Journal of Interactive Online Learning
www.ncolr.org/jiol

Volume 9, Number 2, Summer 2010
ISSN: 1541-4914

The Interaction Equivalency Theorem
Terumi Miyazoe
Tokyo Denki University, Chiyoda-ku, Tokyo
Terry Anderson
Athabasca University, Edmonton, Alberta

Abstract
This paper examines the key issues regarding The Interaction Equivalency Theorem positedby Anderson (2003a), which consists of the three interaction elements found in formal
education courses among teacher, student, and content. It first examines the core concepts ofthe theorem and argues that two theses of different dimensions can be articulated in thetheorem, namely, value and amount (or quality and quantity). Prior studies in distanceeducation and blended learning that have tested the validity of the theorem concepts are also
examined: all research results support the first thesis; however, further research is required to
examine the second thesis. The paper highlights the key issues for further exploration as
research schemes.

Introduction
The equivalency theorem was developed by Anderson (2003a) initially to clarify theinteraction mechanism in distance education. It argues that different economies exist between
independent-oriented and interactive-oriented learning strategies and activities, and that theseneed to be taken into consideration when designing and delivering distance education thatmeets the diverse needs of learners in an effective and efficient way. Taking the definition of
Wagner (1994), interactions are first defined as “reciprocal events that require at least two
objects and two actions. Interactions occur when these objects and events mutually influenceeach other” (p.8). This definition focuses more on the “learning events” than the “media” ofinteraction (p.6). The primary goal of this paper is to articulate “a theoretical basis for
judging the appropriate amounts of each of the various forms of possible interaction.” Themain features of his theorem are condensed into the following theses:
Thesis 1. Deep and meaningful formal learning is supported as long as one of the three forms
of interaction (student–teacher; student–student; student–content) is at a high level. The othertwo may be offered at minimal levels, or even eliminated, without degrading the educational
experience.
Thesis 2. High levels of more than one of these three modes will likely provide a moresatisfying educational experience, although these experiences may not be as cost- or timeeffective as less interactive learning sequences.
The main point of the first thesis is the equivalency in value; that is, the quality considerationof interaction. In its extreme case, it proposes that only one of the interaction elements could94

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assure quality learning. For example, a student achieves a quality learning experiencethrough intense interaction with other peers (collaborative or cooperative learning), although
the instructor was not available and the course content was not appropriate. The second
thesis, on the other hand, refers more to the quantity of interaction. That is, there might be an
educational condition in which there is a great deal of interaction with both the course
instructor and the course content, and perhaps, there is high student-student interaction as
well. Such course would likely provide a high quality of learning, but the cost of producing
the content and the time commitments required of the students and the teacher would likely
create a course that is expensive and unsustainable. Figure 1 is a tentative visualization of thetheorem.

Thesis 1

Thesis 2

Figure 1.Visual representation of the equivalency theorem by Anderson (2003a).
The two theses refer to the different dimensions of interaction, and each is likely toassume a different educational delivery context. The first is associated with closed systems inwhich interaction is limited by the design to ensure effective and efficient learning, such as in
the case of a predesigned course in distance education. The second is an open system where
positively accidental surplus of interaction could occur; an example is an unexpected guest
lecturer in a course, although it is possible for a distance course to be planned, providing ahigh level in all three interaction elements in exchange for cost or time.
The theorem puts itself in the mainstream theoretical framework in the history of
distance education, succeeding Moore’s (1989) three-part model of interaction. This isregarded as the first theorem to systematically define interaction in distance education, which
consists of three types of “learner–content interaction, learner–instructor interaction, andlearner–learner interaction” (p.1). Anderson’s theorem advanced and developed the model
into a new conceptual form through the perspective of quality and quantity that he forwarded,
as well as three more dyads of interaction to make the constructs measurable, which will be
explained later.
Research on the Equivalency Theorem
Although studies on interaction that use concepts such as communication andcollaboration are abundant, little attempt has been done to test the core nature of theequivalency theorem. Research that denotes the concept of the equivalency theorem and thatconcerns all three elements of interaction is considered to be more relevant and is therefore
closely reviewed here. Two are doctoral dissertations, and one appeared in the Review of
Educational Research, a leading publication in educational research in the field.
Rhode (2008 and 2009). The doctoral study of Rhode (2008), published as a journal
article in 2009, is probably the first to examine the theorem of Anderson when it phrases twoof its research questions as follows (italics added):
1. What forms of interaction do adult learners value the most in self-paced online
courses?
2. What forms of interaction do adult learners identify as equivalent in self-paced online
courses?

