Piyush Swami, University of Cincinnati

Robert Shields, University of Akron




            Gowin’s Knowledge Vee, a constructivist heuristic, was introduced to undergraduates enrolled in two introductory biology courses at a community college in Ohio and to pre-service education majors at a research university also in Ohio.  Novak’s (1998) procedure for teaching Vee diagraming was employed using a group approach.  In the non-majors biology courses, the Vee was used for critical reviews of science articles while students in science education courses used the Vee in laboratory experiences.  After classroom practice in groups, students constructed individual Vees as appropriate to the course assignments and had them evaluated using Gowin’s assessment rubric (1984).

            Our study suggests the Vee can be used to assist undergraduates to learn science and science education.  Moreover, the students, none of whom were science majors, showed a willingness to try a heuristic they had never before used, a facility to use it and sufficient positive experience to consider using it in their future course work.  Given even this limited experience, we believe that the Vee can be employed in the undergraduate classroom and, in turn, K-12 classrooms.


The Constructivist Theory of Learning

            Whether classic behavior modification or cognitive behavior modification, the classroom has been teacher centered with students treated as passive receivers and learning considered to be a stepwise process.  At the same time that behaviorism was employed as the primary teaching process other research was beginning to point to learning as a constructed process.  In fact, the development of the concept of learning as a constructed process is itself a construction which can, at the least, be traced back to Piaget and Inhelder.  Piaget’s concept of cognitive development, assimilation and accommodation in particular, evolved through the work of others so that today there is a more complete picture of how we learn. 

            Vygotsky introduced the role of social interaction in cognitive development while Bruner proposed that learning is an active process in which learners construct new ideas or concepts based upon their current and past knowledge.  The cognitive structure is a schema or mental model which provides meaning and organization to experiences and can assist the learner to go beyond the information given.  As with Vygotsky, Bruner saw education as a social and interactive process in which the goal was to assist students with their cognitive development rather than a reception process in which they were presented facts to memorize without a well established, if it was at all, context.

            Subsumption, according to Ausubel, is the primary process of learning in which new material is related to similar material already existing in the cognitive structure in a substantive and non-verbatim basis.  To facilitate cognitive development, Ausubel (1963) recommended the use of the advanced organizer.  Advanced organizers are:

            “. . . introduced in advance of learning itself, and are also presented at a

higher level of abstraction, generality, and inclusiveness; and since the

substantive content of a given organizer or series of organizers is selected

on the basis of its suitability for explaining, integrating, and interrelating

the material they precede, this strategy simultaneously satisfies the

substantive as well as the programming criteria for enhancing the

organization strength of cognitive structure.”  (1963, p. 81).

            With the work of Piaget and Inhelder (Gallagher & Reid, 1981), Vygotsky (1978), Bruner (DeBoer 1991) and Ausubel (1963), constructivist learning can be seen as a process in which the student assimilates and accommodates new knowledge and experiences in the context of the prior knowledge and experiences and creates a new and personal or idiosyncratic understanding.

Gowin’s Knowledge Vee, a Heuristic for the Constructivist Classroom

            Until 1984 constructivism in education was a theory for which there did not yet exist methodologies by which it could be applied in the classroom.  Novak and Gowin (1984) introduced two constructivist heuristics:  the concept map which is a tool for helping students to understand the meaning of knowledge, and the knowledge Vee diagram, a tool to help students understand the structure as well as meaning of knowledge.  The Knowledge Vee, also referred to as Gowin’s Vee, is the heuristic which may assist students in understanding science literature as well as laboratory experiences.

Gowin’s Knowledge Vee

            Concerned with the apparent inability of students in science laboratories to place their work in a larger context, Gowin began in the 1970s to develop a process that would help students make those crucial learning connections.  Students were, and still are, familiar with “shake and bake” laboratory experiences which, upon completion, normally require the submission of a laboratory report.  Gowin, as have many science educators, noted that students could easily identify the materials and methods they used and the results they achieved; they could not explain how their results were connected to an underlying theory nor could they generalize their results.  In short, they had disconnected information which, in that form, was of no learning value.  The students were not able to explain the meanings of their results yet “. . . meaning must be constructed, and we must show how all elements interact when we construct new meanings.”  (Novak & Gowin, 1984, p. 56).  Novak (1990, p. 31) described the Vee as a heuristic representing the “. . . constructivist view of knowledge and illustrat(ing) the . . . epistemological elements that interact in the process of new knowledge construction.” 

