The Representation of Space in Mental Models derived from Text

Abstract

The Representation of Space in Mental Models derived from Text

In the experiments that follow we will investigate properties of spatial mental models to answer some of the questions posed above. In brief, we demonstrate that spatial mental models are unlikely to be Euclidean. The experiments are based on three assumptions: 1) Readers will form a mental model when reading a spatial text; 2) This mental model has analogical properties (such that increasing distance in the model is similar to increasing distance in a real environment); and 3) When items are spatially close in the model, readers will encode this relationship. The first two assumptions are shared by most researchers who investigate text comprehension. The third assumption, called the "noticing" hypothesis, is based on the conclusions of Glenberg and Langston (1992). We will discuss empirical support for each of these assumptions below.

Assumption One: Representation in Mental Models

Assumption Two: Mental Models are Constructed in an Analogical Spatial Medium

Denis and Cocude (1989, 1992) demonstrated that scanning a representation of an island produces similar results whether the scan is controlled by a mental representation formed from a linguistic description, a mental representation formed from observing a map, or a physical representation, that is, the map itself. Denis, Gonçlaves, and Memmi (1995) conclude that "These data support the claim that images generated from verbal descriptions can have metric properties..." Finally, Glenberg, Meyer, and Lindem (1987) showed effects of spatial distance between a protagonist and a critical object. In these experiments the critical object (such as "sweatshirt") was described as spatially close to the protagonist in the associated condition, as in "After doing a few warm-up exercises, [John] put on his sweatshirt and went jogging." In the dissociated condition, the critical object and the protagonist were described as spatially separated, as in "After doing a few warm-up exercises, [John] took off his sweatshirt and went jogging." Accessibility of the critical object (e.g., sweatshirt) was assessed after reading another sentence in which John was foregrounded but sweatshirt never mentioned. Accessibility of "sweatshirt" was found to be greater in the spatially close, associated condition than in the spatially separated, dissociated condition.
A frequent interpretation of these findings is that readers construct analog spatial mental models to understand what they are reading, and that these models have properties of Euclidean space: all dimensions are equivalent to one another and there is no intrinsic structure. Thus, degree of spatial relationship between two elements (such as the protagonist and the critical object in Glenberg et al., 1987) is solely a function of Euclidean distance. We will show that this interpretation is unlikely to be correct. Note, however, that ruling out a Euclidean form of mental representation for text does not imply that mental representation of spatial information must be propositional (i.e., not analog). It is possible to have representations that are analog, but not Euclidean. We expand on these ideas in the General Discussion.

Assumption Three: The Noticing Hypothesis

Glenberg and Langston used their results to develop the noticing hypothesis, which sets the stage for the experiments described here. The noticing hypothesis provides one explanation for why forming mental models enhances comprehension: the spatial medium in which the model is constructed supports a type of inference making called noticing. The hypothesis is based on the assumptions that a) mental models are constructed in a spatial medium, such as the limited-capacity visuo-spatial scratchpad identified by Baddeley (1986); b) text-relevant dimensions (e.g. time) can be assigned to spatial dimensions, although the assignment may require expertise in a domain or visual support such as that provided by a diagram; c) text-relevant concepts (e.g., steps in a procedure) are represented by pointers arrayed within the medium and each pointer is associated with information about the concept in memory. Furthermore, the spatial distances between pointers is cognitively meaningful. That is, pointers that are spatially close in working memory represent concepts that are more closely (or strongly) related along the text-relevant dimension assigned to the spatial dimension. d) Mental models are updated by introducing new pointers or rearranging existing pointers to reflect the situation described by the text. e) When an existing pointer is moved, or when a new pointer is introduced into the model, that pointer is attended, and any pointer within the "spotlight" of attention is noticed. "Noticing" means that the relation between the pointers is specifically encoded and added to the associated information in memory. The operation of this noticing process was formalized in a computer simulation described by Glenberg et al. (1994).

We found the noticing hypothesis appealing for several reasons. First, it provides one reason why forming a mental model facilitates comprehension: The mental model allows for a type of inference making (noticing on the basis of spatial contiguity) not easily available to a propositional system. Second, unlike many schemes for inference generation, noticing is highly constrained: It only occurs along text-relevant dimensions assigned to spatial dimensions; it is constrained by the capacity limits of working memory; it occurs only during updating a mental model and then only between spatially close pointers. Third, the simulation model bears at least a family resemblance to models developed by Johnson-Laird (e.g., Johnson-Laird, Byrne, and Tabossi, 1989) to account for reasoning using mental models. Fourth, Glenberg et al. (1994) show how a simulation model incorporating noticing can account for much of the data reviewed above. Finally, the noticing hypothesis is implied by many of the theoretical claims about the operation of spatial mental models (e.g., Denis and Cocude, 1992; Rinck and Bower, 1995). As documented above, hypotheses that assume a Euclidean medium for mental models assume that distance within the medium has functional consequences; items that are farther apart are less likely to interact.

The seven experiments reported here were designed to test the noticing hypothesis. The basic logic was to have participants read (or listen to) a text describing a spatial layout. An example text appears in Table 1. Each text described the relations between some objects explicitly, whereas the spatial relations between other objects were left implicit. A speeded recognition task (Experiments 1-4) or a sentence reading task (Experiments 5-7) were used to assess the accessibility of the items in the layout. The primary manipulation was the distance (in the described spatial layout, not the text) between the probe item and another most recently mentioned item. The most recently mentioned item is an item that is described in the text immediately before the probe is presented. In Table 1, "seaweed" is the most recently mentioned item. Sometimes the most recently mentioned item was near to the probe in the spatial layout (notice condition), and sometimes it was far from the probe (not-notice condition). Importantly, the spatial distance between the probe and the most recently mentioned item was never described explicitly. Instead, the relation between the most recently mentioned item and some other object (the "big rock" in Table 1) controlled the relation between the probe and the most recently mentioned item. In the notice condition, when the most recently mentioned item is near to the probe (in the spatial layout, and hence in the putative spatial model), more noticing of the probe should occur than when the two objects are separated from one another, as in the not-notice condition. We assessed the degree of noticing by measuring the accessibility of the probe soon after the most recently mentioned item was introduced by the text.