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The study was held in a one-year, self-paced online certificate undergraduate program in
educational technology in a private American higher education institution for adult learners.
The students in this study were required to use both a learning management system(Blackboard) and a social networking system (Elgg), so the researcher could examine thestudents’ interaction preferences for formal and informal orientation. Ten students, who wereconcurrently taking two sections in the self-paced program for August 2007 and September
2007, participated out of 15 course takers. Phone interviews were conducted, consisting of 94
predetermined questions and additional follow-up questions for clarification, and these wereanalyzed using a constant comparison approach to find emerging themes (the exact question
statements are found in Rhode, 2008, pp.235–244).
The study found that the students in this study valued interaction with the instructor andcontent most highly, that is, the answer for research question 2. Furthermore, they also
identified a nearly equal value between instructor and content but not with student, that is,
the answer for research question 3. Moreover, its specific research scheme of informal andformal interaction analysis reveals that the students admitted placing equal value to bothinformal blog reading and writing, regarding them as important as formal or required
discussion forums in the course design. However, the students in this study did not support
the concept that interaction with the instructor and content could be “diminished oreliminated” and could be compensated for by other forms of interaction (p.14), which meansthat the student felt the need of having all three interactions although their extent could differ.
This result, although initially contrary to Thesis1, can be understood through Anderson’s
Thesis 2, which states that students felt a course with high levels of all three interactions
would likely be not only more satisfactory but also more costly.
Based on the interview research, Rhode further develops his idea of the equivalency theorem
into a series of matrices, two of which are shown in Figures 2 and 3, giving the tentativemodeling of the theorem by Anderson (2003a).

Figure 2. Interaction matrix core (Rhode, 2008).
In Rhode’s conception, content, learner, instructor, collective, and network are all
essential elements of the learning environment (2008). The network and the collective, which
are conceptualized by Anderson and Dron (2007), express “emerging catalytic components”
where learners interact with one another informally (p.197). In conclusion, Rhode (2008)
proposes Figure 3 to represent the final product of his idea that integrates Anderson’s
equivalency theorem (2003), Dron’s (2007) collective and network, and his formal andinformal dimension of interaction.

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Figure 3. Interaction Matrix (Rhode, 2008).
A point to be argued about this study is its relatively small sample size of 10participants even with the qualitative research approach. Another concern relates to theconcept of interaction that may be uniquely used in this specific paper. Even though 30
questions were prepared to ask research question 2 on the form of interaction the students
valued, further clarification is needed; for example, in which categories (student–instructor,
student–student, and student–content) shall “Course Podcast” (Q.6-3) and “Reflective
activities” (Q.6-24) be classified? Also, the series of questions regarding “Interaction with
Content” (Formal and Informal, Q.50-57) may seem ambiguous if it asks more about
instructional design and preferred format of interaction than the value of interaction between
the student and the content itself; for example, Q.50 asks, “Thinking of all the different typesof instructional content in the course, which aspects of the course content or activities weremost helpful?” This demonstrates one of the challenges and perhaps the value of theequivalency theorem. The multi-media recording and content production capacity of the net
creates opportunities for interaction to morph among student, teacher, and content, as
demonstrated by the production of a podcast by either teacher or students. Finally, as thestudy itself admits, the students’ weak preference for student–student interaction could be asimple reflection of the reason why the students in this study chose the self-paced study
mode; that is, they chose the self-paced program because they had reasons to find difficulty
in synchronizing their schedules to the learning pace of others. This said, Rhode’s (2008)
study claims high value to be the first to test the equivalency theorem in a tangible way, andits significance is its finding a support for the theorem, further suggesting that the forms ofinteraction valued by learners could be different under varying circumstances.

