Theories or Fragments? The Debate Over Learners’Naive Ideas About ScienceMary B. NakhlehDepartment of Chemistry, Purdue University, West Lafayette, IN 47907

Online Symposium: Piaget, Constructivism, and Beyond

Print • Software • Online • Books

Journal of Chemical Education

Journal of Chemical Education, Vol. 78, p 1107, August 2001. Copyright ©2001 by the Division of Chemical Educationof the American Chemical Society.

Owned and Published by the Division of Chemical Education, Inc., of the American Chemical Society

2

THEORIES OR FRAGMENTS: THE DEBATE OVER LEARNERS NAIVE IDEAS ABOUT SCIENCE.

Mary B. Nakhleh, Department of Chemistry, Purdue University, West Lafayette, IN 47907-1393.

The debate. We now have a substantial body of research that provides a solid basis for claiming that

novice science learners actively construct their own ideas about the natural world and that the naive ideas of learners

often differ in content and organization from the ideas of trained scientists (1). However, researchers and theorists

are currently debating the qualitative nature of these novice learners ideas (2). In a nutshell, are students

constructed ideas about science concepts constrained by underlying, coherent naive theories about the natural world

or do students generate ad hoc explanations of phenomena that are fragmented, diffuse, and unconnected?

Michelene Chi and her associates (3) argue that novice learner s ideas are theory-bound and that novice

learners organize their ideas about the natural world into mutually exclusive ontological categories called trees.

McCloskey (4) also argues that students ideas of science are theory-bound. He has studied physics students

understanding of projectile motion, and he asserts that students reason from an underlying naive theory, which is

related to a medieval concept called the impetus theory. At the other extreme of the theory/fragments debate,

Andrea diSessa urges that students rely upon fragmented, diffuse, weakly connected scraps of ideas that he terms

phenomenological primitives , or p-prims (5,6). He has investigated these possible p-prims in the area of

mechanics in physics and demonstrates that physical phenomena, such as tossing a tennis ball into the air, can be

equally well explained from either a theory-driven perspective or a p-prim perspective. He argues that students use

p-prims rather than theory and that eventually these p-prims grow into an interconnected network of ad hoc ideas

that serve the student well in predicting and explaining phenomena. This network may eventually grow into a

theory with a focus on a set of explanatory principles, or it may remain a patchwork of ideas that generates ad hoc

explanations for observed phenomena. This paper briefly reviews that debate and then shows how both the

knowledge in pieces ideas of Andrea diSessa and the naive theories perspective can be applied to chemistry

instruction.

diSessa s p-prims. The core data base for diSessa s ideas is a three-year set of interviews of approximately

20 students in an elementary physics course at MIT. The course content was mechanics. He supplements this core

group with an unspecified number of informal interviews with learners ranging from high school to adult

nonscientists. He asserts that from early childhood on people gradually acquire what he terms a sense of

mechanism, an ability to explain to oneself how the natural world works. His interest lies in exploring the structure

3

of this sense of mechanism, i. e. how knowledge of how things work is organized. He believes that science

learners create explanations of well-known events, like bouncing or tossing a ball, from applying a cluster of p-

prims to explain their observations rather than from an underlying theory.

The classic example of the contrast between p-prims and theories is how to explain the familiar observation

that a ball thrown vertically into the air is seen to rise, halt, and then fall back down to the ground (5). McCloskey

(4), who asserts that students reason from an underlying theory, argues that students explanations seem to be based

on a medieval concept of force called the impetus theory. In other words, the act of throwing imparts a force to

the ball and this force spends itself as the ball rises. When the force is spent, the ball halts and then drops back to

the ground. McCloskey would argue that if students hold this theory, their explanations will be constrained by the

theory. In other words, they will not offer ad hoc explanations that may change over time. They will offer

explanations that are consistent with statements like the force is all gone so the ball falls and their explanations

will consistently refer to something like a force being used up.

diSessa argues that students do not reason from anything so sophisticated as an impetus theory; instead

they apply a cluster of beliefs, which are basically short encoded scripts that have been proven over and over by

experience. One such p-prim is called overcoming, i.e. the idea that a weaker force in conflict with a greater force

will eventually be overcome. Another p-prim is dynamic balance, which is viewed as a conflict between equal and

opposing forces. Therefore, the ball rises into the air because the force of the toss overcomes gravity. Then the ball

halts because there is a dynamic balance between two equal and opposed forces. Finally, the ball drops because

gravity overcomes the upward force of the toss. diSessa claims that if students are invoking p-prims rather than

theory in their explanations, then he would not expect interviewees to give similar explanations, since p-prims other

that these could be invoked. He would, in fact, expect their explanations to be unstable over time and to vary from

student to student.

Of course, to a physicist, the situation is explained very differently from either of these positions. A

physicist would see the toss as imparting momentum to the ball, but as soon as the ball leaves the hand, the only

force acting on the ball is gravity. The physicist might accept that impetus is an imprecise metaphor for

momentum but never for force.