            The Vee heuristic was developed to illuminate the structure of, as well as help students construct, knowledge.  It emphasizes the structure of, and interplay between, the theoretical and methodological dimensions of knowledge.  Gowin’s Vee, which evolved over more than 15 years (Gowin, 1970, 1981), had in its original configuration 16 epistemological elements which, in practice, has been reduced to ten to twelve elements.  The structure of knowledge is in two parts:  conceptual and methodological.  Gowin choose to use the “V” for the form of his heuristic simply because it has two sides, a center and an apex. 

            The left or conceptual side of Vee (Figure 1) is composed of philosophies, theories, principles and concepts; those constructs that provide the foundation or context for further learning.  Philosophy, although we don’t often think of it in everyday science or science education, underlies all that we do.  Gowin described philosophy as the belief about the nature of knowledge and knowing which guide inquiry.  As this is so broad and science laboratories are usually limited in scope, philosophy is usually not used in a Vee applied to a laboratory.  Subordinate to philosophy is theory that is described as “logically related sets of concept permitting patterns of reasoning leading to explanations”  (Novak & Gowin, 1984, p. 56).  Note that the description in Figure 1 differs from that here; this is done to provide for a wider understanding of that concept.  Theories such as that of the diversity of life, cyclogenesis and photosynthesis are usually presented in discussion or lecture sections of a class and are thus included usually as the highest conceptual level in a student’s Vee as noted in Figure 1.  Theories contain one or more principles or constructs which are “ideas which support reliable theory, but without direct referents in events or objects” (Novak & Gowin, 1984, p. 56).  They, in turn are supported by concepts which Gowin describes as “signs or symbols signifying regularities in events and shared socially.” (Novak & Gowin, 1984, p. 56)  It is the conceptual side which provides the meaning of, and foundation for, the methodology and is also the side which as been traditionally overlooked by both students as well as some teachers. 

Figure 1.  Gowin’s Knowledge Vee (after Novak and Gowin, 1984)

Conceptual                                                                                           Methodological


Philosophy:                                           Interaction                                Value Claims:

The beliefs about the                                                                             The worth or value of nature of knowledge                                                                                the inquiry

and knowing guiding the

inquiry                                                    Focus                              Knowledge Claims:

                                                            Question                       Answers to the focus

Theory:                                                                         question(s) - reasonable

The general Principles guiding                                        interpretations of the records

the Inquiry that explain why                                                       and transformed records/data

events or objects what is

observed                                                                                  Transformations:

                                                                                          Reorganized, rearranged

Constructs:                                                                         records  more manageable &

Ideas showing specific relation-                               meaningful representation of the

ships between concepts, without                                         event – tables, graphs etc.

direct origin in events or objects


Concepts:                                                               Raw data:

Perceived regularity in events or objects                  The observation(s) made and recorded

(or records of events or objects)                             from the events/objects studied

designated by a label.


Events & Objects: Description of the event(s) and/or object(s)

to be studied in order to answer the focus question.


The focus question in the center of the Vee is based on the conceptual side and must clearly address an issue specific to the left side.  The apex, especially, points to the events and objects which “. . . are at the root of all knowledge production . . .”  (Novak & Gowin, 1984 p. 57).  Events and objects are the activities and materials which comprise the normal laboratory experience and have as their immediate foundation the focus question.  Although not stated explicitly, Gowin chose to use events and objects in lieu of “materials and methods” to insure that those epistemological elements would not be confused with same named elements of the positivists’ scientific method.  Moving up the right side are the results of the events and objects, first of which is the record or specific results of the experience.  They in turn can be transformed to a more useable format such as graphs or statistical analyses which in turn can be used to create knowledge claims in which new generalizations answer the focus question.  At the top of the methodological side, and supported by the elements below it, are the value claims which identify the worth of the knowledge claims or place them in the context of the underlying theory.  Such worth in the context of the underlying theory is the purpose of Kuhn’s (1970) “normal science”.  Note the “interaction” arrow connecting the conceptual and methodological sides; it is this which calls to the attention of the student and teacher the connections between knowing and doing.   If a laboratory is constructed well the focus question is clearly based on the conceptual side, and the methodological side both answers the focus question and adds more understanding to the conceptual side.  The Vee functions in helping students see the interactions between theory, methods and results.  In its use, the Vee functions much like an advanced organizer in that it enhances the organization strength of the cognitive structure.

