COGNITIVE LEVELS AND MODES OF RESPONSE IN YOUNG STUDENTS'             
EXPLANATIONS OF SIGHT AND REFLECTION.
     
          Brian L. Jones, Kevin F. Collis, Jane M. Watson and 
Kimberley Foster, University of Tasmania.

     (Paper for presentation at AARE Conference, Fremantle W.A., 
November 1993)

ABSTRACT
     The developmental model of cognitive functioning based on 
the updated SOLO Taxonomy (Biggs & Collis, 1991; Collis & Biggs 
1991) is being used to evaluate students' understanding of 
science concepts.  In a pilot study of primary school children, 
conceptions of how objects are seen directly and in mirrors were 
explored by examining students' responses to common phenomena 
depicted in drawings and text using a questionnaire and 
individual interviews. Evidence was sought to support an 
hypothesis for increasing levels of response within one or more 
cycles of learning related to the concepts of sight, light, 
reflection and image.

INTRODUCTION
Research in the area of students' alternative conceptions in 
science has generated many hundreds of papers in the last two 
decades (Pfundt & Duit, 1991). The majority of these papers 
attempt to map the most common conceptions in various school 
science topics and raise important issues about effective 
teaching and learning methods. For example, in the topic of 
'light and vision', students' beliefs about the nature and 
behaviour of light have been described by Stead and Osborne 
(1980). Also, a range of beliefs about how we see objects have 
been reported by Andersson & KŠrrquist (1983) and Guesne (1985) 
from studies involving Swedish and French speaking students 
respectively. More recently, the ideas of Australian students 
concerning phenomena related to light and the process of seeing 
were collected in a questionnaire study conducted by ACER (Adams, 
Doig & Rosier, 1990).  In their analyses researchers have drawn 
attention to the similarity of some students' conceptions to 
those recorded in the history of science and also to their 
persistence in spite of serious teaching of currently acceptable 
scientific views. However, it appears that few analyses in this 
type of study have involved a consideration of the nature of 
cognitive processes involved in the different types of responses 
given by students to stimulus questions or situations.  

The following description outlines the application of a 
developmental model of cognitive functioning based on the SOLO 
Taxonomy (Biggs & Collis, 1982; updated in 1991) in order to 
provide another interpretive window into the nature of students' 
views about aspects of 'vision'.  The theory is illustrated with 
reference to children's responses to questionnaire and interview 
items in a pilot study. 
 
SOLO TAXONOMY AND MULTI-MODAL FUNCTIONING

The SOLO Taxonomy (Biggs & Collis, 1982) has been used to analyze 
the structure of children's understanding of mathematical 
concepts and problem solving abilities over a wide educational 
span from primary to tertiary levels (e.g. Chick, 1988; Pegg & 
Davey, 1989; Watson, Chick & Collis, 1988; Watson & Mulligan, 
1991).  It has been applied in a limited way in the area of 
science (Collis & Davey, 1986; Levins, 1992; Jones, Collis & 
Watson, in press).  The SOLO theory, which was significantly 
updated in 1991 (Biggs & Collis, 1991; Collis & Biggs, 1991) 
builds upon Piaget's stages of development and suggests a five-

level cyclical structure for responses within each of five modes 
of cognitive functioning.  The theory postulates that modes of 
functioning begin to appear sequentially from infancy and each 
one may remain operational and develop further throughout life.  
The modes, abbreviations and common ages of appearance are: 
Sensorimotor (sm: infancy), Ikonic (ik: early childhood to 
preschool), Concrete Symbolic (cs: childhood to adolescence), 
Formal  (fm: early adulthood), Post Formal  (pf: adulthood), but 
they should not be confused with Piagetian stages.  In earlier 
proposals each successive mode, with its increased level of 
abstraction, was seen as replacing its predecessor.  However, 
with the recognition that the sensori-motor and ikonic modes 
provide their own distinctive forms of knowledge in adult life, 
they are viewed as developing throughout life, and in interaction 
with other modes.  Such co-existence of qualitatively different 
forms of functioning provides the opportunity for multi-modal 
learning where learning within one mode is supplemented by 
experiences and activities in concurrent modes (Collis & Biggs, 
1991).

