Inviting Argument by Analogy: Analogical-Mapping-Based Comparison Activities as a Scaffold for Small-Group Argumentation

Analogies Naturally Scaffold Thinking

Analogical comparison can scaffold thinking to make a concept easier to understand or communicate. People use analogies spontaneously to think and communicate (Clement, 1988; Dunbar, 2001; Wong, 1993). For example, Clement (1981, 1988) invited experienced problem solvers to analyze a physics problem. Although they were not instructed to search their own background, Clement expected people to appeal to analogues from their past experiences to solve it. They did this, in fact, through an extended think-aloud process that produced correct reasoning via analogy. The author concludes that reasoning with analogies does not necessarily provide an immediate solution but has the potential to be effective over time. Furthermore, there is “reason to believe that some of these processes [of reasoning and conjecturing with analogies] are learnable, rather than being exclusively a product of genius” (Clement, 1981, p. 9).

Wong (1993) also found, among a class of preservice teachers, that “productive analogical reasoning can occur when the learners themselves assume primary responsibility for the task of generating, applying, and learning from analogies” (p. 1271). For instance, when participants were asked to explain the operation of a sealed syringe, they were found to appeal to self-generated analogies including the idea that air particles are analogous to BBs in a container, people moving in a room, or rubber balls inside the syringe (p. 1270). Participants reached into their past knowledge and experience to explain and understand the problem before them. This frequently resulted in the emergence of new questions, such as how to explain the fact that the syringe returns to its rest position when pulled out or even how to explain air pressure more generally.

In both Wong's and Clement's research, people were found to reason via an analogical reasoning process to understand and communicate ideas they did not fully understand. How have these findings been applied to science instruction? Many researchers have suggested that science students can be invited to use analogy as a process in the classroom (Duit, 1991; Else, Clement, & Rea-Ramirez, 2008; Wilbers & Duit, 2006). Analogies are commonly used as an explaining tool in science education (Brown & Clement, 1989; Coll, 2006; Fogwill, 2010; Heywood, 2002). For example, Brown and Clement (1989) argue for engaging “the student in a process of analogical reasoning in an interactive teaching environment” as opposed to “simply presenting the analogy in a text or lecture” (p. 237).

Various frameworks that have been developed to provide steps for the use of analogy in teaching and learning science (Else et al., 2008; Glynn, 1991; Treagust, Harrison, & Venville, 1998) all include language on analogy as an active process. For example, guidelines of Else et al. for working with analogies called for making “analogy as student-active as possible.” The Focus, Action, and Reflection guide for working with analogies has an “action” phase that consists of “mapping of shared attributes” and “showing students where the analogy breaks down” (Treagust et al., 1998, p. 92). The Teaching With Analogies model also addresses the importance of process; its step four instructs students to “map similarities” (Glynn, 1991, p. 230). These frameworks all implicitly suggest the importance of comparing and contrasting, which has been shown to benefit learning.

The Importance of Argumentation and Scaffolding

To understand the nature and process of science, students must understand the process of argumentation that gives rise to scientific knowledge (Driver, Newton, & Osborne, 2000; National Research Council, 2007; National Research Council, 1996). Without understanding this process, students can perceive science as a body of facts that are self-evident and self-establishing. While engaging in argumentation, students should be doing activities that center on communicating, interpreting, and justifying scientific evidence with an eye toward understanding the scientific concept in question (Jimenez-Aleixandre, 2008). They can thus increase their understanding of the specific content to be argued as well as about science more generally. Although argumentation is important, it seems that learners do not discuss well or argue about what they do not understand (von Aufschnaiter, Erduran, Osborne, & Simon, 2008). They need to be supported in the argumentation process, and scaffolding is one way to do this.

The term scaffolding relates to the Vygotsky (1978) zone of proximal development, which is the theoretical space between what a novice can do without assistance versus what he or she can do with assistance from abler peers. Scaffolding of novices, or in this case science learners, means to temporarily support them to achieve a higher performance than they could achieve alone. It is expected that later, the learners will be able to perform unaided at the higher level (Mascolo, 2005; Wood, Bruner, & Ross, 1976).

