Education-line Home Page

Analogical Reasoning and Map Skills

Jennifer Nock

Paper presented at the Register of Primary Research Seminar Conference "Raising Achievement: Developing Thinking Skills", University College Worcester October 27 2001

Position and address
Research Assistant
Faculty of Education and Language Studies
Open University
Email: j.a.nock@open.ac.uk

Address for correspondence:
43, Clark Street
Stourbridge
W.Mids
DY8 3UF

Available in Occasional Paper: No 2 2002 ISBN 0-9538154-1-2 available from the Editor, 9,Humber Road, Blackheath, London SE3 7LS

Abstract The ability to reason by analogy to facilitate performance is analysed in relation to mapping skills of 5-7 yearolds. Recent literature of evidence of children’s ability to use maps is reviewed. The paper investigates how children can interpret map material, how the skill develops and what factors facilitate their competence? Forty children in Reception and Year 2 were investigated and analysed in various ways. Amongst other conclusions it is shown that very young children can be taught how to apply analogous solutions simply by exposure and experience. The capacity for symbolic representation and consequently, analogical reasoning, appears to be innate, but experience and instruction facilitates performance. Concerns are raised about current teaching and learning approaches.

Introduction

Although analogies are frequently used as teaching techniques or to test reasoning skills in I.Q. tests, they are not generally taught to children as learning strategies. This may be due to the fact that early research (e.g. Inhelder and Piaget, 1955) suggested children under the age of 11 or 12 years were unable to reason analogically. However, contemporary researchers, using child-appropriate concepts, have demonstrated that analogical reasoning skills are present much earlier than was originally proposed. For example, Holyoak, Junn and Billman (1984) found that 4- to 6-year-olds are sensitive to analogical relations, and can use a solution learned from an original problem to solve a target problem. They found that 4-year-olds depend on a higher level of surface similarity than older children, and concluded that younger children may only be able to use analogical reasoning when surface similarity provides a support cue. This substantiates Liben and Yekel’s (1996) finding that young children rely more on perceptual similarity when interpreting ambiguous symbols on maps.

However, under appropriate circumstances, even 2- to 3-year-olds demonstrate that a high degree of perceptual similarity is not always necessary (e.g. Brown, 1990). Goswami and her colleagues (e.g. Goswami et al., 1998) found that 3-year-olds could solve classical analogies in the absence of surface similarity cues. They argue that unfamiliar concepts and relationships prevent recognition of higher-order relations irrespective of age, and in those situations, surface similarity is a significant factor for successful analogical reasoning. Thus, analogy solution is a function of domain knowledge rather than developmental progression. They found compelling evidence to support this theory by using classical analogy tasks based on physical causal relations, such as melting, burning and cutting. Children are highly competent at reasoning about physical causality by the age of 3 or 4 years (Das Gupta and Bryant, 1989), and the experimenters based the analogies on objects that are familiar to young children. Three-year-olds were able to solve the analogies, demonstrating that they can reason about higher-order relations, as long as those relations are understood.

Analogies are often used in the classroom, both as a teaching technique, for example, by using Unifix cubes to demonstrate the decimal number system, or spontaneously used by children to make decisions and predictions in unfamiliar areas, based on knowledge about familiar domains (Goswami, 1992). Inagaki and Hatano (1991) demonstrated that preschool children used analogies based on their understanding of people to facilitate their understanding of biological phenomena such as respiration, growth and pain. Pauen and Wilkening (1997) found that 9-year-olds were able to make spontaneous analogies when reasoning about the principles of physics, and Goswami (e.g. 1990, 1991b) has conducted extensive research on the role of analogy in reading, spelling and comprehension. Occasionally though, a negative learning set occurs, in which children learn a set of flawed routines which inhibit the use of analogy, because it is very difficult to dissemble knowledge learned via direct instruction. This effect has often been found in the area of mathematics. Children may be adept at manipulating concrete representations such as Unifix cubes, but are unable to transfer their expertise to written maths because their calculation routines for written arithmetic are different (and possibly flawed) from their procedures with the cubes (Resnick and Osmanson, 1987).