Table 1: Sample Texts From Experiments 1 and 2
_____________________________________________________________
4-Item Notice version from Experiment 1

Sam was setting up his fish aquarium decorations.
Sam put the castle down first.
Next, he put the plastic diver right of the castle.
Then Sam put the big rock under the plastic diver.
Then Sam put the seaweed left of the big rock.
{Probe: castle}
Next, he put the treasure chest left of the seaweed.
Finally, Sam put the sunken boat over the treasure chest.
When Sam put the fish in, it was scared by all of the stuff.

4-Item Not-Notice version from Experiment 1

Sam was setting up his fish aquarium decorations.
Sam put the castle down first.
Next, he put the plastic diver right of the castle.
Then Sam put the big rock under the plastic diver.
Then Sam put the seaweed right of the big rock.
{Probe: castle}
Next, he put the treasure chest left of the seaweed.
Finally, Sam put the sunken boat over the treasure chest.
When Sam put the fish in, it was scared by all of the stuff.

4-Item Far Notice version from Experiment 2

Sam was setting up his fish aquarium decorations.
Sam put the castle down first.
Next, he put the plastic diver way right of the castle.
Then Sam put the big rock under the plastic diver.
Then Sam put the seaweed way left of the big rock.
{Probe: castle}
Next, he put the treasure chest left of the seaweed.
Finally, Sam put the sunken boat over the treasure chest.
_____________________________________________________________

Table 2 summarizes the results of the seven experiments, and it provides a guide to the detailed exposition that follows. The two dependent variables that we used are listed in the DV column. One dependent variable was speeded recognition, the time to recognize the probe word as an item that occurred in the text. The probe word occurred immediately after the most recently mentioned item. Speeded recognition is a commonly used measure of accessibility that is sensitive to spatial relations (e.g., Glenberg et al., 1987; de Vega, 1995; see also Experiment 4 for a specific test of sensitivity). The other dependent variable was time to read an about sentence. The about sentence followed the most recently mentioned item, and the sentence referred to the target item. Hence the time to read the sentence included the time needed to make an anaphoric reference to the target item. Sentence reading time is a common measure of accessibility of the referents of anaphors that also appears to be sensitive to spatial relations (e.g., Rinck & Bower, 1995). Most of the experiments used visual presentation of the text (as indicated in the Modality column of Table 2), but we also report one experiment (Experiment 3) that used auditory presentation. The next column (Item/Dim) indicates the item number of the most recently mentioned item. Thus, across the experiments, the spatial layout of 3, 4, or 6 items was described before accessibility of the target item was assessed. The number following the slash mark indicates whether the spatial layout was in one or two dimensions¹. In most of the experiments, the distance in the spatial layout between the most recently mentioned item and the target item was confounded with number of intervening items (in the arrangement). That is, no items intervened in the notice condition, and several items might intervene in the not-notice condition. This confound was removed in those conditions labeled "far" in Table 2. For those comparisons, we computed the noticing effect as the difference between the notice-far and the far conditions (see Experiment 2). In those conditions, the spatial distance (in the layout) between the target and the most recently mentioned item was manipulated without intervening items. The column labeled "Picture" indicates whether the verbal description of the layout was accompanied by a picture illustrating the layout of the first three items. The "unlabeled" picture condition in Experiment 2 illustrated the layout using tokens (boxes), but did not label the tokens with the item names.

Table 2: Summary of the Experiments

					Noticec	t medd	t mede	tzf	tzg
Exp	DVa	Modality	Item/Dimb	Picture	Effect	Standard	Loose	Standard	Loose
1	Recognition	visual	4/2	no	21.7	1.33 (41)	1.20 (41)	.72 (36)	.32 (41)
			4/2	yes	17.3	-.29 (38)	.75 (39)	.11 (36)	.61 (39)
			6/2	no	6.7	-.45 (41)	.28 (41)	-.32 (36)	.74 (41)
			6/2	yes	28.0	.66 (38)	1.51 (39)	.65 (36)	.97 (39)
2	Recognition	visual	4/2	no	-21.1	-.61 (27)	-.99 (29)	.37 (9)	.57 (29)
			4/2	yes	10.8	2.11 (27)	.53 (29)	1.22 (17)	1.88 (27)
			4/2	unlabeled	30.0	.04 (27)	1.13 (27)	.41 (17)	.89 (27)
			4/2 (far)	no	-23.3	.80 (27)	-1.09 (29)	.16 (9)	-1.32 (29)
			4/2 (far)	yes	-0.4	-1.03 (27)	-.02 (29)	.35 (17)	.27 (27)
			4/2 (far)	unlabeled	-14.4	.13 (27)	-.68 (27)	.61 (17)	-1.17 (27)
			6/2	no	54.4	3.00 (27)	1.35 (29)	.98 (9)	2.43 (29)
			6/2	yes	19.9	-.65 (27)	.67 (29)	-.44 (17)	-.64 (27)
			6/2	unlabeled	-45.7	-.76 (27)	-1.67 (27)	-1.18 (17)	-1.21 (27)
			6/2 (far)	no	4.3	-.14 (27)	.15 (29)	.57 (9)	-.35 (29)
			6/2 (far)	yes	-11.5	-.84 (27)	-.42 (29)	-1.18 (17)	.49 (27)
			6/2 (far)	unlabeled	-54.4	-1.26 (27)	-1.44 (27)	-1.07 (17)	-2.11 (27)
3	Recognition	visual	4/2	no	7.3	.60 (17)	.23 (17)	.60 (17)	.13 (17)
		visual	4/2	yes	36.1	.43 (17)	.92 (17)	-.08 (17)	-.09 (17)
		auditory	4/2	no	-47.3	-.34 (17)	-.23 (17)	-.48 (17)	-.51 (17)
		auditory	4/2	yes	45.4	.97 (17)	.67 (17)	-.19 (16)	-1.12 (16)
4h	Recognition	visual	3/1	no	-11.7		-.36 (22)		-1.10 (22)
5	Reading	visual	4/2	no	1.8	1.09 (45)	.03 (50)	.72 (45)	1.26 (50)
6i	Reading	visual	4/2	no	36.9	.13 (36)	.65 (39)	.21 (36)	1.29 (39)
7j	Reading	visual	3/1k	no	50.4	.72 (37)		1.18 (37)
			3/1l	no	34.9	.42 (37)		1.57 (37)