In thinking about these p-prims, it becomes apparent that several combinations or clusters of these p-prims

could be invoked by students to explain the vertical ball toss. In fact, some of the p-prims that diSessa discusses

could have large areas of overlap, although diSessa states that he believes that the p-prims are encoded separately

4

(6). diSessa s p-prims may cluster and be somewhat persistent (5), but he believes that these clusters are not

selected by theory.

Different models, different goals . diSessa argues that these two very different models (theories vs. p-

prims) lead to very different goals for instruction. He claims that if students operate from an underlying theory, i.e.

an organized system of ideas that imposes constraints on acceptable explanations, then effective instruction would

consist of helping students identify their underlying theories and then confronting those theories with the currently

accepted scientific theory. In other words, the ideal technique would be to persuade/force students toward

conceptual change.

If, however, students employ p-prims, i. e. loose clusters of ideas that do not impose constraints on

explanations, then instruction is best accomplished by encouraging students to examine and connect their ideas.

The goal here is to help students grow their ideas into scientifically acceptable networks by giving high value to

useful p-prims and low value to unhelpful p-prims (5).

diSessa also strongly urges that instruction must make connections between the ideas of science and the

real world of the students because it is this real world of experience that the student uses to develop p-prims.

Thinking about everyday phenomena is not just making an analogy or providing helpful scaffolding; it is invoking

the very resources out of which expertise is built, and it is also exercising a component of developing knowledge

not engaged in more schematic problems (5, page 207). If we accept diSessa s argument that these opposing

views of learning lead to very different instructional goals, it becomes important to investigate the issue.

What is needed is data from other scientific disciplines. diSessa developed his ideas within the domain of

physics, but every scientific discipline has its own core concepts, processes, and structure. It is not at all clear that

theories of learning developed in one discipline (physics) can transfer totally to another discipline (chemistry). The

final section of the paper briefly describes two studies of learners chemistry ideas, one in the area of bonding and

one concerning the nature of matter. The findings of these studies may shed some light on the theories vs.

fragments debate.

Data from bonding study. Taber (7) investigated pre-university A-level British students ideas of the

fundamental chemistry concept of bonding. He interviewed 15 students over a period of three years on this topic

and developed cases studies of how each student s understanding of bonding changed and developed over that time.

He then constructed a composite model of these students misconceptions and developing conceptions that he called

5

an alternative conceptual framework. He was interested in reporting his composite framework, but, for our

purposes, two of his findings bear upon the theories vs. fragments debate which is the concern of this paper.

First, he clearly demonstrated that the students had an overall pervasive reliance on the octet rule. He

supported his argument by listing 12 bonding topics, among them covalent bonds, ionic bonds and metallic bonds,

which were explained by a reference to the octet rule. For example, on the topic of stability, Taber explained that

one of his students thought that once an electron had been removed to give the stable ion, it would then not be

possible for further electrons to be removed (page 603). He reports that another student wrote that If an atom has

been filled up or [is] all ready full up [of eight outer electrons] it becomes stable and therefore it is unreactive. The

atom will stay that way forever and not react or loose [sic] or gain any electrons (page 603). Students also used the

octet rule to explain metallic bonding. Taber reports that one [student] described how metals haven t got full

outer shells, then by electrons moving around they re getting, a full outer shell, but then they re sort of losing it,

but then like the next one along will be receiving a full outer shell (page 603). Seen from the theories/fragments

debate perspective, this reliance on the octet rule functioned as a theory because the octet rule was invoked to

explain many subtopics and concepts and because students could make logical connections from each topic back to

the underlying theory, i.e. the octet rule.

However, at the very end of the paper, Taber reported another interesting finding. He found that there was

a tendency to discount anything that could not be explained in terms of the full shells explanatory principle as just a

force, and not a proper bond. In a metal, for example, there would be a force between the atoms but not a bond.

Similarly, solvation was considered to be like a bond but just an attraction really. Even in the cases of hydrogen

bonding (where the name might be expected to be somewhat suggestive) students thought that adjacent molecules

don t actually bond and the hydrogen bond would be a lot weaker than the proper bond (page 605).

This notion of force-as-attraction-not-bond seems to function very much like one of diSessa s primitives.

This explanation is invoked as a fall-back answer if the students find that the octet rule cannot be invoked. This

explanation does not seem to be very elaborated; it seems to be loosely defined as an attraction. However, this

force is differentiated from bonding, which is also an attraction in the scientific view. The only elaborations

reported are statements that a force is a weak attraction, which is not as powerful as a bond.

As a composite picture of this study s students, the octet rule emerged as a naive theory that was logically

connected, elaborated across many concepts, and had explanatory power. Force-as-attraction-not-bond seemed to

6

function as a p-prim on the composite level. Force-as-attraction-not-bond seemed not to be logically connected to

the rest of the framework nor well elaborated, and it had little or no explanatory power.

