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INTRODUCTION
This paper is the first in a series on Spreadsheets Across the Curriculum (SSAC),
an educational-materials development project (NSF
DUE 0442629) to build a
resource to facilitate student learning of mathematics in context. The purpose of
this paper is to describe the resource library and its basic element, the spreadsheet
module. In addition, the SSAC story told here illustrates a couple of points
relevant to a goal of the NNN—finding and disseminating “what works” for the
grass-roots spread of teaching quantitative literacy (QL). First, the notion of
teaching with spreadsheets has wide appeal for combining mathematics and
context—regardless of whether that means bringing context to math or bringing
math to context. Second, workshops, such as those hosted by NNN, PKAL,
1
PREP,
2
and NAGT
3
in this instance, can play a vital role in shaping a QL idea and
turning it into an educational resource.
BACKGROUND
The Washington Center for Improving the Quality of Undergraduate Education at
The Evergreen State College (TESC) was one of the four centers and programs
that received funding from the National Council on Education and the Disciplines
(NCED) as part of its initiative to build a national network to support education in
numeracy (Madison and Steen 2008, p. 7-8). The role of the Washington Center
in that NCED-era precursor to the present NNN was to “create professional
development opportunities for faculty from two- and four-year colleges to learn
about QL and incorporate it into the curriculum of their courses” (Madison and
Steen 2008, p. 8). The SSAC project is a direct outgrowth of one of those
activities: a 2003 institute on QL across the curriculum, funded jointly by the
NCED grant and PREP. The goals of that workshop were to help participants
develop a richer understanding of the centrality of QL in a democratic society; to
integrate their work in developing QL materials with ongoing national
conversations about the need to reform traditional math curricula; to become
familiar with QL materials developed at a range of institutions; and to adapt and
create QL materials for use on their own campuses.
The workshop attracted some 50 participants from about a dozen institutions
mainly from the state of Washington. The legislators in Washington State had
recently asked two- and four-year colleges to identify learning outcomes. They
1
Project Kaleidoscope http://www.pkal.org/ (accessed June 12, 2010).
2
The Mathematics Association of America’s Professional Enhancement Program
http://www.maa.org/prep/ (accessed June 12, 2010).
3
National Association of Geoscience Teachers
http://nagt.org/index.html (accessed June 12,
2010).
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Vacher and Lardner: SSAC: Idea and Resource
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specifically asked public colleges and universities to make quantitative and
symbolic reasoning one of four accountability measures. Many two-year colleges
followed suit and included quantitative literacy or quantitative reasoning as one of
their institution-wide learning outcomes.
Resource faculty for the workshop were drawn from the advisory group of
the NCED numeracy network along with directors of the other centers. One of
the representatives of the advisory group was Len Vacher, who presented an NSF
project, “Spreadsheet Exercises for Geological-Mathematical Problem Solving”
(DUE 126500). The purpose of that project was to create a small set of
spreadsheet modules in which students would engage their mathematics while
addressing a geological problem. Participants responded enthusiastically—
“spreadsheet modules would work in my class!” Inspired by that response, we
proceeded to write the proposal for the SSAC project. Whereas the collection of
Geological-Mathematical Problem Solving modules was aimed at one course
(Computational Geology, for junior- and senior-level geology majors) at one
institution (USF), SSAC envisioned a library of modules for diverse courses and
many institutions, albeit with a focus on the state of Washington as a germination
site.
RATIONALE FOR SSAC
Even a casual browse of the QL literature in this journal and elsewhere shows that
there are many flavors of numeracy. For example, there is numeracy for the
needs and responsibilities of citizenship (e.g., Steen 2001); numeracy and social
statistics (e.g., Best 2008; Sweet et al. 2008); numeracy to support argumentation
(e.g., Lutsky 2008; Grawe and Rutz 2009); numeracy to better understand health
information (e.g., Ancker and Kaufman 2007); numeracy for consumers of
financial information (Huhman and McQuitty 2009); numeracy for decision
making (Peters et al. 2006); numeracy for the business world (Taylor 2008).
The original Spreadsheet Exercises for Geological-Mathematical Problem
Solving took a flavor that is not on that list: numeracy to enhance student learning
of geology. The thinking was two-fold:
1. In performing a calculation within the context of solving a geological
problem, students would learn the underlying geological concept better.
2. The students would practice the mathematics that they had already
learned, thereby reinforcing it and becoming more comfortable with it and,
therefore, better prepared to be geologists.
This thinking was amidst a backdrop in which many in the geoscience education
community, particularly the NAGT, were working to create an environment
through faculty development workshops and educational resources development
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to enhance quantitative skills of geoscience majors (see Hancock and Manduca
2005; Wenner et al. 2009). At the same time, there were many in the geoscience
education community making a parallel argument: geoscience educators must
stop avoiding elementary mathematics (such as relationships expressed in simple
equations) in introductory, service-level geology courses (Goforth and Dunbar
2000; Wagner 2000; Vacher 2001), no matter how much the students complained
on students evaluations about “doing math.”