^aDependent variable, either speeded recognition of a probe (Recognition) or time to read an about sentence (Reading).
^bNumber of items before the probe or about sentence, and the number of spatial dimensions required to arrange the items. "Far" indicates that the noticing effect was computed as the difference between the notice and far conditions (see description of Experiment 2 for details).
^cDifference between medians (in msec) for the not-notice and notice conditions in the loose analysis
^dValue of the t statistic (and sample size) for the medians in the standard analysis
^eValue of the t statistic (and sample size) for the medians in the loose analysis
^fValue of the t statistic (and sample size) for the z-scores in the standard analysis
^gValue of the t statistic (and sample size) for the z-scores in the loose analysis
^hData are collapsed across items 1 and 2; because there was no comprehension question, the standard analysis could not be performed.
ⁱData are from the condition in which the target was item 1
^jBecause correct responding was forced, there is no distinction between standard and loose
^kData are from the condition in which the frame is on item 2
^lData are from the condition in which the frame is on item 3

One index of the noticing effect is the difference between the median value of the dependent variable in the not-notice condition and the median value of the dependent variable in the notice condition. The noticing hypothesis predicts a positive difference. This index is provided in the column labeled "Notice Effect." The final four columns present statistical assessments of the generalizability of the notice effect. A noticing effect that is significantly different from zero is italicized. The first two columns report the value of the paired t-statistic comparing the medians. The Standard analysis eliminated individual observations if a) response to the probe was incorrect, or b) response to a comprehension question presented after the text was incorrect. The Loose analysis eliminated observations according to condition a, but not condition b. Thus, the medians computed in the Loose analysis are based on more observations. Bush, Hess, and Wolford (1993) have demonstrated that comparisons based on medians may not be statistically powerful. Hence, we also include two analyses (Standard and Loose) based on a set of transformations that Bush et al. found to be the most powerful without sacrificing protection against Type 1 errors. The transformations are intended to achieve power by a) elimination of outliers by removing the longest and the shortest observations in each condition for each participant and then using means rather than medians, b) normalization of skewed reaction time distributions by using the logarithm of the speeded recognition or reading times, and c) elimination of between-subject variability in the size of the effect by using z-scores computed for each participant. Thus, after elimination of outliers, the individual observations were converted into logarithms. Next, a single mean and standard deviation was computed for all of a given participant's scores (regardless of condition), and the participant's mean and standard deviation were used to compute z-scores for all of the observations. Finally, a mean z-score was computed for each participant in each condition. The mean of these mean z-scores will always equal zero (so that there is no between-subject variability), but within-subject differences among conditions are still preserved. The last two columns in Table 2 present the results of the dependent sample t-test comparing the mean z-scores of the notice and not-notice conditions. For each analysis, the number of participants entering into the analysis is noted in parentheses.

Thus, over the course of the seven experiments we manipulated several independent variables that should have directly affected the amount of noticing. The size of the noticing effect was sometimes substantial, but it was never consistently statistically significant. Although the direction of the noticing effect was often that predicted by the noticing hypothesis (positive), we believe that this should be discounted for several reasons. First, the effect was rarely statistically significant, and it was sometimes significantly reversed. Second, as we will describe more fully in the discussion of Experiment 6, there is reason to believe that many of the small positive effects in Table 2 are due to a subtle confound: the layouts in the not-notice condition tend to be a bit more complicated than the layouts in the notice condition, leading to longer responding in the not-notice condition. Third, an analysis of variance of the Loose z-scores using Experiment as an independent variable indicated that the variation in the size of the notice effect across experiments is not reliable, F(6, 371) = 1.14, MSE = .32. Fourth, although statistical power is modest in any individual experiment, the power over the set of experiments is very high. Based on the Loose z-score analysis, the power to detect a small effect of 0.2 standard deviations is .97. The power to detect an effect as small as .14 standard deviations is .80. In fact, however, over all of the data (when the number of items is 3 or 4), the mean Loose z-score noticing effect is .04, the standard error is .03, and t(387) = 1.25 is not significant. Thus, if there is a noticing effect, it is likely to be very small. Our conclusion is that spatial mental models do not support noticing, and hence they are not likely to be Euclidean.

Experiment 1

Two manipulations were used to encourage participants to form a spatial model of the layouts. First, half of the participants read the texts accompanied by pictures that illustrated part of the spatial layout. The reasoning was that the pictures might serve as a frame to guide participants' spatial representations (Glenberg & Langston, 1992). Stronger noticing effects were expected in the with-picture condition than in the no-picture condition. Also, all participants performed a diagram verification task. After reading each text, participants were presented with a diagram of the layout of the items, and their task was to verify whether or not the diagram portrayed the same layout as described in the text. This task was used to encourage participants to attend to the spatial aspects of the texts.

