In press: Journal of Visual Impairment and Blindness



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In press: Journal of Visual Impairment and Blindness

Teaching visually impaired children to make distance judgements from a tactile map
Simon Ungar, Mark Blades and Christopher Spencer

Department of Psychology,University of Sheffield, Sheffield, S10 2TN, UK


Abstract


Estimating the distance between places when walking through an environment is an important skill for people with visual impairments. Tactile maps can provide useful information about the distance between places in unfamiliar environments, but the distances on the map need to be scaled to estimate distances in the real environment. There has not been any previous research into children's ability to estimate distances from a map and therefore we investigated this skill in 59 children aged 5 to 11 years. Three groups of children were included in Experiment 1 (children with total blindness, with residual vision and with sight). They were given a map and asked to place an object along a path in a position which corresponded to that object's position on the map. Children with visual impairments performed less well than children with sight, and an analysis of the children's strategies indicated that the majority of children with visual impairments did not know an effective way to work out distances from the map. In Experiment 2, the children with visual impairments were given a 30 minute training session in using maps and then re-tested. After training the children's performance improved. The implications of these results for teaching map skills to children with visual impairments is discussed.

Introduction

Estimating distance accurately is an important mobility skill for people with visual impairments. A knowledge of the distance between two places can be gained in at least three ways. First, an appreciation of distance can be gained from the direct experience of walking between place A and place B. Second, even without travelling directly between two places it may be possible for a person to infer the distance between them; for example, a person who knows the relationship of place A to several other features in the environment, and the relationship of place B to the same features may be able to work out the distance between A and B. The latter process depends on the person having an accurate knowledge of the relationships between features in the environment (i.e. an accurate cognitive map of the area), from which such inferences can be made. The third way that distances, especially novel distances, can be known is from indirect sources of information - for instance, a person could be told the distance ('it's ten paces between A and B') or could use a scale map showing the distance between A and B.

There have been many studies of people's ability to judge distances, but most of these have investigated distance judgements in the context of research into cognitive maps. If a person is asked to make judgements about the distances between places which they have not directly experienced, the more accurate they are at making such judgments the more likely it is that they have an effective cognitive map of the area (for a review of this research, see Montello, 1991). Much of this research has been carried out with people with sight, but a few studies with visually impaired people have demonstrated that both visually impaired adults and children can make accurate estimates of distances in familiar environments (e.g. Byrne and Salter, 1983; Rieser, Lockman and Pick, 1980; Ocha’ta and Huertas, 1993; Ungar, Blades and Spencer, in press). A little research, with sighted people, has also considered how factors such as the type of route can influence distance judgements; for example, Sadalla and Magel (1980) found that routes with more turns were judged as longer than routes of the same length which had fewer turns.

The studies of inferred distance from cognitive maps, or distortions in distances depending on route characteristics have concentrated on testing people's memory for distances, but as pointed out above there is another important way that a knowledge of distances can be gained, and that is from indirect sources of information. One such source is a map, because a scale map provides immediate information about the relationships between different places in the environment, and maps are particularly important for providing information about unfamiliar environments.

Maps are especially useful for people with visual impairments, because a tactile map provides a view of a novel environment which can help to compensate for lack of vision (Golledge, 1991; 1993). Information about the distances between places in the environment can be gained much more rapidly from a tactile map than from direct experience of the environment itself. However, little is known about how people with visual impairments use maps to work out distances. Most of the research related to tactile maps has concentrated on the design and production of maps rather than on how they are used (e.g. Bentzen, 1977; Dacen-Nagel and Coulson, 1990; Horsfall and Vanston, 1981).

The few studies which have investigated the use of tactile maps by adults with visual impairments have shown that maps can be an important mobility aid (e.g. Yngstršm, 1988). More recently experiments have also shown that children with visual impairments can use simple maps to learn the direction of places in a novel environment (e.g. Ungar, Blades, Spencer and Morsley, 1994). However, previous studies have usually tested people's ability to use a map to follow a route or point to places in the environment. There has been little consideration of how people make distance judgements from a tactile map.