Interaction with the participants at the 2003 workshop brought the
introductory, non-majors courses to the forefront. Infusing QL across the
curriculum would involve a different way of thinking about the interplay of
mathematics content and non-mathematics context. Whereas geological concepts
(context) were given primacy in the modules developed in the original
Spreadsheet Exercises for Geological-Mathematical Problem Solving project, the
mathematics content would need to be primary in the new modules; the context
would be what would make the mathematics worth doing from the student
perspective. Further, if the goal was to be to get all students who “do not do
math” to experience “doing it” in their courses beyond the walls of the
mathematics building, we would be expanding into a different—more
foundational—kind of mathematics.
It was not difficult in the proposal to argue the need for a project to get non-
mathematics students to do math. We made the point in a preamble in the
proposal.
The national news media could not contain their delight on the evening of Nov 15, 2001,
after Premier Putin and President Bush met with children at Crawford Elementary
School. Their delight was in the remarks that Putin and Bush interjected when the
Principal, while performing the introductions, told the children that their distinguished
guests had agreed to answer their questions. Putin, with an impish grin, said “So long as
it’s not math.” Bush added, “No fuzzy math.” What fun, according to the nightly
newscasters. Famous people don’t do math either!
SSAC takes the position that, whatever the flavor, numeracy is active, not passive.
“Doing math” is a crucial part of being numerate. When confronted with a problem
involving numbers, a numerate person can calculate or graph, or somehow explore the
numbers. How do we get students comfortable with doing math to explore problems?
SSAC answers, “Spreadsheets!”
WHY SPREADSHEETS?
In the inaugural issue of the open-access journal Spreadsheets in Education,
editors John Baker and Steve Sugden published a review with 205 references on
how spreadsheets have been used in education (Baker and Sugden 2003). To set
the time frame (Power 2004; Baker and Sugden 2003): VisiCalc, which appeared
in 1979, was the first electronic spreadsheet; Lotus 1-2-3 was developed in the
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Vacher and Lardner: SSAC: Idea and Resource
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early 1980s and bought out VisiCalc in 1985; Microsoft Excel, which was
originally written for the 512 Apple Macintosh in 1984-1985, added a graphical
interface and point-and-click technology; it zoomed to prominence in 1987 when
Microsoft launched its Windows operating system. As electronic spreadsheets
evolved in the 1980s, papers on their educational merits began to appear in
professional educational journals such as The College Mathematical Journal
(Arganbright 1984), Mathematics Teacher (McDonald 1988), Computers in
Physics (Dory 1988; Misner 1988), School Science Review (Elliot 1988; Brosnan
1989), Journal of Economic Education (Adams and Kroch 1989), The Computing
Teacher (Parker and Widmer 1989); Collegiate Microcomputer (Watkins and
Taylor 1989). The extent of their penetration into a discipline can be illustrated
by earth science; 38 papers in the Journal of Geoscience Education from 1986
through 2003 incorporate spreadsheets as a teaching activity (Fratesi and Vacher
2005). Examples of contexts include two-dimensional modeling of groundwater
flow (Ousey 1986), U-shaped glacial valleys (Harbor and Keattch 1995), the size
of our galaxy (Shea 2003), and heat loss from a building (Frey et al. 2003).
Baker and Sugden (2003 p. 19) cite a very early paper (Hsiao 1985) that
makes the obvious point about why spreadsheets would become so popular:
…while computers are clearly useful tools for education generally, one of the main
disadvantages is having to program them. In many cases, (at least in 1985), students had
to learn a programming language in order to benefit from computers…. Use of
spreadsheets helps to get around this problem.”
The authors go on to cite many virtues of using spreadsheets educationally and
assemble an extensive and impressive array of quotations. We select the
following as an example;
Spreadsheets…. have a number of very significant benefits many of which should now be
apparent. Firstly, they facilitate a variety of learning styles which can be characterized by
the terms: open-ended, problem-oriented, constructivist, investigative, discovery oriented,
active and student-centered. In addition they offer the following additional benefits: they
are interactive; they give immediate feedback to changing data or formulae; they enable
data, formulae and graphical output to be available on the screen at once; they give
students a large measure of control and ownership over their learning; and they can solve
complex problems and handle large amounts of data without any need for programming.
(Baere 1993)
The references and quotations in the Baker and Sugden review—and articles
in subsequent issues of Spreadsheets in Education—argue that teaching with
spreadsheets can be a successful strategy when teaching mathematics, physics,
chemistry, economics, and other quantitative, computational subjects. The
context of that teaching, however, is in courses of those subjects. Students in
such courses would not be characterized as math-avoidant. We do not know of
studies involving students who “don’t do math.” On the other hand, when we
wrote the proposal, we did know of two developments in the preceding decade
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that make one think that spreadsheets would be more palatable than alternatives
for getting math-avoidant students to do hands-on quantitative activities in the
context of their non-quantitative, non-mathematical courses. First, spreadsheets
were ubiquitous; if students owned a computer, they probably had a spreadsheet
program (now, if they have an iPod, iPhone, or Blackberry they do indeed have a
spreadsheet program). Second, facility with spreadsheets was becoming
increasingly an expectation of employers. We suspected that peer pressure alone
would convince students to get over their resistance to using a spreadsheet to do a
calculation that was within their range mathematically.
Figure 1. Spreadsheet calculating the distance to a lightning strike.