Glenberg and Langston (1992) assumed that spatial mental models are constructed using the spatial component of working memory. To test this assumption, an additional manipulation was included: size of the putative mental model at the time of the probe. For half of the texts, participants were probed after the fourth item was added to the layout (but the text then continued with a description of the other two items). For the other half, participants were probed after the sixth item. We reasoned that participants are likely to have enough capacity to represent four items, but that six items would be likely to exceed this capacity. So, we expected to find a larger noticing effect in the four-item condition (because the target item should still be represented in the model when the probe is presented) than in the six-item condition.

Method

Participants

Materials

Each text described an arrangement of six items. Sample texts are presented in Table 1. Associated with each text was a seventh item that could plausibly be a part of the arrangement in the text, and this item was used when the correct answer to the speeded recognition probe was "no, this item was not mentioned in the text."

For with-picture participants, the texts were accompanied by a picture depicting the spatial arrangement of the first three items in the text (the entire arrangement was never illustrated). For the sentence describing the first item, the picture was a box surrounding the name of the first item. When the sentences describing the second and third items were presented, the picture was updated by adding boxes appropriately located relative to the first box. The picture remained on the screen, with no further changes, while additional items were described. The picture was not visible when the probe appeared. Thus, although the picture could aid memory, in two ways it forces noticing to be based on a cognitive model. First, the critical most recently mentioned item (fourth or sixth item) was not displayed in the picture. Second, the picture was not visible when the probe appeared.

Participants also verified a diagram after each text. The diagram was composed of six boxes arranged on the screen with the names of the six items written in the boxes. Half of the time these diagrams corresponded to the layout described by the text. When the diagram did not match the description in the text, the same spatial layout was used, but two items were chosen at random and their locations in the diagram were switched.

The 48 experimental texts were randomly ordered to begin the experiment (the same three texts were always used for practice). The texts were then randomly assigned to one of the conditions. Conditions were assigned such that in each block of six texts there was one text from each of the critical conditions plus two filler texts. These six conditions were randomly ordered in each block, and there were a total of eight blocks.

For filler texts, the probe was either the name of a seventh item (which did not appear in the text), or it was the name of some item in the text other than the first. Approximately two thirds of the filler texts used the seventh item as the probe (because all of the critical texts required a "yes" response, the majority of the fillers required a "no" response to provide some balance). The remaining one third of the filler texts used an item other than the first as the probe. Probes in the filler texts could appear after any sentence except those describing the fourth and sixth items (to break up the pattern of always probing after these sentences).

Design

Procedure

Texts were presented to the participant one sentence at a time. Participants were instructed to imagine the layout on the table in front of them. At a predetermined point during the presentation of the text, a single word (or very short phrase) probe appeared on the screen with three asterisks on either side of it. Participants answered "yes" or "no" to the question "was this word or phrase in the text you're currently reading?" participants were instructed to respond to these probes as quickly as possible without making errors. Affirmative responses were made with the participant's dominant hand.

For critical texts, the probe word was always the first item in the text. For 4-item texts, the probe appeared immediately after participants read the sentence describing the placement of the fourth item. These texts continued after the probe with the placement of the fifth and sixth items. For 6-item texts, the probe appeared immediately after participants read the sentence describing placement of the sixth item. After the entire text was presented, participants verified whether the arrangement of items in a diagram matched the arrangement in the text.

Results

As the results of these four analyses were very similar for all of the experiments, we have elected to report in the text only the results from the loose medians analysis. We chose this analysis because it discarded few observations and because median reaction times are easier to interpret than z-scores. Nonetheless, the critical notice versus not-notice comparisons from the other analyses are reported in Table 2. For all analyses, the significance level was set at 0.05.

The data were analyzed using a three-way analysis of variance. The noticing hypothesis predicts a main effect for noticing: Participants should respond faster in the notice condition than in the not-notice condition. This main effect was not significant, F(1,78) = 3.06, MSE = 8883, although participants did respond faster in the notice condition (M = 1008 msec) than in the not-notice condition (M = 1026 msec). None of the other main effects or interactions was significant.

A second analysis was conducted using percent correct on the probe as the dependent variable. In this analysis, none of the main effects or interactions was significant. Overall accuracy was 93%.

A final analysis used performance on the diagram verification task as the dependent variable. In this analysis, the main effect for size was significant, F(1,78) = 28.38, MSE = 0.03. participants were more accurate in the four-item condition (M = 78%) than in the six-item condition (M = 68%). The interaction between picture and notice was marginally significant (p<.06), F(1,78) = 3.82, MSE = 0.02. No-picture participants responded approximately equally accurately in the notice and not-notice conditions, whereas with-picture participants responded more accurately in the notice condition than in the not-notice condition.

Discussion

Nonetheless, there was a hint (given the direction of the difference between notice and not-notice) that a noticing effect was present. One possibility is that noticing does take place, but that the distance manipulation in the first experiment was too weak. It might be that in both conditions, notice and not-notice, the two objects were either too close together or too far apart for a noticing effect to be detected. The plan for Experiment 2 was to refine the distance manipulation to better cover the range of distances between the most recently mentioned item and the target item.

Experiment 2

The third distance was the far condition. Texts in this condition described a layout with a gap, but in this case the gap separated the most recently mentioned item and the target item. For this condition, the target item and the most recently mentioned item were not adjacent (in the layout), but there were no intervening items between them. The fourth distance was equivalent to the not-notice condition of Experiment 1: The target and most recently mentioned items were not adjacent, and there were intervening items between them. The fifth distance was the not-notice-far condition. For this condition, the most recently mentioned item was not adjacent to the target item, there were intervening items between them, and there was a gap in the arrangement.