Scaffolding need not be provided directly by another person who is present. Rather, it can be embedded into the environment to support a novice. One way of doing this is to structure and problematize science content for students (Reiser, 2004). To problematize content means to make it a situation in need of resolution as opposed to presenting it outright. (Note that this use of “problematizing” differs from other uses in such fields as technological design in which students come to form, understand, and articulate a problem to be solved.) Structuring content, on the other hand, involves making a task more doable by breaking it into steps. The two can be in tension at times; to structure too much can be to problematize too little, and vice versa. The goal of task-embedded scaffolding (i.e., structuring and problematizing) is to channel and focus student attention and action (Pea, 2004). When scaffolded well by problematizing and structuring content, student attention will be focused and channeled throughout the task.

With respect to scaffolding argumentation specifically, various strategies have been attempted, with encouraging results. One strategy is to scaffold students with computer software that can prompt students to attend to data in a specific order or that can arrange, represent, or graph data (Walker & Zeidler, 2007; Zembal-Saul, Munford, Crawford, Friedrichsen, & Land, 2003). Another is to provide students with various prompts or criteria for making their arguments (Jimenez-Aleixandre, 2008).

Design Rationale

Scaffolding students’ argumentation in science can improve their argumentation skills as well as their content learning (Walker & Zeidler, 2007; Zembal-Saul et al., 2003). Analogy and argumentation, when put together, have the potential to yield benefits. Analogy serves as a scaffold for exploring new concepts in rich, mappable contexts. If groups are invited to make an argument by analogy, this work hypothesized, they may be scaffolded and better able to learn content through argumentation. Simple machines can be regarded as natural analogues that lend themselves well to this type of activity.

This project explores the scaffolding of argumentation with analogical-mapping-based comparison activities. Specifically, students in small groups were invited to make an argument by analogy about simple machines that are all, to various extents, analogous in function. This study specifically asked: What does it look like when argumentation and analogy are blended in the study of simple machines? How do comparison and analogical mapping affect communication and learning? What problems do students have? These questions were answered using the method of discourse analysis.

Context

This research took part in a science elective course for preservice teachers at a large research university. The three-hour-per-week course met twice weekly and had the dual aim of teaching science concepts via inquiry and designing inquiry-based activities. This research took place during the 8-week unit on simple machines in which simple machines were offered together as part of guided inquiry activities in a course for preservice elementary teachers to learn the science content, and to learn how to create and teach with guided inquiry lessons. Small groups of students built, used, modified, and made measurements of levers, pulleys, inclined planes, gears, and other simple machines. These activities asked small groups of about four students each to build the machines using Legos®. They were then used to lift something of known weight while students measured and recorded effort force, resistance force, and their corresponding distances. Various quantities could then be calculated. Questions embedded within the activity prompted students to summarize what they had learned about the simple machine under study. Finally, students designed a way to apply a combination of machines to lift a prescribed load. Class discussions, notebooking, and test questions generated reflections on the guided-inquiry, lesson-design principles employed.

Fifty-five students from three sections (14 groups of about four students each) elected to take part in the study, agreeing to be videotaped and have their written work used as data. The instructors were Betsy (two sections) and Mark (one section), both of whom had taught the course or a similar one for about one year prior. They helped to design the specific interventions.

Activity Development

When learning about simple machines, students are often given the chance to use the machines and asked to make measurements of and compare input and output forces and distances (i.e., effort force, resistance force [or load], effort distance, and resistance distance) (e.g., Hewitt, 1999; Roth, 2001). Then, in making, applying, and representing a given simple machine in various configurations (e.g., varied: loads, mechanical advantages) and/or varied simple machines (e.g., a pulley and a lever), students are guided toward a notion of mechanical advantage (as the multiplier through which effort and resistance forces and effort and resistance distances relate) (Hewitt, 1999; Roth, 2001).

