The role of the graphics calculator

Marian Kemp, Teaching and Learning Centre, Murdoch University, Australia

Barry Kissane, School of Education, Murdoch University, Australia

Jen Bradley, Department of Mathematics and Statistics, Murdoch University, Australia

The graphics calculator has found many advocates impressed with
its capacity to support student learning related to algebraic
functions and calculus. In this paper, we suggest that the graphics
calculator may well be a useful alternative to the computer statistics
package for student learning of statistics, especially in the
early undergraduate years. This is not to deny the importance
of students learning statistics eventually becoming familiar and
competent with computer use; rather, we suggest that the graphics
calculator may provide a more convenient and effective place to
start.

**Changes in the statistics curriculum
**Statistical analysis has undergone a revolution, in
a remarkably short time, primarily as a result of developments
in computing. Three aspects of this revolution merit comment.
Firstly, statistical computations have come to be performed by
computers rather than by people armed with devices such as mechanical
calculators, table books and slide rules. Secondly, statistical
analysis has become much more visual, as computers have acquired
capabilities to represent images as well as perform calculations.
Thirdly, much statistical analysis has become more speculative
and exploratory than previously, rather than being pre-determined,
because of the flexibility provided by computer software. Computer
software for statistics has become widely available and is now
routinely used in applied work. It thus seems inevitable that
the undergraduate statistics curriculum will be influenced by
these developments as well.

In parallel with these changes (and perhaps even partly as a consequence
of them), statistics has continued to increase in significance
in the undergraduate curriculum. For example, Moore *et al*,
(1995 p.259) reported that statistics enrolments at US two-year
colleges had risen from 10% to over 50% of calculus enrolments
in 25 years. While there are still many undergraduate students
who undertake first and second level calculus courses to support
other undergraduate majors, there is an increasing group for whom
the study of some statistics is the main, or even the only, mathematics
they encounter after secondary school. Although many students
undertake courses offered by mathematics and statistics departments,
there are also many students who study statistics in courses within
the natural sciences, the social sciences, education and business.

It might seem inevitable in these circumstances that undergraduate
statistical study should routinely incorporate work with computers;
however there have been some difficulties in doing so successfully
in practice. Not the least of these has been the provision of
sufficient access to computer hardware, especially in large introductory
units at the first year level. Frequently, students have had access
to computers mainly in formally scheduled laboratory sessions;
security and scheduling issues have tended to reduce opportunities
for student work outside regular classes. In addition, large,
flexible and multi-purpose software packages, such as Minitab,
Statistica, SPSS and SAS are relatively expensive to purchase
in bulk and maintain, as well as being time-expensive in the sense
of requiring student learning time devoted to operating the software
effectively.

**Calculators for statistics
**It is generally accepted, even expected, that all students
studying undergraduate statistics have access to a scientific
calculator with statistical capabilities. Such calculators certainly
changed expectations and the learning process for many; before
their availability, a great deal of time was spent by students
essentially doing arithmetic and substituting values into formulae
to compute such statistics as variances, standard deviations,
correlation coefficients and linear regression coefficients. Despite
these advantages, scientific calculators have several limitations
for data analysis relating to the detection and correction of
data entry errors, visual display of data and access to inferential
tests.

Graphics calculators, first available around twelve years ago,
offered very significant improvements. These stem mainly from
the fact that data were stored in the calculator and thus could
be examined, edited, deleted, transformed or augmented relatively
easily. Data could be simulated using calculator commands as well
as entered directly. A stored data set could be analysed in more
than one way, allowing and expecting students to make choices
about what kind of analysis is appropriate. As the name suggests,
the graphics calculator also opened the possibility for analyses
to involve graphical displays, such as scatter plots or histograms,
as well as numerical ones.

These advances made the graphics calculator an attractive device
for secondary schools, which have long included the rudiments
of descriptive statistics in mathematics curricula, at least in
countries such as Australia and the UK. (For example, about 20%
each of Kissane (1997) and Kissane, Bradley & Kemp (1997)
is concerned with data analysis and probability simulation for
secondary school students.) However, the recent addition of inferential
capabilities to the suite of statistical commands available on
graphics calculators has bridged the gap between upper secondary
and lower undergraduate requirements. Modern calculators produced
by three major companies (Casio, Texas Instruments and Sharp)
include a variety of commands for inferential tests (such as z,
*t*, F, ANOVA and c2) and associated confidence intervals,
as well as access to tables and graphs of the relevant probability
distributions. The programmability of calculators allows users
to customise a calculator by adding additional tests (such as
non-parametric tests or two-way ANOVA, for example).

At first glance the prospects for acceptance of this new generation
of calculators into the undergraduate learning and teaching of
statistics appear promising, especially when issues of access
and economics are considered. The portability of the calculators
potentially overcomes one of the main difficulties with access
to computers on campus, at home, in the field and in examinations.
The costs of calculator access are very much less than those of
computer access; further, as students are increasingly likely
to already own or want to purchase their own calculator, the costs
to institutions may be significantly eased. Since calculators
have inbuilt software, software purchase and maintenance costs
are also saved.