We were also a bit worried that the picture condition used in Experiment 1 may have been misleading or confusing. That is, the pictures used boxes surrounding the names of the items, rather than analog representations of the items. Perhaps the participants were confusing the boxes with the items themselves. To try to alleviate this problem, we added a third picture condition that used unlabeled boxes. We hoped that participants would treat the boxes as simple spatial markers, rather than the objects themselves.

Method

Participants

Materials and Procedure

Design

Results

The main effect for picture was significant, F(2,82) = 5.36, MSE = 392815. participants responded faster in the with-picture (M = 912 msec) and unlabeled-picture (M = 954 msec) conditions than in the no-picture condition (M = 1078 msec). The main effect for size was significant, F(1,82) = 13.55, MSE = 17056. participants responded faster when the probe occurred after four items (M = 965 msec) than six items (M = 998 msec). None of the interactions was significant.

A second analysis was conducted using percent correct on the probe as the dependent measure. In this analysis the main effect for size was significant, F(1,82) = 9.00, MSE = 0.013. participants responded more accurately in the 4-item condition (M = 90%) than in the 6-item condition (M = 88%). The interaction between size and distance was also significant, F(4,328) = 2.41, MSE = 0.010. For the 4-item conditions participants were approximately equally accurate at all five distances, but in the 6-item conditions participants were more accurate in the far, not-notice, and not-notice-far conditions than in the notice and notice-far conditions. None of the other main effects or interactions was significant.

A final analysis used performance on the diagram verification task as the dependent variable. In this analysis, none of the main effects or interactions was significant. Overall accuracy on the diagram verification task was 65%.

Discussion

Experiment 3

Method

Participants

Materials and Procedure

Texts were presented to the participants one sentence at a time. In the auditory condition, the texts were played through the Macintosh's internal speaker. The presentation rate in the visual condition was set to approximate the presentation rate in the auditory condition. For both conditions, probe words appeared on the screen.

Design

Results

A second analysis was conducted using percent correct on the probe as the dependent variable. In this analysis, none of the main effects or interactions was significant. Overall accuracy was 93%.

A final analysis used performance on the diagram verification task as the dependent measure. In this analysis, the main effect for picture was significant, F(1,64) = 10.92, MSE = 0.03. Participants were more accurate in the with-picture condition (M = 85%) than in the no-picture condition (M = 75%). The main effect for modality was also significant, F(1,64) = 25.58, MSE = 0.03. Participants were more accurate in the auditory condition (M = 88%) than in the visual condition (M = 72%). The main effect for notice was also significant, F(1,64) = 7.08, MSE = 0.01. Participants were more accurate in the not-notice condition (M = 82%) than in the notice condition (M = 77%). The interaction between picture and modality was marginally significant, F (1,64) = 3.81, MSE = 0.03, p = .06. Participants in the with- and no-picture conditions were more accurate with auditory presentation than visual presentation, but the effect was more pronounced for participants in the no-picture condition. None of the other interactions was significant.

Discussion

Experiment 4

Table 3: Sample text from Experiment 4
___________________________________________________________
Text
Alan was arranging some modes of transportation according to how comfortable they seem to him.
Alan started with trains.
Then way in front of trains Alan placed planes because they seem more comfortable.
Then immediately in back of planes Alan placed cars because they seem less comfortable.
Probes
Notice: trains
End: planes
Item 3: cars
"No": buses
Verification sentences
trains seem more comfortable than planes (F)
trains seem more comfortable than cars (F)
planes seem more comfortable than cars (T)
planes seem more comfortable than trains (T)
cars seem more comfortable than trains (T)
cars seem more comfortable than planes (F)
___________________________________________________________

Experiment 4 was designed to address these objections. All of the texts described arrangements of three items. An example is given in Table 3. To correct the first problem, half of the notice and not-notice probes were item one and half of the notice and not-notice probes were item two. Item three was also used as the probe item with the same frequency as items one and two to eliminate any potential focusing strategy that might be employed by the participants. However, data from the item three probes did not enter into the analyses. To correct the second problem, there were an equal number of "yes" and "no" probes.

To correct the third problem, we used a set of "spatial" probes² to demonstrate that the item recognition probes are tapping into a spatial representation. From the participant's point of view, these spatial probes were identical to the notice and not-notice probes; that is, the spatial probes were item recognition probes. Half of the spatial probes involved an item at an end of the dimension and half of the spatial probes involved an item in the middle of the dimension. Note that "end of the dimension" refers to the dimension formed by comprehension, that is, a dimension in a spatial representation, and it does not correspond to the literal order of mention. Items one and two were used as the spatial probes equally often. If there is a difference between response times to items from the end of the dimension and items in the middle, this would indicate that the item recognition task is sensitive to spatial location. If there is an effect of spatial location in the absence of a noticing effect, this would indicate that the lack of a noticing effect is not due to insensitivity of the item recognition probe to spatial representations.

Experiments 1-3 demonstrated that readers formed spatial models with a diagram verification task. To demonstrate that readers are forming a spatial representation for Experiment 4, we replaced the diagram verification task with a symbolic distance task. The symbolic distance effect is that when items are arranged along a dimension (the dimension is "comfort" for the example in Table 3), judgments about pairs of items that are near on the dimension take longer than judgments about pairs of items that are far apart on the dimension (Potts, 1972; Moyer, 1973). For the text in Table 3, participants should verify "planes seem more comfortable than trains" faster than "planes seem more comfortable than cars" since planes and trains are farther apart on the dimension of comfort. If participants in this experiment are forming an appropriate representation of the spatial arrangement of the items in the text, then we ought to get a symbolic distance effect. Note, again, that because the order in which the items are described in the text is different from their order on the dimension, correct performance on the symbolic distance task requires forming the appropriate spatial ordering.

