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 Editor’s Note: Instructional design, learning management, and a different philosophy make this online statistics course an acceptable alternative to its classroom counterpart. The author clearly outlines the steps taken and provides statistics to report the results.

Teaching an Introductory Graduate Statistics Course Online to Teachers Preparing to Become Principals:
A Student-Centered Approach

Gibbs Y. Kanyongo


This article discusses the teaching of an eight-week statistics course that is delivered entirely online and how it promotes student-centered learning. Students enrolled in this class are school teachers who are working towards certification to become principals. This course is one of the several courses they are required to take for them to fulfill the requirements of the program. The course is intended to equip students with the skills that enable them to read and understand the statistical information in research literature relevant to school problems and issues.

The paper begins with a brief introduction of some of the benefits of online learning, with an acknowledgement of some challenges that online learning poses. Next, the paper presents the framework for student-centered learning and contrasts that to teacher-centered learning; then the link between student-centered learning and Web-based learning is illustrated. Finally, the paper shows how the two concepts were integrated into teaching a statistics course online. This paper is not advocating student-centered learning as being superior to teacher-centered learning, but recognizes the two approaches as being on two ends of a teaching philosophy continuum.

Key Words
: correlation; regression; web-based learning; student-centered learning; teacher-centered learning; collaboration; statistics.


Smith (2001) listed many of the benefits that online distance education provides for students and faculty members. Some of the benefits for students include accessibility, flexibility, participation, absence of labeling, written communication experience, and experience with technology. On top of these benefits, faculty members also enjoy employment advantages derived from newly gained skills. However, there are challenges as well, notably issues concerning team building, security of online examinations, absence of oral presentation opportunities, and technical problems. From the faculty perspective, there is a lot of time involved, and activities include designing courses, learning new technologies, and resolving technological problems. The benefits of online learning contribute to the strong support for and rapid development of distance education in many settings, while the challenges cause the indifference or hesitation in others.

Teaching statistics concepts in an online environment presents major challenges to both the instructor and the students. It is a challenge to the instructor because the instructor should be able to communicate the statistical concepts in a manner that students understand. It is a challenge to students because of their varying levels of preparedness, complexity of content and technological expertise. Despite all these challenges, the experiences of this author are that teaching statistics online can be effective if the course is properly designed.

Student-Centered Approach

In student-centered environments, the content change involves a dual function: (a) establishing a knowledge base and (b) promoting learning. Weimer (2002) points out that in learner-centered approach, content becomes the means whereby learning outcomes are advanced. She points out that there are three ways in which instructors can use content to teach students about learning. First, instructors should “use” content not “cover” content as a vehicle to develop learning skills. This means that instructors help students acquire a repertoire of strategies, approaches, and techniques that they can use when they need to learn material in a particular discipline. These may be basic skills, like time management, collaboration, communication and computational skills, important to learning almost any sort of material.

Second, content should be used to promote self-awareness of learning. Students need to be made aware of themselves as learners and develop confidence in their ability to work on learning tasks. They should be able to have a self- assessment of their strengths and weaknesses as learners, and then develop strategies that help build on their strengths and make up for the weaknesses. Weimer (2002) sees self-awareness as the foundation on which further development as a confident, self-directed, and self-regulated learner grows.

Third, content promotes learning when students are given the opportunity to use content so that they learn and experience it firsthand. In learner-centered environments, active learning strategies should be used all the time. Students should have hands-on learning experiences, not just listen to the instructor explain some concepts. For example, rather than having the instructor tell them about the outcome of an experiment, students are given the data and challenged to perform analyses, and come up with meaningful results. These three features promote active learning by students that allow them to have firsthand experience with the content.

Most people mistakenly believe that learning skills develop by osmosis; for example, if an instructor solves problems on the board, students learn problem-solving skills. Research does not support that notion. Woods (1987) found that in a four-year engineering program, students observed instructors working more than one thousand problems. The students themselves solved more than three thousand homework problems, and yet despite all this activity, they showed negligible improvements in problem solving skills. He pointed that what they acquired was a set of memorized procedures for about 3,000 problem situations that they could, with varying degrees of success, recall.

