure of the complexity of the expression. This expression has nine “math words.” The number of math words in a passage was then compared to the number of total words (math + text) to yield the mathematical density.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Overall Chapter Text Examples
Fundamentals of Physics 3rd Edition
Fundamentals of Physics 7th Edition
University Physics 11th Edition
Other
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Textual Readability formulae do not account for mathematics in text – a complimentary readability formula was needed to measure the readability of the mathematics.
 Scientific passages including various amounts and levels of mathematics were given to University Physics I and II students at the University of Arkansas to read.
 Students were asked to recall 10 missing words/numbers/equations from the passages.
 Their answers were combined with the statistics from the passage and statistical analysis software (SAS) was used to determine a mathematical readability formula by a multiple linear regression.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Math Readability = 0.6113 – 5.9074 + 5.9886 - 0.8993
= inline math objects per total objects
= math objects per total objects
= math words per total words
The mathematical readability score gives the projected fraction of questions students will answer correctly for a given passage.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Math objects include a count of the number of equations, numbers, and symbols in a passage.
Inline math objects are in the flow of the text, not set aside.
Possible scores range from 0 to 1
Texts with scores closer to 0 are more difficult to read.
Texts with scores closer to 1 are easier to read.
A larger amount of math set apart from the text usually leads to a higher mathematical readability score.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

0.51
0.5
0.49
0.48
0.47
0.46
0.45
0.44
0.43
0.42
0.509
0.456
0.459
Fundamentals of Physics 3rd
Edition
Fundamentals of Physics 7th
Edition
University
Physics 11th
Edition
A higher score signifies an easier to read passage.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

 Designed to determine the comprehension difficulty of a passage.
 Higher scores are easier to read
 Lower scores are harder to read
90-100 – understandable by 11 year old
60-70 – understandable by 13-15 year old
0-30 – understandable by college graduates
Flesch Reading Ease Score:
206.835 – 1.015(words per sentence) – 84.6(syllables per word)
Rudolf Flesch, Journal of Applied Psychology ( 1948)
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Fundamentals of Physics 3 rd Edition
61.9
Chapter Text Examples Other
57.7
70.4
59.0
Fundamentals of Physics 7 th
58.2
Edition
Chapter Text Examples
55.9
62.7
Other
54.4
University Physics 11 th
57.7
Edition
Chapter Text Examples
53.8
62.4
Other
58.2
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Between the 3 rd and 7 th editions of Fund. of Physics, the total page area increased by ~ 23%. In the same time frame, the blank area increased by 104%. (That equates to about 5 extra blank pages for every 5-6 chapters in the text.)
The textual and mathematical readability tests reveal the difficulty of Fundamentals of Physics has increased over the 16 year period. They also reveal that texts published in approximately the same year yield similar readability scores.
Over the same time, the mathematics also became somewhat less readable. This is due in part to an increase in the amount of math imbedded in the text.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

The mathematical readability will continue to be studied.
The mathematical expressions (previously treated as proper names for LEX) will be translated into English sentences and analyzed with LEX software.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell

Textbooks
Halliday, Resnick, Fundamentals of Physics 3 rd Edition, Wiley Publishing. 1988
Halliday, Resnick, Walker, Fundamentals of Physics 7 th Edition, Wiley Publishing. 2004
Young, Freedman, University Physics 11 th Edition, Addison Wesley Publishing. 2003
LEX
Donald P. Hayes, "The Growing Inaccessibility of Science", Nature, (1992) 356, pp 739-40.
Jonathan Knight, “Scientific Literacy: Clear as Mud”, Nature, (2003) 423, pp 376-78.
Flesch Reading Ease
Rudolf Flesch ,A new readability yardstick, Journal of Applied Psychology, Vol. 32, (1948) pp. 221-233
Force Concept Inventory
David Hestenes, Gregg Swackhamer, and Malcolm Wells. Force concept inventory. The
Physics Teacher, 30:141–158, 1992.
APS Meeting – April 2008 – St. Louis, Missouri Jennifer Campbell