Mathematical modelling in the discourses of the KOM and PISA frameworks and teacher interviews

Figures & data

Figure 1. Mathematisation cycle of the PISA 2003 framework (OECD, 2003, p. 38).

Table 1. Analytic tool, adjusted from Morgan and Sfard (2016).

	Aspects of discourse	Questions guiding the analysis	Textual indicators
Word use	Specialisation	To what extent is specialised language about educational mathematical modelling used?	Terms from the theory of educational mathematical modelling (e.g. mathematising), including different perspectives of mathematical modelling. Depth of engagement in a real-world context. Aim to solve a problem or create a mathematical model?
	Objectification of the discourse	To what extent does the discourse speak of properties of objects and the relationship between them rather than of processes?	Are, for example, properties of the modelling process depicted, or are models mentioned as objects?
		Is the mathematical modelling connected to specific mathematical content?	Which mathematical content is mentioned explicitly?
Visual mediator	The presence of multiple visual mediators	Is a modelling cycle included?	Visual mediator included in a framework or mentioned by teachers.
		To what extent does the discourse make use of specialised mathematical modes?	Refers to graphs, function expressions, tables, etc.
		How are multiple visual mediators incorporated into the discourse?	Are the mediators provided by students, teachers or textbooks?
	Transitions between visual mediators	What transformations need to be made between different modes?	Presence or demand of two or more modes of communication-equivalent information (e.g. both function expression and graph?)
		How are transformations indicated in the discourse?	Provided by a teacher or to be produced by students?
Routines	The types of action demanded of students	What areas of mathematics are involved?	Are the routines connected to special mathematics content?
		What are the characteristics of the routine procedures?	Are the students supposed to perform an algorithm, or do they have to engage in the situation at a different level?
Endorsed narratives	The origin of mathematical knowledge	What is the degree of alienation of the discourse?	Mathematical objects as agents in processes: Non-finite verb forms? Passive voice?
		To what extent is mathematics construed as involving material action or as atemporal objects and their properties?	Mathematical objects involved in material processes or relation/existential processes.
		To what extent is mathematics presented as a human activity?	Is mathematics expressed as useful and necessary knowledge? Is mathematical modelling included in mathematical knowledge?
	The status of mathematical knowledge as absolute or contingent	To what extent does the text indicate that decisions or choices are possible during mathematical activity?	Modifiers indicating a degree of certainty (may, can, will) Conditional clauses (if … or when …) Explicit decisions have been or need to be made

Organisation for Economic Co-operation and Development. (2003). The PISA 2003 assessment framework – Mathematics, reading, science and problem solving knowledge and skills. https://www.oecd.org/education/school/programmeforinternationalstudentassessmentpisa/33694881.pdf

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Morgan, C., & Sfard, A. (2016). Investigating changes in high-stakes mathematics examinations: A discursive approach. Research in Mathematics Education, 18(2), 92–119. https://doi.org/10.1080/14794802.2016.1176596

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