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Miyazoe (2009). Although held without knowledge of Rhode’s study, this study canbe regarded as a follow-up to the unanswered questions of Rhode in that it attempted to test
the validity of the theorem in different learning modes and content orientations. This study
was executed in an Asian context in Japan and Taiwan over the period 2007– 2008 in a
blended learning form in higher education and involved four universities and four instructors.
It asked the priority order of interaction elements among instructor, student, and content todetermine the students’ perception of learning quality. Blended learning in this study isdefined as a mixed course design of face-to-face and written online interaction components:
the participants had experienced the blended learning form for a minimum of ten weeks to
one year, and the online interaction intervention was the threaded forum discussion regularly
done throughout the course at all institutions. Following the two theses posited by Anderson(2003a), a tentative equivalency theorem indicator questionnaire was made and tested with a
total of 236 valid respondents with consent for analysis and publication (255 questionnaire
distributions; 100% collection rate; out of 236 valid samples, Japanese 200: Taiwanese 36).
The questionnaire consists of two pair questions comparing (1) the different learning modesof face-to-face versus online class, and (2) skill-based versus knowledge-based course
content orientations. The inventory configuration tested the combinatory concepts ofAnderson’s Thesis 1 and 2. It hypothesized that (1) if one of the interactions is valued over
the others, students could rank the three interaction elements, with one being the mostvalued–referring to Thesis 1, and (2) customizing a course design of varied focus fittings to
the priority order could produce higher learning for the least cost and time–referring to
Thesis 2. Below is the model answer quoted here in order to give the basic idea on how theinventory works.
2. For you, when comparing face-to-face class (during the class) and online class (theclass developed on Moodle), the “interaction” elements that are important are, inorder of importance:
Face-to-face class:

Online class (on name of LMS):

Teacher1

Teacher3

Students

2

Students

2

Content

3

Content

1

The data were coded into six patterns of priority order of interaction as in Table 1, whichwere processed usong SPSS for analysis.
Table 1
Six patterns of priority order of interaction
Pattern
1
2
3
4
5
6

Rank 1

Rank 2student
content
teacher
content
teacher
student

teacher
student
content

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Figure 4 expresses the study’s understanding of the theorem: this considers that firstrank interaction can differ depending on the learning modes and other factors if Thesis 1 is
supported. However, it implies that the increased level of more than one kind of interaction
may not increase learning effectiveness proportionally, but the degree of effectiveness will
gradually decrease with the combination of more than one kind of interaction.

Thesis 1

Thesis 2

Figure 4. Equivalency Theorem Thesis 1 and 2 in Miyazoe’s study.
Figure 5 highlights the findings of the study: the number from one (left) to six (right)
in the X-axis in each graph corresponds to the pattern number of the above-mentioned
priority order; for example, in the figure in the middle, the higher percentage of categories 5
and 6 signifies that the most number of students valued student-content interaction the most.
Four universities are named University A, B, C, and D; A to C are Japanese and D is
Taiwanese.

