Jürgen Symanzik and Natascha Vukasinovic
Utah State University
Journal of Statistics Education Volume 14, Number 1 (2006), www.amstat.org/publications/jse/v14n1/symanzik.html
Copyright © 2006 by Jürgen Symanzik and Natascha Vukasinovic, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent from the authors and advance notification of the editor.
Key Words:Key Words: Computer; Interactivity; Statistical Concepts; Undergraduate Course; Web-enhanced Course.
The idea to incorporate software, in particular teaching software (or “teachware”), at an early stage of the statistical education of students has become very popular during the last few years. An increasing level of computer literacy among students and the availability of necessary equipment in classrooms have stimulated developing and using teachware in introductory statistics courses. Interactivity, hands-on exercises, colorful applets, visualization of statistical concepts, well-documented real-life examples, reduced need for manual calculations, and the possibility of self-assessment and immediate feedback may be the most valuable features of statistical teaching software. They should stimulate the student's activity in class, ease understanding of statistical concepts, and make the whole course more attractive and fun for the student.
Using software when teaching statistics in the classroom varies from occasional interactive exercises and in-class software demonstrations to completely Web-based courses without any use of “traditional” teaching tools or even pen and paper, as in Kent L. Norman's courses cognitron.umd.edu/cognitron.html. An overview of teachware evolution in past years can be found in Symanzik and Vukasinovic (2002).
Currently, there are many statistical teachware packages and electronic textbooks accessible via the Web. Some of them are freely available, such as the Globally Accessible Statistical Procedures (GASP) educational procedures (West, Ogden, and Rossini 1998; West and Ogden 1998a), accessible at www.stat.sc.edu/rsrch/gasp/. Entire (introductory) statistical textbooks have been designed for the Web. Examples of Web-based textbooks that are freely available are David M. Lane's HyperStat (Lane 1999), accessible at davidmlane.com/hyperstat/ and David W. Stockburger's two books Introductory Statistics: Concepts, Models, and Applications (www.psychstat.missouristate.edu/sbk00.htm) and Multivariate Statistics: Concepts, Models, and Applications (www.psychstat.missouristate.edu/MultiBook/mlt00.htm). The UCLA Statistics e-book by Jan de Leeuw, titled Statistics: The Study of Stability in Variation (de Leeuw 1997), formerly freely accessible at www.stat.ucla.edu/textbook/, is currently unavailable since the editor(s) “are unable to maintain it nor complete it at this time due to lack of funds”. Interestingly enough, a page counter, if working properly, indicates that this Web site has been visited more than 70,000 times in about two years since counting started on 10/1/2003. Other electronic textbooks such as Seeing Statistics (www.seeingstatistics.com/) or CyberStats (www.cyberk.com) are commercial packages that allow Web access upon registration. Some of the commercial electronic textbooks are distributed on a CD-ROM in addition to Web access, e.g., MM*Stat (www.quantlet.com/mdstat/mmstat.html), or on a CD-ROM only, e.g., ActivStats (www.dat.txtadesk.com/products/mediadx/activstats/).
In this paper, we report about our experiences in teaching an introductory statistics course to undergraduate students at Utah State University in the Fall 2001 semester using the electronic textbook CyberStats. We will commonly speak of the Web-enhanced course when referring to this course. Symanzik and Vukasinovic (2002) contains a preliminary version of our teaching experiences with CyberStats, as well as a comparison of CyberStats with other popular teaching software packages. In contrast, Utts, Sommer, Acredolo, Maher, and Matthews (2003) describes a “hybrid” offering of an introductory statistics course that combines a regular textbook with CyberStats. Utt's class met once a week, but students were required to learn the material on their own using Web-based materials and a textbook.
CyberStats possesses all the features of a traditional statistics textbook: coverage of statistical concepts with text, graphics, and exercises. It also includes an interactive table of contents, an interactive index, an interactive glossary, and self-assessment tools. In addition, CyberStats provides all tools necessary for complete course management, such as instructor's and students' course Web pages, electronic submission of homework assignments, a message board, and a chat room for students. CyberStats has an automatic timeout feature that terminates a user session if there is no user input for more than 30 minutes (15 minutes when the course was taught).
CyberStats targets students at an introductory statistical level, especially non-science majors. CyberStats emphasises concept understanding, data visualization, and data analysis. Less emphasis is put on formulas and mathematical components of statistics.
Figure 1. Contents Page of CyberStats.