Clearly, the ability to reason by analogy facilitates performance in many areas. A recent study attempted to demonstrate that children who are able to reason by analogy are more likely to be able

Figure 1: Stimuli used for cutting analogy.

An A4 size map of the school playground was used for the map reading task. A five-point route was drawn on the map, and the points numbered 1 to 5. A cross was marked on the map to indicate the starting point of the route. A key to the symbols is shown in Figure 2. A reduced version of the map is shown in Figure 3.

to interpret map material than those who cannot reason by analogy (Nock and Plester, 2001). The evidence of children’s ability to use maps, with various levels of skill is compelling:

The important questions then, are not if young children can interpret map material, but rather how they can, how their skill develops, and what factors facilitate their competence? Nock and Plester (2001) argue that the ability to reason by analogy is an essential component in understanding and using spatial representations such as maps and models because the map is consulted, and the information contained therein is transferred to the analogous situation. The relational similarity, or analogy, between the representation (the map) and the real space must be understood in order to use the map appropriately. Reasoning and learning by analogy involves finding particular similarities or correspondences between two events, situations or domains of knowledge and then transferring knowledge from one to the other. Psychologists have used two types of analogy to investigate the development of analogical reasoning. Classical analogies are frequently seen in IQ tests and are framed in the A:B::C:D format, for example, bird:nest::dog:kennel. A, B and C are provided, and the D element is selected from several options. The C and D terms should be related in the same way as the A and B terms. Problem analogies have been used to investigate children’s ability to reason by analogy in problem-solving tasks. The solution depends on the ability to perceive the relational similarity between a problem that has already been solved (the base), and a current problem. Both types attempt to measure the ability to recognise not only surface similarities (appearance), but also relational similarities.

In order to interpret a map, it is necessary perceive the relationship between the representation and the actual space, and to frame it in the A:B::C:D format. Thus, A is a symbol or feature on the map, B is another symbol or feature on the map, C is the parallel object or feature in the real space, and D is the parallel object or feature to B in the real space. For example, circle on the map:triangle on the map::tree in the real space:bench in the real space. Therefore, the geometric relationship between A and B on the map is equivalent to the geometric relationship between C and D in the actual space. If this relationship is recognised, then the map can be used both to detect objects and locations within real space, and to move through real space.

Forty children (15 boys and 25 girls) in two age-groups (Reception and Year 2) participated in Nock and Plester’s (2001) study. In order to determine the contribution of other factors (verbal and non-verbal IQ) the block design and verbal task subsets from the Wechsler Intelligence Scale for Children (WISC-R) was used. The effects of age and gender were also considered. In order to measure analogical reasoning ability, the researchers designed a task based on the picture analogies used by Goswami and Brown (1989). There were eight picture cards for each analogy, each based on physical causality. The causes used were cut, break, wet, burn, open, melt, dirty and switch on. The objects in the A:B pair were not from the same semantic category as the C:D pair. The appropriate picture to complete the A:B::C:? sequence was selected from five alternatives. These were as follows:

For example, to complete the cutting analogy cake:cut cake::apple:?, the available choices were: cut apple (D), cut bread (E), rotten apple (F), ball (G), banana (H). An example of the stimuli used is shown in Figure 1.

When the data were analysed (using multiple regression analysis), overall, analogical reasoning ability was linked with map reading skill. None of the other factors (verbal and non-verbal IQ, age and gender) were significant predictors of map reading ability. The Y2 girls were the only sub-group in which the relationship did not occur, and in both year groups, the relationship was stronger for the boys than the girls. Thus, the study supported the research hypothesis that analogical reasoning ability is related to map reading ability. The relationship was more apparent in the younger age-group, and several factors may contribute to this difference. Firstly, the Y2 group were much more familiar with the playground than were the YR children, as they were beginning their third year in school, compared to only the second or third week for the younger children. The Y2s were therefore moving through a familiar space, in which the map information would be more clearly recognised as representative of the real space, even without highly developed analogical reasoning ability. In contrast, the YR children needed to work much harder to establish a clear understanding of the higher-order relations between the map and the real space. Without the ability to reason by analogy, the task would be almost impossible for this age-group, as was clearly demonstrated by the data. Eight reception children failed to reach the first landmark, and their analogical reasoning scores were consistently low. When asked to explain their choices for incorrect analogy solutions, replies tended to be vague (e.g. "Because I did"), or related to personal preference (e.g. "Because I like baby chicks"), or semantic associates of the C term (e.g. "Because it matches"). With the exception of one child, those who scored 3 or over on the map task achieved between 63 and 100 per cent on the analogy task, and their justifications of correct choices were specific and accurate (e.g. " Because it’s cutted up and it’s an apple"). Even when an incorrect choice was made, there was an attempt to find a relationship, although this usually depended on surface similarities (e.g. "Because it’s the same because it’s melted").