The design of the experiment is not ideal for examining the symbolic distance effect. The problem is that there is a confounding of "distance" between items on the dimension and whether the items are on the ends of the dimension. This confounding is not a problem here, however, because whether the symbolic distance effect is due to end items or distance is irrelevant. In either case, observing the effect is sufficient to conclude that readers were constructing the appropriate spatial representation because both "end item" and "distance" are defined in terms of the constructed representation, not the order of occurrence of the items in the text.

Method

Participants

Materials

Each text described an arrangement of three items. Item one and item two probes were either notice, not-notice, spatial-end or spatial-middle probes. There are two features to note about these texts. First, the relation between the last mentioned item (item three) and the target is always implicit, rather than given directly in the text. Thus we can ask if accessibility of the target varies with its spatial proximity to the last mentioned item. Second, the locution "way in front of" or "way behind" was used in every text to describe the relation between the first and second items. This was done to leave room (in a spatial layout) for the possible insertion of the object named by the third item. Because the results from Experiment 2 indicated that near versus far in a spatial model (with no intervening items) had little effect on noticing, we were not concerned by the introduction of this locution.

After each text, participants responded to six true/false symbolic distance questions. Each question was a statement about the relative positions of a pair of items from the text on the dimension. Sample questions are presented in Table 3. The six questions contained all possible combinations of the three items in the text, and the order of the questions was randomized independently for each text for each participant. For half of the questions the correct response was "true" and for half of the questions the correct response was "false".

Design

Procedure

Results

If participants are forming a lasting representation of the spatial arrangement, then we ought to see a symbolic distance effect. In particular, participants ought to respond faster to sentences containing pairs of items that are far on the dimension than to sentences containing pairs of items that are near on the dimension. This effect was significant, t(21) = 6.17, SEM = 44.93. The mean for far sentences was 1294 msec, and the mean for near sentences was 1572 msec. These data indicate that participants are forming an appropriate representation of the arrangements described in the texts. An analysis of accuracy data from the symbolic distance questions also showed an effect for distance, t(21) = -3.91, SEM = 0.011. participants were more accurate in the far condition (M = 89%) than in the near condition (M = 85%).

The third analysis investigated the noticing effect. The data were analyzed using a two-way ANOVA³ with notice condition and item (the target item was item 1 or 2) as the factors. If the noticing hypothesis were correct, we would expect participants to respond faster to notice probes than to not-notice probes. This main effect was not significant, F(1,21) = 0.28, MSE = 18782, although participants did respond a bit faster in the notice condition (M = 1074 msec) than in the not-notice condition (M = 1090 msec). The main effect for item and the interaction were not significant. An analysis of the accuracy data showed no main effects or interactions. Overall accuracy was 95%.

Discussion

One component of these data seems a bit unusual. For the spatial probes, responding was faster for items in the middle of the ordering than for items on the ends. The expectation of an advantage for end items arises, in part, from work on the symbolic distance effect: Symbolic distance comparisons involving end items are fast. However, the spatial probes did not involve comparisons, only access. To our knowledge, there is no data demonstrating faster access to end items using a recognition probe. Faster responding to middle items is consistent with a spatial representation if it is assumed that participants are focusing on the middle items in a spatial representation (perhaps looking at them with the mind's eye) in an attempt to keep all items equally available.

Experiment 5

Table 4: Sample notice text from Experiment 5
_____________________________________________________________
Kelly was arranging things on her night table.
She put the book down first.
Then she put the jewelry box to the right of the book.
Next, Kelly put the alarm clock in front of the jewelry box.
Then she put the photograph to the left of the alarm clock.
The book was a gift.
Finally, Kelly moved the book in front of the alarm clock.
Comprehension Question
How was the book obtained?
_____________________________________________________________

Following the about sentence was a move sentence. It described how the protagonist moved one of the previously located items (the target item for the critical texts) to a new location. The move sentence was included to ensure that participants were building a mental model that was capable of being updated, rather than a static representation.

Method

Participants

Materials

Design

Procedure

After reading the text, participants answered the diagram verification question. The diagram verification task was in a multiple choice format. Four layouts for the items in the text were displayed, and the participant selected the one that correctly represented the layout after the move sentence. Participants used the keyboard to type their answers to the comprehension question.

Results

A second analysis was performed using percent correct on the diagram selection task as the dependent variable. The difference between the percent correct for the two conditions was significant, t(49) = 4.94, SEM = 0.03. participants were more accurate in the notice condition (M = .75) than in the not-notice condition (M = .59). Might the degree of noticing be related to individual differences? In several of the earlier experiments we investigated whether noticing was correlated with individual differences in comprehension or individual differences in spatial memory capacity. We did not report this work for the earlier experiments because we did not find any significant relations that replicated across experiments. We take up the question again here, in part because it provides a major motivation for the next experiment. We reasoned as follows. Noticing presupposes that people are building mental models and comprehending the texts. In fact, if individuals are not attempting to comprehend the spatial layouts, it is unlikely that they would show a noticing effect. Thus, we predicted a positive correlation between size of the noticing effect and performance on the diagram selection task. The correlation was not significant, however, r (48) = 0.14.

Discussion

Experiment 6

Method

Participants

Materials and Procedure

Design

Results

A second analysis was performed using percent correct on the diagram selection task as the dependent variable. The main effect for noticing was significant, F(1,76) = 14.58, MSE = 0.02. participants were more accurate in the notice condition (M = .74) than in the not-notice condition (M = .65). No other main effects or interactions were significant.

