The expression Y1 = normalcdf(-4,X,0,1) was inserted
in the Y= Menu to produce the graph shown in Figure 1:
| Adopted from the draft of an article published in The Statistics Teacher Network, Autumn 1997. |
To build a good course, all teachers
need a story to tell and the tools to tell it with. One strategy for teaching
statistics is to allow technology to simultaneously remove some of the drudgery
of mechanical operations and aid in focusing on higher level concepts. Aligned
with recent learning theory, the NCTM and The College Board suggest that
statistics courses should tell their story in a way that allows students
to construct their own knowledge. Computers and graphing calculators play
a large role in allowing students to learn by exploration. Many secondary
school mathematics programs use graphing calculators. Of these, the TI-83
has one of the most comprehensive set of routines for statistics.
Light and lively, TI-83 Enhanced Statistics, is a valuable liaison
between the TI-83 and many of the concepts found in a first course in statistics.
Authors Ray Barton and John Diehl find just the right balance in its 35
activities. Always being careful not to go too far, they provide a conceptual
overview while guiding the reader through the statistics routines of the
TI-83. Their pragmatic activities flow naturally. While not formally grouped
into chapters, the activities lead the reader through:
Each activity follows a similar format. A narrative describing the statistical
concept is integrated with examples which the reader enters into the TI-83.
Each activity ends with a short but interesting and appropriate set of exercises.
Many of the examples and activities contain realistic data. All exercises
have carefully worked solutions located near the end of the book.
TI-83 Enhanced Statistics can be used in different ways. At first
I turned to it when I was about to prepare to teach a topic which I had
not taught before. Each activity helped me develop an overview and provided
a few good examples of a particular concept. In some cases I even modeled
an in-class worksheet on a particular activity.
Then I began to notice that there was a story being told and told well.
I realized that working on an isolated activity missed the succinct but
well organized flow of this book. The flow can be gleaned from the activity
titles. For instance, near the center of the book, activities such as Binomial
Distribution, Simulation, Normal Approximations to Binomial Distributions,
Normal Distribution, Assessing Normality, and Random Sampling & The
Central Limit Theorem suggest that this book is much more than a list of
how to push the TI-83's buttons.
The Narratives
The narrative section of each activity introduces material and reviews major
points without side-tracking the reader with excessive details which are
more appropriately found in text books. Formulae are well presented without
derivation. The reader is asked to let the calculator apply specific statistics
to illuminating examples. The narratives are experiential. They suggest
that the reader enter data and complete computations. They also ask for
predictions and suggest questions which help the reader confirm understanding.
However needed details are given when appropriate. For example, the method
which the TI-83 uses for computing outliers from a five-number summary is
explained. Also, a complete but compact presentation of how to determine
a median-median line by hand is provided1
. This is appropriate since this relatively new
topic is often not described in text books . Another example of appropriate
detail is found in an exercise for visualizing "signed area" which
leads nicely to a first understanding of the correlation coefficient. In
addition, the authors are very careful to demonstrate that the outputted
r for log, exponential, and power regressions is "actually measuring
the linearity of the transformed data." This is a point that
first-time teachers are often not aware of. The authors have left the reader
with the desire to make sure that he or she clarified this concept.
Even as a very experienced TI-83 user, TI-83 Enhanced Statistics
reminded me of features that had slipped my mind. For example, somehow I
had forgotten that the last of the six "Stat Plot" options was
a normal-quantile plot. I was reminded of this feature as I prepared
this review! Ironically, my students used Minitab to create these plots
last year. In addition, I learned that the coordinates of the three summary
points for a median-median line are available in the VARS menu and that
there is an optional parameter in Sinusoidal Regression which estimates
the period.
There are some areas of the narratives which could be improved. Occasionally,
the organization and narrative style left me hanging. Within a particular
activity, there were times when I was not sure if I was about to start a
new concept or if I was finishing up the last. To some degree this is a
function of the authors' goal of not overdoing the book's structure or details.
As often happens with good experiential material, the trick with TI-83
Enhanced Statistics is to continue reading and to continue doing the
examples.
Unfortunately, the most confusing presentation is in the first activity:
Data and Lists. The TI-83's ability to store an enormous number of
named lists makes the initial entry of data confusing to many first-time
users. The authors tried to cover two different approaches to entering data
into lists plus the idea of relative lists in the first activity. As a result
the reader's attention is split between too many concepts. It might have
been better to choose one approach for the first activity and then insert
an additional activity to introduce the second approach and relative lists.
In addition, a more complete explanation of the use of the "SetUpEditor"
command would ease confusion later on. This command determines which lists
are displayed in the Stat List Editor .
There are also times when more information would be helpful. For example,
while a solid activity on the Poisson Distribution is included, the reader
is not sure when the Poisson Distribution should be used2. In a similar fashion, there
is a strong activity on how to handle a Goodness-of-Fit test for a one-way
table and even a program to compute the appropriate Chi-Square statistic.
However, the reader is not informed that the TI-83 lacks a function to perform
this operation. In addition, there is a wonderful example of using data
extracted from the Internet in the Data and Story Library (http://lib.stat.cmu.edu/DASL)
to do a test of homogeneity. Yet there is no mention of how this test relates
to the previous example which is a traditional test of independence for
two-way tables.
One interesting choice the authors make is to use a matrix approach to determining
the Least Squares Regression line. Those readers hoping to find more insight
into what is squared and what is minimized will only be more
confused after reading this discussion. On the other hand, the authors continue
to build an interesting story by extending this matrix process in explaining
polynomial regression a few activities later. Perhaps both the traditional
approach to minimizing the sume of the squared residuals and a matrix approach
could be included in future editions.
The Exercises
Activities usually end with between two and six exercises. Most are basic
but illuminating. Often they contain one or two very good examples that
could be used in class, in a worksheet, or on a test. There are little
gems scattered throughout. For example, the following questions are found
at the end of an activity on Normal Distributions:3
The expression Y1 = normalcdf(-4,X,0,1) was inserted in the Y= Menu to produce the graph shown in Figure 1:
A. What do the X and Y coordinates displayed on the graph tell you about the normal curve with mean 0 and standard deviation 1?
B. This graph appears to have a horizontal asymptote of Y=1. Explain why.
In a phone conversation, the publisher, George
Best, mentioned that the authors are considering adding additional exercises.
Conclusion
TI-83 Enhanced Statistics is a valuable resource. It tells the story
of much of a first year statistics course and concurrently explains how
to use the TI-83 statistics routines. It uses an experiential style that
does not bog down the reader with excessive detail. It contains easily missed
or forgotten technological details. Valuable teaching ideas are found in
many of its activities. It has realistic data sets and some unique exercises.
TI-83 Enhanced Statistics would be a valuable review for teachers
who are about to teach statistics for the first time. It would be a valuable
reference for each of us who teaches introductory statistics using the TI-83.
It also would pull together concepts for students who need an overview or
more exploration. I recommend it with enthusiam to you.
1 For a fuller explanation, see
Contemporary Precalculus through Applications. Gloria Barrett et al.
Janson. 1991 .
2 For a description and examples of the use of the Poisson
Distribution, see A Data-Based Approach to Statistics. Ronald L.
Inman. Duxbury. 1994.
3 Reproduced with the permission of the Publisher: George
Best, Venture Publishing.