            Gowin’s Vee in the Laboratory

            Novak and Gowin contended that the Vee heuristic is a useful constructivist tool and field studies by others support their contention.  In keeping with the purpose for which the Vee was originally developed Gurley-Dilger (1992), in one of the earliest articles on the Vee, used it in a high school laboratory by having her students fill in the conceptual side before a laboratory experience and then completing the methodological side following the experience.  The completed Vee served as their laboratory reports and were easier for the teacher to respond to than the traditional laboratory report.   She reported that they learned better in that they could not only see the interaction between the two sides, prior and new or constructed knowledge, but the teacher could easily identify to them any problems they appeared to have with that interaction.  Her results were supported by other studies:  Qin (1997), Lebowitz (1998) and Passmore (1998) also found the Vee to be effective in college science laboratories.  Novak (1984) also noted that Gowin’s Vee had been tried with some success in elementary schools although there is little in the literature on this.  The limited number of articles and even fewer dissertations concerning the Vee are primarily focused, as was Gurley-Dilger’s, on the use of the Vee in science laboratory experiences. 

            Gowin’s Vee Used With Preservice Teachers

            If Gowin’s Vee is to be used in the classroom it has to be introduced to students by their teachers.  Novak (1998) suggested a method by which students can be introduced to and learn to use the Vee.  His method has, however, yet to be tested as the majority of Vee studies occurred prior to the publication of his 1998 book and studies conducted subsequent to his book do not reference his method.  That Novak choose to suggest a method acknowledges its importance if the Vee is to find wider use in science education. 

            Okebukola (1992) found that preservice teachers of mathematics and science can learn to use the Vee but find it difficult to teach students how to use it.  Wandersee (1990) noted the same problem and suggested that of the constructivist heuristics, the Vee was the most difficult to use.  Its difficulty notwithstanding, teachers in Okebukola’s study did have a positive attitude towards using Gowin’s Vee.  Roth and Roychoudhury (1993) found that preservice elementary teachers could learn to use the Vee, they had a positive attitude towards its use and it helped them to “reflect on the process of learning and teaching science” (p. 243).  They also found that the Vee could be used in collaborative situations.  Nelson and Epps (1996) also found that preservice elementary teachers could learn to use the Vee and were willing to use it in laboratory investigations but, as found in other studies, the students had difficulties with the higher order elements such as value claims and principles. 

            Gowin’s Vee Used for Analyses of Science Literature

            Gowin suggested however (Novak & Gowin, 1984) that “Papers, texts, literary works, lectures, and other forms of exposition can be analyzed and critically evaluated using the Vee” (p. 117).  The literature provides only one article (Stewart, 1997) which examines that use of Gowin’s Vee and thus there is a need to further examine Gowin’s contention.

Current Study of Gowin’s Vee

            With the belief, based on available research, that Gowin’s Vee can be a very useful tool in the science classroom and recognizing that there yet remains a dearth of research concerning it, we engaged in a two pronged study of how to teach it as well as determine, to a limited degree, its efficacy.  The results reported herein are preliminary and will serve as the basis for future studies.  Our primary interests in these preliminary studies is to learn best how to help students use it as well as learn how receptive students are to this heuristic to which they had not been previously exposed.  With such knowledge further research on its efficacy will be less influenced by the variable of teaching the tool.  That said, we did take an non-rigorous look at its efficacy.

            In this study he Vee was introduced to undergraduates enrolled in two introductory biology courses at a community college in Ohio and to pre-service education majors at a research university also in Ohio.  Novak’s (1998) procedure for teaching Vee diagraming was employed using a group approach.  In the non-majors biology courses, the Vee was used for critical reviews of science articles while students in science education courses the Vee was introduced for use in laboratory experiences.  After classroom practice in groups, students constructed individual Vees as appropriate to the course assignments and had them evaluated using Gowin’s assessment rubric (1984).  Students were also asked to respond to a survey concerning the Vee.


            In the community college introductory biology classes, students were required to read assigned articles from science magazines and then write a paper which illustrated their understanding of the topic as well as present a critique of the article.  The treatment group prepared the required narrative only after receiving instruction on the use of the Vee and preparing a Vee on their article.  The control group did not receive such instruction nor were they required to prepare a Vee prior to writing their narrative.  Both groups were further assessed through the use of an exam essay based on yet another science article.

            This part of the study utilized a static-group comparison, quasi-experimental design, (Table 1) a design also referred to as pre-experimental (Newman, personal communication).   This design was chosen as the participants could not be truly given random assignments to a treatment or control group and that a posttest was administered to both group but no pretests were used.    Convenience sampling was used to determine which class would be the control and which would be the treatment group.