The class in which this research took place did this as well. But from past semesters’ experience, even with about 8 weeks to build, use, and compare simple machines, the instructors had observed that students did not see the connections between all simple machines (i.e., all have calculable mechanical advantages, trade distance for force, have effort forces and distances, move a resistance through a distance, are to various degrees analogues to one another, etc.). Since the design of the course repeated not only simple-machine science content (and other science content) but also guided-inquiry lessons, the course allowed for machine–machine and lesson–lesson comparisons. Thus, it was unfortunate that the instructors felt that students were not achieving coherent understanding of the simple-machine content. For example, they were sometimes able to calculate ideal mechanical advantage for one machine but not for another, in spite of the similarities. The synergy hoped for from the repeated use of simple machines was not achieved. To address these concerns, this study focused on the simple-machine content of the course rather than the guided-inquiry pedagogical aspect. By inviting students to make an argument by analogy and to have us scaffold those arguments with an invitation (and training) to compare and map the simple machines as analogues, it was hoped that a more coherent understanding could be developed in which one machine's structure and function could support the students’ learning of other machines.

Activities were created to address this by inviting explicit comparison between simple machines by asking, “Is this (first) simple machine more analogous to this (second) simple machine or more analogous to that (third) simple machine? Why?” Figures 2-4 show actual handouts used for this research. During these activities, groups were asked to make an argument for a better analogue from among two possibilities: “Is science concept X more like possible analogue-concept A or possible analogue-concept B?” They had prior familiarity with two of the three concepts. The third was new to them. Before doing the activity in Figure 3, for example, students had already built, used, and made measurements with the pulley and the first-class lever, but they had not yet used or studied the wheel and axle.

The specific goal of this research was to learn and describe how small groups of students engage in argumentation when they are scaffolded with analogy-based comparison activities. By asking students to make an argument in favor of one simple machine as a best analogue, the simple-machine content was problematized, and by asking students to use analogical mapping to make that argument, it was structured.

The instructors and the principal investigator designed the activities to offer simple-machine juxtapositions that had the power to make important underlying concepts salient and invite student reflection on superficial similarities through the analogical mapping process and subsequent argumentation. For example, consider the shape- and position-based similarities between the lever and the inclined plane in Figure 4. They look similar, as do the wheel-and-axle and pulley in Figure 3. In both cases, however, these are not the best analogues. One must look deeper than shape or orientation. In spite of superficial shape similarities between the pulley and the lever (Figure 3), one looking to analogically map the axis of rotation of the wheel and axis would find a stronger analogue in the lever's fulcrum than anything the pulley might offer. While the pulley might seem to have a fulcrum (or perhaps more than one), these are quite different from those found in the other machines; they do not map well to the first-class lever, as they are not good analogues. Also, the wheel's radius affects the machine's mechanical advantage in a way that is analogous to the length of the effort arm of the lever—as both increase in length, the effort force required to lift is reduced. It was thought that analogical-mapping-based comparison activities such as this have the potential to scaffold this process of looking deeper in a systemic one-by-one way in which elements of one machine are considered in relation to another's.

Implementation

Student groups were trained to do analogical mapping by doing simple analogical-mapping activities (e.g., Figure 1) during the unit on simple machines. The training activities, each lasting about 15 minutes, were done in small groups, and then discussed as a whole class over two class periods. After the training, students in their groups completed, as in past years of the class, inquiry-based labs on simple machines in which they built, used, and made measurements. Interspersed with these, once per week, groups would do an analogical-mapping-based comparison activity, such as those in Figures 2-4, which would introduce a new machine not yet otherwise studied. (See the timeline in Table 1.) These took 30 to 60 minutes. After these activities, the small groups presented posters (roughly the same format as the handouts) with their analogical maps and final arguments to the rest of the class. Then, the whole class would discuss the groups’ arguments and analogical maps and any problems they had doing them.