Sensorimotor functioning is associated with the performance of 
skilled motor activities and relates to tacit knowledge, although 
one may be unable to explain how one interacts with the physical 
world.   The ikonic mode is associated with intuitive knowledge, 
that which is perceived or felt directly and which involves the 
imaging of objects and events.  Functioning in the concrete 
symbolic mode involves the use of symbol systems which have 
referents in the material world and facilitate the communication 
of declarative knowledge.  Lastly, the formal and postformal 
modes are the most abstract ones and involve theoretical 
constructs having no material referents. Within these modes 
individuals are able to consider not only what is perceived to be 
real but what may be possible.

The cyclical structure for responses within each mode, in order 
of increasing complexity, features
(i)   prestructural responses (P) which represent no use of 
relevant aspects of the mode in question;
(ii)  unistructural responses (U) which represent the use of only 
one relevant aspect of the mode;
(iii) multistructural responses (M) in which several disjoint 
aspects are processed, in sequence;
(iv) relational responses (R) in which several aspects of the 
mode are related into an integrated whole; 
(v)  extended abstract responses (EA) which make use of higher 
order principles and may take the whole process into a new mode 
of functioning at the unistructural level.  Figure 1 (adapted 
from Biggs & Collis, 1991) shows the transition between modes of 
functioning and the equivalence of the extended abstract response 
of one mode with the unistructural response of the next mode.

Recent work in mathematics on Volume Measurement (Campbell,Watson 
& Collis, 1992) and Fractions (Watson, Collis & Campbell, 1991) 
suggests that there are in fact two major cycles for this kind of 
content within the concrete symbolic mode.  The first shows heavy 
reliance on the IK mode to develop the concrete concept and the 
second uses the CS mode as such but utilises ikonic support for 
problem solving


   MODE                       FORM  OF  KNOWLEDGE


OVERVIEW AND METHOD OF THE STUDY
Probing Students' Understanding About Vision. 
Visual sensing is a dominant part of everyday experience from 

early childhood and thus the topic of 'sight and light' has much 
potential for the engagement of children in interesting 
activities in school science across a wide age range.  It also 
has potential for responses over the range of modes of 
functioning. Consequently, as a first step in our study we 
obtained random samples of scripts from the large ACER 
questionnaire study (Adams et al.,1990). Children's responses to 
those items concerning 'light and vision' were re-analysed in 
terms of their structure according to the SOLO Taxonomy and its 
recent theoretical developments relating to modes of functioning. 
On the basis of this analysis (Jones et al., in press) further 
questionnaire items have been developed to fill gaps in the 
available data.  

The Questionnaire and its Trial
A set of nine questionnaire items, in cartoon format, were 
generated to explore children's beliefs about how people see 
objects and the role of light in this process. The first item 
portrayed a four part scenario concerning the use of a torch to 
see objects in a dark room and the remaining items portrayed 
common circumstances involving the formation of virtual images by 
mirrors and mirror-like surfaces. 

In order to test the effectiveness of each item to determine 
children's understanding of the key phenomena, the questionnaire 
was administered to whole classes from Grades 2 to 6 (n=106) in a 
suburban primary school near Hobart. After an inspection of the 
written responses, two children from each grade were selected for 
individual interviews on the basis of their answers to one or 
more of three items which seemed to prompt the most response. 
Children were selected where it was thought that conversation 
might clarify certain written responses or validate inferences 
made. The same questionnaire was used as the basis for individual 
interviews with 12 children from Grades K, Preparatory and 1 
whose verbal responses were recorded on audiotape and later 
transcribed. For the purposes of this paper Item 3 only, and the 
analysis of responses to it, will be reported in detail. 

Questionnaire Item 3
The cartoon sketch in Item 3 (Fig. 1) shows a rear view of a girl 
looking into a mirror with her right hand raised. Her image is 
drawn in the mirror except for her hand. The children were asked 
to draw how she would see her raised hand in the mirror and then 
to write an explanation of why they drew it where they did. 
                              