In CyberStats, the course content is divided into seven sets of units: collecting and visualizing data, modelling random behaviour, inference, regression, design of experiments and ANOVA, time series, and statistical process control. Each set of units consists of one to fourteen units (Figure 1). Units resemble chapters in traditional printed textbooks. Each unit in CyberStats begins with a “Summary”, followed by a set of motivational questions related to the topic (“Think first”). The actual chapter is presented in form of “Three Keys”: “Basics”, where the basic concepts are presented; “Uses”, where a student has a chance to work through a set of examples and exercises; and “Warning”, where potential dangers of wrongly used statistical concepts are discussed. Each of these three keys is accompanied by plenty of examples and exercises and followed by a self-assessment test. In each exercise set, a student can submit the answers to the system, which are automatically recorded on the CyberStats server and can be accessed by the instructor and the student.
To analyze more complex, “real” data sets, advanced electronic textbooks are commonly linked to some full-scale statistical software package. CyberStats was linked to Data Tools, a simplified version of the popular WebStat software (West, et al. 1998; West and Ogden 1998b). Since 2002, the full WebStat 3.0, recently renamed StatCrunch 3.0 (www.statcrunch.com/), is tightly integrated into CyberStats.
The core of CyberStats are “Interactives”. “Interactives” are usually invoked in a new window by clicking on one of the many “Interactive” buttons located throughout the CyberStats units. Some of the “Interactive” buttons will start up WebStat and load a data set to analyze. Other “Interactive” buttons will start up “Calculators” or other interactive tools. Here, the user can type in or modify values, use sliders, add points to a graphic by mouse clicks - and immediately see the result of their actions. For students, the CyberStats “Interactives” are considered fun and highly educational at the same time.
A review of CyberStats Version 2.0 can be found in Dear (2001). Comparisons of CyberStats with two other popular teachware packages, ActivStats and MM*Stat, can be found in Symanzik and Vukasinovic (2002) and Symanzik and Vukasinovic (2003). A recent review of six online instructional materials, including CyberStats, can be found in Larreamendy-Joerns, Leinhardt, and Corredor (2005).
In the Fall 2001 semester, USU ran two sections of its introductory statistics course STAT 2000. One section of STAT 2000 in the Fall 2001 semester was a regular textbook-based section, using Moore and McCabe (1999). The other section was a Web-enhanced section using CyberStats only. Students had a choice which section they wanted to attend. The regular section (8:30 - 9:20am) on Monday, Wednesday, and Friday (MWF) had 17 students and the Web-enhanced section (10:30 - 11:20am) on MWF had 14 students. One student who was initially enrolled in the Web-enhanced section changed to the regular section early in the semester, claiming that he did not want to participate as a guinea pig in an untested version of this course. There were 42 lectures at 50 minutes each. Almost all lectures of the Web-enhanced section were held in an electronic classroom. Each student individually had access to a PC during the entire lecture, as well as during the exams. Thus, in contrast to the “hybrid” offering described in Utts, et al. (2003), our Web-enhanced course can best be summarized as an “Web-enhanced face-to-face” course that makes use of computers and a Web-based textbook, but still has the same number of contact hours between instructor and students as the regular textbook-based section. The course Web pages that contain links to the syllabus, homework assignments, and other information posted throughout the semester can be found at www.math.usu.edu/~symanzik/teaching/2001_stat2000_2/stat2000.html for the Web-enhanced section and at www.math.usu.edu/~symanzik/teaching/2001_stat2000_1/stat2000.html for the regular textbook-based section.
The fact that the Web-enhanced section took place only one hour after the regular section three days a week is a potentially very important confounding factor for the results, given that the same instructor taught both sections. Ideally, even if an instructor tries to present the course material as similarly as possible in consecutive sections of the same course, we have to assume that the material presented is most likely not the same. Sometimes the second class may benefit due to insights gained from the first lecture, but sometimes the second class may also be disadvantaged because the instructor may skip something already taught that day to the first class. But, because Moore and McCabe (1999) and CyberStats use quite different methods to introduce “similar” topics and the order of these topics is different, one should really treat these two sections as unrelated. Nevertheless, we frequently refer to the regular textbook-based section to highlight similarities, differences, and possible confounding factors.
The reason why we had to run two sections of STAT 2000 in the Fall 2001 semester (instead of just a Web-enhanced section) whereas only one section of STAT 2000 had been offered in previous semesters was due to capacity limitations of our electronic classrooms - the largest available computer classroom at USU could not hold the 40 students expected to attend STAT 2000. Even the 31 students that actually attended these two sections surpassed the maximum cap size of 25 students for the electronic classroom that was used.
