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Spreadsheets in Education –The First 25 Years



Spreadsheets made their first appearance for personal computers in 1979 in the form of VisiCalc, an application designed to help with accounting tasks. Since that time, the diversity of applications of the spreadsheet program is evidenced by its continual reappearance in scholarly journals. Nowhere is its application becoming more marked than in the field of education. From primary to tertiary levels, the spreadsheet is gradually increasing in its importance as a tool for teaching and learning. By way of an introduction to the new electronic journal Spreadsheets in Education, the editors have compiled this overview of the use of spreadsheets in education. The aim is to provide a comprehensive bibliography and springboard from which others may develop their own applications and reports on educational applications of spreadsheets. For despite its rising popularity, the spreadsheet has still a long way to go before becoming a universal tool for teaching and learning, and many opportunities for its application have yet to be explored.The basic paradigm of an array of rows-and-columns with automatic update and display of results has been extended with libraries of mathematical and statistical functions, versatile graphing and charting facilities, powerful add-ins such as Microsoft Excel’s Solver, attractive and highlyfunctional graphical user interfaces, and the ability to write custom code in languages such as Microsoft’s Visual Basic for Applications. It is difficult to believe that Bricklin, the original creator of VisiCalc could have imagined the modern form of the now ubiquitous spreadsheet program. But the basic idea of the electronic spreadsheet has stood the test of time; indeed it is nowadays an indispensable item of software, not only in business and in the home, but also in academe. This paper briefly examines the history of the spreadsheet, then goes on to give a survey of major books, papers and conference presentations over the past 25 years, all in the area of educational applications of spreadsheets.
Spreadsheets in Education (eJSiE)
|Issue 1Volume 1 Article 2
Spreadsheets in Education –The First 25 Years
John Baker
Natural Maths,
Stephen J. Sugden
Bond University,
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Spreadsheets in Education –The First 25 Years
Spreadsheets made their first appearance for personal computers in 1979 in the form of VisiCalc, an
application designed to help with accounting tasks. Since that time, the diversity of applications of the
spreadsheet program is evidenced by its continual reappearance in scholarly journals. Nowhere is its
application becoming more marked than in the field of education. From primary to tertiary levels, the
spreadsheet is gradually increasing in its importance as a tool for teaching and learning. By way of an
introduction to the new electronic journal Spreadsheets in Education, the editors have compiled this
overview of the use of spreadsheets in education. The aim is to provide a comprehensive bibliography and
springboard from which others may develop their own applications and reports on educational applications
of spreadsheets. For despite its rising popularity, the spreadsheet has still a long way to go before becoming a
universal tool for teaching and learning, and many opportunities for its application have yet to be explored.
The basic paradigm of an array of rows-and-columns with automatic update and display of results has been
extended with libraries of mathematical and statistical functions, versatile graphing and charting facilities,
powerful add-ins such as Microsoft Excel’s Solver, attractive and highlyfunctional graphical user interfaces,
and the ability to write custom code in languages such as Microsoft’s Visual Basic for Applications. It is
difficult to believe that Bricklin, the original creator of VisiCalc could have imagined the modern form of the
now ubiquitous spreadsheet program. But the basic idea of the electronic spreadsheet has stood the test of
time; indeed it is nowadays an indispensable item of software, not only in business and in the home, but also
in academe. This paper briefly examines the history of the spreadsheet, then goes on to give a survey of major
books, papers and conference presentations over the past 25 years, all in the area of educational applications
of spreadsheets.
Spreadsheet, education, mathematics education, statistics education, survey.
This regular article is available in Spreadsheets in Education (eJSiE):
Spreadsheets in Education–The First 25 Years
John E Baker
Director, Natural Maths
Stephen J Sugden
School of Information Technology, Bond University
July 24, 2003
Communicated by S. Abramovich.
Submitted June 2003; revised and accepted July 2003.
Spreadsheets made their rst appearance for personal computers in 1979 in the form of VisiCalc
[45], an application designed to help with accounting tasks. Since that time, the diversity of
applications of the spreadsheet program is evidenced by its continual reappearance in scholarly
journals. Nowhere is its application becoming more marked than in the eld of education. From
primary to tertiary levels, the spreadsheet is gradually increasing in its importance as a tool for
teaching and learning. By way of an introduction to the new electronic journal Spreadsheets in
Education, the editors have compiled this overview of the use of spreadsheets in education. The
aim is to provide a comprehensive bibliography and springboard from which others may develop
their own applications and reports on educational applications of spreadsheets. For despite its
rising popularity, the spreadsheet has still a long way to go before becoming a universal tool for
teaching and learning, and many opportunities for its application have yet to be explored.
The basic paradigm of an array of rows-and-columns with automatic update and display of results
has been extended with libraries of mathematical and statistical functions, versatile graphing
and charting facilities, powerful add-ins such as Microsoft Excel’s Solver, attractive and highly-
functional graphical user interfaces, and the ability to write custom code in languages such as
Microsoft’s Visual Basic for Applications. It is dicult to believe that Bricklin, the original
creator of VisiCalc could have imagined the modern form of the now ubiquitous spreadsheet
program. But the basic idea of the electronic spreadsheet has stood the test of time; indeed it
is nowadays an indispensable item of software, not only in business and in the home, but also
in academe. This paper briey examines the history of the spreadsheet, then goes on to give a
survey of major books, papers and conference presentations over the past 25 years, all in the area
of educational applications of spreadsheets.
Keywords: Spreadsheet, education, mathematics education, statistics education, survey.
Paper-based spreadsheets have been around for centuries, primarily for use as record-keeping and
accounting tools. The rst electronic spreadsheet, VisiCalc [45], [36] appeared in 1979, created by
Dan Bricklin (concept) and Bob Frankston (programmer) for the Apple II platform. It was conceived
and developed as a tool to do repetitive calculations for Bricklin’s studies at Harvard Business School.
They formed a company, Software Arts, to market the product. In 1981, Bricklin received the Grace
Murray Hopper Award from the Association for Computing Machinery (ACM) for the creation of
VisiCalc. It has been said that VisiCalc was the application, more than any other that sold millions
of Apple II computers. Houghton [87] notes:
The invention of the spreadsheet made personal computers have real value in the marketplace
and legitimated the personal computer industry. Without the invention of this software category,
spreadsheets, the impact of the personal computer might have been delayed for years.
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Baker and Sugden: Spreadsheets in Education
Produced by The Berkeley Electronic Press, 2003
J. Baker and S. Sugden
Bricklin and Frankston sold the rights in VisiCalc to Lotus Development Corporation, which
developed Lotus 1-2-3, a huge killer application for the new IBM PC in 1982. This product introduced
rudimentary database and graphics functionality into the spreadsheet domain, and it dominated
the market for most of the 1980s. Then came Microsoft Excel, which was developed rst for the
Apple Macintosh, but which was also the rst real Microsoft Windows application. In fact, the
earliest versions of Excel ran under MS-DOS, but with a special Windows runtime environment [193].
Other major spreadsheets were SuperCalc (1980, for CP/M operating system), Multiplan (Microsoft),
PlanPerfect (WordPerfect Corp.), Quattro Pro (Borland), VP-PLANNER and AsEasyAs. Since the
mid-1990s, Microsoft has held the dominant market share, and now commands in excess of 90% of
the spreadsheet market [193].
The basic paradigm of an array of rows-and-columns with automatic update and display of re-
sults has been extended with libraries of mathematical and statistical functions, versatile graphing
and charting facilities, powerful add-ins such as Microsoft r
°Excel’s Solver, attractive and highly-
functional graphical user interfaces, and the ability to write custom code in languages such as Mi-
crosoft’s Visual Basic for Applications r
Useful summaries of spreadsheet history are given by Power [154] and Walkenbach [194] and
the authors gratefully acknowledge these sources in preparing the present very brief section on the
historical background and emergence of electronic spreadsheets. Dan Bricklin’s own website [45] has
some very interesting titbits of information and, at the time of writing, also includes a downloadable
copy of VisiCalc. Bob Frankston’s website [71] is also interesting.