     The girl is looking into the mirror and puts her right hand 
up.
     Draw how she would see her hand in the mirror.
     Why have you drawn it where you have ? Explain.   

          Fig. 1 Questionnaire Item 3.

RESULTS
Children's responses to the item were grouped in terms of their 
relevance to the question and the degree of complexity of the 
explanation given.  Four groups of responses were readily 
identifiable ranging from those who did not, or said they could 
not, offer any explanation to those whose explanations of a 
correctly drawn hand made reference to image reversal by mirrors.  
However, it should be noted that none of the explanations 
involved any direct reference to light, either in relation to the 
object or the mirror. 
The number of children responding in each of the four groups is 
set out by Grade level in Table 1 and is based on a consensus of 
a group of the authors. The various responses were later 
associated with ikonic and concrete symbolic SOLO modes of 

functioning. Table 2 shows the number in each Grade who drew the 
hand correctly on the right hand side of the mirror.

TABLE 1
 PERCENTAGES OF CHILDREN BY GRADE IN EACH SPECIFIED GROUP OF 
RESPONSES
(Number of children is shown in brackets)

     GRADE =   K-1  2    3    4    5    6    Total
_____________________________________________________________
Group 1.            
Correct or incorrect.    25   47   23   22   21   11   24
No explanation.     (3)  (7)  (7)  (5)  (4)  (2)  (28)

Group 2.            
Hand correct.  67   33   27   39   21   21   32
Experience recalled.     (8)  (5)  (8)  (9)  (4)  (4)  (38)

Group 3.
Hand incorrect.     0    13   37   22   33   32   26
Image reversal used.     -    (2)  (11) (5)  (6)  (6)  (30)

Group 4.       
Hand correct.  8    0    3    9    21   37   12
Reversal mentioned. (1)  -    (1)  (2)  (4)  (7)  (14)
Based on experience.

Unclassified.  0    7    10   9    5    0         6
          -    (1)  (3)  (2)  (1)  -         (7)
______________________________________________________________
Number in Class     (12) (15) (30) (23) (19) (19) (118)
______________________________________________________________

TABLE 2
 PERCENTAGE OF CHILDREN IN EACH GRADE WHO DREW HAND CORRECTLY    
                         (Number of children is shown in 
brackets)

     GRADE =   K-1  2    3    4    5    6    Total
     _________________________________________________________
          %    92   60   50   61   63   68   63
          n =  (11) (9)  (15) (14) (12) (13) (74)
     _________________________________________________________

In the following description of the groups, each typical example 
of the responses is followed by an indentification code in which 
the 'v' and 'x' indicate correct and incorrect placement of the 
hand, m and f refer to gender and the last digit is the 
respondent's Grade.
   
Group 1. No explanation was given. Whilst a large majority of 
children in this group drew the hand on the correct side of the 
image, no one offered an explanation in terms of a mechanism as 
to why they drew it there. Typical responses were of the 
following type; "I'm not sure." x(010f3) 
     "...that's how you might have to put it up there because it 
might have a sore arm." 'v'(112fP)
     "Because it's shown there." v(045m3) 
     "That's where our hands go." x(006f2) 
     "Because she's looking into it." v(067f4)
Many were statements of what the world is like, from ones' 
experience, rather than why it happens the way it does.

Group 2. The hand was drawn correctly and at least one element of 
an explanation was given. Some made a logical connection between 
aspects of the girl and her image e.g. 

     "Because her hand is on the right." v(054m4)  
     "Because she put up that hand." v(027m3)
Others referred to the concept of reflection, but generally as a 
name for what is perceived in the mirror. e.g. "Because it's a 
reflection of her." v(093m6) 
Some appeared to refer to an elementary type of reflection 
process, e.g. 
     "Because when you hold your right hand it reflects." 
v(003f2) 
     "The mirror reflects exactly the same thing as you do." 
v(088m6) 
     "Because it reflects on the same side." v(033f3)
These statements also appear to arise directly from experience of 
what the world is like, and incorporate primitive elements of why 
it happens the way it does.