Face-to-face course

Online course

Blended learning course

Figure 5. Priority of interaction elements in different learning modes.
The study found that the perceived priority order of interaction elements by thestudents clearly had certain patterns: the students place a higher value on the teacher element
for the face-to-face mode and content for online courses; however, the preference is divided
in all three elements for the blended learning form with increased online interaction among
students. It also found that a skill-based course called for a high value on teacher elements,
whereas the preference is divided with knowledge-based course. These suggest that thevalued interaction elements differ in learning modes and content orientations. Varying theemphasis on the interaction elements in our course design depending on the contexts istherefore more efficient and hence is recommended.
In conclusion, this study supports both Theses 1 and 2: the students did admit more valued
interaction elements over others, and the kind of first priority interaction differs depending on
the other variables; that is, they admitted equal value on all three interactions (Thesis 1).
Furthermore, the varied rank order of interaction suggests that the customization of a course
following the priority order of the interaction pattern of a specific context will possibly
produce a better learning environment in the most effective and efficient way (Thesis 2). A
caveat to be clarified in this study is reliance on the students’ perceptions of the priority
order, which is similar to other research that relies on the participants’ self-reports. Also, the99Journal of Interactive Online Learning

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study did not reach the point of elucidating the correlational mechanism with time and costvariables. On the other hand, insofar as the inventory directly asks the students about theirlearning quality assurance interaction elements, this helps quantify and answer the questionof learning quality in a quite straightforward way. This study was published in a research
paper by Miyazoe and Anderson (2010).
Bernard et al. (2009). As the most recent comprehensive approach to the issue, thismeta-analysis (Glass, 1976; Lipsey & Wilson, 2001; Shadish et al., 2002) examined distanceeducation research from January 1985 to December 2006. It uses the special term interaction
treatments (ITs) for interaction intervention, which are defined as “the instructional and/or
media conditions designed into DE [distance education] courses, which are intended tofacilitate student–student (SS), student–teacher (ST) or student–content (SC) interactions”(p.2).
In accordance with the interpretation that the present paper articulated above, Bernard et al.,(2009) use the term value (or importance) for Thesis 1 and strength (or magnitude) for Thesis
2 for its conceptualization. Six research questions are broken down as follows:
1. What are the effects of the three kinds of interaction (student–student, student–teacher,and student–content) on achievement?
2. Does more overall interaction treatment strength promote better achievement?
3. Do increases in treatment strength of the three different forms of interaction result inbetter levels of achievement?
4. Which combinations of student–student (SS), student–teacher (ST), and student–content(SC) interaction affect achievement the most?
5. Are there differences among synchronous, asynchronous, and mixed forms of DE interms of the effects of ITs on achievement?
6. What is the relationship between treatment strength and effect size for achievement
outcomes in asynchronous-only DE studies?
The first four questions are directly relevant to the theorem testing: the first relates to Thesis
1 and the second, to Thesis 2; the third and fourth further break down the sub-issues
regarding Thesis 2. The fifth and sixth questions come from another parameter ofasynchronous versus synchronous distance education that is derived from another major
meta-analysis identified by the same authors (Bernard et al., 2004).
The analysis includes the blended type of distance courses (less than 50% of face-to-facecomponents), following strict criteria for analysis inclusion. Out of 1,034 potential courses, a
total of 77 satisfied all the criteria for the final analysis; the total number studies examined
for inclusion/exclusion was more than 6,000. The kinds of interaction treatment of SS, ST,
and SC are codified, and two categories of achievement and attitude are focused on as theoutcome of calculating the effect size. Table 2 below summarizes their findings (Bernard etal., 2009).

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Table 2
Summary of the findings for achievement and attitude outcomes for each research question
Research Questions
Question 1: Categories
of interaction (SS, ST,SC)

Findings
Achievement
All categories > 0.25, SS and
SC > ST.

Attitudes
SS > ST and SC.

Question 2: Overall
strength of interaction
categories

Increase in strength formoderate and high strength
over low strength. Regression
is significant.

Increase in strength formoderate over low strength.
Not enough data to evaluate
high strength. Regression is
not significant.

Question 3: Strength ofindividual categories

Increase in strength for highover low and moderate for SC
only.

Increase in strength formoderate over low for SC
only.

Question 4:
Combinations of
categories

Increasing relationshipbetween strength and effectsize for SS + SC and ST + SC.