A key part of a strategy for SSAC, then, would be to use straightforward,
easy-to-follow, unintimidating spreadsheets to do a calculation. Use a spreadsheet
like one would use a calculator. Lay out the steps line by line like one would on a
sheet of paper. Figure 1 shows an example. The spreadsheet answers the
following question: given the speed of light and the speed of sound, how long
after the lightning flash does the thunder arrive if you are 1.2 miles away from the
lightning strike? The spreadsheet starts (Row 4) with the distance and works
through a succession of one-step calculations. First it converts the miles to
kilometers (Row 5) and then meters (Row 6). Next it writes 300 million as
300,000,000 (Row 7). Then it converts the speed of sound in feet/second (Row 8)
to meters/second (Row 9). Then (Row 10), it divides the distance in meters (Row
6) by the speed of light in meters/second (Row 7), and (Row 11) the distance in
meters (Row 6) by the speed of sound in meters/second (Row 9) to find the travel
times for the light and sound, respectively. Lastly, it finds the answer (Row 12)
by subtracting the travel time for light (Row 10) from the travel time for sound
(Row 11). The answer is 5.6 seconds. Students working through the calculation
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Vacher and Lardner: SSAC: Idea and Resource
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would be doing unit conversions and manipulating speed = distance/time to time
= distance/speed.
Students would see immediately that the lightning flash arrives
instantaneously. The travel time of the flash is negligible relative to the thunder.
They could also use the spreadsheet to solve the reverse problem and experience
the power of spreadsheets: once you solve the first problem, finding the answer to
a similar problem is a breeze because the spreadsheet does the work. For
example, how far away is the lightning strike if you count “Mississippi 1” to
“Mississippi 8’ between seeing the flash and hearing the thunder? Using the
spreadsheet, the student can guess the distance (in miles) until the 8 appears in
Cell C12 (seconds). And, then the student can manipulate the velocity equation
again and use distance = speed × time to check the work with pencil and paper
(and, optionally, explore significant figures).
The spreadsheet of Figure 1 can be put into context in a variety of courses.
Earth science, weather, and geography are obvious examples. For people from
the Tampa-Orlando corridor (the country’s statistical leader for lightning strikes),
additional choices come to mind: golf; parks and recreation; journalism; Florida
living; campus safety.
4
Prompting students to step through a simple, straightforward spreadsheet
such as this lightning example is the basic concept of SSAC. In essence, SSAC
modules are elaborate word problems with a computational component using
technology.
THE SSAC LIBRARY
The SSAC project included three annual summer institutes (2005, 2006, and
2007) in Olympia WA where faculty came for intensive one-week workshops to
learn about spreadsheet modules and make a first draft of one for a class that they
teach. After review, revision and editing, selected modules were posted on the
SSAC Web site.
5
The modules are housed in the General Collection
6
of the
SSAC Library. At the conclusion of the project (March 31, 2010), the General
Collection included 55 modules by 40 authors from 21 institutions in 11 states
(Table 1). The 55 modules are classified into 26 Library of Congress (LOC)
categories ranging from BF (Psychology) to WY (nursing) (Table 2).
Modules
SSAC modules are short (ca. 15−20 slides) PowerPoint presentations that prompt
students to build one or more Excel spreadsheets to solve and examine a mathe-
4
Richard Stessel, a popular USF engineering professor, was struck and killed by lightning while
walking on campus, August 2001.
5
http://serc.carleton.edu/sp/ssac_home/index.html (accessed June 12, 2010).
6
http://serc.carleton.edu/sp/ssac_home/general/index.html (accessed June 12, 2010).
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Table 1
Module Authors
State Institution Author Modules
A. Mathematics faculty
AZ Chandler-Gilbert CC Frank Murphy 1
IA Buena Vista University Nasser Dastrange 1
Lawrence Couvillion 1 LA Southern University
Joseph Meyinsee 1
MI Davenport University Gary Franchy 3
MO Metropolitan CC - Longview Bridget Gold ½
NH Colby-Sawyer College Semra Kilic-Bahi 3
NY Alfred University Eric Gaze 1
PA Indiana Univ of Pennsylvania Yu-Ju Kuo 1
Central Washington Univ. Aaron Montgomery 1
Vauhn Foster-Grahler 1 The Evergreen State College
David McAvity 1
WA
South Seattle CC Jian Zou 1
B. Non-Mathematics faculty
CA San Jose State University Mike Pogodzinski 1
Eckerd College Laura Wetzel 1
Dorien McGee 1
Christina Stringer 1
FL
University of South Florida
Len Vacher 5
MI Delta College Loretta Sharma 2
Metropolitan CC - Longview Rebecca Foster ½ MO
Truman State University Tony Weisstein 1
Maryann Allen 2
Nicholas Baer 1
Cheryl Coolidge 3
Shari Goldberg 1
Jodi Murphy 1
Ben Steele 2
NH Colby-Sawyer College
Bill Thomas 2
NY Manhattan College Bernadette Garam 1
Paul Butler 2
Rob Cole 1
Martha Rosemeyer 1
The Evergreen State College
Rebecca Sunderman 1
Highline CC Eric Baer 1
Lower Columbia College Armando Herbelin 1
Michael O’Neill 2 Seattle Central CC
Ylin Sun 1
South Seattle CC Sara Baldwin 1
Polly McMahon 1
WA
Spokane Falls CC
Rachel Wang 1
matical problem in non-mathematical context. The modules are intended to be
problem-solving activities.
In working through the modules, students work
through the disciplinary problem of the context as well as the mathematics
embedded in it. The immediate hands-on activity is that students need to recreate
the spreadsheets. They need to figure out the cell equations to populate the
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spreadsheets that apply the mathematics. Then they proceed to “end-of-module
problems.”