Making accurate distance judgements from a map depends on an understanding of scale and the ability to translate distances from a map into distances in the environment. One study has investigated whether people with visual impairments can use a model of a space to work out the relationships between objects in the real space. Herman, Herman and Chatman (1983) tested a group of 12 participants who were totally blind; their mean age was 17 years and the age range within the group was from 12 to 24 years. The participants were asked to examine a table top layout of four miniature items (a box, a chair, a wagon and a hoop), and given practice in tracing the distance from the box to the other three objects. Then they were taken into a large room which contained a real box where they were led from the box to the position of the hoop. By considering the actual distance between the box and the hoop in the room and the distance between those objects in the model the participants could work out the scale of the model and hence the distances between other objects in the room. Herman et al then removed the real objects from the room and tested the participants' knowledge of distances in the room by asking them to walk between the positions where they supposed the objects to be. Herman et al found that although the participants were generally accurate in estimating the distances between objects, they tended to underestimate the correct distances. Although a wide age range of participants was included Herman et al did not report any developmental differences in performance.

The experiment by Herman et al (1983) demonstrated that people with visual impairments could benefit from using a scale model to work out distances in a real space, but the study was limited to a single layout, and the participants only had one opportunity to calculate the scale relationship between the model and the real space (based on just walking the distance between the box and the hoop in the room). The participants' limited experience of the task may have been one of the reasons why they were not always accurate in making distance estimates.
Rationale for the present study

To investigate the use of small-scale representations, we tested children's ability to use tactile maps to estimate distances. Children were given a map which showed the positions of a number of objects along a path. They were asked to walk along the path and place one object at the correct relative distance from the others by reference to the map. A path, rather than a layout, was chosen as the test environment to reduce errors which can occur as the result of veering when walking. The children carried out a number of trials, rather than just a single trial, to overcome any effects due to lack of familiarity with the task.

As there has been little previous related research and the youngest participants in Herman et al's (1983) study were 12 years old, nothing was known about the development of the ability to estimate distances. Therefore, to investigate possible developmental differences in performance we included a wide age range of younger children with visual impairments (from 5 to 11 years). There has been no previous research into sighted children's ability to estimate distances from a map so we also included a control group of children with sight.




Map

Scale

Distance on map (cm)




Distance on path (m)










AB

BC

AB

BC

1

4:1

4

2

1

0.5

2

4:1

4

4

1

1

16


2:1

8

16

4

8


Table 1. Description of maps used in Experiment 1. One set of 16 maps showed the symbol for the ball first and a second set of 16 showed the brick first. Therefore there were 32 different maps used in the experiment.

Experiment 1 was designed to find out about untrained children's ability to use a map, and in Experiment 2 children were given a short training period in making distance estimates to find out if specific teaching could improve their performance.

Experiment 1
Participants

There were 59 participants in the experiment (with a mean age of 8 years 6 months, and range: 5 years 1 month to 11 years 10 months). These included three sight groups: 10 children who were totally blind, 16 who had some residual vision (light perception or better) and 33 children who were fully sighted. The children with visual impairments attended a school for the visually impaired and the children with sight attended mainstream schools. Although the children had recieved mobility training they had not been given specific training in the use of maps.

Each sight group was divided into two ages - children who were younger than 8 years and children who were 8 years or older. The children who were totally blind included 8 older and 2 younger children; in the group with residual vision there were 7 older and 9 younger children and in the group with sight there were 20 older and 13 younger children.



Figure 1. Example of map shown to the children. The map had raised symbols for the ball, brick and tambourine, and the fence was shown as a raised line.
Materials

For the children with sight a 14 metre path was marked out in chalk on the floor of their school playground. The objects used in the experiment (see below) were placed on the ground along this path. The children with visual impairments were tested on a 14 metre long path in their school grounds on one side of which was a wire mesh fence which was used as a guide to help the children walk in a straight line. For the children with visual impairments the objects had hooks attached to them so that they could be hung from the fence (this avoided having objects on the ground which might have impeded the movement of the children). Three objects were used in the experiment: a plastic brick, a ball, and a tambourine.

Thirty-two maps of the path were made. For the children with sight the maps were made from strips of card with a line representing the path and three differently coloured symbols representing the three objects. For the children with visual impairments the maps were made using the thermoform process; each map had a raised line running the length of one side which stood for the fence along the path, and three different raised symbols, one for each of the three objects (see Figure 1). All the maps were 28 cm long by 3 cm wide. Importantly, the maps did not show the full length of the path, only the relative positions of the three objects (see Figure 1).

On half the maps the symbol for the ball was the first symbol at the start of the path and the symbol for the brick was the second, and on the other half of the maps the brick was shown first and the ball second. The symbol for the tambourine was always the symbol furthest from the start of the path. In the following discussion the first object will be referred to as object A, the second as object B and the third (the tambourine) as object C.