2 Programming vs Spreadsheets
As early as 1984, just one year after Lotus 1-2-3 made its presence felt in the commercial market,
educators were beginning to discuss their experiences with using spreadsheets in education [25], [26].
Hsiao [88] makes the point that 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 benet from computers. Hsiao observes that use
of spreadsheets helps to get around this problem. This view is still supported by other writers; for
example, Morishita et al [133] state that:
Our experience in computing was that it took a very long time to learn computer languages
and it was sometimes very hard to obtain proper results in a limited time. The spreadsheet,
however, is rather easy to use and almost instantaneous numerical simulations are possible.
Hsiao considers examples such as function tabulation and plotting, integration by Simpson’s rule,
and makes a brief mention of the possibility of matrix computations, including the Gauss-Jordan and
inverse matrix methods of solving linear algebraic systems. Although this is quite an old paper, it is
clear that the potential for educational uses of spreadsheets wherever mathematics is involved was
obvious to many people even in the early 1980s. The author makes some interesting closing remarks.
1. The rst is that the spreadsheet has allowed teachers to adopt a middle course, compared to
the extremes of fully coding an algorithm in some programming language such as BASIC or
Pascal, or using an o-the-shelf package with a canned solution. It is argued that neither of
these methods is ideal for learning and the spreadsheet approach is recommended.1
2. The second one concerns the absence (in 1985) of a number of desirable features, such as
transposition of rows and columns, absence of regression lines on scatter graphs, 3D graphs, and
so on; all of these features are available in modern versions of spreadsheets such as Microsoft’s
1In many instances, at least, the present authors are in agreement.
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Essentially the same points are made in a more recent paper by Steward [176]:
I would suggest that when both are possible, students nd it easier and quicker to use a
spreadsheet than write a computer program. Moreover, once written a program can often mask
the mathematics that it is intended to represent, while on a spreadsheet the procedure is constantly
In this paper [176], the author considers three examples illustrating his claim: linear regression
from rst principles, convergence of recursive sequences, and rst-order ordinary dierential equa-
Relf and Almeida [157] give the example of the spreadsheet being used to (comprehensively) solve
the Birthday Problem, which can be stated as nding the least number of people in a group for which
there is a probability 0.5 that two will have the same birthday. In comparing the cost/benets of
programming vs spreadsheets, they say:
...theprimeneedis foramediumwhich will facilitate consideration of conceptual issues while
requiring minimal technical expertise, will provide insights into the mathematical context without
necessitating attention to extraneous distractions, will permit modication without the need for
major changes in design and will ag and encourage the pursuit of connected enquiries.
It is the spreadsheet that meets all of the above.
With access to VBA (Visual Basic for Applications), educators are also nding great benetin
tying programming to spreadsheet use, thereby overcoming much of the time spent in organizing data
input and output. For example, Martin [121] outlines a course for Operations Research students in
which he reports that:
...using the spreadsheet as a platform, the student is led to a position where they can write
virtually a stand-alone program to support a simple OR application, even from a position of little
previous spreadsheet or computing experience.
From the above, it appears that if the goal is not to teach a programming language, but to achieve
understanding of a concept/topic for which some sort of program is needed to show, for example,
variation over time, then the spreadsheet should be the rst choice.
3 Packages vs Spreadsheets
The Association for Educational Communications and Technology (AECT) has a useful website, and,
in particular, an interesting page [201] entitled Spreadsheets as cognitive tools. On it, we read the
following quotation from the doctoral dissertation of Leon Argyla [109]:
Spreadsheets are powerful problem-solving tools. However, the diculty in using spreadsheets
for problem solving depends on the amount of abstractness and information processing the problem
contains (Leon-Argyla, 1988).
At the same time as spreadsheets, a number of computer packages have been developed that
parallel business and educational applications. In the arenas of statistics and geometry, sites such as
CTI2[202] and CIGS3[203] show that specially designed packages are preferred to the computational
and graphical features of spreadsheets.
However, on the benet side, we would suggest that:
3Corner for Interactive Geometry Software
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1. Building spreadsheets requires abstract reasoning by the learner.
2. Spreadsheets are rule-using tools that require that users become rule-makers (Vockell and van
Deusen [192]).
3. Spreadsheets promote more open-ended investigations, problem-oriented activities, and active
learning by students (Beare [31]).
Feicht [67] describes the use of Excel to investigate relationships between matrices and geomet-
ric transformations, and in doing so, opens up a very rich eld for further investigation. Today’s
mathematical syllabus has little time for geometry, but it may see a resurgence if it can be shown
that electronic versions of theorems have the power to excite the imagination and enthusiasm of
learners–see the mathematics site of Bogomolny [204], which is testimony to the power of animating
concepts in mathematics and statistics. For an example hosted in Microsoft Excel, consider the work
of Staples [175]. We have seen that when it comes to programming, spreadsheets have desirable
features; it may be that in the future, the animation of concepts is an area in which spreadsheets
will have an increasingly inuential role over computer packages.
For applications of spreadsheets in mathematics education, especially that of mathematics educators,
Abramovich, along with co-workers, is the most prolic author ([1]—[22], [110]). Indeed, Abramovich
and co-workers are leading the eld in this area. The website [1] for Abramovich’s course “Using
Spreadsheets in Teaching School Mathematics” contains a number of useful links, and is well-worth
investigating. Abramovich and Brantlinger [11] examine the suitability of spreadsheets for mathe-
matics teacher education. They note that the typical classroom is not well-equipped when it comes
to a range of mathematical software.
The appearance of computers as alternative instructional tools has created serious problems in
undergraduate pedagogy. This is particularly the case for mathematics teacher education, because
technology as a mathematical/pedagogical tool is not always used appropriately in schools. Indeed,
some teachers who attempt to incorporate technology into the curriculum limit its use to routine
computations only due to a lack of experience with this technology. The mathematics education
community views this problem as a great challenge to educational reform [11].
In [10], the same authors give examples of the use of recursion in a spreadsheet, the visualization
of the limit of a sequence, and cobweb diagrams. The paper concludes that, given the wide avail-
ability of spreadsheets, a toolkit of computer resources (such as a scientic calculator, a graphing
package and a database program) can be just one program: a modern spreadsheet. Abramovich and
Norton [15] extend this work to investigation of chaos, and associated basic concepts of convergence,
divergence, cycling and period doubling. They further argue that for mathematics education majors,
the spreadsheet is the ideal vehicle for the illustration of mathematical fundamentals such as these.
Similar topics are covered in another paper by Abramovich et al [13].
4.1 Collaborative Constructivist Learning
D’Souza and Wood [200] investigate the benets of spreadsheets in a collaborative learning environ-
ment at secondary school level, with the application being elementary nancial mathematics. The
authors state that:
Spreadsheets have enormous potential for assisting in the learning of algebraic concepts. They
can be of great benet at all levels. Spreadsheets enable students to concentrate on thinking about
the subject matter at hand rather than on the software. There are many mathematical applications
of spreadsheets as noted by Beare [32].
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It is worth repeating the relevant citation from Beare [32]:
Spreadsheets.... have a number of very signicant benetsmanyofwhichshouldnowbe
apparent. Firstly they facilitate a variety of learning styles which can be characterised by the
terms: open-ended, problem-oriented, constructivist, investigative, discovery oriented, active and
student-centred. In addition they oer the following additional benets: 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.
