Using Mathematical Competencies to Predict Item Difficulty in PISA: A MEG Study

Quality Teaching of Mathematical Modelling: What Do We Know, What Can We Do?

“…In the language of competencies according to Niss and colleagues (see Niss 2003), the ability to carry out those steps corresponds to certain competencies or sub-competencies such as understanding a given real world situation or interpreting mathematical results in relation to a situation (Blomhøj and Jensen 2007;Maaß 2006;Kaiser 2007;Turner et al 2013). Cognitively speaking, an individual's competency is his/her ability to carry out certain actions in a well-aimed way.…”

“…The PISA Mathematics Expert Group has shown that the empirical difficulty of PISA mathematics tasks can indeed be substantially explained by the competencies needed to solve these tasks (see Turner et al 2013).…”

Identifying Competency Demands in Mathematical Tasks: Recognising What Matters

“…The emergence of competency frameworks coincides with the increased focus on the acquisition of competencies in education (Pikkarainen, 2014;Westera, 2001) and competencies and competence-based curricula have been embraced 'as a new standard for curriculum design' (Westera, 2001, p. 75). A parallel emergence of assessment frameworks can be observed, such as the frameworks developed for large international comparative studies (Kilpatrick, 2014;Turner, Dossey, Blum, & Niss, 2013). One framework in particular has influenced mathematics curricula and assessment reforms in several European countries: the Danish KOM project (Kilpatrick, 2014).…”

“…This scheme has been used to identify and rate the mathematical competencies needed to solve mathematical problems targeted at 15-year-old students (Turner, Blum, & Niss, 2015) and those necessary to succeed in college courses (Tucker, 2013). Applying the scheme to analyse 48 mathematics items used in both the PISA 2003 and PISA 2006 surveys, Turner et al (2013) found that it could be used effectively by experts to identify the competency demands of PISA items. Turner et al (2015) also argue that the mathematical competencies described in the scheme 'should legitimately be taking a prominent place in mathematics teaching and learning ' (p. 108) and that the scheme can be used by teachers to select and devise appropriate assessment items.…”

“…All PISA 2012 mathematics items were included in the present study. Furthermore, 48 of the included items were previously analysed in the MEG study; when comparing the teachers' analysis to those of the PISA MEG, the reports from the MEG study (Turner et al, 2013) indicate a higher proportion of ratings at levels 2 and 3.…”