There are some evident disadvantages associated with graphics
calculator use as well. Large data sets cannot be handled, the
range of analyses offered is limited, printing of results is awkward
(although not impossible) and the small screen resolution is relatively
poor and monochromatic. It is clear that even a modern graphics
calculator can never be a complete substitute for a modern statistics
package on a computer, although it may serve as a useful learning
and teaching aid for introductory work.

**Prospects for change
**In order to gauge the likely place of graphics calculators
in undergraduate courses involving statistics at Murdoch University,
we have canvassed the views of a range of University teachers.
The courses involved include toxicology, animal behaviour, tourism,
social science research methodology, business and statistics itself.
Our discussions have been both informal and informative, but certainly
do not reflect a rigorous statistical sampling process. Our intention
has been to identify issues of importance, rather than make secure
generalisations about them.

Interviewees were generally very familiar with statistical software
on computers but most were generally unfamiliar with graphics
calculators, and few reported any personal experience with them.
Consequently, they were not yet able to make informed decisions
about the potential place of graphics calculators in their courses.
It seems likely that opportunities for personal use and exploration
with graphics calculators would be needed before significant student
use would be contemplated.

Despite this unfamiliarity, those interviewed were enthusiastic
about the prospects for calculator use in the early undergraduate
years, once they were acquainted with sample graphics calculator
models and their operations. A brief analysis of the statistical
content of the courses concerned suggested that the capabilities
of modern calculators in almost all cases met student data analysis
needs, both for practical purposes and for learning purposes.
It seems that the few exceptions would be fairly easy to program
into the calculators. New opportunities for teaching and learning
might arise if staff felt that they could take advantage of technology,
rather than being constrained by limited student access to it.

Although many students owned computers, many others did not, and
so it was necessary to provide on-campus access to computer software
for teaching and assessment purposes. Several interviewees expressed
concern about the costs of providing students with adequate computer
access, especially in courses with large enrolments. At least
one course was contemplating using a sophisticated spreadsheet
program (Microsoft Excel) for data analysis in preference to a
dedicated statistics package, because it was more likely that
students would have access to it at home as well as on campus.
The graphics calculator was seen as providing an economical alternative
to computers for data analysis, and to potentially provide a more
significant use of technology in student activities within a course.

Despite the attractions of graphics calculators, it is clear that
computers will continue to be important in courses at this level.
Computers provide access to capabilities not easily available
on graphics calculators (such as web-based databases). While graphics
calculators might be useful devices for helping students to learn
about statistics, they could not be expected to replace entirely
the need for students to learn to use computers for data analysis
purposes. Indeed, it was reported that some employers of graduates
routinely expected competence with computer data analysis.

None of the interviewees reported student use of computers during
formal examinations. For examination purposes, it seems that graphics
calculators may have a clear advantage over computers, due to
their portability and potential accessibility to all students.
Some preference was expressed for examination questions that did
not involve students in conducting analyses from raw data, since
these might create potential risks of exaggerating differences
in key-punching abilities among students. To date, examinations
often have been designed to reduce calculation demands and to
focus on interpretations, partly for the same reason. Some interviewees
reported that they expected students to develop some expertise
at interpreting computer printouts, a common expectation in several
fields, and noted that their examinations reflected this. Such
problems (and solutions) are less evident with other forms of
assessment, such as assignments and projects, for which the time
constraints are less important. In these situations, students
are frequently expected to deal with raw data, both choosing and
carrying out suitable analyses, for which a graphics calculator
may be a suitable alternative to a computer.

**Conclusion
**In summary, the case for use of the new generation
of graphics calculators at the early undergraduate level seems
to be a strong one. The prospects of students learning more about
statistics seem promising, and the fresh opportunities for good
teaching seem at least as promising. While it is very unlikely
that technology of this kind will replace computers and statistical
software for undergraduate learning, it seems that it may provide
a very useful adjunct to existing practice. To realise this potential,
it seems clear that many university staff are likely to need some
help to become familiar with the nature, operations and educational
uses of modern graphics calculators.

**References
**Kissane, B. 1997,

Kissane, B., Bradley, J. & Kemp, M. 1997,

Moore, D.S., Cobb, G.W., Garfield, J. & Meeker, W.Q. 1995, Statistics Education Fin de Siècle,

Please cite this paper as:

Kemp, M., Kissane, B. & Bradley, J. (1998) Learning undergraduate statistics: The role of the graphics calculator. In

Proceedings of International Conference on the Teaching of Mathematics, JohnWiley: Samos, Greece, pp xx-xx.

(http://wwwstaff.murdoch.edu.au/~kissane/greece.html)