Herrington and Standen [84] consider that many multimedia educational packages tend to present
material in an instructivist manner, thus placing the learner in a passive role. They would prefer to
see learning posed in an authentic setting to provide a constructivist learning environment, and it is
the spreadsheet that provides just such an environment4.
In a 1997 conference presentation, Sher [165] asserts that:
The spreadsheet is the ideal environment for software that follows the Harvard ap-
In a nutshell, the so-called Harvard approach [for mathematics teaching] is that every topic should
be presented geometrically, numerically, and algebraically. Such an approach is exemplied in the
work of Hughes-Hallett [89] and many others. Similarly, Friedlander [72] suggests that:
Spreadsheets build an ideal bridge between arithmetic and algebra and allow the student free
movement between the two worlds. Students look for patterns, construct algebraic expressions,
generalize concepts, justify conjectures, and establish the equivalence of two models as intrinsic
and meaningful needs rather than as arbitrary requirements posed by the teacher.
Thus, in mathematics education, we are seeing the emergence of the spreadsheet as a key compo-
nent of the constructivist teaching repertoire. There is no doubt that this role will grow in importance,
as students become more and more competent in the mechanics of using spreadsheets.
We close this section with some comments from a relatively modern work, that of Ainley et al
Over recent years, we have explored the conjecture that particular pedagogical settings that
exploit immediate and continuous access to computers can change the way in which knowledge
about graphs is constructed.
...the spreadsheet provides the facilities that allowed Clara and Colin to construct these mean-
ings for trend ...
...Through activities with spreadsheets in this pedagogic setting, children expressed new mean-
ings in which scattergraphs became increasingly powerful tools for analysing ongoing experiments.
4.2 K-12 mathematics
Lewis [114] notes that:
Spreadsheet assignments oer concrete ways to explore abstract concepts in mathematics and
other subjects.
4We are not implying here that spreadsheets are the silver bullet that will transform traditional classrooms into
constructivist ones. Indeed, it is quite possible to imagine students being taught to program spreadsheets in teacher-
centred ways.
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Lewis [115] has also produced a spreadsheet resource book for mathematics teachers of grades
K-8. Nowhere is the exploration of an abstract concept more fully researched than in the study of
Sutherland and Rojano [184] in which the potential of the spreadsheet to enable students to form a
correct understanding of algebraic concepts such as pronumerals is investigated. This frequently cited
work, in a sense, sets the benchmark for educational studies of spreadsheet potential. Sutherland
[187] has much more recently used the spreadsheet environment to allow secondary school students
in the UK to develop basic concepts of algebraic dependency. Since the students have trouble with
the abstract nature of algebra, the spreadsheet is used to develop relationships with point-and-click.
Note the following remarks from Sutherland’s paper [187]:
The more traditional approach to teaching algebra often involved imposing an algebraic
method with an over-emphasis on the manipulation of symbols and with no acknowledgement
of the value of the pupils’ own approaches. This way of teaching algebra was only successful for
the minority of pupils.
Our experimental work has shown that most pupils do not spontaneously engage in the alge-
braic processes of expressing generality, acknowledging and manipulating the unknown, focusing
on structure, using an analytic algebraic method.
One way to help pupils move from a non-algebraic to an algebraic approach can be through
work with spreadsheets. . . ..Pupils use the mouse to support the expression of general relationships
and to move from thinking with situation-based to more abstract algebraic objects. . . ..Mouse
pointing becomes a way of supporting pupils to express general relationships, which are then
represented automatically in spreadsheet code. Pupils become aware of this spreadsheet code
without explicit instruction and interact with it when they need to modify their constructions.
They begin to use the spreadsheet code in their talk when communicating with their partner and
can write it down when communicating with others. In this way the algebra-like spreadsheet code
is learned eortlessly without explicit teaching. Pupils use the spreadsheet specic calculations
to help in the construction of general rules and often verify their general rule with reference to
specic numbers. In this way links between symbols and general numbers are established.
Similar comments are made by Abramovich [12]. Referring to a spreadsheet model to support an
inductive proof, it is stated that the model:
...allowsforthevisualizationofaninductive proof of combinatorial identity, and it cognitively
supports a transition from computing to a formal language of mathematics.
Ruthven & Hennessy [162] give an account of the use of various forms of computer technology and
software to support mathematics learning in seven English secondary schools, in the year 2000. In
this rather lengthy paper, although there is much interesting material, we generally conne ourselves
here to aspects relevant to spreadsheets. Some of the major points are:
1. Students are nowadays more familiar with basic IT applications, including spreadsheets, so that
much less time is spent on trivial matters in Excel, and the class can spend most of its time on
mathematical activities within the spreadsheet. This is in contrast to the graphics calculator,
which is not as ubiquitous as the spreadsheet, and is typically only used in mathematics classes,
whereas the spreadsheet could be used in IT skills courses, business, economics, etc.; it is a
more generic tool.
2. Teacher and students have more control over spreadsheet models, e.g., sequences, than for other
3. In a comparison of classes of software used for mathematics instruction and modelling in the
seven schools (courseware, graphware, Logo, spreadsheet), the spreadsheet was the only one in
use at all the schools.
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4. A teacher at one school had his year 11 students doing statistical text processing in Excel:
some text from newspaper website was transferredintoExcel,thenanalyzedstatistically,in a
short space of time.
In hindsight it seems obvious, but probably one of the most profound, clear benets of using
spreadsheets that emerges from this study is just that of saving time. The time gained can then be
spent on investigating properties of the mathematical objects created in the spreadsheet environment:
the so-called what-if scenarios. There is huge scope for investigation of dependence on parameters in
almost any spreadsheet model of a mathematical process. This includes not only the “traditional”
mathematics that we might classify under the headings of algebra, calculus, trigonometry, geometry
etc., but also more modern and discrete areas such as string processing, language theory, automata
theory, and of course, combinatorics and recurrence relations. Note the following comments from a
teacher of years 7 and 8:
We’ve used spreadsheets in Year 7 and 8, to enable them to look at handling data, because
they can quickly get tables and produce charts that are much better quality than those that they
can produce themselves. I’ve got the bottom set in Year 7 and it can take them the whole lesson
to draw a bar chart. So it’s particularly successful from that point of view because they don’t
have to draw all the axes so much, and it doesn’t take them so long to develop the ideas because
they’re not having to spend a whole lesson drawing something. They can draw twenty graphs in
a lesson and actually see connections, rather than spend twenty minutes drawing the axes and
then twenty minutes talking and then twenty minutes drawing all the graph.
It saves a lot of time as well with the Further Maths and the graphing that we did. It would
have taken forever to actually plot all the points and see what happens when you transform certain
shapes. Whereas it was done in a ash and they could see and they learnt an awful lot. So then
they were ready and they’d accepted it because they’d seen it happening... Whereas it would have
taken many lessons if we’d actually plotted all these graphs, they’d have just got bored by it. So
that denitely helped, just kept the pace going. [162]
It needs to be added that, despite the growing number of studies that show positive results for
the use of spreadsheets, curriculum goals such as those produced by State and National Education
Departments place less emphasis on the role of spreadsheets than on that of calculators as a tool for
social constructivism in mathematics. There is little doubt that the main reason for this emphasis
on calculators is based on educational administrators being constrained by the number of computers
that are available in any given classroom. As a referee of this paper has noted: “it is not that
graphing calculators are a superior tool it is rather that graphing calculators are a more accessible
tool.” However, curriculum administrators are beginning to acknowledge the enormous potential of
the modern spreadsheet program to enhance learning opportunities.
For a review of the K-12 uptake of spreadsheets, the ERIC digests by Ozgun-Koca [145] for
the years 2000 and 2001 make a good starting point, as they contain numerous links to web-based
resources. The book [101] is a good source of spreadsheet examples for grades 3 to 8. See also the
work of Dugdale [59].