Although the results described below are only the outcome of an observational study and not of a controlled experiment (because students could decide themselves which section to attend), we have made some interesting observations. These may be of interest not only for instructors using CyberStats but also for instructors interested in working with other electronic textbooks.
Student attendance was similarly high in both sections in the Fall 2001 semester (although no exact counts were taken) and the dropout rate (0%) was exceptionally low in both sections, compared to previous offerings of this course. Because this was observed in both sections, it cannot be attributed to any of the two course formats. More likely, the overall small class size and closer interaction between instructor and students in both sections may have been a major confounding factor here.
No major difference in the grade distribution for the Web-enhanced section and previous grade distributions by the same instructor can be noticed for the A, B, C, and D grades. The relatively high percentage of A grades (five out of fourteen students, i.e., 36%) in the Web-enhanced section can be easily explained by chance, recalling that there were only fourteen students in that section. However, the lack of any F grades in both Fall 2001 sections is noticeable. Confounding factors such as smaller class size (previous offerings had between 32 and 48 students in a section), closer interaction between instructor and students, and overall higher attendance may lead to this outcome in both Fall 2001 sections.
Due to the different arrangement of lecture topics in Moore and McCabe (1999) and CyberStats, it was not possible to provide identical exams for the two sections. However, about 50% of the questions in all exams were identical for both sections. There was no noticeable difference in the students' exam performance between the two sections.
Homework assignments in both sections accounted for 300 points out of a total of 1000 points, i.e., 30% of the course grade. Thirteen homework assignments (at 25 points each) consisting of multiple questions were assigned throughout the semester. Each question in each homework assignment was graded on a done/not done basis (rather than a correct/incorrect basis), thus resulting in zero points or full points for this question. The sum of these points was the weekly homework score. Only the highest twelve of the thirteen weekly homework scores were used for the total homework score. The idea of awarding points for working on and turning in answers to homework assignments (rather than awarding points for correct answers only) was previously found to be an effective means of motivating students to work more independently on the assignments and turn in their own answers rather than working on assignments as a group or simply copying answers. Because homework assignments were not graded in detail, solutions by the instructor were provided for each assignment.
The homework assignments for the Web-enhanced section consisted of CyberStats and non-CyberStats questions. Non-CyberStats questions included old exam questions (from previous regular course offerings) and questions from other sources. The homework assignments for the regular section included the same non-CyberStats questions, whereas the CyberStats portion of the assignment was replaced with questions from the Moore and McCabe (1999) textbook. A closer look at the homework scores reveals some interesting results: Except for one outlier (196 points), all homework scores in the regular section ranged from 263 to 300 points, with a median of 299 points. Similarly, the Web-enhanced section had two outliers (38 and 184 points). The student with the 38 points missed many classes and only submitted answers to two homework assignments, but nevertheless performed well enough in the exams to obtain a “D” grade overall. The remaining homework scores in the Web-enhanced section ranged from 259 to 300 points, with a median of 290 points. Some small differences could be observed between the two sections when looking at student grades. While all “A” and “B” students from the regular section had almost perfect homework scores (298 through 300 points), this was the case only for the “A” students from the Web-enhanced section. The “B” and “C” students from this section lost most of their homework points on non-CyberStats questions. It should be noted that CyberStats homework questions had to be submitted electronically while working with CyberStats while the non-CyberStats questions had to be e-mailed, faxed, or turned in during class. One possible explanation for a slightly lower submission rate of non-CyberStats questions might be that it was more convenient to answer questions electronically and less convenient to turn in additional written answers. Another possible explanation might be that the non-CyberStats questions were not related too well to the Web-enhanced course content, but better matched the regular course content.
However, it was not possible to discuss all material that was initially planned in the Web-enhanced section. Units B-11, C-1 through C-4, C-6, and mosaic plots were omitted in the Web-enhanced section, whereas all planned material was discussed in the textbook-based section. There are several reasons for these omissions from the Web-enhanced section:
Overall, working with CyberStats requires a careful reevaluation of what can be taught in one semester. Although it is unlikely that other instructors will encounter the same technological problems, one should expect unavoidable delays to occur over the course of a semester when using technology in class. This includes problems with computers, Web access, and related technology such as projection devices. In case of such problems, it might be helpful to have some additional course material at hand to cover part of, or, in the worst case, an entire lecture. This can be review material (on topics such as probability, regression, or normal distribution) that otherwise would be discussed before an upcoming exam or optional course material that can be discussed without the classroom technology (such as examples of statistical graphics that go beyond the electronic textbook and can be introduced via handouts).
