Kevin F. Collis

Towards a Model of School-Based Curriculum Development and Assessment Using the SOLO Taxonomy.

One factor preventing the wider acceptance of school-based curriculum development and assessment is the problem of comparing performances of different students, in different schools, in different areas of study. A framework is needed to describe the complexity of learning outcomes in a language that is generally applicable across the curriculum. Such a framework is provided by the SOLO taxonomy which describes the growth in complexity of performance in many learning tasks, from the earliest engagement in the task to expertise. Learning grows along at least two dimensions: (a) the level of abstraction, or mode, of the contents learned (five such modes are recognisable from infancy to adulthood); and (b) the cycle of increasing complexity that learning undergoes within any given mode. It is possible, by specifying both the mode or modes to be used and the level of the learning cycle to be attained, to state the desired level of performance in many important curriculum topics in a way that can be used (a) for criterion-referenced assessment in particular subjects, and (b) for discussing comparable levels of attainment across different subjects and different schools.

The development of chance measurement

This paper presents an analysis of three questionnaire items which explore students’ understanding of chance measurement in relation to the development of ideas of formal probability. The items were administered to 1014 students in Grades 3,6 and 9 in Tasmanian schools. The analysis, using the NUD•IST text analysis software, was based on the multimodal functioning SOLO model. An analysis of the results and a developmental model for understanding chance measurement are presented, along with implications for curriculum and teaching practice.

A Model for Assessing Higher Order Thinking in Statistics

ABSTRACT As in other areas of the school curriculum, the teaching, learning and assessment of higher order thinking in statistics has become an issue for educators following the appearance of recent curriculum documents in many countries. These documents have included probability and statistics across all years of schooling and have stressed the importance of higher order thinking across all areas of the mathematics curriculum. This paper reports on a pilot project which applied the theoretical framework for cognitive development devised by Biggs and Collis to a higher order task in data handling in order to provide a model of student levels of response. The model will assist teachers, curriculum planners and other researchers interested in increasing levels of performance on more complex tasks. An interview protocol based on a set of 16 data cards was developed, trialed with Grade 6 and 9 students, and adapted for group work with two classes of Grade 6 students. The levels and types of cognitive function...

Some Methodological Considerations

This chapter discusses the SOLO taxonomy and the way in which it may contribute toward meeting the problem of evaluating quality. The chapter focuses on the methodological issues such as the reliability and validity of SOLO and the implications of the taxonomy for psychological theory. There are several meanings of reliability given in the psychometric literature. Those that may apply to SOLO are consistency across items, test-retest, that is, whether students tested on an item tend to give similar levels of response when the same item is attempted on a later occasion, and interjudge agreement. While considering the different aspects of reliability as applied to SOLO, it is important to remember that SOLO is a response measure and not a measure of a personological characteristic of a student. SOLO level is intended to be sensitive to instruction; therefore, whether SOLO levels are stable from occasion to occasion would depend upon the amount of instruction that may have intervened between occasions, or across content areas, and upon the students motivation at the particular occasion of testing.

Visual processing during mathematical problem solving

This study investigated, in the context of mathematical problem solving by secondary school students, the nature of the visual schemata which Johnson (1987) hypothesises mediate between logical propositional structures and “rich” specific visual images. Four groups of grade 10 students were studied, representing all combinations of high and low operational ability in mathematics (equivalent to Johnsons logical propositional structures) and high and low vividness of visual imagery (corresponding to Johnsons “rich” images). The results suggested first, that success at problem solving was related to logical operational ability, but not to vividness of visual imagery. Second, a variety of visually based strategies were used during problem solving which differed in their level of generality and abstraction, and use of these strategies appeared related to either logical operational ability or vividness of visual imagery, depending on their level of abstraction. The results supported Presmegs (1992b) continuum of abstraction of image schemata.