4.3 Number Theory
In spite of number theorist G.H. Hardy’s claim [82] that “I have never done anything useful”, the
utility of number theory nowadays is undeniable, with prime applications being mathematical cryp-
tography and cryptology. Modern CS/IT graduates need to know at least the basics of cryptographic
computer security systems, and the use of spreadsheets in particular for the illustration of number-
theoretic concepts appears to be on the rise. Just a few examples are the work of Abramovich and
co-workers, cited earlier, and that of Sugden [182]. Sugden uses Excel for illustration of Euler’s
ϕ(n)(totient) function, τ(n)(number of divisors), the Möbius function µ(n),aswellasthebasic
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operations of modular arithmetic, including modular inverse, modular exponentiation, leading to a
32-bit implementation of the RSA public key cryptosystem in Excel.
Abramovich [7] also considers the use of Excel for some basic investigations into number theory,
and gives an implementation of the Sieve of Eratosthenes using a few very simple formulas. He goes
on to consider gaps between primes, primes in arithmetic progression, even showing how to tabulate
and graph the function π(x)(numberofprimeslessthanx), all in Excel. His formula for this latter
task is very long but consists of a sequence of very similar sub-formulas, and one suspects that this
could be simplied somewhat, given the modern facilities of, for example, Microsoft Excel XP. In his
article, Abramovich quotes earlier authors MacKinnon [119]:
...thebest use of computers in mathematics education is to runprofessional software written
for real purposes.
and Steward [176] (op cit, p20).In a later paper, Abramovich and Brantlinger [11] present further
topics in elementary number theory within the spreadsheet environment. These include Pythagorean
triads, Euclidean algorithm, Bride’s Chair, and the representation of integers as the sum of perfect
4.4 Combinatorics
Neuwirth [135] showed that:
...spreadsheets as a model for mathematical relations can help gaining insight into recursive
relations for combinatorial formulas.
This paper and Neuwirth [136] use the very fundamental features of a spreadsheet to illustrate
the structure of elementary recursive combinatorial identities, introducing an arrow diagram notation
to demonstrate the concept:
We see immediately that in this graphical notation the formula is the same for any case in a
very intuitive sense.
Neuwirth aims to avoid algebra as much as possible as the students have trouble with this and
with the closely related concept of mathematical induction. Sugden [179] also uses Excel to assist
with investigations into mathematical induction and recursive implementations of arithmetic and
geometric sequences (directly applicable to simple and compound interest respectively). The concept
of a recursive relation is one that lies at the heart of Microsoft Excel’s Fill Handle implementation,
which takes a range of cells in which formulae apply and spreads them over a range in a way that
replicates the recursive process. We believe that an investigation into student understanding of
recursion can be greatly enhanced by implementing such a process on the spreadsheet. For example,
Sugden [179] uses this technique for his discrete and business mathematics classes to implement a
full superannuation model, complete with rollover and schedule of net worth, in Microsoft Excel,
with just one addition and one multiplication–no exponentials or intrinsic functions. Given such an
environment, the traditional conceptual diculty of recursion is replaced by the visual simplicity of
a single-step formula (one recursive step) and Excel’s ll-down. Hvorecký and Trencansky [94] use
cell insertion in Excel, under VBA/macro control, to investigate graphs of functions of one and two
variables, and to the generation of fractals. As further cells are inserted (their requirement for extra
cells grows exponentially), graphs and fractals of higher precision are obtained.
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4.5 Numerical Analysis
There is a healthy literature on the uses of spreadsheets in numerical analysis (NA). A topical example
would be Lawson and Tabor [108], in which a model arithmetic and geometric growth is presented
using a spreadsheet. Their application is to model the spread of Variant Creutzfeldt-Jakob disease
(mad-cow disease, or vCJD). In all references located, the positive aspects of spreadsheet use recur.
For example, Soper and Lee [178] conclude:
The versatility of computer spreadsheets makes them a very suitable means of accurately
undertaking numerical calculations. The formulae required are easily entered into the spreadsheet,
and the approach has the further advantage that the users can see what is being calculated, so
enhancing their understanding of the method. With the availability of graphical facilities, a plot
of the value of a variable at successive iterations can easily be displayed. A further benetof
the approach is that students become procient in the use of a very popular business computer
Another two examples of using spreadsheets for numerical analysis are from Australia: Smith
[174] describes an entire NA course at Monash University, Australia (1989) taught entirely using the
spreadsheet program VP-PLANNER, and McLaren’s book [126] has been used to support his NA
course at LaTrobe University.
Sequences, a key element of numerical modelling, are a natural for a program such as Microsoft
Excel. There is no doubt that the modelling of sequences is one of the great strengths of the modern
spreadsheet program; in fact, even the very early versions such as VisiCalc were almost as good.
Sequences can be dened by just listing the terms, by a direct formula, or by a recurrence. For the
most basic of sequences (arithmetic and geometric), the most natural denition is the recursive one:
start anywhere and either keep adding a constant or keep multiplying by a constant. From the point
of view of student understanding, such a prescription is almost too easy to implement in a modern
spreadsheet such as Microsoft Excel.
For the 21st century, IT-literate student, it must seem like a total a waste of time that the teacher
has to write a recurrence relation to express such a simple operation as ll-down ! Students familiar
with spreadsheets already know all about this. The challenge for the teacher is, of course, to relate
the mathematical formalism of a recurrence relation to the readily comprehended spreadsheet notion
of ll-down. Student reaction to the translation of mathematical formalisms such as the algebraic
expression of a recurrence relation such as that of Equation 1 into the spreadsheet environment are
discussed briey by Sugden [179]. Equation 1 represents a superannuation model with $100,000
rollover (initial value), 1% interest per month, and $500 contribution per month. It is interesting
that many students have diculty even understanding Equation 1 (let alone solving it), yet have
very little trouble implementing the corresponding model in Microsoft Excel. Clearly, there is ample
scope for future research here.
an=½1.01an1+ 500 if n>0
100,000 if n=0 (1)
It is clear that immediate application of such recursion is to be found in the area of elementary
mathematics of nance. Coupled recurrence relations (dierence equations) relating to population
dynamics, for example, are also easily handled. Since many sequences are most naturally dened
recursively (arithmetic, geometric, Fibonacci etc.), the spreadsheet oers a very rich environment for
investigation of sequences, in most instances, with no coding required. Further discussion may be
found in [180].
4.6 Mathematics not otherwise cited
Due to limitations of time, it was not possible to obtain a copy of every publication considered
relevant to the application of spreadsheets to mathematics teaching and learning. However, in the
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interests of providing as complete a bibliography as possible in the present survey paper, the following
additional works are cited: [30], [41], [58], [60], [61], [62], [63], [85], [86], [93], [96], [97], [117], [118],
[120], [122], [127], [125], [132], [138], [139], [142], [143], [148], [151], [152], [158], [159], [161], [164],
[172], [173], [185], [190], [191], [195], [197] and [199].
5 Statistics
Does the spreadsheet have advantages that make it a more acceptable tool for teaching and learning
than the use of statistical packages? In this respect, Hunt [91] refers to teacher belief as follows:
Many teachers now believe that a spreadsheet provides a better educational environment
in which to teach statistics at an elementary level. The spreadsheet can be made much more
transparent to the student, allowing them to look inside the black box.
Overall, however, the jury is still out on this question–at least at the tertiary level. Although
Neuwirth [137], for example, has demonstrated that spreadsheets may be employed to assist statistical
learning beyond just that of using intrinsic functions (he writes about visualizing correlation), there
is a good deal of negativity in the literature when it comes to statistical computations. For example,
writing about versions of Excel 5.0 and earlier, Nash and Quon [134] conclude that:
Spreadsheet vendors must be encouraged to do better. Closer attention to statistical issues
would result in tools better suited to data exploration and analysis, and cleaner software design
would avoid some obvious sources of error.