Data Collection and Analysis

Data were collected during the analogical-mapping-based comparison activities in the form of video and audio recordings, individual students’ written analogical mapping tables, and posters of small groups. From among all 15 groups doing all activities, 48 hours, 38 minutes, and 6 seconds of video data were collected—an average of 43 minutes per group per activity. Because of equipment issues, one group's data were not transcribed for two of the activities. Only the video relevant to the research was transcribed. Side conversations longer than about five utterances and long periods of silence were not transcribed. Teacher comments and directions to the class were transcribed only once (as opposed to on each group's recording). This resulted in 24 hours and 21 minutes of transcripts. Transcripts were made by the principal researcher in StudioCode® and then pasted into Microsoft Excel.

The idea units within “reasoning sequences” (Pontecorvo and Girardet, 1993) were used as the unit of analysis for the transcripts. These are parts of the student argumentation in which “particular epistemic actions (or subactions) are performed” (p. 370) and only one thing is discussed. They last from two utterances (many seconds) to several dozen (several minutes). Within these reasoning sequences, Pontecorvo and Girardet (1993) offer the term “idea units,” which they refer to as “the smallest units in which the discourse is analyzed” (p. 370). An utterance may have zero to several idea units. Reasoning sequences were identified and highlighted in all transcribed data. These were reviewed by two instructors and the principal researcher together over several meetings to determine any patterns that could be labeled with codes. Next, they were shared with, critiqued, and modified by the other authors of this paper. Finally, they were applied to all data and evaluated again by the researchers. Disagreements were resolved through discussion.

The importance of discernment was noted by the researchers after reviewing videos and transcripts for early activities. Discernment for our purposes meant differentiating one thing (in this case one simple-machine element) from another. When it was not present, miscommunications between group members usually resulted. When it was present, communication was less problematic.

Miscommunications Resulting from Insufficient Discernment

The group in the following reasoning sequence had a miscommunication caused by insufficient discernment in an early activity in which they were comparing an inclined plane to a screw. In this case, this group considers a correspondence between the resistance distance of the inclined plane and an analogue element of the screw. By not discerning the differences between “resistance,” “resistance force,” and “resistance distance,” communication about these features was hindered. Even physically pointing to these on the actual machines did not resolve the miscommunication issues, as the excerpt will show. First, however, some explanation is in order. See Figure 5. The upper and lower parts of Figure 5 are positioned similarly to show how they align analogically. (Note: the groups did not receive this labeled diagram.) The length of the screw shaft and the “resistance distance” as labeled on the inclined plane both represent the distance that a load would move up (imagine a block of wood moving up the screw while turning or conversely, the screw moving down into it). The force from friction and the need to split the wood would impart a resistance force on the screw. This means that although the load would travel along a larger distance (along the ramp length labeled “effort distance”) at reduced force, it has really moved much less in terms of useful distance (just the vertical distance from the ground). This vertical distance or height of the inclined plane (or length of the shaft of the screw) can be called “resistance distance.” The word “resistance” itself means essentially the same thing as load.

It is important to point out that the term “resistance distance,” however, is different from the word “resistance.” In the case of the inclined plane, the “resistance” would be the weight of the load at the bottom left. For the screw, the “resistance” would be something into which the screw was being turned—a wall for example. Both these resistances would exert a force on their respective machines, which can be called a “resistance force.” Thus, it is important to distinguish between “resistance,” “resistance distance,” and “resistance force,” as these are different things.

In the reasoning sequence below, group members Serena and Sheri use the word “resistance” to mean “resistance force,” whereas Evan uses it to mean the “resistance distance.” In the transcript, ideas relating to resistance are italicized for emphasis. The group begins talking about the screw:

Serena starts off stating the “resistance is gonna be whatever [the screw is] going into.” This is partially correct. A wall or a board, etc., puts a resistance force on the screw. She and other group members, however, do not discern that “resistance,” what they are saying, is different than “resistance distance” or “resistance force.” Evan follows up with “The shaft would be…”. Although grammatically incomplete, he does bring up the “shaft.” This is appropriate, since the shaft length of the screw corresponds analogically to the resistance distance of the inclined plane.

In this analysis, inferences must be made about some of the meanings intended. However, given the benefits of hindsight, correct scientific understanding, the fact that students seemed convinced of their respective positions, and that student argumentation positions are correct if interpreted in this way, these assumptions are reasonable.