Student-centered and instructor-centered practices are viewed as representing opposite ends of the teaching philosophy spectrum. Student-centered practices are considered to have an underlying constructivist philosophy while the teacher-centered approach is grounded in the positivist philosophy (Knowlton, 2000). Three constructivist notions are the basis of student-centered approach. The first notion is that, knowledge acquisition is an active process where the student makes sense of the world rather than merely accumulating facts. The second one being, students internalize new knowledge in personal ways, by creating relationships to existing knowledge thus enabling application; and third, knowledge has a cultural aspect that relies on collaboration and social negotiation to give shared meanings (Grabinger, 1996).

Students in the teacher-centered environment receive knowledge from the instructor, internalize the knowledge, and later, reflect the knowledge back during assessment. The meaning, personalization of the knowledge, and linking of new knowledge to the student's existing knowledge structures are left entirely to the student and take place outside of the teaching process. The teacher-student relationship is one of disseminator and recipient which assume that the teacher has ‘monopoly’ over knowledge. This does not imply that the "facts" are different for learner-centered approaches; only that intentional effort is applied to providing students an opportunity to individualize the context and meaningfulness of the knowledge within the context of the teacher-learner interaction.

The Internet and Web-based Learning

With the internet’s rapid growth, the web has become a powerful and interactive medium of learning and teaching. The web provides the opportunity to develop learner-centered instruction and teaching. Recent studies have shown that the internet can be an efficient instructional technology in higher education. For example, studies by Corrent-Agostino, Hedberg, and Lefoe, (1998) showed that the internet facilitated graduate students understanding of problem-based learning principles. A study by Lockyer, Patterson, and Harper, (1999) showed an improvement in undergraduate students’ understanding in a health-education course. Liou, (1997) showed that the reading of comprehension and writing skills of English as a Second Language of college students improved when supportive web-based materials were used.

Web-based instruction is a hypermedia-based instructional program which utilizes the attributes and resources of the World Wide Web to create a meaningful learning environment where learning is fostered and supported. (Khan, 1997). Gillani and Relan (1997) define Web-based instruction as the application of a repertoire of cognitively oriented instructional strategies implemented within a constructivist and collaborative learning environment, utilizing the attributes and resources of the World Wide Web. They suggest the Web may be used as a:

  1. resource for identification, evaluation and integration of information

  2. medium for collaboration and communication of ideas

  3. platform for expression of understandings and meanings

  4. medium for participating in simulated experiences, apprenticeships and cognitive partnerships.

They point that these uses exploit the release of learning from the constraints imposed by traditional modes of delivery while changing the roles of teacher and learner and the way in which knowledge is structured.

Web-based teaching tools help reduce teachers' administrative duties, allowing them to focus more on teaching and meeting students' needs. Teachers can assign notes, documents, projects, homework and other student evaluations as far ahead as they like, with the students taking more responsibility for keeping track of their own work schedules.

Web-based learning provides students tools that give them more ownership of their grades and work with demonstrable results. Web tools help in improving the students' ability to learn. Students can write their teachers after school hours asking questions regarding their assignments, and teachers are there for the students during any part of the day. In addition, the Web tools have also been an aid to students who are less inclined to play a vocal role in class. Some students are just not "classroom" people; hence web tools help teachers make the connection between teacher and student.

Bostock (1997) contrasts the use of the Web for transmission of information to passive learners in a traditional framework with an active, collaborative learning approach. He offers a summary of the nature of active learning from a constructivist viewpoint. He provides a list of features identified by Grabinger and Dunlop (1996):

  1. Student responsibility and initiative to promote ownership of learning and transferable skills

  2. Intentional learning strategies, explicit methods of learning, reflection on learning processes, meta-cognitive skills

  3. Goal-driven, problem-solving tasks and projects generating products of value

  4. Teachers as facilitators, coaches and guides, not sources of knowledge, requiring discussion between teachers and learners

  5. Authentic contexts for learning, anchored in real-world problems

  6. Authentic assessment strategies to evaluate real-world skills

  7. Cooperative learning


Collaboration is an important part in most of the more innovative courses delivered via the Web. Groups of learners interact and develop the attributes of a 'virtual learning community', even though they may never meet in the same place or time. Shrage (1991) defines collaboration as the process of shared creation of two or more individuals with complementary skills interacting to create a shared understanding that none had previously possessed or could have come to on their own.