Group 3. The hand was drawn but NOT correctly. These responses 
appeared to indicate that they had applied, albeit incorrectly, a 
concrete symbolic notion of lateral inversion. e.g. 
     "Because if you put your right hand up it would look like 
your left hand." x(016f3)  
     "The mirror reflects the opposite side." x(046f4) 
     "It reverses your image; so say you had a freckel on your 
left, it would still be on your left in             the mirror 
for example." x(086m5)
     " Because the mirror reflects. If you put up your right hand 
in the mirror it would be your left              hand because it 
has been reflected backwards." x(096f6)
     "Because if you ... look in a mirror with writing on your 
clothes it is back to front." x(094m6)

Group 4. The hand was drawn correctly and explanations were given 
which made reference to some aspect of the phenomenon of lateral 
inversion by mirrors. It would appear that these children were 
able to imagine the image as another person (inside the mirror as 
it were) with a left hand raised, as well as to perceive the 
image directly from outside the mirror. That is, they were able 
to handle the two perspectives without confusion although the 
basis of their drawings appeared to be their recollection of past 
visual experiences. Typical responses were as follows.
     "Because the reflection is showing it on that side. She can 
see it on that side but the reflection            has it on its 
left." v(061m4)
     "Because that's how she'd see her hand but if you turned to 
look the way the reflection is               looking, it's the 
left hand. She is putting up the right hand but the reflection is 
doing the       opposite." v(100f6)
     "when you look in the mirror like if you write 'toH' in the 
mirror it would be 'Hot'." v(057m4)
     "Because the right becomes left and left becomes right." 
v(103f6)
     "The mirror reflects the image on the wrong side but the 
right hand in the mirror, (?) because                the mirror 
reflects the right with the right and the same with the left." 
v(090m6)
     "I've drawn it there because when you look in a mirror it 
gives you a mirror image. It's like            looking face to 
face with yourself." v(081f5)
     "If I said to put your right hand up it would be opposite to 
my right hand but a mirror is               different it will be 
the same side." v(044m3)
     "The mirror isn't like a person facing you." v(073m5)
A more extended response made during the interview of a Grade 1 
girl elaborated the insight expressed in the last quotation about 
images in mirrors: 
     "There's something not the same about reflection. Because if 

you have something like a school  jumper you can see it back to 
front. And that's probably left (pointing to the right side of 
the    image) that would be if it was real, and that (pointing) 
would be right; but that's right and that's     left (pointing in 
reverse). v(115f1)

An inspection of the frequency data across the grades reveals a 
change in the distribution of children between the four groups. 
This is shown graphically in Figure 1 which is a plot of the data 
from Table 1.  The frequency of Group 1 responses across the 
grades is generally low (11%-25%) except for a sharp peak to 47% 
in Grade 2. The frequency of Group 2 responses drops off sharply 
from 67% in Grades K-1 before decreasing gently to 21% in Grade 6 
while Group 3 responses have a similar but inverted change, 
rising sharply to Grade 3 and generally leveling out just above 
30% in Grades 5 and 6. Group 4 responses decrease from 10% in K-1 
to zero in Grade 2 before increasing in a smooth curve to 37% in 
Grade 6. The possible significance of these apparent trends is 
discussed below.     

The percentage of correct responses is relatively low in the 
middle primary grades of the school declining from almost 100% in 
the K-P-1 group to 50% in Grade 3 before rising to 68% in Grade 
6. This is shown graphically in Figure 2 and suggests that a U-
shaped development of understanding about mirrors may occur in 
the population of which the school is a sample of convenience.


Fig.1  Percentage of responses within four groups by Grade level. 
 
     
Fig. 2  Frequency of correct hand drawings in each Grade level. 