Evan is influential in this argumentation, yet he is unable to hold sway without proper discernment between “resistance” and “resistance distance.” Serena reiterates, “But that's the resistance.” Evan, likely knowing that the shaft length relates to the resistance distance but insufficiently discerning, asks, “Is the shaft not the resistance?” Serena answers, “I don't think so.” Note that he also is insufficiently discerning with the word “shaft.” It is likely that he means “shaft length,” as these would correctly correspond analogically.

Sheri continues, stating, “I think this (she points back and forth along the resistance distance on inclined plane) would be like the shaft.” Unfortunately for Sheri, none of the other group members directed their attention to her physical pointing during her use of deictic language (context-dependent language including pointing; e.g., this, here, that, there). Serena agrees, stating, “Yeah.” Again, this is nearly correct, but it again lacks discernment. Note that Sheri's use of “this” and her pointing along the inclined plane where the resistance distance is, suggest that she is talking about—but not saying—the resistance distance. Sheri's word, “resistance,” is not sufficiently discerning. Had she said that “resistance distance” was like the “shaft length,” this would have been correct and discerning. It is likely, since Sheri referred to “the shaft” of the screw and pointed to the resistance distance of the inclined plane, that she thought she was conveying this correct idea.

During the next few utterances, the opportunity for discernment was provided; however, it did not happen. Evan asks, “Why would that [resistance distance, as Sheri had mentioned] be the shaft?” Sheri states, “I don't know cause it's constant.” This is an unclear response to Evan's question. Evan states, “Yeah but—the only reason thee—the threads are—have to do with the effort distance is cause they're going up the shaft. So, I feel like—the shaft would have to do with this piece [points to resistance distance on inclined plane].” This utterance has two important functions. First, Evan situates the new potential correspondence within another previously agreed upon one (not shown in this reasoning-sequence transcript)—that of the length of the screw thread and the length of the inclined plane (or effort distance). This attempt to give support to the new correspondence might have been effective. Evan even hedges somewhat with his use of a less-than-specific “the shaft would have to do with this piece.” The “would have to do with” suggests the need for further discernment through argumentation. Evan still has not uttered the term resistance distance, though he has pointed along it on the inclined plane, but here again, as with Sheri's earlier use of deictic language, none of the group members direct their eyes to where Evan is pointing. Thus, although communication might have benefited because of it, it does not.

Evan believes the group is talking about resistance distance, or the distance a resistance is moved. Sheri and Serena believe the group is talking about resistance force, the force applied by the resistance, such as a wall. At utterance 00:21:11:29 Evan questions their right to assert that a wall exists when it is not pictured. The argumentation continues on this idea for about 54 seconds (not shown due to space limitations). And finally, the reasoning sequence ends in dissatisfaction when Sheri states, “I don't care what we write. I don't understand this.”

The frustrating ending for the group is unfortunate, especially since there were many assertions that would have been correct had more discernment been used. Nonetheless, given the near correctness of their assertions, it is all but certain that all three members maintained key correct understandings (a fourth member was present and paying attention but did not participate during this reasoning sequence).

This reasoning sequence is representative of a class of such miscommunications caused by insufficient discernment that occurred in every one of the 15 groups. Some were longer. Some were shorter. But the key elements were the same: lack of discernment in communication causes a miscommunication. While doing the same activity, all but four groups had nondiscernment-caused miscommunications nearly the same as the one analyzed here (i.e., dealing with resistance). All groups, however, had at least one miscommunication due to lack of discernment.

Madeleine took “larger” to mean “a thicker screw,” whereas another group member took it to mean longer threads (and thus finer) on the same screw shaft, which would reduce the effort force; and another member took this to mean farther apart (requiring more effort force). The word “larger” is insufficiently discerning. Only four groups (of 15) made this particular correspondence between “threads” and “effort distance” without problem or apparent miscommunication. Nonetheless, these four groups show that some groups did accept an analogical correspondence even with an insufficiently discerning word choice without much apparent difficulty.