Data from the nature of matter study. Another study using a very different population of learners also

found this same mix of theory-like explanations and other explanations which functioned more like p-prims.

Nakhleh and Samarapungavan (8) investigated elementary school children s understanding of the nature of matter.

They individually interviewed 15 children (ages 7-10) about their understanding of the nature of matter in its

various physical states, in simple phase changes, such as melting/freezing, and in dissolving. The materials used in

the interview were objects familiar to young children: a sugar cube, a toothpick, water, a copper wire, a clear

helium-filled balloon, an ice cube, and table salt. The students were first asked to describe the objects in terms of

both physical appearance and composition. Next, they were asked to explain differences in properties, such as

flowing vs. rigidity (water vs. wood) and malleability vs. rigidity (copper wire vs. toothpick). Third, their

understanding of phase change was explored by asking them to explain the melting/freezing of water. Finally,

students were asked to explain what happens when table salt (NaCl) is dissolved in water.

They found that students seemed to hold one of three sets of beliefs: macro-continuous (matter has no

particle nature), macro-particulate (matter is made of tiny particles, but the students still reason only on a bulk

property level), and micro-particulate (matter is made of very tiny, invisible particles called atoms and/or

molecules). Nakhleh and Samarapungavan reported that some students explanations of physical states of matter

were theory-like because their explanations were consistent for different objects in different physical states, but other

students explanations were somewhat fragmented and not entirely consistent across physical states.

They also found that most students explanations of melting or dissolving were more like elaborate p-

prims. P-prim-like explanations were also sometimes given when students explained some observation in terms of

an invariant intrinsic property. For example, a student might explain why a metal wire bends by simply stating

that wire bends because it s made of metal and metals bend. In other words, the property of bendability seems to

function in this type of explanation as a p-prim.

However, overall, the students did not seem to generate the variability in answers predicted by diSessa s p-

prim model. For example, the p-prim model would indicate that, faced with the task of explaining some

phenomenon that the student did not know, the student would spontaneously generate some sort of explanation by

falling back on familiar p-prims. Nakhleh and Samarapungavan s data indicate that in these cases, the students

simply stated that they did not know. This response was interpreted to be the result of a constraint imposed by an

7

underlying theory-like structure. Students operating in a p-prim model would have been likely to generate ad hoc

explanations on the spot rather than stating that they did not know an explanation.

Implications for chemistry instruction. In sum, the data from these two studies indicate two major

conclusions. First, in both studies the students explanations and predictions seemed to be a mixture of theory-like

and p-prim-like explanations. Second, these studies show that students of widely different ages and backgrounds

are capable of offering explanations that in some instances are theory-like but in others are more like p-prims.

Indeed, these studies indicate that one can usefully think of knowledge acquisition in chemistry as most like a

spectrum, with students knowledge structures ranging from p-prims to fully developed theories. Therefore,

chemical educators at all levels can probably assume that their students reflect a mix of theory-like and p-prim-like

knowledge structures.

In that case, how can instruction take these models into account? It is helpful to think of these models as

really being different ends of the same continuum. Our task is to provide opportunities for students to move their

understanding along this continuum more toward scientific beliefs. From the theory proponents we can take the

idea that instruction should provide opportunities to challenge students misconceptions and to help students

clearly articulate their explanations and predictions. From diSessa s p-prims we can gain a renewed appreciation of

the importance of bringing the real world of experience into our instruction. He argues that these p-prims are a

necessary first step along the road to theory and that these p-prims are developed by students meaningful

interactions with real world phenomena. Seen this way, connecting everyday phenomena to our lecture topics is not

just adding flavor to our lectures, it may be providing students with vital clues as to what we re really talking

about!

Acknowledgments. The author gratefully acknowledges Bill Robinson s thoughtful comments and

suggestions, which contributed greatly to this paper s development.

Literature Cited

(1) Nakhleh, M. B. J. Chem. Edu., 1994, 71, 494-499.

(2) Brewer, T. & Samarapungavan, A. In Cognition and the Symbolic Processes: Vol. 3. Applied and Ecological

Perspectives; Hoffman, R. R. & Palermo, D. S., Eds.; Erlbaum: Hillsdale, NJ, 1991.

(3) Chi, M. T. H., Slotta, J. D. & de Leeuw, N. Learning and Instruction, 1994, 4, 27-43.

(4) McCloskey, M. In Mental Models; Gentner, D. & Stevens, A., Eds., Earlbaum: Hillsdale, NJ, 1983.

(5) diSessa, A. A. Cognition and Instruction, 10(2 & 3), 105-225, 1993.

8

(6) diSessa, A. A. In Constructivism in a Computer Age; Forman, G. & Pufall, P. B., Eds., Earlbaum:

Hillsdale, NJ, 1988.

(7) Taber, K. S. Intl. J. of Sci. Edu., 1998, 20 (5), 597-608.

(8) Nakhleh, M. B. & Samarapungavan, A. J. Res. in Sci. Teaching, 1999, 36 (7), 777-805.