They would like to see options for:
1. Histograms, possibly with unequal class intervals.
2. Stem and leaf diagrams.
3. Boxplots, especially with multiple boxplots on the same scale.
4. Quality-control charts.
5. ppand qqplots for distributions, especially the Gaussian distribution.
If the requirement, even at tertiary level, is to cover only elementary concepts, others nd that the
spreadsheet serves admirably. For example, in teaching an engineering subject, Hall [81] concludes
This approach to teaching mathematics, with an intimate mix of mathematical theory, nu-
merical examples and graphical representations, together with the use of modern computing aids,
seems appropriate for engineers.
Warner and Meehan [196] express similar support, stating that:
Individual instructors will need to weigh the costs and benets of using a spreadsheet program
versus specialized statistical package, but we believe a spreadsheet, such as Excel, will prove more
attractive in many situations.
Hunt [92] reasserts the belief of teachers, concluding that although Microsoft Excel has a great
deal to oer at the elementary level, it is of limited use to serious students of the subject. He points
to features such as NORMDIST(1.96) which returns the tail probability of 0.975 and commends the
function NORMSINV(RAND()) which can be used for simulating a standard normal random deviate.
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Features such as these really do make the spreadsheet a simple-to-use tool for the constructivist
learning environment. Hunt also identies two types of computer-assisted learning activities that are
well-supported by spreadsheets. There is the ‘do-it-yourself’ type of activity favoured by Callender
and Jackson [49], and the ‘Blue Peter5’ activities where students experiment with pre-set spreadsheets
such as the DISCUS materials of Hunt and Tyrrell [90].
Callender [48] demonstrates how the spreadsheet, with simple-to-write macros, can be used to
demonstrate the normal distributions and the central limit theorem. He suggests that a benetof
using spreadsheets to introduce such key topics in statistics is:
The normal distribution has been introduced without ‘denitions’ being needed and all the
components of the Central Limit Theorem are demonstrated as a consequence of probability
However, a recurring complaint is that Microsoft Excel does not cater for exploratory data analy-
sis. We would question the value in Excel’s catering for such a specic and small audience as that
for whom exploratory data analysis is an issue. Features such as box and whisker plots can readily
be constructed on XY-scatter charts, and once the framework for such a plot has been made, it can
be quickly copied for use with dierent data. To make a histogram with uneven intervals, our advice
would be ‘Don’t!’ and if you have data that needs to be summarized on a histogram, the Pivot Table
facility provides a very speedy way of generating the required data table. It would appear that the
true value of these educational oddities of exploratory data analysis have not been recognized by the
wider business community, and hence not implemented by Microsoft programmers.
More serious is the common complaint that Excel statistical functions are unreliable [123], [124],
[104]. Indeed the present authors would hesitate to recommend any version of Microsoft Excel
for professional statistics work, although the second author has done much consulting work based
(stochastic modelling) in Excel [181] and the package performed very well. But, from a pedagogical
standpoint, it is here argued that a collection of totally robust algorithms for computing statistical
functions and distributions is not the principal requirement for students when learning basic statistical
techniques and functions. Provided the implemented functions are reasonably accurate for normal
ranges of the parameters, it is far more important that the student is able to understand the operation
of such functions and so see the many connections, patterns and properties; these are amply illustrated
in the spreadsheet environment. However, a revamp of the statistical functions appears to be on
Microsoft’s wish list for Excel 2003 [193].
In this context, please forgive us for slipping in a positive comment about the MODE function; one
that is taught in very elementary statistics courses, never again to rear its head. In Excel, however,
we nd that the MODE function is a powerful tool for locating duplicates in a list, particularly when
combined with conditional formatting (e.g., if the value of this cell is =MODE(range) then format
the cell to have a blue colour). Some further useful information concerning the use of conditional
formatting with Excel’s MODE function was pointed out by an anonymous reviewer, and is included
here, with permission.
It appears that in the case of poly-modal array of numbers, the MODE function recognizes the
rst number that appears most in this array. For example, using conditional formatting jointly
with this function, in the array {2,1,3,2,1,5,5,3,4,4}twos will be highlighted only, whereas in
the array {1,2,3,2,1,5,5,3,4,4}ones will be highlighted only.
It would be inappropriate to complete this section without mentioning the Association of Statistics
Specialists Using Microsoft Excel (ASSUME) [205] whose main interest appears to be the use of Excel
in higher education. Queries to the ASSUME list will almost always receive an answer from someone
who knows.
5This name refers to the English children’s TV program ‘Blue Peter’ catchphrase — “Here is one that I
prepared earlier".
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6 Physical Sciences
Spreadsheets have long been used both for teaching mathematical principles of physical science and
analysis of empirical results; for example [27], [31], [34], [35], [39], [40], [42], [43], [44], [46], [47], [50],
[51], [52], [53], [56], [57], [65], [66], [68], [69], [75], [77], [79], [80], [99], [100], [102], [103], [105], [108],
[111], [128], [129], [130], [131], [133], [140], [141], [144], [149], [153], [163], [169], [188], and [198].
However, in his 1992 paper, Smith [171] notes the comparative rarity of using the spreadsheet as a
mathematical teaching tool. He goes on to mention some uses of spreadsheet in teaching physics, and
cites the texts of Misner & Cooney [130] and Crow [52]. In his closing remarks, Smith predicts three
positive outcomes for students:
1. Reversal of the declining interest in mathematics.
2. Improvement of technological literacy and enhancement of career preparation.
3. Revitalization of mathematical skills through problem solving.
Some textbooks, not mentioned elsewhere, and which employ spreadsheet-based models, algo-
rithms and solutions are [25], [26], [27], [33], [37], [38], [54], [55], [83], [106], [107], [150], [155], [170],
[183], and [186].
An interesting modern paper is that of Lim [116], which describes how spreadsheets are used to
support the teaching of quantum chemistry. It is reported that students with weak mathematical
backgrounds have proted from this approach.
This author prefers the use of spreadsheets for weaker students for the following reasons. The
symbolic mathematical packages depend on the use of a symbolic, quasi-programming language,
which can present an additional learning obstacle for many students....
Furthermore, the access to symbolic mathematical packages is usually more limited than
that of spreadsheets, which are widely available in home, business and community settings. The
“worldware” ...also called “application-software” ... nature of spreadsheets means that students
will have greater opportunities to use and become familiar with spreadsheets than with (eg)
symbolic mathematical packages, leading to greater utility and expertise. Software that isn’t
designed for instruction can still be good for learning....
A “straw poll” of physical chemistry faculty suggests that signicantly more faculty use spread-
sheets in teaching and learning activities than symbolic mathematical packages [116].
Shinners-Kennedy [166] reports on the use of early work in which spreadsheets provide a host envi-
ronment for teaching assembly language programming. Even as early as 1986, he notes:
It is surprising the range of applications that have been coaxed into this format.
In another paper [167], the same author describes computer programming and data structures and
algorithms courses and refers to the well-known obstacles to comprehension of run-time behaviour of
programs for "weaker students". The response of several educators to this problem is the creation of
run-time visualization environments. Similar considerations are expressed by Rautama et al [160].
Once again, the authors state that many students have trouble understanding basic algorithms, and
it is a signicant challenge to inspire them to investigate why and how a given algorithm works.
Examples they cite are binary search, and edit distance for string editing. Rautama et al use
Microsoft Excel as an algorithm animation environment, and also point out that such an approach
leads to useful tools for algorithm research too. Shinners-Kennedy [167] recommends the use of
spreadsheets for construction of such visualization systems, and goes on to describe the benets of
the Microsoft Excel Object Library for such endeavours:
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The spreadsheet concept is deceptively simple.
