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A synthesis of existing frameworks used to analyse mathematics curricula

This paper is concerned with the development of a framework for analysing the mathematics curricula of different examination boards in Pakistan. The analysis is being undertaken in order to explore how students’ preparation for the examinations conducted by different examination boards influences their approach to solving questions that they consider as non-routine. The study assumes that an examination system, through its written (curriculum documents and textbooks) and tested (past exam papers) curricula, creates a particular teaching and learning culture. It sets accepted norms and values, and establishes a context which dictates what is and is not appropriate within that culture. Ultimately, this culture manifests itself in the students’ way of responding to problems. This study chooses the problem-solving behaviour of students from a particular examination background as a window on the processes of teaching and learning enculturated through the written and tested curriculum of the examination. The first step in the study requires a review of the literature to develop a framework for analysing the curricula. Later the study will examine students’ responses to non-routine questions, and interpret their problem-solving behaviour through the ‘lens’ of their examination background. The curriculum analysis also provides guidelines for preparing questions which might be assumed non-routine for students belonging to different exam backgrounds. The literature review indicates that most of the frameworks (e.g. Bloom 1956; Smith et al 1996; Porter 2002) offer overlapping as well as discrete categories of cognitive processes. Overall it may be implied that these frameworks recognise three levels of mathematical thinking: assimilation of knowledge; transformation of knowledge; and generation, or validation, of knowledge. Under these fundamental levels there exist several categories of cognitive processes. Apart from the above mentioned frameworks, Anderson and Krathwohl (2001) have added another dimension to Bloom’s taxonomy. The new dimension has four types of knowledge namely factual, procedural, conceptual and meta-cognitive. Each piece of a curriculum can be placed at the intersection of the cognitive process domain and the knowledge domain. Following on Anderson and Krathwohl (2001), this ongoing study attempts to use a two-dimensional framework to analyse exam questions, textbook material and curriculum documents of the secondary mathematics curricula in Pakistan. One dimension of the framework has categories of cognitive processes specific to each level of mathematical thinking obtained through the synthesis of the above-mentioned frameworks/taxonomies.