Table 2
Number of Modules in the General Collection by Subject
Library of Congress category Modules
BF Psychology 1
DT History, Africa 1
E History of the Americas 1
GB Physical Geography 1
HB Social sciences, economics, general 2
HE Transportation and communications 1
HF Social sciences, commerce (including accounting) 5
HG Finance 3
HN Social history and conditions, social problems, social reform 1
HV Social pathology, social and public welfare. Criminology 1
JF Political institutions and public administration 1
LB Education, practice 2
LC Education, social aspects 1
PN Literature (including Star Trek) 2
Q Science, general 1
QA Mathematics 5
QC Physics (including atmospheric science) 1
QD Chemistry 5
QE Geology 8
QH Natural history. Biology 3
QP Physiology 2
QR Microbiology 2
QV Pharmacology 1
S Agriculture 1
TC Hydraulic engineering 1
WY Nursing 2
Design. The Power-Point presentations are self-contained (e.g., requiring no
textbooks), and they are written for the students, not the instructors. The first slide
is a title slide that includes a list of the quantitative concepts and skills that come
into play in completing the module (Fig. 2). The prominence of the list aims to
make it clear to the students that mathematics is a learning goal, an integral part of
the activity, and that they need to take it seriously. The list can serve as a prompt
to discerning students who wonder "what is going to be on the quiz?"
A typical module starts with a few slides that pose the problem and give
some background on the context and relevant mathematics content. The module
typically ends with a few slides of wrap-up and end-of module questions.
The
end-of-module assignments, which are intended as homework, commonly include
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Figure 2. Title slide of a module
one or more questions that ask the students to change some of the parameters in
the spreadsheets that they made while working through the module.
The core of the module is the sequence of slides that take the students
through the construction of the spreadsheets. The spreadsheets do the calculations
that address the in-context problem. In many cases, this part of the module
involves graphing. The modules that are aimed at beginning spreadsheet users
include Excel instructions.
Figure 3. Slide 5 in “Driving across town for cheaper
gas: Is it worth the effort?” by Gary Franchy.
The slides are strongly color-coded (Fig. 3). Blue text boxes contain
information in the mainstream of the narrative. Green text boxes signify a
"command" such as "Recreate this spreadsheet." Red text boxes give sideline
information that may be interesting or useful (e.g., a hint).
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The spreadsheets, which are embedded as pictures in the student version of
the modules, also are strongly color-coded. For example, numbers appear in
yellow and orange cells—the yellow cells contain data or known values, and the
orange cells contain cell equations (Figs. 1, 3). Students use the numbers that
appear in the orange cells as checks on the cell equations they have to enter into
their own copy of the spreadsheet. Instructor versions, which are available by
request on the SSAC Web site, are the same as the student versions except that the
spreadsheets are embedded as Excel spreadsheets that can be activated to reveal
the equations.
Code number. Each SSAC module has a three-part code such as
SSAC2006.QP301.LS1.2 that appears on the first slide of the module (Fig. 2).
The SSAC2006 segment indicates the year of the series. The SSAC2005,
SSAC2006 and SSAC2007 series are from the SSAC workshops of Summer
2005, 2006, and 2007, respectively. SSAC2004 indicates modules reformatted
from Spreadsheets for Geological-Mathematical Problem Solving.
The second
part of the code is a subject indicator following the LOC classification. The third
part of the code indicates the author. LS1.2 in this case means that it is the second
module produced by author LS1 (Loretta Sharma), the first SSAC author using
the initials LS
Web Site
A month before the second workshop in 2006, SSAC was invited by Cathy
Manduca, Director of the Science Education Resource Center (SERC) to become
a partner in SERC’s new Pedagogical Services project
7
(NSF DUE 0532768).
The intent of that project was to build a library of pedagogical methods together
with collections of activities that exemplify them. SERC’s goal was to support
educators who wish to explore new teaching strategies and methods. Pedagogical
Services saw SSAC as a new pedagogy “based in creative use of PowerPoint and
Excel resources.”
8
In essence, SSAC was asked to contribute a Web site
containing the spreadsheet modules developed at the workshops to the portal of
educational resources the Pedagogical Services project was developing. In return,
SSAC would use their content management system
9
and be networked with other
projects and groups who were developing new materials. That arrangement
caused the creating of an SSAC Web site to be a much larger component of the
project than we had anticipated, with a much more fully developed result.
The home page (Fig. 4) describes the project under three headings: The Goal,
The Pedagogy, and The Library. The navigation column on the right side of the
7
http://serc.carleton.edu/sp/service/index.html (accessed June 12, 2010).
8
http://serc.carleton.edu/sp/service/partners.html (accessed June 12, 2010).
9
http://serc.carleton.edu/serc/cms/index.html (accessed June 12, 2010).
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page has six links. “SSAC and Quantitative Literacy” expands on the goal of the
project. “Teaching with SSAC” is a group of pages that brings SSAC into the
shared design of other pedagogies in the Pedagogical Services project portal.
“The SSAC Library” describes the design of the modules, the code numbers, and
the cover Web pages (described below) that introduce the individual modules.
Figure 4. Screen shot of home page.