The main task for an instructor when using CyberStats in a classroom setting is to integrate the given technology, in particular the “Interactives” and Data Tools/WebStat, into the overall course material. CyberStats states on the instructor screen: “We strongly recommend that you [do] not start a CyberStats course before investing a few hours in organizing it.” Finding an optimal teaching style that incorporates technology probably requires more effort than designing a good regular course.
Clearly, to teach a course in this “Web-enhanced face-to-face” format, an instructor should be generally familiar with current Web technology and features. While a regular textbook is often straightforward to transfer into a lecture, a Web-based textbook such as CyberStats provides far more material and options than what can be discussed in class and therefore requires a more rigorous selection by the instructor. This includes a large number of readily available data sets and “Interactives” in CyberStats that require a detailed screening. Also, an instructor should be somewhat prepared to solve at least minor technical problems that may occur during the classroom sessions.
Finally, it should be stated that the instructor should not expect that many students work on “Interactives” prior to a lecture unless credit is given. When asking students to work on a particular “Interactive” for the next lecture (without providing credit for doing so) with the intention of discussing the students' observations and results during that lecture, there was rarely any student who did the work prior to class. Eventually, towards the end of the semester, all “Interactives” worth discussing have been discussed in class or have been assigned as a homework assignment with credit. Possibly, assigning most “Interactives” from the beginning on as homework assignments with credit might have freed enough class time to cover content similar to a regular course. The reader should be reminded that most of the attending students were undergraduates. Graduate students might be more mature and willing to do some extra work even without getting immediate credit for it.
In addition, students could comment on aspects of the teaching or content of this course that were especially good and suggest changes to improve the teaching or the content. In the Web-enhanced section, four students listed CyberStats (and the “Interactives”) and its combined use with handouts in a lecture format as “especially good”. In the “changes” question, six students of the Web-enhanced section had no suggestion at all. None of the suggested changes was listed more than once and only one student suggested not to use CyberStats.
In addition to the official teacher/course evaluation, an additional CyberStats questionnaire with extra questions related to CyberStats had been handed out in the Web-enhanced section. This questionnaire was designed by the authors of this paper with the intention to learn more about students' opinions and suggestions regarding CyberStats. It was not intended to duplicate questions from the official teacher/course evaluation discussed above that was handed out in both sections. Thirteen (out of fourteen) students answered the additional CyberStats questionnaire. It should be noted that some students listed more than one feature. The questions and most frequently given answers follow below:
Problems that were mentioned all over again relate to the nature of a Web-based textbook: problems to access it at all, slow access, problems to work on homework assignments if no computer is available at home, difficulties to find something in the electronic version, and no possibility to mark and highlight important facts in an electronic book. One of the cited problems was immediately fixed during the semester: students are no longer automatically logged out of CyberStats after 15 minutes of idle time. Because CyberStats is undergoing continuous revisions and updates, one can assume that most of the other listed inconveniences have disappeared by now. Furthermore, the general accessibility of the Web has become much easier for students and instructors now. Based on the experience with the Web-enhanced section and the students' suggestions, one should definitely consider CyberStats (or any other electronic textbook) for future use in Utah State's STAT 2000 class.
Even though the additional questionnaire suggests that CyberStats was popular among the students, it can be noticed that the overall performance of students and the overall course/instructor evaluation was within the range of previous courses. Only subjectively, students had the impression that CyberStats is better than a regular textbook. Nevertheless, as stated in the Introduction, electronic textbooks are important to better motivate students and teach statistical ideas and concepts in a more convenient manner.
Not having a printed version of a textbook (as was the case for CyberStats when this course was taught) is inconvenient for the instructor as well. It is very difficult to determine on the computer screen which exercises to assign, in particular when there is more than just one set of exercises for a unit or when a homework assignment consists of questions related to several units. Eventually, all available exercises (and solutions) were printed out to obtain a better overview of available questions before assigning selected exercises. Also, looking up a definition or an example in a Web-only textbook is time consuming, in particular when this is done from home and a network connection has to be established, the Web page has to be accessed, and the required information needs to be searched. Finding a definition or an example in a printed textbook is much faster. So, many students ended up printing the entire course material from the Web. Recently, the CyberStats developers have addressed some of these problems. Instructors and students can now purchase a “print companion” to CyberStats containing a selection of units discussed in their course. Also, further progress in technology will resolve some of these limitations.