Table 1

The Static-Group Comparison Quasi-Experimental Research Design                                             


                                       Action prior to treatment                Treatment given         Posttest                                               


Treatment Group                                  -                                               X                         O


Control Group                                      -                                               -                           O                


Key:      - = no action taken

            X = treatment administered

            O = posttest administered


            The hypothesis being tested was:  there is not any difference in the quality of understanding of science article between students who have learned and used Gowin’s Vee and those who have not as expressed in the form of a written review and critique, and in the form of an examination essay question. 

            Participants in this study were students attending an Ohio community college during the fall semester of 2005.  All were enrolled in a section of an introductory (100) level biology course taught by one of the authors, Shields.  The students were either recent high school graduates, adults returning to college or were high school juniors and seniors enrolled through the post secondary education  opportunity program.  As such there was a wide age range from 16 to over the age of 40.  The demographics of the students was generally representative of the county in which the college is located.

            During the study each group was assigned to read and respond to specific articles from first Science News and later Scientific American.  Students in the treatment group received an initial introduction to and instruction in the use of Gowin’s Vee for 80 minutes when they received their first writing assignment.  Classroom instruction followed that recommended by Novak (1998) and included an overview of the structure and use of the Vee as well as examples of the Vee, developed by the instructor, as applied to science articles.  It should be noted that examples of such a use of the Vee do not exist in the literature.  In addition to the classroom instruction they were given a four page handout which included a description of the Vee, a sample of the Vee and a blank Vee for their use.  The students in the control group received an assignment that did not include information specific to the Vee.  The students in the treatment group were required to complete a Vee for their assigned article and submit it for critique.  Upon return of the Vee they were allowed to discuss it among themselves but no further instruction or class critique was provided as it was believed it would confound the results by providing each student in the treatment group with, in essence, an instructor developed Vee for the article.  The Vees were evaluated using the rubric developed by Gowin (Novak and Gowin, 1984, pp. 71-71).  The reviews were assessed using an instructor developed rubric.

            Examination essays were based on a specific article from Scientific American.  Students in the treatment group were encouraged but not required to produce their own Vee for the essay article and to share their Vees and discuss the articles prior to the exam.  For both groups the articles were provided a week before the exams. 

            The pre-service teachers enrolled in a methods course received their introduction to the Vee also using the method recommended by Novak (1998).  An analysis of the efficacy of the heuristic was not conducted in this part of the study.  The Vees produced by the preservice teachers were for laboratory exercises and were evaluated using Gowin’s rubric (Novak and Gowin, 1984).  At both the community college and the research university students were asked to respond to a survey concerning their perceptions of the Vee.

            In the community college part of the study there was a difference in the quality of the article reviews and critiques and examination essays between the treatment and control groups but the differences were not significant.  The surveys indicate that most of the students thought using the Vee for both articles was difficult but they would be open to continue using it.  This finding is in agreement with Lebowitz’s (1998) findings.  The students’ comments from this study also support the continued use of the Vee and, again, are very similar to the comments provided by the students in Lebowitz’s study.  Some of the comments were: 

            “. . . it definitely made me grasp the material.”


            “I can also see myself using the V in the future for my own

            purposes/helping to get a paper together.”


            “I wouldn’t say it was amazing, but it was helpful.”


            The Vee was very helpful and a good tool.  At first it was very

            confusing but then I got it.”


            “It made me read the article more.”


            “It helped me organize my info . . . I will use Gowin's Vee in the future.”


Conclusion and Recommendations

Although preliminary, this study provides us first with support for the usefulness of the Vee, second, a better understanding of the difficulties students found with the Vee and, finally, it suggests the need for improvements to how we teach and evaluate the tool.

            Although there was not a significant difference between the treatment and control groups in the community college part of the study, that there was a difference suggests the Vee may be useful.  Certainly, in their critiques of the Vee, the students opined that the Vee is useful.  With a more critical review of Novak’s methods for teaching the Vee and more practice at doing so we may more effectively introduce Gowin’s Vee to students.  Of particular interest is the difficulty students have determining value claims and theories, and to a lesser but still notable degree, knowledge claims and principles/constructs; this is consistent with the findings by Nelson and Epps (1996).  They had few problems identifying focus questions, events and objects, raw data and transformations and, in spite of the problems identifying theories and value claims, they were able to make the connection between the conceptual and methodological sides of the Vee.  In this, we agree with Wandersee’s (1990) assessment that the Vee is difficult to use and Novak’s contention that “. . . using the Vee requires significantly more training, incubation time, and reorientation in the way most people think about knowledge and knowledge creation.” (1998, p. 110). 