The last three links on the home page—“General Collection,” “Geology of
National Parks Collection,” and “Physical Volcanology”—access the three
collections composing the current SSAC Library. The General Collection is the
product of the SSAC project, as discussed in this paper. The Geology of National
Parks collection is being developed in a new project,
10
which, in contrast to
SSAC, focuses on a single course (Geology of National Parks) at a single
university (USF). The Physical Volcanology collection is another special-purpose
collection, this one developed by two geologists (at USF and Penn State) who got
caught up in the spirit of SSAC module making and, without funding, created a
collection for a new, advanced undergraduate, physical volcanology course that
they were developing at their respective universities.
10
Geology of National Parks: Spreadsheets, Quantitative Literacy, and Natural Resources (NSF
DUE-0826566).
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General Collection. The General Collection link on the home page accesses the
index page that introduces the collection.
11
The page lists the authors and LOC
categories of the modules and includes a link to a spreadsheet version of a card
catalog organized by LOC category. Most important, the index page contains the
link, “SSAC General Collection Modules,” on the navigation column which
accesses the browse pages
12
for the collection.
Figure 5. Screen shot of browse page for the General Collection.
The browse pages (Fig. 5) list and give a one-sentence description of each of
the modules in the collection—ten to a page and in no obvious order. One can
search for modules with “Narrow the View” boxes that list index terms used in
the content management system to tag the modules. There are three categories for
these search boxes: Quantitative Concepts; Subject; and Excel Skills.
Alternatively (or additionally), one can search by author or keyword by using a
search box (upper left of the browse page, Fig. 5) which activates a full-text
search of the cover Web pages of the individual modules.
Cover pages. Clicking the link on the module listed on the browse page produces
the cover Web page that introduces the module (Fig. 6). The format of these
cover pages was prescribed by the Pedagogical Services project. To be included
11
http://serc.carleton.edu/sp/ssac_home/general/index.html (accessed June 12, 2010).
12
http://serc.carleton.edu/sp/ssac_home/general/examples.html (accessed June 12, 2010).
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in the Pedagogical Services portal, a pedagogy would need a site with a title such
as “Teaching with x” (in our case, x = SSAC) (see home page, Fig. 4). The site
would be a cascade of pages starting with “What is Teaching with x?” and ending
with “Examples”—activities illustrating the use of the x-pedagogy. These
examples would be listed and indexed on one or more browse pages linking to
activity sheets of a preset design (Fig. 6) describing each of the activities. In the
language of SSAC, the example activities are “SSAC modules” and the activity
sheets are the “cover pages.”
Figure 6. Screen shot of cover page for SSAC206.WY100.SG1.1.
These cover pages describe the modules under seven headings formulated by
Pedagogical Services project: Summary; Learning Goals; Context for Use;
Description and Teaching Materials; Teaching Notes and Tips; Assessment; and
References and Resources. In general, our pages were completed by the authors
of the modules after they had made their module and before they had used it in
class, and so only the first three sections contain much information. The
summary describes what the students do in the activity and the context and
quantitative content that the module covers. Learning Goals describe what the
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author intends for the students to experience and get out of the activity. Context
for Use identifies the course for which the module is prepared.
The Teaching Materials section contains the link to the particular module.
The short section includes a statement that the online module is the student
version and that instructor versions are available by request. The main difference
between student and instructor versions is in how the spreadsheets are
embedded—as pictures in student versions so that the cell equations do not show,
or as Excel worksheets in instructor versions so that the cell equations are
accessible. Instructor versions of the SSAC2006 and SSAC2007 series also have
a short quiz that was prepared by the authors for pre- and post-module
assessment.
Who’s Asking?
The Teaching Materials section of the cover page includes a link to an online
form to request the instructor version of the module. The request form asks for
the requester’s name, contact information, institution, and department. It also
asks for information about the course in which the module may be used: the
number and title of the course, number of students, a brief description, and how
the module will be used.
From mid-October 2006 to mid-October 2009, SSAC received 121 requests
for instructor versions of modules in the General Collection (Fig 7). The requests
came from 72 different people from 26 states in the US as well as 12 other
countries. Forty-two (76%) of the 55 modules in the General Collection were
requested at least once.
Figure 7. Spreadsheet listing and graphing the number of modules produced and requests for
instructor versions by year through mid-Oct, 2009.
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Table 3A
Mathematics Courses Identified in Requests for Instructor Versions of
SSAC Modules
Type of Institution Course Students Modules
Calculus (Laboratory) 20 2
Math Reasoning 90 1
University
In-service for Teachers (math) 20 1
College Algebra 20 3
College
Quantitative Literacy 100 1
College Algebra 60 2
Elementary Algebra 40 1
Two-Year College
Elementary Algebra 25 1
Basic Math Concepts 75 6
Geometry (including Trigonometry) 125 1
Consumer Math 20 1
Statistics 10 1
Computer Math 74 1
Secondary Schools
8
th
Grade Mathematics 120 1
Community Math 60 1
Community (Adult)
School
Community Math 20 1
The vast majority (108 or 89%) of the requests were associated with specific
courses at specific institutions (Tables 3A and 3B). In all there were 64
institutions. They break down into categories as follows:
• Universities: 28, including 19 in the US, and one each in Canada, Jamaica,
El Salvador, Venezuela, Peru, Sweden, Italy, The Slovak Republic and
Sudan.
• Colleges: 12, all in the US.