Clearly, a Web-based textbook has an immediate advantage: errors and typos can be fixed immediately. It does not take several months (or years) before the next updated edition of a textbook on CD or in print is being published. Certainly, in the case of CyberStats, this is attributed to its very efficient and helpful technical support, who almost instantly fixed every problem reported by the instructors.
However, as experiences with MM*Stat show Rönz, Müller, and Ziegenhagen (2000), about 48% of the students prefer the CD-ROM version, 40% prefer the Web version, and 12% have no preference. The CD has the advantage that it is independent from a network connection and can be run on virtually any computer. Servers that are down, slow connections, a telephone line for a modem that is shared by three or four roommates - these are features the CD does not depend on. Unfortunately, CyberStats cannot be offered on CD-ROM due to its current implementation.
Another main advantage of a Web-based textbook, compared to a CD or a printed version, is the possibility for students to upload homework answers to the main server and for instructors to download these answers after the submission deadline. After some initial technical difficulties with timeout problems and the access to the server, the homework upload was well accepted among the CyberStats students. As described before, the “B” and “C” students from the Web-enhanced section turned in the CyberStats questions but often did not turn in the additional homework exercises on paper. CyberStats offers a possibility to give students an entirely electronic exam: the “Test Bank” allows instructors to write electronic exams that include the instructor's own questions, CyberStats questions, and questions from other instructors who use CyberStats. However, this feature was not used during this offering of the Web-enhanced course.
To summarize, the main advantage of electronic textbooks on the Web (or on CD), such as CyberStats, clearly is the interactivity (as provided by the CyberStats “Interactives”) that allows students to actively learn statistics. Also, the ability to work on homework problems on the computer and upload answers to a server from which they can be downloaded by the instructor after the due date is a major advantage for students and the instructor.
Ideally, an electronic textbook (Web-based or on CD) should not be used alone, but accompanied by a printed book and optionally with the other electronic format. An additional printed textbook such as the CyberStats “print companion” has several benefits. In particular, it is faster to “access” a textbook and find the desired information. The textbook can be read while commuting in buses or trains, it can be taken back home over the weekend, and it can be read during short breaks at the university when no computer lab is at hand. Otherwise, a Web-based electronic textbook has the advantage to include corrections quickly and the convenience to answer homework questions electronically and upload them to a server.
Based on this summary, the current version of CyberStats is already very close to an “ideal” electronic textbook. Additional features are added regularly by the CyberStats developers and its publisher. However, instructors still have to consider carefully whether CyberStats is appropriate for use in a particular course. Its developers suggest that CyberStats can be used (i) instead of a regular textbook, (ii) in addition to a regular textbook, and (iii) for distance education.
Clearly, CyberStats is ideally suited for distance education, i.e., option (iii). When a regular textbook (that usually costs between $50 and $100) is being used, it seems to be doubtful whether students are willing to pay an additional amount of $33 for the CyberStats access - so option (ii) may not be selected frequently.
When CyberStats is used instead of a regular textbook, i.e., option (i), we would highly recommend its use in an electronic classroom setting, in particular for undergraduate students. Based on our experience, it is doubtful whether undergraduate students are motivated enough to work through the electronic course material just by themselves. When teaching a class based on CyberStats in an electronic classroom, the instructor can assure that the most relevant CyberStats Web pages, exercises, and “Interactives” are visited and further explained during class time. The instructor may assign additional exercises and “Interactives” as homework.
In conclusion, it seems that using CyberStats in a classroom could be considered a useful way of combining advantages of technology with in-class instruction. Both the instructors and the students have experienced a somewhat different kind of a statistics course. Based on the positive, encouraging feedback from the Web-enhanced section, we would like to continue experimenting with CyberStats in our introductory STAT 2000 course. Unfortunately, high enrolment numbers in STAT 2000, beyond the capacity of our largest electronic classroom, have prevented us from further experimenting with CyberStats at Utah State University in recent semesters in this “Web-enhanced face-to-face” format although CyberStats is currently being used for the distance education versions of STAT 2000 and STAT 2300. We hope, however, that additional resources will become available in the future - either in form of expansion of the existing computer classrooms or engaging new personnel to teach an additional course section, which would make it possible to permanently transform the campus version of STAT 2000 into the “Web-enhanced face-to-face” format.
We want to finish our discussion with a list of open questions that deserve further investigation:
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Jürgen Symanzik
Department of Mathematics and Statistics
Utah State University
Logan, UT 84322
U.S.A.
symanzik@math.usu.edu
Natascha Vukasinovic
Department of Mathematics and Statistics
Utah State University
Logan, UT 84322
U.S.A.
nvukasin@charter.net
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