DISCUSSION
In relation to knowledge and understanding about mirrors and its 
hypothesized U-shaped development with increasing age of children 
(Fig. 2), three possibly confounding factors are acknowledged. 
First, the data comes from an across grade study rather than a 
longitudinal one yet it is reasonable to accept it as prima facie 
evidence with a view to exploring the matter further as such 
development has been documented before in a number of cognitive 
domains (Strauss, 1982). Second, as the school is relatively 
small there is a greater chance of variation between nominal 
Grades, although this is reduced somewhat by the fact that all 
classes above Grade 1 are composite of two Grade levels i.e. 2/3, 
3/4, 4/5 and 5/6, thus variance due to different teachers is 
reduced. Third, the high success rate in K-1 Grades could be 
associated with the fact that the children were individually 
interviewed, however, this is unlikely as the questionnaire was 
read aloud to all other grades and its wording was used as the 
basis of conversation for the interviews. Should the U-shaped 
success curve for this task be validated one might find a reason 
for it in the nature of the explanations offered by the children, 
that is, in relation to the four groups of responses, as follows.

It is proposed that the reason why most children in the youngest 
grades (K-1) had the highest success in drawing the hand 
correctly is that they relied upon ikonic functioning alone. They 
readily recalled past visual experience of seeing their image in 
a mirror and probably had no other knowledge to divert them from 
its application to answer the simple question. It is the most 
appropriate mode of functioning in this context. As children get 
older their developing knowledge can lead to confusion through 
its inappropriate application. It appears that after Grade 1, 
children are developing concrete symbolic knowledge about lateral 
inversion by mirrors and begin to apply rules such as 'mirrors 

reverse your image' and 'left becomes right and right becomes 
left' to answer the question under discussion. However, this 
knowledge about lateral inversion does not help one explain why 
the raised right hand appears on the right side of the mirror 
and, indeed, it leads many to arrive at an incorrect answer 
particularly in Grade 3. Over the succcessive years an increasing 
proportion of children appear to  revert to ikonic functioning to 
provide a correct drawing, nevertheless they still make reference 
to this irrelevant concrete symbolic knowledge in their 
explanations and accept an anomaly with the perceived correct 
position of the hand.  The image reversal phenomenon itself is a 
dominant perception which appears to affect the personal 
interpretation of what is seen in the mirrors.

Thus, in respect of the children whose answers were allocated to 
Groups 3 and 4, it is claimed that there is evidence of 
interaction between concrete symbolic and ikonic modes of 
functioning, albeit in relation to knowledge about two different 
aspects of mirrors. Answers resulted from the dominance of the 
concrete symbolic mode in the case of  Group 3, and the ikonic 
mode in Group 4. Those in the latter group show evidence of 
having resolved, at least in part, the confusion between two 
types of functioning.

It is interesting that none of the children's explanations 
involved any direct reference to light, either in relation to the 
object or the mirror. This is consistent with the findings in a 
related study by three of the current authors (Jones, et al., In 
Press) that very few Grade 9 students use the idea that light is 
reflected from objects to explain how one sees them. Many appear 
to use an alternative framework to explain vision such that 
objects become bright or 'lit up' and are thus visible. In such 
ikonic functioning dominated by perception no object eye 
connection, in terms of light rays for example, seems to them to 
be required. 

One would not expect primary school children to have much 
knowledge about angles of reflection from mirrors and certainly 
not of the declarative (concrete symbolic) type. However, one 
might have expected a few to have referred to intuitive 
experiences of mirrors to see around corners where object and 
observer are aligned appropriately with a mirror's surface. 
Aspects related to this are currently under investigation and two 
other problem scenarios involving mirrors have been devised to 
explore the development of related declarative knowledge in the 
concrete symbolic mode. 

CONCLUSION
As this research proceeds hypotheses will be developed about the 
order of, and influences on, the development of concepts, and 
typical ages (if any) at which critical shifts in modal 
functioning occur. It is believed that the updated SOLO theory, 
when applied in relation to specific science topics, may be 
sufficiently fruitful to contribute to the design of more 
effective teaching approaches which enhance a student's 
scientific understanding of the topics and their ability to make 
higher level responses in appropriate modes. 
 
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