In essence the spreadsheet system is a toolkit (emphasis ours) for exposing and explaining the
principal concepts associated with the object-oriented methodology.
Fone [70] demonstrates the value of using Excel to model neural networks. In an end-of-course
survey, Fone found that:
Unlike previous groups, there were no comments suggesting the need for better models. How-
ever, ve comments typied by the statement, “I found the Excel example particularly helpful, not
only in helping me understand the networks but with aspects of other modules” were of particular
Other applications of spreadsheets in computer science are described in [95] (programming),
[112] (arithmetic unit simulation), [113] (automata), [168] (object-oriented programming), [64] (ani-
8 Economics and Operations Research
Thiriez [189], in an invited review of the role of spreadsheets in operations research teaching begins
by pointing out that there is: point in demonstrating the eciency of the spreadsheet as a tool for teaching basic
modeling and programming.
Thiriez also notes that there are less well-known features of spreadsheets that turn out to be
powerful, so long as you know how to use such features. He goes on to give examples in decision
theory, linear programming and simulation:
The spreadsheet is the best tool for teaching deterministic simulation.
Suggestions are also made that users should view the Solver capabilities with caution. However,
A major asset of spreadsheets resides in the speed with which a model may be designed.
Recently, I had the opportunity to build a simulation model for the automatic handling of luggage
at the Paris Roissy airport. When the model (totally developed in Excel) was nished, I learned
that all other proposals for the tender oer of this application, all of them based on the use of
professional simulation software, had all been at least vetimesasexpensiveasourproposal.
Many other examples of the use of Excel’s Solver are to be found on the WWW; for example, see
Jones and Judge [98] support the general views of Thiriez in a paper that gives examples from
micro-economics and macro-economics, illustrating how a spreadsheet can be used to assist in the
development of a student’s understanding of dynamic models and their properties. Adams and Kroch
[23] point to the value of the graphical component of spreadsheets:
The linkage between algebraic, numerical and graphical presentations in spreadsheet programs
on the personalcomputeris asignaladvantage for theteaching of macroeconomics...toillustrate
the principal elements of macrotheory.
Goddard et al [78] note the way in which spreadsheet usage supports a shift from active to passive
learning by enabling students to explore what happens to income-expenditure economy models (the
IS-LM model) as equilibrium is disturbed.
Barreto and others use Excel for the teaching of Economics and Econometrics at Wabash College
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9 Some spreadsheet esoterica
9.1 Conditional formatting
An interesting feature, introduced in Excel 97 is that of conditional formatting. It may be viewed
as a generalization of the common accounting practice of colouring amounts of money red or black,
depending on their natures as debits or credits (negative or positive). Microsoft Excel is able to
automatically format (colour, border, font etc.) a cell based on its current value. A simple example
of the use of this feature is solving f(x)=0without algebra, but by just observing change of sign
(change of colour). Those interested in the use of this facility will nd downloadable models on
the Spreadsheets in Education (SIE) eJournal site [28]. The literature on the use of this feature for
educational applications within the spreadsheet environment is scant indeed, although applications
abound. One reference to its use is that of Sugden [179], who uses it for solving f(x)=0without
algebra, and illustrating the solution of simultaneous linear congruences, among many others.
9.2 Names
One of the most benecial features of the modern spreadsheet is the facility to dene a Name. Such
a feature allows the spreadsheet user to refer to a cell or collection of cells by a single identier; this
is similar to the use of variable names in programming languages rather than hard addresses (relative
or absolute). Many benets accrue with the use of names; some of these being:
The troublesome, but sometimes necessary, absolute references are handled automatically.
Models may be expressed in notation very close to that of standard algebra. Instead of using
an obscure formula with hard cell references such as = A2*$E$3, one may write something like
= GrossPay*TaxRate.
Large areas of the worksheet such as tables or lists may be easily selected by just going to the
Name box (Microsoft Excel)
Models become at least partially self documenting and tend to be easier to debug.
Despite the fact that problems with relative and absolute addressing simply vanish, and that
formulasmaybeexpressedintermsverycloseto an algebraic model when one uses names, it is
rather surprising how rarely these are used in published examples.
9.3 Auditing and debugging
In this paper, we have trumpeted the benets of spreadsheets for educational purposes. What is the
downside? There exist quite a number of papers which highlight negative aspects of spreadsheets,
and in the interests of a more balanced presentation, it seems only fair that our survey should
include some of these papers too. The main objection appears to be debugging (touseacomputer
programmer’s term), or auditing (to use an accounting term). When applied to spreadsheets, these
two terms refer to much the same thing: the problem of ensuring that a given model is correct.
The diculties of auditing spreadsheets are well-known, and the level of complexity seems to be
comparable to that of debugging a moderate-sized computer program; this problem is well-known to
be hard [73], [74], [146], [147], [156].
To put our negative remarks about spreadsheet auditing in perspective, we note that modern
spreadsheets such as Microsoft Excel have some quite useful auditing tools; for example, even without
invoking the auditing toolbar, just a double-click in a cell will highlight immediate antecedents, that
is, cells which directly aect the value of the current cell. Secondly, spreadsheet models developed for
educational purposes tend to be founded on a sound mathematical model, and if wrong results are
produced, or a limitation of the model is reached, then students can be asked to investigate why such
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a happening has occurred. In other words, in an interactive learning environment, it is often possible
to turn an apparently negative outcome to a positive one. For an example of this, see Sugden [179].
10 Conclusion
In this brief outline of spreadsheets in education, one of our principal aims has been to provide
arguments and motivation for further research in this area. There is no longer a need to question
the potential for spreadsheets to enhance the quality and experience of learning that is oered to
students. Traditional barriers (particularly the lack of facilities to use spreadsheets in assessment
contexts) need to be removed, either by ensuring that access to computers is improved or by changing
assessment methods. Further expansion is needed of the types of topics that can be eectively covered
by spreadsheet examples; for example, one of the authors has recently completed a spreadsheet to
enable the investigation of cellular automata as described by Gardner [76].
Hence the electronic journal Spreadsheets in Education! The goals of the journal [28] are:
1. To create a forum in which ideas on the use of spreadsheets can be exposed and explored.
2. To provide an avenue for scholarly research into the use of spreadsheets at all levels of education
to be reported to a receptive, practising audience.
3. To enable teachers to take on board a technology which can rightly claim to be one of the
founding fathers of the personal computer and which is a tool for life to which all students
should be exposed.
The electronic medium was chosen over print so as to provide a facility to discuss spreadsheets
in education and at the same time giving access to the spreadsheets under discussion. In the view of
the authors, to do otherwise would be inappropriate in this age of technology.
The authors are grateful to the reviewers for many useful comments and suggestions, and espe-
cially to Sergei Abramovich, State University of New York, for coordinating the review process.
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... It has been more than three decades since computer spreadsheets became known as a tool of education [1]. Designed in 1979 for non-educational purposes on the foundation of the computer program VisiCalc, the spreadsheet, nonetheless, was conceptualized in educational terms as "an electronic blackboard and electronic chalk in the classroom" [2]. ...
... 7); namely, the invariance of the limiting value of the ratio of two consecutive terms of the (Fibonacci-like) sequence a, b, a + b, a + 2b, 2a + 3b, 3a + 5b, 5a + 8b, . . . (1) to the change (a numeric transformation) of the initial values of a and b. When a = b = 1, sequence (1) turns into Fibonacci numbers. ...
... Put another way, the sums of the coefficients in a and b in the terms of sequence (1) are Fibonacci numbers. A recursive definition of sequence (1) has the form ...