No finding.

Question 5:
Asynchronous versus
Synchronous versus
Mixed DENo difference among types ofDE.

Synchronous andasynchronous greater thanmixed DE.

Question 6:

Strength of SC affects
outcomes in asynchronous
settings more than in othersettings.

N/AInteraction in
Asynchronous DE only
(achievement outcomes)

The basic findings regarding the theorem of the study are as follows: (1) Thesis 1 was
supported, especially SS and SC interaction treatments showing a higher value than ST for
both achievement and attitude; (2) not all combinations of interaction treatments necessarily
strengthen achievement and attitude, but (3) only SC shows a certain level of contribution tohigher achievement and attitude, and (4) among three possible combinations of SS+ST,
ST+SC, and SS+SC, the combinations of SS+SC and ST+SC contribute to the increase ofachievement; however, SS+ST and attitude items did not support the thesis regarding
increased effectiveness.
With the study’s particular focus relevant to the equivalency theorem, it found that (5)asynchronous, synchronous, and mixed modes did not show any difference in achievement;
moreover, the mixed mode of classroom instruction and distance education in one course wasmore weakly received than the other two modes, and (6) among three interaction treatments,a higher SC leads to a higher achievement in asynchronous DE.
Regarding by-products, the sampling process found that 68% of achievement studies and
80% of attitude studies were conducted between 2000 and 2006 (p.36). This signifies that thetraditional classroom instruction versus distance education research scheme has seen a rapid
shift in focus, and also, there is lack of research data on synchronous and mixed-mode
contexts.
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One point to be noted is that research questions 5 and 6 are based on the categorization of
distance education into three delivery modes, namely, asynchronous, mediated synchronous,
and mixed (or blended or hybrid) modes in this study. The mixed mode is defined as the
combination of classroom instruction and distance education (pp.9–10). This is congruent tosome extent to the study of Miyazoe (2009) reviewed above, if we consider that the online
instruction outside the classroom is equivalent to that in distance education. Hypothetically,
there should be more variations in the combination of mixed modes in distance education
because now, we have such cases as the combination of the bulletin board system(asynchronously mediated) and live conference (synchronously mediated), or as in the casein Rhode’s study, a combination of two different kinds of formal and informal asynchronous
mediated systems. More and more studies that do not fit the three categorizations ofasynchronous, synchronous, and mixed face-to-face and distance education would have been
rapidly executed. Accordingly, a re-examination of the coding categories for distanceeducation meta-analysis would be required.
Another concern is the meta-analysis coding process at the general level. The process
requires setting up the experimental versus the control group to compare the effect size,
consisting of the sample number, standard deviation, and means. Although the study foundhigher effect sizes on SS interaction treatment over SC and ST, this could be a reflection of
the research and instructional design development where the increased human intervention of
SS interaction has been increasingly executed in distance education, and therefore, morestudies that bore higher effectiveness are more likely to have been reported in recent years. If
this is the case, although the support by meta-analysis for the theorem is intact, it would bepossible that a larger sampling with the traditional interaction components of SC and ST may
bring different priority results than the ones reported by this study.
Implications and Further Suggestions
The three studies, applying different research methodologies held in different
contexts arrive at the same conclusion; Anderson’s first thesis regarding interaction
equivalency is so far supported. All admit that one kind of interaction can be given a higher
value than the others not only in distance education but possibly in a blended learning
context as well. Also, the form of interaction valued most differs among these studies:
instructor and content in Rhode’s study, different elements depending on learning modes andcontent orientations in Miyazoe’s study, and student and content in Bernard et al.’s study as
Thesis 1 supposed. The second thesis was also supported by the meta-analysis of Bernard etal. and partially by Miyazoe’s study: the increased interaction brought by a combination ofdifferent interaction treatments could lead to higher achievement, although the effects it
found were more minimal than proportional.
Besides the original theorem of Anderson, each of the three studies has contributed toadvancing the research scheme by adding an original dimension to the theorem: formal
versus informal interaction with Rhode, learning modes and content orientations with
Miyazoe, and synchronous versus asynchronous learning with Bernard et al.
The first two studies and the meta-analysis help fortify the Theorem complementarily: thefirst two verified the Theorem in specific contexts at the expense of generalization, whereas
the strength of meta-analysis is its test of generalizability at the expense of numerous
different variables in numerous research contexts. Both approaches are needed for a higher
level of verification of the Theorem especially in educational settings where no one single
educational event could be repeated in reality.
There are arguments to be developed further regarding the research methodology. Although
this paper articulates the core concepts of the theorem, that is, value and strength (or quality
and quantity), it is still a question whether or not the current research scheme has
successfully measured the two learning qualities defined by Anderson (2003a) above, that is,“deep and meaningful” learning and “satisfying” educational experience. There may be a gap
between whether or not a student felt that learning occurred and if he/she was satisfied–that
is, if quality learning indeed happened–and whether or not a high course grade given by a102

