Planning teaching an unfamiliar mathematics problem: The role of teachers’ experience in solving the problem and watching pupils solving it

Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers

“…Major differences were identified in the ways in which knowledge played out during their lessons, with Anna, by means of extensive and tightly managed activation of prior knowledge, appeared to believe that her students would be unable to address the problem unaided, while both Stelios and Eleni felt no such need, seemingly trusting that their students were appropriately prepared by their previous learning of mathematics. In other words, confirming earlier research, undertaking a problem prior to teaching it does not always translate into higher expectations for learners (Leikin & Kawass 2005).…”

“…While it is desirable that those who are expected to help students become effective problem solvers should be competent problem solvers themselves (Silver 1985), it is equally important that teachers are motivated to engage in such work (Leikin & Kawass 2005). This is a not insignificant issue as studies have shown that even in Finland, where PISA has reported consistently high 'mathematics' achievement, teachers seem unprepared to engage their students in mathematical problem solving (Ryve, Hemmi & Börjesson 2011).…”

“…Typically, the literature indicates that research on teachers' problem solving-related beliefs, whether preservice or in-service, has been framed by the traditional versus reform dichotomy (see, for example, Handal & Herrington 2003;Anderson, Sullivan & White 2005;Chapman 1997). Moreover, there is much research on belief modification and practice as part of, typically, teacher education programmes (for example, Higgins 1997; Leikin & Kawass 2005;Silver et al 2005), which is not discussed here.…”

“…Osana, Lacroix, Tucker and Desrosiers (2006) found not only that the higher the level of problem complexity the more difficulty preservice teachers had in classifying problems but that decisions were frequently made on superficial characteristics like problem length. Perhaps most worryingly is research showing that when they undertake a problem solving task prior to teaching it, many teachers lower their expectations of their students' success, although the most successful problem solvers are more convinced that their students will succeed also (Leikin & Kawass 2005). However, in all such research, the more profound teachers' knowledge of mathematics the more likely they were to identify and respond to problem complexity (Osana et al 2006) and plan appropriate teaching-related prompt questions (Leikin & Kawass 2005).…”

Defining mathematical problems and problem solving: prospective primary teachers’ beliefs in Cyprus and England

“…In the first, participants are treated as teachers, and the main focus is enhancing their pedagogical knowledge and skills for problem solving in classrooms. Such examples are the studies of Lam (2006), and Leikin and Kawass (2005). In the second, participants are seen as both learners and teachers.…”