A second factor may be that of prior learning. The National Curriculum for England and Wales requires that children in Key Stage 1 (4- to 7-years-old) should learn about their local environment in several ways. The document suggests that in order to develop geographical skills, children should have opportunities for recording information on school or local area maps, for making maps of real or fictitious locations, and for following designated routes on maps (Department of Education, 1995). The Y2 children had constructed and followed maps on several occasions during their time in school. Thus, prior learning may have facilitated their use of maps, despite relatively low analogical reasoning ability. Conversely, even high levels of analogical reasoning may have been insufficient to aid map reading if a negative learning set had already been acquired in the field of map reading, as was found in the mathematical field by Resnick and Omanson (1987). Obviously, it is much more difficult for children to use analogies successfully if they also have in place a practised set of flawed systems that the analogy needs to supersede.

The reasons for the weaker link between analogical reasoning and map reading skill in the girls than in the boys is less obvious. Although there was a significant relationship across the whole sample, and in the sub-samples of class and gender, the results of the Y2 girls showed no such relationship, and the only relationship in that sub-group was between verbal skill and analogical reasoning. Clearly, the girls were using other cues in order to inform their actions, and this is an area that would benefit from further exploration, given that even in the YR group, analogical reasoning ability is not as strong a predictor of map reading skill for girls as it is for boys. If the girls were using other cues and skills, their dependence on analogy would not be so strong. Further investigation of the different techniques and cues used by boys and girls would be interesting.

Such findings have important educational implications, not only in the realm of geographical education, but in all areas that benefit by analogical reasoning. Goswami (1992) claims that analogical reasoning is a fundamental element of human cognition, involved in learning, classification, problem solving and discovery. It is therefore somewhat surprising that developmental and educational psychology has largely ignored the potential of analogical reasoning in early learning. Early beliefs that suggested children under the age of 11 or 12 years were unable to reason analogically (e.g. Inhelder and Piaget, 1955) are not supported by current psychological findings, including the evidence reported above. Recent research has demonstrated that young children’s abilities are being seriously underestimated (Lidster and Bremner, 1999), Chen, Sanchez and Campbell (1997) found that children as young as 13 can perceive similarity in the goal structures of different problems and transfer solution strategies from one context to another, even when surface features are different. The researchers conclude that 1-year-olds can build flexible, abstract mental representations, and that reasoning by analogy is possibly one of the principal achievements of the first year of life.

A number of studies have shown that children actively search for underlying commonalities, demonstrating the learning-to-learn phenomenon (e.g. Brown and Kane, 1988, Brown, 1990). Where children fail to use analogy spontaneously, they can be encouraged to recognise relational similarities by direct instruction or ‘hints’. The provision of multiple analogies increases the chance that relations will be recognised. Reflection on their learning, for example by teaching someone else how to solve the same problems, or by describing how two problems are the same also facilitates children’s ability to focus on relations. Brown et al. (1989) found that where multiple analogies are combined with instructions, 7-year-old children rapidly learn that the problem-solving goal is to apply an analogous solution, and this meta-knowledge will facilitate the extraction of the relational structure from the base problem and the application of the analogy.