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course instructor in a distance education could, in reality, refer to very different experiences.
Furthermore, the three studies reviewed in this paper did not examine the cost and time
variables to correlate interaction and learning quality, which consist of the core elements of
Thesis 2. This will be a challenging and meaningful research question to be further
undertaken, as will be noted later.
It is noteworthy that the research made has so far covered only partial events of interaction
rather than the whole vision of interaction concept developed by Anderson: that is, theresearch has tested three combinations of interaction, which are pairs with students’perspective only. As phrased in another book chapter by Garrison and Anderson (2003), as
well as Anderson (2003a) and Anderson (2003b), three more pairs of interaction elements(teacher–content, teacher–teacher, and content–content) exist, which could be further
developed into the following new theses:
Thesis 3: Deep and meaningful formal teaching is supported as long as one of the threeforms of interaction (teacher–student; teacher–content; teacher–teacher) is at a high level.
The other two may be offered at minimal levels, or even eliminated, without degrading the
educational experience.
Thesis 4: Deep and meaningful formal teaching and learning is supported as long as one of
the three forms of interaction (content–student; content–teacher; content–content) is at ahigh level. The other two may be offered at minimal levels, or even eliminated, without
degrading the educational experience.
Teacher-teacher and content-content interaction may sound counter-intuitive at first look;however, the recent emphasis on faculty and professional development in education is afamiliar example for teacher-teacher interaction to improve teaching, and consequently, thestudents’ learning. Also, the recent intelligent programs that compile information on specificindividual learning styles such as unit study progress and scores, and that propose acustomized study plan may be a familiar example of preinstalled content-content interaction
before student-content interaction. By finding ways to quantify these theses, we may be able
to look at educational events in much different ways than we have always been accustomed
to.
Several directions regarding the equivalency theorem are suggested for the next step of theresearch scheme:- clarifying the concepts of “learning quality” in the Theses in measureable ways
- testing Thesis 1 in varied contexts to detect the predicators that lead to higher
learning quality- testing Thesis 2 to identify if it can claim validity- testing Thesis 2 with the cost, time, and interaction variables- finding the way to test the new Theses 3 and 4 and check their validity.
Although the research so far reviewed supports Thesis 1, further examination of Thesis 2 isalso important because if in reality, doubling or tripling the quality interaction elements bringlittle or no effect on improving the learning, it would be much wiser and more effective toconcentrate on pursuing the Thesis 1 mechanism to customize the most valued interactionthat the students hope to have in an instructional design beyond the distinction of distanceeducation and other modes of learning. In this regard, testing Thesis 1 may eventually resultin the most efficient and effective instruction with the least time and cost.
There is reason to believe that further studies related to the equivalency theorem are being
undertaken and will soon be published. As far as the core interaction components of teacher,
student, and content in education remain, the value of exploring the equivalency theorem
remains promising.

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