These activities and their use of analogical mapping and simple machines easily allowed for and permitted the determination of nondiscernment-based miscommunications. Many aspects of simple machines had similar or closely related terms (e.g., resistance distance and resistance force, effort arm, effort distance, and effort force) that, when combined with nondiscerning word choice, can allow space for miscommunication. This limited space combined with the benefit of hindsight, complete transcripts, and knowledge of correct analogical correspondences, made identification of such miscommunications possible as shown in the previous analysis.

Instruction Toward Discernment: Prompting a Shift

During the activities, the instructors and the principal investigator were walking around the room. From listening to student small-group argumentation and the subsequent whole-class discussions, it became evident that lack of discernment was a problem. In the first activity on simple machines, as mentioned earlier, all groups made a correspondence between the “threads” (instead of “thread length”) of a screw and the “effort length” on their posters. Not even the two groups that were helped by instructors used “thread length” on their posters. Instructors addressed this. For example, after students shared their posters with their analogical maps and arguments with the whole class, the instructors commented that all groups had used the word “threads” when making a correspondence to the “effort distance” (or in some cases just “effort”). They stated on that day that “thread length” would have been more appropriate as “threads” are a concept or idea, whereas “thread length” can be measured. Instructors made similar mentions to individual groups about the need to differentiate between “effort distance” and “effort force” and other related terms during following activities as well.

Reasoning Sequences from Activities Showing Explicit Discernment

In the following section, two reasoning-sequence excerpts of groups showing explicit discernment will be shown and analyzed. In the first reasoning sequence, the group argues about a correspondence between the effort forces in both the lever and the wheel and axle. Although groups had measured and used the concepts they are about to discuss (effort force and effort distance) in earlier lab activities, the concepts remained problematic. The activities, as will be shown, invite the group to discern the difference. The handout for this activity is shown in Figure 2. Interestingly, the term “effort forces” relates to all simple machines in the same way (i.e., the distance over which the hand applies the input force). Nonetheless, the group needed to engage in argumentation to confidently make the connection and locate these on the different machines. The group was able to do this due to the explicit discernment made between “effort force” and “effort distance.”

Beth begins the reasoning sequence by suggesting a relationship between the “hand pulling down” and the “hand pushing down.” (Figure 6 provides a superimposed lever and wheel illustrating the concepts in this reasoning sequence.) She states, “Well.—Let's stick to the lever and the wheel-and-axle—because I think the hand pulling down could be equal to the hand pushing down so maybe the effort. See now what do you call that?” In this last phrase, Beth explicitly directs the group's focus to what they should call “that.” Here again we see the use of deictics in Beth's “that.” The rich context provided by the simple machines comes to the fore. At the beginning of the reasoning sequence, the contextual “that” becomes a seed for further discernment when combined with her question on what to call it. In her utterance, she had also used the word “hand” to center her thoughts on “effort.” Consider the rest of the excerpt given below.

Picking up on Beth's question, Bree offers “Effort force. (2 s) Right?” The next three utterances convey confidence in Bree's assertion. Melissa follows with, “Yeah.” Next, Beth adds, “Wow. Look at you!” Bree then states, “Yeah. I know. Sometimes I get them right.” The “effort force” has been correctly discerned and the term appropriated and the group members know it.

The next few utterances serve to verify the fact that the label applies to both hands, not just one. (The “hands” can be seen in Figure 2.) Beth asks, “What would you call the other one, effort force?” And Bree says, “Yeah. Actually.” Then Beth apparently hedges somewhat; perhaps the words “effort force” might be insufficiently discerning. She says, “I'm just gonna put hand coming down, hand pulling in parentheses.” Bree, in spite of her previous utterance, solicits further verification; “They're both effort forces, right?” Combined with the previous several utterances, perhaps this utterance was made to further convince other group members of the correctness of her idea, or perhaps it was made to refute Beth's need for the additional detail “in parentheses.”