• Two-Year Colleges: nine, all in the US.
• High School: 11, nine in the US, one in Portugal, one in Thailand.
• Boarding School: one in Australia.
• Community Schools (adult education): two in the US.
Only four of the 64 institutions of Tables 3A and B overlap with the 21
institutions of the module authors (Table 1): one university (USF), two colleges
(Colby-Sawyer; Evergreen) and one TYC (Spokane Falls). Therefore, modules of
the General Collection were produced and/or requested by individuals from 81
institutions, meaning that the partnership of SSAC within the Pedagogical
Services project increased the known reach of the SSAC project by some 286%
(from 21 institutions to 81) as of October 2009.
The 108 requests in Tables 3A and B are for a total of 67 courses. Taking
account of duplicates (two courses each in Environmental Geology,
Macroeconomics, College Algebra, Elementary Algebra, and Community Math),
there are 62 different titles. Thirteen (21%) of these titles are math courses in
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Table 3B
Non-Mathematics Courses Identified in Requests for Instructor Versions
of SSAC Modules
Type of Institution Course Students Modules
Systems Analysis 40 13
World Agriculture 170 4
Administration Science 20 3
Introductory Geology (seismology) 15 2
Karst Geology 8 2
Introduction to College 37 1
Introduction to Engineering 70 1
Introduction to Computers 60 1
Numerical Tools (engineering) 40 1
Statistics (economics) 30 1
Physics 18 1
Mechanics 12 1
Chemical Engineering 25 1
Radiation Biology 50 1
Agroecology 50 1
Plant Ecology 55 1
Physical Geology 40 1
Planet Earth 10 1
Earth Resources 32 1
Volcanoes and Earthquakes 72 1
Environmental Geology 100 1
Environmental Geology 30 1
Geomorphology 25 1
Seismology 8 1
Math Applications for Earth Science 10 1
University
Economics 20 1
Historical Geology 20 7
Earth Systems 18 3
Climate Change 13 2
Landscape Processes 50 2
First-Year Seminar 18 1
Educational Technology 22 1
Introductory Biology 65 1
Genetics 24 1
Macroeconomics 45 1
Macroeconomics 20 1
College
Honors (non-math) 28 1
Excel Basics 18 1
Introduction to Natural Resources 32 1
Earth Science 150 1
Microeconomics 40 1
Nursing 100 1
Two-Year College
Human Services 25 1
Personal Finance 25 3
Geology 25 2
Chemistry 15 1
Introduction to Business 150 1
Record Keeping 20 1
Accounting 20 1
Secondary Schools
Professional Development 100 1
Boarding School
Health Studies 21 1
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mathematics departments (Table 3A). The other 49 courses are distributed across
the curriculum (Table 3B), as was the intent of the project. Many (15) of the non-
mathematics courses are geology courses, reflecting the geoscience-education
heritage of SERC and its continuing workshops and other activities in that arena
(e.g., Wenner et al. 2009).
The 67 courses of Tables 3A and B reach a total of 2,988 students. Those
students are fairly evenly distributed between (1) universities and colleges (1618
students or 54% of the total) and (2) the others, namely, two-year colleges and
secondary and community schools (1370 students or 46%) (Table 4).
Table 4.
Distribution of Students in Courses for Which Instructor Versions of
SSAC Modules Were Requested (10/2006-10/2009)
Type of Institution
Math
courses
Non-math
courses
Totals
TYC, HS, community schools 629 741 1370
Universities and four-year colleges 250 1368 1618
Totals 879 2109 2988
Table 4 shows how the numbers of students split between math courses and
non-math courses. The 13 math titles (21% of the 62 titles) have 879 of the 2988
total students (29%), reflecting more students per math title (68) than non-math
title (43). More interesting is the uneven split of the two types of courses with
respect to the two categories of institution (Table 4): the 879 students in the math
courses are mostly (72%) in two-year colleges and secondary and community
schools, and the 2109 students in the non-mathematics courses are mostly (64%)
in the universities and four-year colleges. Thus, although SSAC modules
obviously have appeal both to instructors interested in bringing context to their
mathematics courses and instructors interested in bringing mathematics to their
context courses, in terms of numbers of students reached, the potential impact of
the first (mathematics courses with context) appears to be higher in high schools
and two-year colleges than in universities and four-year colleges, whereas the
potential impact of the second (context courses with mathematics) appears to be
higher in universities and four-year colleges than in high schools and two-year
colleges.
In addition to the requests associated with specific institutions and courses,
SSAC has received numerous and diverse requests that we characterize as “none
of the above.” These include:
• An elementary school teacher interested in self-education.
• A young wife interested in home schooling her children and helping her
husband prepare for a GED.
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• A mother of an elementary school child researching Excel ideas in
collaboration with her child’s teacher.
• A TYC faculty member getting ideas for using Blackboard.
• A high school math coordinator for a school district investigating
classroom resources.
• A research evaluator for another school district doing the same for a
course in data analysis.
• A university Center for Education Research preparing for a teacher
workshop.
• A project evaluator for another NSF-supported QL project.
This diversity shows the potential broad appeal of spreadsheet modules—even
beyond the classroom.
Reflections
The subtitle of this journal is “Advancing Education in Quantitative Literacy.” In
that regard, what works? The SSAC experience suggests that we can put two
items on the list: spreadsheet exercises in which students do math to solve
problems, and workshops or workshop sessions that focus on educational
materials.