Half the maps were made at a scale of 2:1 and half were made at a scale of 4:1 (the children were not told the scale of the maps). The position of the objects on the path was varied systematically: the distance between A and B could be one, two, three, or four metres, and for each of those distances the distance between B and C could be 50%, 100%, 150% or 200% the distance from A to B. Table 1 describes the 16 combinations of scale and distance which were used. Each combination was used twice (once on a map showing the ball as the first object on the path and once on a map showing the brick as the first object) to create a total of 32 different maps.
Procedure

Each child was tested individually, in two sessions one week apart. In each session a child was presented with eight maps (selected randomly from the 32 maps, with the constraint that each map was used an equal number of times in the experiment). Each map was presented in a separate trial. The task was explained in the form of a game - the children were asked to imagine that they were in the castle of a very fussy giant who only owned three toys: the brick, the ball and the tambourine. The child was to asked to make sure that tambourine was placed exactly where the giant wanted it to be, and it was explained that the correct place was shown on the maps.

Each map was presented at the start of the path next to object A fixed to a table at about the child's chest height. The map was always aligned with the path and children stood behind the map so that they were facing in the direction of the path (see Figure 2). The child was asked to examine the map and pay particular attention to the distances between the three symbols. Then the child was directed to object A which had already been placed on the path (for the children with sight) or hung on the fence (for the children with visual impairments) by the experimenter. The child was asked to walk from object A to object B which had also been placed in position. Then the child walked back to object A. After this experience the child was allowed to consult the map again and was encouraged to think about the position of the actual objects on the path while she examined the symbols on the map.



Figure 2. Position of child when looking at the map at the start of the path. Objects A and B were already placed on the path.
The child was then given the tambourine; and walked along the path from object A to object B. After reaching object B, the child was asked to continue walking and put the tambourine on the path in the position indicated by the map. When the child had placed the tambourine on the path, its position was measured to the nearest centimetre. The performance of the children with visual impairments was videotaped, and after both sessions had bee completed they were asked to describe how they had worked out the correct distance for the tambourine.
Results

For each child in each trial and error score was calculated as the difference between the true test distance and the child's estimate expressed as a proportion of the true test distance. The use of proportions allowed comparison across long and short test distances. From the raw error scores, three types of mean error scores were calculated as dependent variables; absolute error (mean unsigned error score), constant error (mean signed error score) and variable error (mean standard deviation of the error scores). These provide, respectively, a global measure of accuracy, a measure of any constant tendency to over- or under-shoot and a measure of the variability of response accuracy (see Guth, 1995, for more detailed discussion of these measures). For each measure, a 3 (sight group: totally blind, residual vision or sighted) x 2 (age: younger or older children) analysis of variance was carried out.


Absolute Error

The mean absolute error scores for each sight group and age group are shown in Table 2. There was no difference between the performance of the children who were totally blind and the performance of the children who had residual vision, but the children with sight performed better than the children with residual vision (mean absolute error: TB = 0.42, RV = 0.56, S = 0.34; F(2,53) = 6.29; p<0.01). The older children performed better than the younger children (mean absolute error: Older = 0.33, Younger = 0.55; F(1,53) = 13.07; p<0.001). There were no other significant results.



Table 2: Absolute error scores by age and vision groups for Experiments 1 and 2.







Totally Blind




Residual Vision




Sighted










Older

Younger

Older

Younger

Older

Younger

Experiment 1

Mean

.357

.690

.480

.623

.261

.461




SD

.158

.000

.174

.301

.147

.170



SD

.122

.064

.143

.166

-

-

Constant Error

The mean constant error scores for each sight group and age group are shown in table 3. There were no differences between the scores of the different sight groups (mean constant error: TB = -0.11, RV = -0.18, S = -0.08; F (2,53) = 0.89, p > 0.05). A significant difference between the scores of the older and younger children suggested that the younger children tended to undershoot while the older children's estimates were centred around the correct distance (mean constant error: older = 0.00, younger = -0.28; F (1,53) = 10.94; p < 0.01). There were no other significant results.


Table 3: Constant error scores by age and vision groups for Experiments 1 and 2.