After about 36 seconds of unrelated dialogue, Dory, who had not yet spoken in this reasoning sequence, sought additional discernment in asking, “But is there a difference between effort and effort distance? I think there is.” Melissa responds, “There's effort force and effort distance.” Interestingly, once the discernment between “effort distance” and “effort force” had been offered, Bree seems to question her prior utterances stating, “Yeah. So I don't know which one it is.” It is possible that when she had stated “effort force” in her earlier utterance that she did not realize there was an “effort distance”. Or, maybe she simply did not mentally juxtapose the two. More likely, however, she did not know what exactly was best represented by the hand (see Figure 2). Melissa reaffirms her initial assertion stating, “Well that's effort distance (points along effort distance). Effort force is what—the force that it takes to pull the thing up the effort distance.” This utterance comes full circle in answering the question posed by Beth in the first utterance: what to call it. Melissa offers an important final discernment with deictics (i.e., pointing and using “that's”) between “effort distance,” “effort force,” and just “effort,” the earlier used word, which is unclear.

The comparison activity and related instruction scaffolded the students’ discourse toward the discernment of a definition for effort force in context as can be seen in this reasoning sequence. First, Beth began the sequence using context-specific language and the word “hand” in an attempted correspondence that suggested that these might relate to “effort.” She then asked for more discernment around the word “effort.” Bree then offered “effort force.” Dory explicitly next asked the group to discern between “effort” and “effort distance.” Melissa offered further discernment to Dory's “effort,” stating there's “effort force” and “effort distance.” Finally, Melissa offers a clearly discerned and pointed out definition of both “effort force” and “effort distance.”

The analogical-mapping-based-comparison activities created a need for discernment and a context within which it could take place. Both simple machines offered a perspective from which to view “effort force” (and “effort distance”). In addition, the coconstructions made possible between group members allow for easy changes back-and-forth between those two perspectives.

A Second Example of Discernment

The next excerpt, from Haley, Nathan, Audrey, and Jenn, shows another example of explicit discernment. The group is engaged in argumentation on the same activity (Figure 2) as the group in the previous excerpt. They are attempting to find simple-machine element correspondences between the lever and the wheel and axle.

Audrey begins by asking, “The fulcrum and—the—the thing–isn't that the same as the (points to wheel-and-axle) pivot point. Not pivot point. The center of the thinger.” Consider the transcript below.

Audrey's utterance serves two functions. First, she introduces a possible correspondence between the lever's fulcrum and the wheel. Next, she questions her own use of “pivot point” as an acceptable term to make a correspondence to the lever's fulcrum. The word “thinger” combined with deictic pointing also promoted the need for discernment early in the reasoning sequence. This questioning makes it acceptable to the rest of the group to engage in discernment around finding a better term. Her questioning of the term also allows her to save face should a better term emerge from further argumentation. Haley agrees, stating, “Yeah.” Audrey tries to clarify with, “Wheel and axle.” It is not apparent whether this was a question or a statement.

With Haley's “So the fulcrum—Should we just call it that the thinger? (laughs),” the dialogue next turns explicitly toward discernment. Clearly, “the thinger” is insufficiently specific to correspond with the fulcrum. Audrey states, “There has to be a smarter word for that. Center thingy. Come on Nate. We need your big words here.” The contiguous reasoning sequence ends here. The group did, however, take up the matter in a follow-up reasoning sequence when attempting to write final choices on poster paper for sharing approximately 25 minutes later, offering a final two utterances. Haley states, “OK. The fulcrum and the center are the same because…” to which Audrey responds, “because that's like the pivot point of the… machine.” The simple machine element in question would best be called the axis of rotation. The members of the group likely had heard this term at some point before. Regardless, their definition was exact and well discerned, pointed out, and referred clearly to the axis of rotation in spite of the use of different words.

Although the argumentation in the end yielded a product much like the one in the first utterance, the “center” of the wheel and axle or the “pivot point” of the wheel and axle are specific and unique enough to not be confused with any other element. Therefore, it is considered that discernment took place between the words “thinger,” “pivot point,” and “center.” And although “pivot point” ultimately was adopted, the other terms, as well as the physical pointing, added to the communication and discernment process.