Spreadsheets
Spreadsheets offer a readily accessible cross-disciplinary platform for
dissemination of numeracy. The appeal of modules that prompt students to build
spreadsheets to solve problems was apparent throughout the project. At the
Washington Center’s 2003 Institute on QL across the curriculum, the enthusiasm
of the participants for spreadsheet modules developed in the phase-1 project (one
course, one institution) led directly to the proposal for the phase-2 SSAC project
to develop modules conjoining math and context in courses across the curriculum.
The 55 modules created in the project are cataloged into 26 different Library of
Congress categories—and were created by 13 mathematics faculty and 27 non-
mathematics faculty from 21 different institutions. Among the visitors to the
online library housing the modules, 72 went to the trouble of filling out a form to
request instructor versions of one or more modules. Sixty of those were from
institutions not represented by the module authors. The requests indicated that the
modules were considered for at least 62 different courses (different titles)—13
math courses and 49 non-mathematics courses. Whether the goal is to bring
context to mathematics courses or to bring mathematics to non-mathematics
courses, the SSAC experience shows that educators are interested in materials that
have students using spreadsheets to do math.
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Workshops
There were two crucial steps in the story of the SSAC project. The first was
the 2003 Washington Center institute where the simple idea of spreadsheet
modules found a receptive audience: a group of educators who had come to the
workshop to find out about QL and were looking for ideas and resources. The
second was connecting SSAC to SERC, and thereby gaining a ready-made
framework for the creation and dissemination of an Internet resource. That step,
though definitely a stroke of good fortune, was not fortuitous; it was the direct
outgrowth of NAGT workshops that had built an activist community of
geoscience faculty interested in more effective pedagogy and the materials to
make it happen. The actual SERC connection occurred at a 2006 NAGT
workshop focused on quantitative reasoning in geology courses. The connection,
in time for the second SSAC workshop, set a goal for the participants at
subsequent workshops: make a module that will be published on the SERC portal.
By the end of the project, 35 workshop participants and five workshop faculty
including two graduate students published a QL educational resource on the
SERC/SSAC site.
Upstream from those workshops, there were others. The authors, for
example, met at the 2002 PKAL institute, “Quantitative Literacy: Everybody’s
Orphan.” Cathy Manduca and Len Vacher began working together on QL in
geology at a 1999 PKAL workshop, “Building the Quantitative Skills of Non-
Majors and Majors in Earth and Planetary Science Courses.”
The SSAC project clearly did not happen in isolation. It was part of a
process. The process involved workshops, networking, and communities.
Conclusion
Spreadsheets Across the Curriculum is based on a simple idea, the spreadsheet
module. A spreadsheet module is a short PowerPoint presentation that guides
students to build a spreadsheet to do a calculation to solve a problem. The idea
originated in a geology course. It grew to a library of modules crossing 26 LOC
“disciplines.” From idea to Internet resource—it was not a random walk. It was
island-hopping: from workshop to workshop. The intended destination was to
join mathematics and context. After the journey, it appears the strategy that
worked was networking and community-building.
Subsequent papers will discuss the SSAC workshops that produced the
modules, our efforts to find out whether the modules had any effects on module
makers (workshop participants) and/or module users (students), and what we have
learned in the process about the various meanings of quantitative literacy.
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Acknowledgments
We thank our colleagues Cathy Manduca of SERC and Gilles Malnarich of the
Washington Center for their help and encouragement throughout the project, our
program officer Lee Zia for his interest and encouragement, and the reviewers and
editor for their helpful feedback on the submitted version of this manuscript.
References
Adams, F. G. and E. Kroch, 1989. The computer in the teaching of
macroeconomics. Journal of Economic Education 20(3): 269−280.
Ancker, J.S. and D. Kaufman. 2007. Rethinking health numeracy: A
multidisciplinary literature review. Journal American Medical Information
Association 14(6): 713−721.
Arganbright, D. 1984. The electronic spreadsheet and mathematical algorithms.
The College Mathematics Journal 15: 148−157.
Baker, J.E. and S.J. Sugden. 2003, Spreadsheets in education – The first 25 years.
Journal of Spreadsheets in Education 1(1): 18−43.
Beare, R. 1992. Software tools in science classrooms. Journal of Computer
Assisted Learning 8: 221−230.
——— 1993. How spreadsheets can aid a variety of mathematical learning
activities from primary to tertiary level. In Technology in Mathematics
Teaching: A Bridge Between Teaching and Learning, ed. B. Jaworksi.
117−124. Birmingham U.K.: University of Birmingham.
Best. J. 2008. Beyond calculation: Quantitative literacy and critical thinking
about public issues. In Calculation vs. Context, ed. B.L. Madison and L. A.
Steen, 125−135. Washington DC: Mathematics Association of America.
http://www.maa.org/Ql/calcvscontext.html (accessed June 22, 2010)
Brosnan, T., 1989. Teaching chemistry using spreadsheets – I: Equilibrium
thermodynamics. School Science Review 70: 39−47.
Dory, R.A., 1988. Spreadsheets for physics. Computers in Physics 2(3): 70−74.
Elliot, C., 1988. Spreadsheets in science teaching. School Science Review 70:
87−93.