Full-text available
The paper promotes the notion of computational experiment supported by a multi-tool digital environment as a means of the development of new mathematical knowledge in the context of education. The main study of the paper deals with the issues of teaching this knowledge to secondary teacher candidates within a graduate capstone mathematics education course. The interplay of mathematics and education is considered through the lens of using technology to enhance one’s mathematical background by advancing ideas from mostly known to genuinely unknown. In this paper, the knowns consist of Fibonacci numbers, Pascal’s triangle, and continued fractions; among the unknowns are Fibonacci-like polynomials and generalized golden ratios in the form of cycles of various lengths. The paper discusses the interplay of pragmatic and epistemic uses of digital tools by the learners of mathematics. The data for the study were collected over the years through solicited comments by teacher candidates enrolled in the capstone course. The main results indicate the candidates’ appreciation of the need for deep mathematical knowledge as an instrument of the modern-day pedagogy aimed at making high schoolers interested in the subject matter.
... Tabellenkalkulationsprogramme zum Modellieren werden im Physikunterricht bereits ähnlich lang eingesetzt wie imperative Programmiersprachen. 1979 wurde VisiCalc für den Apple II entwickelt (Baker & Sugden, 2003), was dann bereits 1984 für den Unterricht genutzt wurde (Arganbright, 1984). Auch aktuell wird Excel häufig im Physikunterricht eingesetzt, da das Programm den meisten Lehrkräften geläufig ist und für verschiedene Dinge genutzt werden kann (Herman, 2009). ...
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Newtons laws of motion are known to be difficult to understand for students. Many persistent preconceptions exist, that are incompatible to the physical theory. Those preconceptions hinder the progress in conceptual understanding of Newtons laws. One reason for the persistence of those conceptions is the focus on idealized situation is physics class. Students have difficulties with those situations and a gap between physics class and the real world can arise. Complex motions from everyday life are too mathematically difficult for physics lessons in school. The computer as a tool can help to bridge that gap. This pre-post-design study with N = 274 students from 11th grade of German (Hessian) schools investigates two different ways of using the computer to discuss complex motions with friction regarding their efficacy in improving the conceptual understanding of Newtons first two laws after the school lessons. For that, two equivalent interventions were designed that only differ in the way the computer is used. In each intervention, four different experiments are discussed. The students always work in groups of two after the respective experiment is shown in the plenum. The test, which was used to measure conceptual understanding and other variables, is partly based on known tests. Other parts of the test were created and piloted for this study. Additionally, screen recordings in combination with the conversations of N = 45 students were used to investigate, among other things, the way students use the software. A significant difference with large effect size between conceptual understanding in the pre-test and post-test was found in both cohorts. A comparison showed no difference between computational modelling and video motion analysis in the overall conceptual understanding. However, a significant difference in items regarding Newtons first law was found. The computational modelling cohort improved significantly more. It was also found that the common preconception, that a force in the direction of motion is necessary, was reduced further in the computational modelling cohort. An analysis of the screen recordings reveals that this preconception is expressed more often in that group as well. This leads to the conclusion that modelling forces students to activate the preconception which is then disproved by the comparison of the model and the data in the software. This cognitive conflict leads to a bigger reduction of the preconception which in turn leads to a larger improvement in the items regarding Newtons first law. The computational modelling cohort also improves in model understanding. More differences (e.g. cognitive load and different affective variables) were found and are being discussed. A linear hierarchical model shows that the pre-test score, the interest in theoretical relations in physics, the cognitive load and the physics grade influence the post-test score. Additionally, a comparison between more successful and less successful pairs shows that the phase of discussing the results could be an important factor for the learning gain. The more successful pairs also used the data or model more often to derive end results.
... Sin embargo, su uso se ha diversificado y masificado a partir de la incorporación de nuevos recursos que incluyen bibliotecas de funciones matemáticas y estadísticas, complementos potentes, funciones e interfaces gráficas altamente funcionales y la capacidad de escribir código personalizado. En consecuencia, se ha convertido en un software indispensable en los más diversos campos, incluyendo su uso cada vez más extendido en el ámbito educativo (Baker y Sugden, 2003). ...
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Se presenta una propuesta para reconstruir el movimiento diario del Sol en el cielo local a partir de observaciones realizadas por los estudiantes desde sus propias casas en épocas de no presencialidad escolar. Cada estudiante debía medir la dirección y el largo de la sombra de una estaca vertical en cuatro distintos momentos del día y se programó una planilla de cálculo para representar dichas mediciones en un gráfico polar. Se analizaron los datos de todo el curso y se representó el desplazamiento solar. Se detalla la propuesta, la metodología y los resultados obtenidos en su implementación con un grupo de estudiantes de nivel secundario. Se elaboran conclusiones respecto al uso de este recurso para la modelización de un mismo fenómeno al ser medido por distintos observadores. La secuencia permitió vincular a los estudiantes con la observación del movimiento solar tal como es percibido en su propio entorno celeste, además de favorecer el desarrollo de competencias científicas relacionadas con los procesos de medición, representación gráfica, análisis de datos y modelización.
... Teaching aids need to be accepted as they can affect the outcome in terms of the students' results. Baker and Sugden (2003) mentioned that the spreadsheet was likely becoming a universal tool for mathematics. Particularly, Lee and Rha (2009) demonstrated that students exposed to interactive materials achieved higher scores. ...
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The main purpose of this paper is to examine the use of online learning tools as a Personal Learning Environment for self-regulated learning for a statistic course. This study was carried out on students at a private university in Malaysia. This paper examines the data collected in a pilot study. The preliminary analysis of the data will be used to refine the questionnaire for a full-scale study. The data collected was processed and analysed using SPSS. The study's results indicate many learners are connected with the internet but not many use it for learning purposes. Using social network for learning is found to be correlated with a stronger intrinsic motivation. Instructors have to adopt an attractive and innovative social media content that is integrated in the Learning Management System. The results show that learners prefer a blended learning method with both online and offline formats. The implication-of this results is that there is a growing trend of the use of social media in learning, and at the same time there is still a demand for the conventional offline approach where there is an indication that a blended learning approach is still a better option.
... There are studies showing that also higher education students have a less positive opinion about their skills to work with spreadsheets than other ICT skills (De Wit et al., 2014). Spreadsheets have, however, found to promote several skills in mathematics education (Baker & Sugden, 2003), such as algebraic thinking (Nobre et al., 2012). Knowing the pros of using spreadsheets in mathematics education, it is suggested that students in vocational schools are supported with appropriate learning materials more in the future. ...
Hydrology teaching currently relies upon educators' background, requiring a change in training future professionals to manage water resources to address climate change, among other issues. In the teaching experience described in this paper, traditional lectures in a postgraduate civil engineering master's degree were replaced by the development and assessment of a lumped hydrological model implemented into an Excel spreadsheet. Although the primary activity evaluated the long‐term impacts of climate change on streamflow in a watershed, the students were required to address several specific issues such as calibration and validation processes, goodness‐of‐fit metrics, uncertainties of parameters, and sensitivity analysis. The learning experience's efficacy was assessed by conducting two surveys comparing the participants' knowledge before and after the exercise. The results revealed that 92.3% of the students considered that their hydrological skills had improved significantly following the exercise. Furthermore, the acquisition of hydrologi- cal modeling concepts was satisfactorily appreciated by all the participants, 97.6% of whom considered it useful or highly useful. Using a spreadsheet as a complementary tool in hydrology teaching increases student participation and motivation provided it is a contemporary and appealing issue, and the teacher clearly defines, monitors, and follows up on the class objectives.