Description of the Course

The course title is “Statistics in behavioral research”, and the main goal of this course is to provide students with tools to be able to read, interpret and communicate clearly statistical concepts in their fields. In this particular section of the course, a total of 15 students were enrolled and the course was delivered entirely online. All the students enrolled in this course were in the process of being certified to become principals. Thus, the course was particularly focused on the needs of school principals to: (a) understand the data they use to make decisions in schools and districts; and (b) read and understand the statistical information in research literature relevant to school problems and issues. Specifically, the  student will be able to:

  1. accurately define and understand basic vocabulary commonly used in quantitative inquiry.

  2. read and interpret basic descriptive statistics.

  3. read and interpret basic inferential statistics.

  4. apply research results to problems of professional practice.

The course is offered through special web-based software (First-Class). Students enrolled in this class receive the software which they install on their computers at home or work. The software is user-friendly that no special training is required before they use it. All course information such as syllabus, with detailed course objectives, course requirements, assignments, and projects are available on the course site. The course site provides links to various resources useful to the course. For example, there are links to some online statistics books for students to use as references. Other sites the course is linked to include: Center for Research on Evaluation, Standards and Student Testing site, American Institutes for Research site, and a RAND Corporation site that publishes reports on educational issues.

A timeline with due dates for assignments and projects is also on the course site so the students know exactly when a particular project or assignment is due. Students only have access to a particular week’s activities, and can not work ahead since those materials are not available. Activities for a following week are made available on a Friday afternoon so that students have the weekend to review the material.

In the course, students are required to: (a) work on individual assignments, based on a statistics workbook, (b) work on group projects, (c) participate in weekly chat sessions with instructor, d) participate in group discussions with fellow group members on projects, and e) participate in the general bulletin board for the course where the instructor posts questions for discussion. A pictorial layout of the course environment is shown in Figure 1 below. The design of the course and the learning environment are such that they are user-friendly, providing the students the opportunity to explore with ease and contribute meaningfully to the activities of the course.

Figure 1. A pictorial layout of the course environment.


Learner-Centered Practices Online

The most critical task is to understand the essential characteristics necessary for each of the learner-centered practices. The important questions in this regard are: What elements are necessary for collaborative learning? What are the necessary elements for problem-based learning? What must be done to employ self-directed learning? Each of these strategies includes a process or sequence of activities and specific practices that make the method successful. We must incorporate the required elements of the practice in the online version. The challenge is not just replication, but enhancement using the technology’s unique advantages. The following class activities illustrate how the students are at the center of the learning universe with the instructor playing the role of a facilitator.

Class Projects

Students are divided into three groups of five students in each group, and each group is assigned a simulation project. There are a total of three simulation projects for the course that the students work on in groups. After each project, the groups are dissolved and new ones formed for the next project. By the end of the course, each student would have had the opportunity to work with several members in the class. Each group has a discussion site where they ‘meet’ to discuss the group projects. Because the transcript is automatically archived, the instructor has the ability to check the site for the discussion transcript to see each student’s contribution to the discussions. Each of the three projects provides the students the opportunity to apply the statistics concepts learned in this course to their situations as school administrators. As an example, in the first project, students are provided with aggregated and disaggregated data for 5th grade Math and Reading scores for a virtual school district. In the project, students are required to:

  • Decide what story the data are telling (interpret the data)

  • Decide what kind of statement(s) they will make

    (a) to district administration and

    (b) to the public based on the data

  • Decide what, if any, actions they will take in their school (or advocate for taking, if district level involvement is necessary)

In this project, students should show the ability to interpret basic statistics concepts like mean, percentages, and histograms and how these apply to test scores.

In the second project, students are required to apply knowledge of such topics like sampling, test scores, correlation, and regression. They are given research articles on educational issues; for example, “The relationship between grade inflation and proficiency.” Such an article incorporates concepts like sampling and sample size, correlation, correlation coefficient, and regression. Students should be able to show their knowledge of these concepts by interpreting correctly the research articles and critiquing them.

In the third project, students are required to conduct their own research on a topic of their interest. Each group agrees on a research topic, and they then conduct literature search of their topic. The third research project specifically teaches students to conduct online research of various research databases. They should also be able to interpret the statistical analyses used in the different articles they researched. They should be able to evaluate the information they get to determine what is relevant and what is not relevant to their particular topic of interest, and be able to synthesize their findings into a concise document. This is important because, according to (Weiner, 2002) “today’s learners must be able to access information, find resources, organize them, and, perhaps most important, evaluate the ocean of information that now exists in that electronic sea” (p.50).