Fratesi, Sarah E., and H.L. Vacher. 2005. Using Spreadsheets in Geoscience
Education: Survey and Annotated Bibliography of Articles in the Journal of
Geoscience Education through 2003. Spreadsheets in Education 1 (3):
190−216:
http://epublications.bond.edu.au/ejsie/vol1/iss3/3 (accessed June
22, 2010).
Frey, S. T., W.R. Moomaw, J.A. Halstead, C.W. Robinson, K.A. Marsella, and
J.J. Thomas. 2003. Home energy conservation exercise. Journal of
Geoscience Education 51(5): 521−526.
20
Numeracy, Vol. 3 [2010], Iss. 2, Art. 6
https://digitalcommons.usf.edu/numeracy/vol3/iss2/art6
DOI: http://dx.doi.org/10.5038/1936-4660.3.2.6
Goforth, T.T. and J.A. Dunbar. 2000, Student response to quantitative aspects of
instruction in an introductory geology course. Mathematical Geology 32:
187−202.
Grawe, Nathan D. and Carol A. Rutz. 2009. Integration with writing programs:
A strategy for quantitative reasoning programming development. Numeracy
2(2): Article 2.
http://dx.doi.org/10.5038/1936-4660.2.2.2 (accessed June 22,
2010).
Harbor, J.M. and S.E. Keattch. 1995. An undergraduate laboratory exercise
introducing form-development modeling in glacial geomorphology. Journal
of Geoscience Education 43(5): 529-533.
Hancock, G., and C. Manduca. 2005. Developing quantitative skills activities for
geoscience students. Eos, Transactions of the American Geophysical Union:
86(39),
http://dx.doi.org/10.1029/2005EO390003.
Hsiao, F.S.T., 1985. Micros in mathematics education – Uses of spreadsheets in
CAL. International Journal of Mathematical Education in Science and
Technology 16(6): 705−713.
Huhmann, Bruce A. and S. McQuitty. 2009. A model of consumer financial
numeracy. International Journal of Bank Marketing 27(4): 270−293.
Lutsky, N., 2008, Arguing with numbers: Teaching quantitative reasoning
through argument and writing. In Calculation vs. Context, p. 59−74.
Madison, Bernard L. and Lynn Arthur Steen. 2008. Evolution of numeracy and
the National Numeracy Network. Numeracy 1(1), Article 2.
http://dx.doi.org/10.5038/1936-4660.1.1.2 (accessed June 22, 2010).
McDonald, J. 1988. Integrating spreadsheets into the mathematics classroom.
Mathematics Teacher 81(8): 615−620.
Misner, C. W., 1988. Spreadsheets tackle physics problems. Computers in
Physics 2(3): 37−41.
Ousey, J.R., Jr. 1986. Modeling steady-state groundwater flow using
microcomputer spreadsheets. Journal of Geoscience Education 34(5):
305−311.
Parker, J. and C. Widmer 1989. Using spreadsheets to encourage critical
thinking. The Computer Teacher: 27−28.
Peters, E., D. Vastfjall, P. Slovic, C.K. Mertz, K. Mazzocco, and S. Dickert. 2006.
Numeracy and decision making. Psychological Science, 17(5): 410−413.
Power, D.J., 2004. A Brief History of Spreadsheets.
http://dssresources.com/history/sshistory.html (accessed June 22, 2010).
Relf, S., and Almeda, D. (1999), Exploring the birthdays problem and some its
variants through computer simulation. International Journal of
Mathematical Education in Science and Technology 30: 81−91.
Shea, J.H. 1993. An exercise for introductory earth science classes on using
globular clusters to determine the size of the Milky Way and our position in
21
Vacher and Lardner: SSAC: Idea and Resource
Published by Digital Commons @ University of South Florida, 2010
it. Journal of Geoscience Education 41(5): 490−496.
Steen, Lynn Arthur, ed. 2001. Mathematics and Democracy: The case for Quantitative
Literacy. Washington, DC: Woodrow Wilson National Fellowship Foundation.
http://www.maa.org/ql/mathanddemocracy.html
Stephen Sweet, Susanne Morgan, and Danette Ifert Johnson, 2008. Using local
data to advance quantitative literacy. Numeracy 1(2): Article 4.
http://dx.doi.org/10.5038/1936-4660.1.2.4 (accessed June 22, 2010)
Taylor, C. 2008. Preparing students for the business of the real (and highly quantitative)
world. In Calculation vs. Context, ed. B.L. Madison and L. A. Steen, 109−124.
Washington DC: Mathematics Association of America.
http://www.maa.org/Ql/calcvscontext.html (accessed June 22, 2010).
Vacher, H.L. 2001, Better math, better geology: Geotimes 46(3): 13, 31.
Wagner, J.R. 2000. Sneaking mathematical concepts through the back door of the
introductory geology classroom. Mathematical Geology 32: 217−229.
Watkins, W. and M. Taylor 1989. A spreadsheet in the mathematics classroom.
Collegiate Microcomputer 7(3): 233−239.
Wenner, Jennifer M., Eric M. Baer, Cathryn A. Manduca, R. Heather Macdonald,
Samuel Patterson, and Mary Savina. 2009. The Case for Infusing
Quantitative Literacy into Introductory Geoscience Courses. Numeracy 2(1),
Article 4. http://dx.doi.org/10.5038/1936-4660.2.1.4 (accessed June 22,
2010).
22
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