Correlations between the size of the noticing effect and performance on the diagram selection task were computed separately for target-item-one and target-item-two conditions. They were -.11 and -.04, respectively, and neither was statistically significant.

Discussion

Experiment 7⁴

Table 5: Sample texts from Experiment 7

_____________________________________________________________
Introduction
Doug was setting up for a picnic.
First, he positioned the cake.
Notice Text, Frame of Reference on Item 3
Then he put the picnic basket to the right of the cake.
Next, he put the box of chicken directly to the left of the picnic basket.
So, the picnic basket is on the box of chicken's right.
The cake was strawberry.
The picnic basket broke.
Notice Text, Frame of Reference on Item 2
Then he put the picnic basket to the right of the cake.
Next, he put the box of chicken directly to the left of the picnic basket.
So, the box of chicken is on the picnic basket's left.
The cake was strawberry.
The picnic basket broke.
Not-Notice Text, Frame of Reference on Item 3
Then he put the picnic basket to the right of the cake.
Next, he put the box of chicken directly to the right of the picnic basket.
So, the picnic basket is on the box of chicken's left.
The cake was strawberry.
The picnic basket broke.
Not-Notice Text, Frame of Reference on Item 2
Then he put the picnic basket to the right of the cake.
Next, he put the box of chicken directly to the right of the picnic basket.
So, the box of chicken is on the picnic basket's right.
The cake was strawberry.
The picnic basket broke.
Test Questions
Is the cake anywhere to the right of the box of chicken?
Is the picnic basket anywhere to the left of the cake?
Was the cake chocolate?
Did the picnic basket break?
_____________________________________________________________

A second issue was in how we encouraged participants to maintain a spatial layout. In the previous experiments, we tested memory for spatial layout and depended on the participant's motivation to do well on the test. In this experiment we upped the motivational ante. After reading a text, participants responded to two questions about the spatial layout and two questions about the about sentences. If the participant missed one or more of these questions, the condition was repeated later in the session. Participants were forewarned of this, and they were given feedback following each text. Of course, we did not want to have some participants continuing indefinitely, and so (unbeknownst to the participants) the maximum number of texts that could be repeated was 10.

Method

Participants

Materials

Design

Procedure

Results

The times to read the initial about sentences were analyzed using a two-way analysis of variance. The frame-of-reference-modified noticing hypothesis predicts a) a main effect of noticing condition and b) an interaction between notice and frame of reference. The main effect was not significant F(1,36) = .62, MSE = 107867, nor was the interaction significant, F(1,36) = 0.02, MSE = 110841. In the item-three-frame-of-reference condition, participants read the initial about sentence faster for notice texts (M = 1762 msec) than for not-notice texts (M = 1797 msec). The same was true for the item-two-frame-of-reference condition, notice text M = 1762 msec, not-notice text M = 1812 msec.

Discussion

General Discussion

It is also clear from our data, as well as the data from many other laboratories, that readers encode spatial relations and that they are functional. Notice the good performance on the various types of spatial comprehension questions as well as the symbolic distance effect reported for Experiment 4. It appears, however, that the sorts of spatial relations encoded from text are all explicitly stated in the text, are based on past experience, are depicted in an accompanying picture, or are based on repeated presentations of the text and task demands to form a detailed spatial representation (e.g., Denis & Cocude, 1992; Glenberg & Langston, 1992; Rinck, Hähnel, Bower, & Glowalla, in press; Wagener & Wender, 1985). There is little evidence that readers infer spatial relations on the sole basis of contiguity in a spatial mental model; that is, there is little evidence for noticing.

These experiments join a growing body of literature questioning the assumption that the representation of spatial information is Euclidean. That is, mental models are more than simple, unstructured spaces in which proximity alone can drive inference making. McNamara (1986) demonstrated that after learning locations of objects, objects near to one another primed each other more effectively than those farther away. However, objects in a single bounded region led to greater priming than equally distant objects in two regions. In other words, spatial priming was not a simple function of distance; region also affected the degree of relation. McNamara, Hardy, and Hirtle (1989) were able to show that subjective regions (as opposed to those marked explicitly on a map) also affected spatial priming. The conclusion is that spatial information is not represented in a system that is
Euclidean, but that hierarchical or topological relations (e.g., regions) also affect performance.

Tversky and her colleagues (e.g., Bryant, Tversky, and Franklin, 1992; Franklin and Tversky, 1990) have proposed that spatial descriptions are retrieved (and perhaps encoded) using a "spatial framework" that is decidedly not Euclidean. Their basic findings come from a paradigm in which readers first read about and memorize a three-dimensional spatial layout of objects. The reader is then instructed to imagine facing one of the objects (or the protagonist in the text is described as facing one of the objects). Finally, the reader is instructed to retrieve the names of objects in various directions such as up/down, front/back, and left/right. The basic finding is that retrieval times are a function of the direction, with the fastest times being for up/down and the slowest for left/right. Once again, the conclusion is that the representation of spatial layout (or the retrieval of objects from the representation) does not reflect an unstructured space.