Totally Blind




Residual Vision




Sighted










Older

Younger

Older

Younger

Older

Younger

Experiment 1

Mean

.005

-.585

-.021

-.312

.009

-.215




SD

.301

.064

.315

.526

.200

.372



SD

.134

.170

.122

.233

-

-



Variable Error

The mean variable error scores for each sight group and age group are shown in table 4. A significant effect of vision revealed that the variable error of the residual vision group was significantly higher that that of the other totally blind group and the sighted group (both at p<0.05, Tukey test) who did not differ (mean variable error: TB = 0.38, RV = 0.53, S = 0.32; F (2,53) = 7.06; p < 0.01). There was no difference between the scores of the two age groups (mean variable error: older = 0.36, younger = 0.43; F (1,53) = 0.45; p > 0.05). There were no other significant results.


Table 4: Variable error scores by age and vision groups for Experiments 1 and 2.







Totally Blind




Residual Vision




Sighted










Older

Younger

Older

Younger

Older

Younger

Experiment 1

Mean

.317

.440

.537

.526

.291

.355




SD

.120

.085

.221

.237

.142

.200



SD

.154

.057

.179

.286

-

-



Strategies

When interviewed, all the children with visual impairments were able to give some information about how they had calculated the position of the tambourine. From the children's responses and an analysis of their videotaped performance it was possible to identify nine different strategies used by the children. These strategies are summarized in Table 5.


Table 5: Summary of the strategies used by children with visual impairments.

Strategy

Description

Frequency

1

Full Ratio Calculation

2

2

BT judged relative to length of AB

4

N


No explicit strategy

1

Two visually impaired children (both aged 10 years) used a full ratio calculation (strategy 1). They calculated the ratio between the distance AB and the distance BC on the map by working out the number of fingers they could fit between the symbols. Then they applied the ratio to the actual distance (number of steps) they had walked between A and B on the path in order to calculate the required number of steps between B and C. This strategy resulted in very accurate performance.

Four children (all in the older age group) carried out a less precise version of the ratio calculation by comparing the length of BC on the map to the length of AB on the map, typically by running the tip of a finger between each pair of symbols, and using terms like 'much shorter', 'a bit shorter', 'a little longer', or 'much longer'. Taking the actual distance from A to B into account they were then able to walk from B to C based on their interpretation of the relative distance from the map (strategy 2).

One child (aged 8 years) overcame the problem of calculating the distance by adjusting the length of his stride so that the number of steps between A and B was equal to the number of fingers he could fit between A and B on the map. He then found how many fingers he could fit between B and C on the map and walked the same number of steps from B to C on the path, making sure that he kept the length of his stride constant (strategy 3). This resulted in fairly accurate performance, though some trials required very long strides.

Another child (aged 11 years) calculated the difference between the number of fingers he could fit between A and B on the map and the number of steps between A and B on the path. Then he subtracted this difference from the number of fingers which he could fit between B and C to work out the number of steps from B to C (strategy 4). This strategy proved to be an ineffective way of working out the required distance as some calculations resulted in a negative number of steps.

Twelve children examined the length BC on the map (usually by running a finger between B and C) and, without reference to the distance AB, classed BC as long, medium or short. They then walked what they thought to be a long, medium or short distance from B to C along the path (strategy 5). Five other children simply placed object C immediately after object B on all trials without considering distance at all (strategy 6).

One child just placed object C next to its position on the map, and as the map was always set up at object A this meant that the child always placed object C between A and B (strategy 7).

Only one child could not describe the strategy she used fully enough to be classified.


Discussion

The results indicated that when children with visual impairments were asked to make distance judgments from information provided by a map they were generally poorer than children with sight. Considering the performance of all the children with visual impairments as a whole their average error in placing the third object on the path was more than 50% of the actual distance. From the analysis of the strategies used by the children it was clear that most of the 26 children with visual impairments had no effective strategy for using the maps. Only two of the children explicitly employed a strategy (the full ratio calculation) which would always give the correct distance along the path. The two children who used this strategy were in the older age group, but other children in the same age group were unaware of such a strategy and relied on ineffective methods to work out the actual distance of objects represented on the maps.

As pointed out in the introduction it is important for people with visual impairments to be able to estimate distances accurately when moving through the environment, but this is something which most of the children seemed unable to do when translating distances from a map to the area which it represented. The fact that two of the visually impaired children had a very effective means of performing the distance estimates suggests that visually impaired children do have the potential to perform this task. In order to explore this possibility we carried out a second experiment to find out if the performance of children with visual impairments could be improved if they were given training in the use of maps to make distance estimates.

Experiment 2


Participants and procedure

All 26 children with visual impairments who took part in Experiment 1 were included in Experiment 2, which took place two weeks after Experiment 1.