In each of the projects, students assign each other particular sections that individuals work on for the project. Before the final document is submitted to the instructor, members of the group circulate their sections to all the members of the groups for suggestions and changes. Each of the projects show an increased level of complexity compared to the one before it. Project one asks students to interpret data that were "handed" to them; Project two asks them to interpret data in articles that were handed to them; and project three asks them to find data in articles relevant to something they want or they need to know about. They then use statistical concepts they have learned in the course and the application skills they have been practicing.

Individual Exercises

For individual exercises, students complete exercises in a statistics work book, and submit to the instructor electronically for grading. The instructor provides written feedback to each student with detailed explanation on the wrong answers. The exercises are discussed during chat sessions with the instructor, and if there are any misconceptions arising from the exercises, they are clarified. Students do not have to wait for chat sessions to ask questions, since they can email the instructor any time. The instructor provides detailed feedback to any question/concern from a student within a reasonable time frame, usually, the same day.

Participation in weekly chat sessions with the instructor is done in one-hour long sessions. The students are put in groups (not the same as project groups). Each group meets with the instructor in a chat session on a particular day of the week. Chat sessions for any particular week seek to achieve clearly laid out objectives, usually tailored towards that week’s individual exercises. Participation in online chats is strictly enforced, and students require prior permission from the instructor if they are to miss a chat. If they do miss, they are encouraged to join the chat for the other group for that week.

When students are online working on individual exercises, they have the ability to check and see who is online at that particular time. If other students are online as well, they can invite someone for a chat and can ask questions to the instructor in real time situations, if the instructor is online at that same time.

Course Content

The major topics covered in this course are:

  • Percentages

  • Mean percentages

  • Frequency distribution

  • Mean, median, mode

  • Variance, standard deviation, range,

  • Interquartile range

  • Cumulative percentages and percentile rank

  • Histograms

  • The normal distribution curve

  • Standardized scores

  • Effect size

  • Correlation and regression

  • Multiple correlation

  • Linear regression

  • T-test

Evaluating Students Learning

Use of multiple assessment techniques is necessary to derive reliable results when evaluating students learning outcomes. In this course, students’ learning outcomes were assessed by a variety of means that include individual assignments, group projects, participation in weekly chat sessions, participation in bulletin board discussions and participation in group discussion sessions. In each of the activities, students are graded based on a rubric which is specific to that particular activity. The rubric for each activity is available to students at the beginning of each activity so that they know exactly what areas they will be assessed on. Table 1 shows a rubric that was used to grade the first simulation project. The assessment techniques are quite comprehensive and thorough, and because of the fact that comments are written, which usually requires more effort from both the students and instructor, it means there is a lot of detail involved.

One of the advantages of this is that all communication between instructor and students is automatically archived. Faculty members and students can access transcripts of past chats to determine levels of participation and accuracy or to review guidance and explanations. Providing students with immediate feedback is another practice that helps students derives maximum benefit from the online learning experience. Actually, in this course students consistently pointed out that the one thing they appreciated most was the immediate feedback they received on their assignments and projects.

Table 1.
An example of a grading rubric used for the simulation project






Active, substantive (contributes to the work, not just its format)

Active, at least partly substantive


of  the Data:


Multiple (3 or more) correct conclusions, no major misinterpretations

One or two correct conclusions, any misinterpretations are minor

Major misinterpretations of the data

of the Data:

Statistical Reasoning

Clear, correct, and complete descriptions of percentage and measures of central tendency and variability, clear and complete descriptions of the logic used to interpret them, including the logic behind any comparisons

Partially complete or partially correct descriptions of percentage and measures of central tendency and variability, partially complete descriptions of the logic used to interpret them

Incorrect descriptions of percentage and measures of central tendency and variability, and/or lack of clear logic used to interpret them

Student Evaluation of the Course and the Instructor

Student learning was evaluated using the Teaching Effective Questionnaire (TEQ). The TEQ instrument consists of 10 items that ask students to rate the instructor and the course on a Likert scale ranging from 1 to 5 with 1 being strongly disagree and 5 strongly agree. The items and the mean scores on each item are shown in the Table 2 below. The mean scores are reasonably high (the lowest being 4.07 out of 5.00), and comparable to those obtained by the author for a similar course taught in a face-to-face classroom. Table 3 shows the mean scores for a similar class taught by the same author in a face-to-face environment.