There is also reason to question the analogical interpretation of the distance effects observed in the Morrow and Bower paradigm (e.g., Morrow et al., 1989). For example, in Rinck and Bower (1995) and Rinck et al. (1995, from which the following examples are taken), participants memorized the spatial layout of a building and then read about the movements of a protagonist through the building. A motion sentence such as "Then he walked from the storage room into the lounge" described the movement of the protagonist from a source room (storage room) to a goal room (lounge), and the sentence implied a path that traversed an unnamed path room (in this case, a repair shop). After reading the motion sentence and a motivating sentence that provided a context for the target sentence, the participants read a target sentence that referred to an object in the source, path, or goal rooms. An example of a target sentence is, "He decided that the cart should not be so dirty tomorrow." Time to read the target sentence was a monotonically increasing function of distance of the room containing the object from the protagonist's location in the the goal room. This result is consistent with the claim that spatial distance from the protagonist is a critical factor in comprehending reference to objects. However, Rinck et al. (in press) report data that strongly question the idea of a Euclidean representation affecting text comprehension. In these experiments, the memorized layout included "path" rooms that were either divided (so that there were two path rooms implied by the motion sentence) or undivided. The divided and undivided path rooms contained the same objects and occupied the same space. Rinck et al. tested if the time to read a sentence referring to an object in the path room was sensitive to distance of the object (in the path room) from the protagonist. In fact, when the path room was divided, distance affected reading time so that sentences about objects in the path room far from the protagonist took longer to read than sentences about objects in the path room closer to the protagonist. This effect could either be due to distance or a category effect based on the number of (divided) rooms. The critical conditions involved the undivided path room containing objects that were literally as far from the the protagonist as when the path room was divided. In this case, distance played no role in reading time. Apparently, number of rooms, rather than distance, produces the effect. Interestingly, Rinck et al. did find evidence that spatial representations can incorporate analogical components. When the participants were asked to judge the relative distance of objects from the protagonist, the speed of the judgments was inversely related to distance between the objects. This result corresponds to the finding in Experiment 4 that participants performance on the symbolic distance task seemed to reflect distance. Overall, the results from the Rinck et al. experiments imply that spatial information derived from a memorized layout may be represented with analogical properties, but that those properties do not affect text comprehension processes (simple distance is not the whole story).

Much of the data appear to be covered by a relatively simple generalization. Cognitive representations derived from perception, pictures, or many repetitions of a text (see Denis & Cocude, 1992), may well have Euclidean components, but the Euclidean nature of those components does not necessarily affect text comprehension. This is consistent with work by Zwaan and van Oostendorp (1993) demonstrating that when readers are understanding a real (but edited) mystery novel, they have difficulty answering questions involving spatial inferences without special instructions emphasizing constructing models. Furthermore, on the basis of the experiments reported here, reading in the absence of pictures or multiple passes at the text is unlikely to result in a representation that is Euclidean.

We began this investigation with questions about the nature of mental models. Can we say anything positive about that nature? Again, one conclusion is clear: For texts read without the support of pictures and multiple passes, the representation of space is not Euclidean. An alternative is to conclude, along with van Dijk and Kintsch (1983), that mental models are intrinsically propositional. There are strong grounds to question this alternative, however (see Barsalou, 1993; Glenberg, in press; and Lakoff, 1987). In brief, propositions are composed of abstract symbols that are difficult or impossible to associate with external referents. Thus, propositional systems are inherently syntactic and represent only relations to other propositions, not relations to the world. Mental models, on the other hand, are quintessentially semantic; they encode our understanding of particular situations in the world, not just relations among abstract symbols.

After discounting propositional and Euclidean representations, there are still many possibilities, although none are currently as well-developed as the propositional account. Several of these are related to the concept of embodiment (Johnson, 1987; Lakoff, 1987; see Rinck et al., in press, for other possibilities). In contrast to propositional representations, embodied representations are not constructed from abstract symbols. Instead, the basic elements of the system are shaped by how the body interacts with the environment. Thus, Johnson (1987) describes how the physical nature of our bodies leads to consistent, structured, experiences of in-out, such as putting food into our bodies and moving into and out of rooms. This sort of basic bodily experience is proposed to underlie our understanding of concepts such as containment, as well as our understanding of more metaphorical uses of spatial terms such as to wake out of a deep sleep. In contrast to representations built out of Euclidean space, embodied representations are highly structured. For example, Lakoff (1987) describes the structure of the container schema as having an inside, an outside, and a boundary. Importantly, the schema specifies how being in a container carries many implications (e.g., that what is in the container is under the control of the container). Embodied accounts of meaning are being developed by Lakoff and Johnson (e.g, Lakoff, 1987), Barsalou (1993), and Glenberg (in press).

Consider how such an account might handle the contrast between the results of Glenberg et al. (1987, described in the introduction), which suggest a strong contribution of analogical spatial relations to comprehension, and the results of the current experiments suggesting the opposite. When the protagonist, John, puts on his sweatshirt to go jogging, the sweatshirt is spatially close to him. What may be more important, however, is that the sweatshirt is literally attached to John. Attachment is just the sort of relation that can arise from bodily interactions with the world, such as holding hands with one's parents (see Lakoff's discussion of the "Link" schema). One of the consequences of attachment is a dependency, so that that the sweatshirt goes where John goes. When John takes off his sweatshirt, the attachment relation is broken and the dependency no longer applies. Given these functionally different relations, we would suspect that having the sweatshirt on or off would affect comprehension, and it does. In contrast, consider the spatial arrangement described by the sample text in Table 1. Whereas the objects have different spatial relations to one another, there is little or no differentiation in regard to functional, topological, or embodied relations. For example, all of the objects in the text in Table 1 can be considered to be in the same container (the aquarium), and thus all are equally likely to interact with each other and equally likely not to interact with objects outside of the aquarium. On this analysis, and consistent with the experiments reported here, because the objects are not differentiated in regard to embodied relations, they are not differentiated in regard to effects on comprehension.

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Author Note

Footnotes

1. All of the patterns of spatial layouts are available from the first author.

2. There was only one item recognition probe for each text. So, for a given text the probe could be either notice, not notice, spatial end, spatial middle, item three, or some item not in the text (a "no" probe).

3. The noticing effect reported in Table 2 is different from that reported here because the data in Table 2 combine notice and not-notice probes from items one and two whereas the data in the text separate items one and two.

4. Thanks to Morton Ann Gernsbacher and Karen Luh for suggesting many of the novel features of this experiment.