In Experiment 2 children were trained to use the strategy which had emerged as being most effective in Experiment 1 (strategy 5). Children were given a map and shown how they could use their fingers to measure the distances between symbols on the map. They were then asked to consider how much longer one distance was than the other, and they were encouraged to think about the distances in terms of fractions (e.g. that one distance was half the length of the other distance). If they could not understand this idea they were asked to focus on the distance which was longer and decide whether it was 'much longer' or 'only a little bit longer' than the other distance. After this instruction, children were given a number of practices with several maps selected at random from the 16 maps which they had used in Experiment 1. The entire training and practice session lasted for 30 minutes.

One week after the training session children were tested again following the same procedure as Experiment 1. For Experiment 2 each child was tested with the 16 maps (from the set of 32) which they had not used in Experiment 1. The children's performance was measured in the same way as in Experiment 1. For each measure, a 2 (sight group: totally blind or residual vision) x 2 (age: older or younger children) x 2 (Experiment: 1 or 2) analysis of variance was carried out.



Absolute Error

The mean error scores for each sight and age group are shown in Table 2. There was no difference between the scores of the two sight groups (mean absolute error: TB = 0.35, RV = 0.46; F (1,22) = 0.57; p > 0.05). A significant effect of age revealed that the older children were more accurate overall than the younger children (mean absolute error: older = 0.35, younger = 0.52; F (1,22) = 6.32; p < 0.05). There was an effect for experiment; the children made more accurate estimates before they received training than after they received training (mean absolute error: Experiment 1 = 0.51, Experiment 2 = 0.33; F(1,22) = 12.62, p<0.01). There were no other significant effects or interactions. Examination of Table 6 shows that the performance of all groups in Experiment 2 was better than in Experiment 1. In other words, the training had a beneficial effect both for the children who were totally blind and those with residual vision; and for both the older and younger age groups.


Constant Error

The mean error scores for each sight and age group are shown in Table 3. There were no differences between the scores of the vision groups (mean constant error: TB = 0.03, RV = 0.00; F (1,22) = 0.26; p > 0.05) or of the age groups (mean constant error: older = 0.09, younger = -0.09; F (1,22) = 3.24; p > 0.05). A significant effect of training revealed that the children tended to over-shoot after training whereas they tended to under-shoot before training (mean constant error: Experiment 1 = -0.16, Experiment 2 = 0.18; F (1,22) = 24.22; p < 0.001).

There was a significant interaction between age and experiment (F (1,22) = 7.38; p < 0.05).There were no other significant results.
Variable error

The mean error scores for each sight and age group are shown in Table 4. A significant effect of vision revealed that the performance of the residual vision group was more variable than that of the totally blind group (mean variable error: TB = 0.33, RV = 0.50; F (1,22) = 4.85; p < 0.05). There was no difference between the age groups (mean variable error: older = 0.38, younger = 0.51; F (1,22) = 0.98; p > 0.05) or between Experiments 1 and 2 (mean variable error: Experiment 1 = 0.47, Experiment 2 = 0.39; F (1,22) = 2.05; p > 0.05). There were no other significant effects.


Discussion

In Experiment 2 the children with visual impairments were trained to use an effective strategy to work out distances from a map. A comparison of the children's performance before and after the training session showed that their ability to use the maps improved, and after the training the two groups performed as well as untrained sighted children in Experiment 1. The latter result indicated that any difficulties which the children with visual impairments had in Experiment 1 were most likely to be the result of limited experience with maps - once the children had been given additional training with maps their performance was equivalent to the sighted children.

The improvement in the performance of both groups with visual impairments, after only a brief training session, demonstrated the feasibility of teaching young children an effective map using strategy for calculating distance - an important skill when using a tactile map.

Summary


The performance of most of the children with visual impairments in Experiment 1 when they were asked to work out distances from a tactile map demonstrated that they did not know any effective method for translating distances from the map to the environment it represented. If they had been using a map as a mobility aid, their inability to work out the distances between places would have very much limited the usefulness of the map. However, as shown in Experiment 2, the children were able to learn how to make ratio calculations - even a brief training period made a significant improvement in the children's accuracy and brought their performance to the level of (untrained) sighted children. In other words, children with visual impairments can be taught how to calculate distances from a map, and this ability can contribute to both their understanding of maps, and to their mobility skills.


Acknowledgements - This research was supported by a research award from the U.K. Economic and Social Research Council. We would like to thank all the staff and pupils of Tapton Mount School, Sheffield, for their kind help and cooperation in these studies.

References

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