            Although not conclusive, this study supports Gowin’s contention, and agrees with Stewart’s (1998) conclusion, that the Vee can be useful for the analysis of science articles.  It also supports the studies by Okebukola and  Roth and Roychoudhury that preservice teachers can develop a positive attitude towards the heuristic and appreciate its usefulness in the constructivist classroom. 

            Another aspect of effectively introducing the Vee to students is the rubric by which their Vees are assessed.  The only rubric developed for evaluating student Vees was done so for use with middle school laboratories and is not an effective tool for evaluating Vees developed for analysis of science articles.  Such a rubric needs to and will be developed.  The importance for this rubric this lies in the focus on scientific literacy as the overarching goal of science education.  Science articles can be used to supplement text books and, after students have completed their formal science education, often become an important if not sole source of science information.  The ability of students to understand articles in commercial and popular magazines such as Scientific American, and the ability of teachers to help students learn to effectively use such sources of science information are critical to the development of a scientifically literate citizenry. 

            As evidenced by the paucity of literature on this heuristic, Gowin’s Vee has long been overlooked as a tool to be used in the constructivist classroom.  The literature which does exist and our initial study suggest this is an oversight that does a disservice to students studying science.  Our initial study also leads us to hope that Novak is not quite on the mark with his guess “. . . that it will take 2 or 3 decades before the power and utility of using the Knowledge Vee for knowledge capture and facilitation of thinking takes hold . . .” (1998, p. 110).  We believe that it need not, nor should not, take that long. 



Ausubel, D.P. (1963).  The psychology of meaningful verbal learning:  An introduction to


school learning.  New York:  Grune & Stratton.



DeBoer, G.E. (1991).  A history of ideas in science education:  Implications for practice. 


New York:  Teachers College Press.


Gallagher, J.M., & Reid, D.K. (1981).  The learning theory of Piaget & Inhelder.  Austin,


TX: Pro-Ed.


Gowin, D.B. (1970).  The structure of knowledge.  Educational Theory, 20 (4), 319-328.


Gowin, D.B. (1981).  Educating.  Ithaca, NY: Cornell University Press.


Gurley-Dilger, L. (1992)  Gowin’s Vee: Linking the lecture and the laboratory.  The


Science Teacher 59(3),  50-57.


Kuhn, T. S. (1970).  The structure of scientific revolutions (2nd ed).  Chicago:  The


University of Chicago Press.


Lebowitz, S.J. (1998, April).  Use of Vee maps in a college science laboratory.  Paper


presented at the annual meeting of the National Association of Research in


Science Teaching, San Diego, CA.


Nelson, M. & Epps, N.V. (1996, January).  An analysis of elementary majors’ pogress


with Vee diagramming.  Paper presented as the annual meeting of the Association


 for the Education of Teachers of Science, Charleston, WV.


Novak, J. D. (1977). A theory of education.  Ithaca, N.Y.: Cornell University Press.


Novak, J. D. (1990).  Concept maps and Vee diagrams: Two metacognitive tools to


facilitate meaningful learning.  Instructional Science.  19: 29-52. 


Novak, J.D. (1998) .  Learning, creating, and using knowledge:  Concept Maps as


facilitative tools in schools and corporations.  Mahwah, N.J.:  Lawrence Erlbaum


Associates, Inc.



Novak, J., & Gowin, D.B. (1984).  Learning how to learn.  New York:  Cambridge


University Press.


Okebukola, P.A. (1992).  Attitude of teachers towards concept mapping and Vee


diagramming as metalearning tools in science and mathematics.  Educational


Research, 34, 201-213.


Passmore, G.G. (1998).  Using Vee Diagrams to facilitate meaningful learning and


misconception remediation in radiologic technologies laboratory education. 


Radiologic Science & Education, 4(1), 11-28.


Qin, Y. (1997).  An investigation of the effectiveness of the Vee heuristic for student pre-


laboratory preparations in chemistry.  Unpublished doctoral dissertation, The


University of Iowa. Ames.


Roth, W-M., & Roychoudhury, A. (1993).  Using Vee and concept maps in collaborative


settings: Elementary education majors construct meaning in physical science


courses.  School Science and Mathematics, 93, 237-244.


Stewart, G. (1997).  The use of Gowin’s Vee to improve post-graduate critical analysis of


research papers.  Retrieved November 2, 2003 from http://www.hsb.baylor.edu/




Vitgotsky, L.D. (1978).  Mind in Society.  Cambridge, MA: Harvard University Press.


Wandersee, J.H. (1990).  Concept mapping and the cartography of cognition.  Journal of


            Research in Science Teaching, 27, 923-936.