Mapping development in students’ understanding of vision using a cognitive structural model

This exploratory study took two items, which were designed to ascertain childrens understanding of the phenomenon of ‘seeing’, and used them to gather data over the K‐10 age range. One item was adapted from an earlier large‐scale survey by Adams et al. (1990); the other was based on a set of metaphors for ‘seeing’ designed by Guesne (1985). The data gathered were analysed in the context of a cognitive structural model. This analysis showed that, in relation to the concept of vision, the cognitive model selected was able to account for the ‘normal’ developmental sequence, as well as indicate some possible sequences which might help to explain the ‘alternative framework’ phenomenon in this case. There seems to be sufficient evidence from this study to warrant more detailed research in two directions. The first, replicating with a larger sample, the variables discussed in this paper, and the second, carrying out exploratory studies on concepts in other areas of science which have also documented the ‘altern...

The Psychological Structure of Creative Writing.

Creative writing is defined as an open-end prose or poetic construction, that is intended to entertain rather than to impart information. Two aspects of writing are distinguished: the process of writing, and the quality of the product. Composition is conceptualized in information-processing terms, and the components of writing are used as a basis for the main concern of the present paper, product evaluation. The SOLO Taxonomy is proposed by the authors to evaluate the quality of learning, in terms of the structural complexity of the product. Five levels of writing structure are referred to: incoherent, linear, conventional, integrated, and metaphoric. Samples of creative writing of high school students are selected to illustrate each level. This analysis has implications for both the psychology and the teaching of writing.

Matriculation, Degree Structures, and Levels of Student Thinking

The functions of universities and colleges of advanced education (CAEs) are examined with a view to describing the general nature of the demands on knowledge and skill that are sought in each sector. These demands are elucidated in a public language by applying a newly developed evaluation technique, the SOLO Taxonomy, which sets out clearly the level and complexity of thought involved in various levels of tertiary study. A clear rationale for matriculation and degree structures emerges, a rationale which may help to clarify issues where college and university structures are in conflict.

Cognitive Functioning in Mathematical Problem Solving During Early Adolescence

Problem-solving in school mathematics has traditionally been considered as belonging only to the concrete symbolic mode of thinking, the mode which is concerned with making logical, analytical deductions. Little attention has been given to the place of the intuitive processes of the ikonic mode. The present study was designed to explore the interface between logical and intuitive processes in the context of mathematical problem solving. Sixteen Year 9 and 10 students from advanced mathematics classes were individually assessed while they solved five mathematics problems. Each student’s problem-solving path, for each problem, was mapped according to the type of strategies used. Strategies were broadly classified into Ikonic (IK) or Concrete Symbolic (CS) categories. Students were given two types of problems to solve: (i) those most likely to attract a concrete symbolic approach; and (ii) problems with a significant imaging or intuitive component. Students were also assessed as to the vividness and controllability of their imaging ability, and their creativity. Results indicated that the nature of the problem is a basic factor in determining the type of strategy used for its solution. Students consistently applied CS strategies to CS problems, and IK strategies to IK problems. In addition, students tended to change modes significantly more often when solving CS-type problems than when solving IK-type problems. A switch to IK functioning appeared to be particularly helpful in breaking an unproductive set when solving a CS-type problem. Individual differences in strategy use were also found, with students high on vividness of imagery using IK strategies more frequently than students who were low on vividness. No relationship was found between IK strategy use and either students’ degree of controllability of imagery or their level of creativity. The instructional implications of the results are discussed.

Singaporean and Australian Students' Understanding of Vision

Abstract A model for the development of an understanding of how people see has been proposed on the basis of a questionnaire and interview study of a cross-section of Australian school students. The model, based on the SOLO model of cognitive development (Collis & Biggs, 1991), involves the building of connections between the eye, light and the object seen in the Ikonic and Concrete Symbolic modes of cognitive functioning. In order to assess the viability of the model across cultures, the questionnaire was administered to 116 primary and secondary school students in Singapore. This paper reports some details of how the model was supported in its most important respects. The few discrepancies might be explained in terms of environmental, linguistic and/or teaching factors.