In conclusion then, very young children can be taught how to apply analogous solutions, in general and map reading situations, simply by exposure and experience. The capacity for symbolic representation and consequently, analogical reasoning, appears to be innate, but experience and instruction facilitates performance. Questions are raised regarding current educational practice, which still functions at a largely pedagogical and didactic level, rather than promoting learning-to-learn principles and providing early opportunities for the development of meta-knowledge.

References

Blades, M. & Spencer, C. (1987). The use of maps by 4-6 year old children in a large scale maze. British Journal of DevelopmentalPsychology, 5, 19-24.

Bluestein, N. & Acredolo, L. (1979). Developmental changes in map reading skills. Child Development, 50, 691-697.

Bremner, J.G. & Andreasen, G. (1998). Young children’s ability to use maps and models to find ways in novel spaces. British Journal of Developmental Psychology, 16, 197-218.

Brown, A.L. (1989). Analogical reasoning and transfer: What develops? In S. Vosniadou and A. Ortony (Eds), Similarity and Analogical Reasoning, 369-412. Cambridge: Cambridge University Press.

Brown, A.L. (1990). Domain-specific principles affect learning and transfer in children. Cognitive Science, 14, 107-133.

Brown, A.L. & Kane, M.J. (1988). Preschool children can learn to transfer: learning to learn and learning from example. Cognitive Psychology, 20, 493-523.

Chen, Z., Sanchez, R.P. & Campbell, T. (1997). From beyond to within their grasp: The rudiments of analogical problem solving in 10- and 13-month-olds. Developmental Psychology, 33, 790-801.

Department of Education. (1995). Key Stages 1 and 2 of the National Curriculum. London: HMSO.

Goswami, U., Leevers, H., Pressley, S. & Wheelwright, S. (1998). Causal reasoning about pairs of relations and analogical reasoning in young children. British Journal of Developmental Psychology, 16, 553-569.

Goswami, U, (1990). A special link between rhyming skill and the use of orthographic analogies by beginning readers? Journal of Child Psychology and Psychiatry, 31, 301-311.

Goswami, U, (1991b). Learning about spelling sequences in reading: The role of onsets and rimes. Child Development, 62, 1110-1123.

Goswami, U. (1992). Analogical Reasoning in Children. Hove: Lawrence Earlbaum Associates.

Goswami, U., Leevers, H., Pressley, S. & Wheelwright, S. (1998). Causal reasoning about pairs of relations and analogical reasoning in young children. British Journal of Developmental Psychology, 16, 553-569.

Holyoak, K.J., Junn, E.N., & Billman, D.O. (1984). Development of analogical problem-solving skill. Child Development, 55, 2042-2055.

Inagaki, K. & Hatano, G. (1991). Constrained person analogy in young children’s biological inference. Cognitive Development, 6, 219-231.

Inhelder, B. & Piaget, J. (1955). The Growth of Logical Thinking from Childhood to Adolescence. In H.E. Gruber and J.J. Voneche (Eds). The Essential Piaget. NJ: Jason Aronson Inc.

Liben, L.S. & Yekel, C.A. (1996). Pre-schoolers’ understanding of plan and oblique maps: The role of geometric and representational correspondence. Child Development, 67, 2780-2796.

Lidster, W. & Bremner, G. (1999). Interpretation and construction of coordinate dimensions by 4- to 5-year-old children. British Journal of Developmental Psychology, 17, 189-201.

Nock, J.A. & Plester, B. Reasoning by Analogy: A Facilitator of Map Reading in Young Children? Poster presentation at ‘Raising Achievement and Thinking skills’ Register of Research in Primary Geography Seminar Conference, October 2001 Worcester, UK.

Piaget, J. & Inhelder, B. (1948). The Child’s Conception of Space. In H.E. Gruber and J.J. Voneche (Eds). The Essential Piaget. NJ: Jason Aronson Inc.

Resnik, L.B. & Omanson, S.F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in Instructional Psychology, Vol 3, Hillsdale, N.J.: Lawrence Earlbaum Associates, pp.41-95.

Uttal, D.H. (1994). Pre-schoolers’ and adults’ scale translations and reconstruction of spatial information acquired from maps. British Journal of Developmental Psychology, 12, 259-275

This document was added to the Education-Line database on 20 February 2006