Table 2. The mean scores for the items for the online class



The instructor explained the course objectives clearly


The instructor was well prepared for class sessions


The instructor made effective use of class time


The instructor explained concepts and ideas clearly


The instructor answered questions in a helpful way


The instructor was willing to meet with students outside of class time


The instructor assigned grades fairly


The instructor made the course content interesting


The instructor significantly increased my understanding of the subject matter


Overall, the instructor is an excellent teacher


Table 3. The mean scores for the items for the face-to-face class



The instructor explained the course objectives clearly


The instructor was well prepared for class sessions


The instructor made effective use of class time


The instructor explained concepts and ideas clearly


The instructor answered questions in a helpful way


The instructor was willing to meet with students outside of class time


The instructor assigned grades fairly


The instructor made the course content interesting


The instructor significantly increased my understanding of the subject matter


Overall, the instructor is an excellent teacher




Teaching statistics online can be as effective as classroom teaching especially when instructors use content to help students acquire learning skills, use content to promote self-awareness of learning by students, and let students use content so that they experience it firsthand. The most important issue is not whether statistics should be taught online or in a classroom. The important issue is whether the course promotes a learner-centered approach. A course is likely to achieve its objectives if students become the center of the instructional universe, and when the content functions as a means as well as an end of instruction.


Bostock, S.J. (1997). Designing web-based instruction for active learning. In Web-based instruction (ed.B.H. Khan), 225-230. Englewood Cliffs, NJ.

Corrent-Agostinho, S., Hedberg, J., & Lefoe, G. (1998). Constructing Problems in a WebBased Learning Environment. Educational Media International. 35, 173-180.

Gillani, B., & Relan, A. (1997). Incorporating interactivity and multimedia into Web-Based instruction. In Web-Based Instruction (ed. B.H. Khan), 231-237. Englewood Cliffs, NJ.

Grabinger, R. S., & Dunlop, J. C. (1996). Rich environments for active learning. Association for Learning Technology Journal. 3, 5-34.

Khan, B. H (Ed.). (1997). Web-Based Instruction. Englewood Cliffs, NJ: Educational Technology Publishers.

Knowlton, D. S. (2000). A theoretical framework for the online classroom. In R. D. Weiss & D. S. Knowlton & B. W. Speck (Eds.), Principles of effective teaching in the online classroom (Vol. 84, pp. 5-14). San Francisco, CA: Jossey-Bass, Inc.

Linn, M., Bell, P., & Hsi, S. (1998). Using the Internet to enhance student understanding of science: The knowledge integration environment. Interactive Learning Environments. 6, 4-38.

Liou, H-C. (1997). The Impact of WWW Texts on EFL Learning. Computer Assisted Language Learning. 10, 455-478.

Lockyer, L., Patterson, J., & Harper, B. (1999). Measuring Effectiveness of Health Education in a Web-Based Learning Environment: A Preliminary Report. Higher Education Research and Development. 18, 233-246.

Shrage, M. (1991). Shared Minds: the New Technologies of Collaboration. New York: Random House.

Smith, L. J. (2001). Content and delivery: A comparison and contrast of electronic and traditional MBA marketing planning courses. Journal of Marketing Education, 23(1), 35-43.

Weimer, W. (2002). Learner-centered learning: Five key changes to practice. San Francisco Jossey-Bass.

Woods, D. D. (1987). Commentary: Cognitive engineering in complex and dynamic worlds. Int. J. Man-Machine Studies, 27 (5-6): 571--585.


About the Author

Dr. Gibbs Yanai Kanyongo

Dr. Gibbs Yanai Kanyongo is an Assistant Professor in the School of Education, Department of Foundations and Leadership at Duquesne University in Pittsburgh, USA. He teaches graduate courses in Educational Statistics and Research Methods. He teaches both face-to-face as well as online courses in these areas.

His research interests are in the areas of factor analysis, attitude assessment and online teaching

Gibbs Y. Kanyongo
Duquesne University
Department of Foundations and Leadership
410A Canevin Hall, Pittsburgh, PA 15237

Email: kanyongog@duq.edu



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