The aim of this paper is to describe a new MS Excel‐based approach for designing driveshafts for stiffness and fatigue strength. We analyze the efficacy of the approach in engaging students in an iterative design process and higher‐level qualitative decision‐making activities in an undergraduate class at Texas A&M University. Compared to conventional fixed cross‐section frames and trusses, there are few tools (barring Finite Element Packages) that facilitate rapid design evaluations of stepped shafts. The approach is based on a novel use of singularity functions to obtain explicit solutions for stepped shafts under concentrated loads. This approach allows for relatively easy implementation into Excel without the need for any numerical integration or other forms of approximation. Currently, the tedious calculations involved in the design of stepped shafts prevent instructors from exploring iterative changes in driveshaft design. The Excel tool that we have developed allows instructors and students to focus on iterative decision‐making. With this tool, open‐ended design questions are assigned even in exams since the entire iterative process takes less than 15–20 min. Student surveys and analysis of exam answers reveal that students have gained a considerable capability to make design decisions. They also indicate areas where improvement in design thinking is needed.
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Conference Paper
think aloud protocol). Οι δραστηριότητες έλαβαν χώρα με τη συνεχή παρουσία της ερευνήτριας-βοηθού και η πλήρης διαδικασία καταγράφηκε σε βίντεο. Ως εννοιολογικό πλαίσιο συλλογής και ανάλυσης των δεδομένων χρησιμοποιήθηκαν οι κατηγορίες δεξιοτήτων και οι αντίστοιχες δραστηριότητες μελέτης τους όπως προτάθηκαν στο πλαίσιο του ευρωπαϊκού ερευνητικού προγράμματος DidaΤab που αφορά τη διδακτική των λογιστικών φύλλων. Τα αποτελέσματα της έρευνας δείχνουν πως οι μαθητές κατέχουν περισσότερο δεξιότητες χαμηλού επιπέδου και λιγότερο δεξιότητες υψηλού επιπέδου. Λέξεις-κλειδιά: λογιστικά φύλλα, δεξιότητες (χαμηλού και υψηλού επιπέδου), δραστηριότητες Abstract This paper reports on a study that investigated the competences that 14 year old students possess in relation to the use of spreadsheets. We organized a case study in which ten students tried to solve problems organized in spreadsheets. These ten students had been taught the specific instructive object, as the suitable curriculum anticipates. The research is done under the constant presence of the researcher-helper of the procedure. His role was to support the students cognitively but also technically. For the analysis of our data we based on the activities and competences that were proposed in the framework of the European research project "DidaTab". DidaTad investigates the use of spreadsheets in the Secondary School. The results that derived from the analysis of our data show that the students possess mostly competences of lower level in always in relation with spreadsheets.
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Utilizar en la enseñanza de la física tanto métodos exactos como numéricos complementándose como un todo, hacen el proceso de enseñanza aprendizaje más efectivo. En este trabajo se ejemplifica un problema de la aplicación de los métodos numéricos utilizando el Excel en problemas de mecánica. El objetivo de la investigación fue implementar los métodos numéricos y el Excel de Microsoft para fortalecer la enseñanza de la física en los estudiantes de la carrera ingeniería agrónoma. En el proceso investigativo se aplicaron métodos del nivel teórico, empírico y matemático-estadístico, Después de la introducción de los métodos numéricos se observa una mejoría del aprendizaje de la física, así como una mayor motivación por el estudio de la misma.
Im traditionellen Unterricht werden für numerische Verfahren eine Programmiersprache oder eine Tabellenkalkulation benutzt und die Grundidee der Methode der kleinen Schritte bzw. des Eulerverfahrens vermittelt. In physikdidaktischen Konzeptionen konzentriert man sich mit speziell für die Lehre entwickelten Modellbildungsprogrammen auf die Physik und nicht auf numerische Verfahren. Wird zur Eingabe eine graphische Oberfläche mit Flussdiagrammen genutzt, dann wird qualitativ deutlich, welche Größe aus welcher berechnet wird. Bei einer Modellbildung mit Animationen ist das Interpretieren von Graphen nicht nötig, da man die Animation beobachten kann und schneller sieht, ob das Modell noch korrigiert oder ergänzt werden muss. Schließlich gibt es Programme, die weniger Schritte erfordern und leichter zu bedienen sind, weil nur noch die Kräfte angegeben werden und man sich nicht darum kümmern muss, wie die Software aus der Beschleunigung die Geschwindigkeit und daraus den Ort berechnet.
What is the first Fibonacci number greater than a million? Can elementary teachers use a challenging problem, such as this, to enhance the algebraic thinking of their students? Even with a calculator, the computations are quite tedious. The computer is certainly the right tool for the job; the problem is to find appropriate software. We have found that elementary school students can productively explore such questions using a computer spreadsheet.
Spreadsheets have become popular and effective tools for the dynamic exploration of recursively defined functions, the generalization of solutions to problems, and the visualization of mathematical ideas. This article discusses a spreadsheet model for approximating square roots then extends that model into the intriguing domain of chaos
Students of the sciences must often integrate large amounts of information into simple, coherent frameworks of insight. They are then expected to use this insight to solve new problems in which the driving principles are obscure. The personal computer may change science instruction by permitting the design of problem sets that enable students to build and interrogate simulations of realistic physical simulations and to exploit these simulations with a full complement of graphical tools. Electronic spreadsheets can serve as a construction kit for such activities.
Traditionally, quantum theory has traditionally relied heavily on the use of mathematics. However, there is a significant cohort of students who are weak in mathematics, for example, students who are majoring in biochemistry, biological sciences, etc. This paper reports on the use of spreadsheets to generate approximate numerical solutions and visual (graphical) descriptions as a method of avoiding or minimizing symbolic manipulations, mathematical derivations and numerical computation. A specific example from quantum theory is provided. Some aspects of educational pedagogy of spreadsheet usage are discussed.
The electronic spreadsheet is now firmly entrenched in the modern business environment. Popular news reports and scholarly studies have found that users are often unaware of flaws in spreadsheet templates. But previously published articles have not identified the factors that lead users to make the mistaken judgment of template reliability. Most models of human information processing include a perceptual "filter" as a precursor to mental processing. Building on the possible existence of template perceptual filtering, this article presents the results of a laboratory experiment that was conducted to investigate some of the factors that influence an individual's assessment of spreadsheet reliability. The study also investigated the subjects' level of confidence in their reliability assessments. Three variables were considered in this study: spreadsheet size, spreadsheet format, and the presence of formula errors. The results of the study indicate that an interaction between large size and elaborate formatting significantly inflated perceptions of reliability. Additionally, the results suggest that the subjects' level of confidence in their reliability assessments was not affected by any of the perceptual factors manipulated in this experiment. The results of this experiment should be considered in the design of end-user training programs designed to help users overcome perceptual filtering tendencies that might allow a misjudgment of spreadsheet template reliability.
Graphical Presentation of Data. Descriptive Methods for Small Data Sets. Probability Methods for Large Data Sets. Binominal and Polsson Probability Distributions. Proportion Defective Charts and Acceptance Sampling. Sampling Distribution. Central Limit Theorem. Statistical Process Control. Analysis of Variance.
The numerical, algebraic, and geometric expressions of basic macroeconomic principles are integrated in this spreadsheet approach.
Conference Paper
Computational Fluid Dynamics is now used daily in scientific and engineering practices. The computation themselves are now based on commercially available software. Personal computers are widely utilized elsewhere these days and many people are using spreadsheets as well as word processors. It is now well-known to the scientific and engineering communities that spreadsheets can be used not only for statistics and data processing calculations, but also for matrix inverse, iteration in a finite difference equation, and for special functions of mathematics. This situation allows us to realize SFD, i.e., Spreadsheet Fluid Dynamics. The authors have demonstrated that the fluid dynamics equations including the Navier-Stokes equations could be solved efficiently by using a spreadsheet. The cells in spreadsheets are viewed as either natural grids in CFD or elements of a matrix. The computational domain corresponds to the real physical shape and/or the computational space by grid generation. The result can be visualized in the same spreadsheet with inherent graphics. The pre- and post-processors are all in one in SFD. © 2000 The American Institute of Aeronautics and Astronautics Inc. All rights reserved.