Case Study on Mathematics Pre-service Teachers’ Difficulties in Problem Posing

Abstract

This research is presented in a way that provides useful knowledge for successful problem posing by mathematics pre-service teachers. We present a review of the concept of mathematical creativity (by different authors) and review studies that underline the relevance of problem posing in teaching mathematics, studies that consider problem posing a way to identify students' learning patterns and to test them, and studies that relate mathematical competences to problem posing. Participants in the study were 10 pre-service teachers who were successful in problem solving. Data were gathered through qualitative techniques: classroom observations, sequences of tasks, questionnaires, student focus groups and discussion. The case study illustrated some of pre-service teachers' difficulties in problem posing: creating problems that students recognize as relevant to their everyday lives, problems adapted to the school curriculum at a specific educational level, and problems that can be self-corrected.

Pre-Service Elementary School Teachers' Awareness of Posing Mathematical Pseudo-Problems

“…In this study, the participants integrated real-life objects into mathematical problems, but the numbers or units of measurement used in the problems are somewhat inappropriate for the context. A similar finding is also discussed by [19], [20] and [30]. [30] found that in most cases, pre-service teachers failed to use daily life stories to express the data in the graphs.…”

“…Previous studies showed various classifications of problem posing in terms of the structure of the problem [15], [16], the cognitive processes involved in problem posing [17], [18], as well as difficulties encountered in posing problems [19], [20]. [21] and [22] established the classification of problem posing activities.…”

Resoluci� de problemes: creativitat i did�ctica matem�tica

“…Els docents haurien de practicar la competència de crear problemes, almenys amb la reformulació dels enunciats d'altres problemes existents, mentre intenten adaptar-los per a un propòsit educatiu. Però resulta que els futurs mestres no hi estan gaire interessats perquè no en saben prou (Mallart et al, 2018). Només li veuen la utilitat a l'hora d'avaluar, però en canvi, crear problemes estimula la creativitat, contribueix a precisar situacions, matisa el llenguatge utilitzat i els conceptes que hi intervenen, afina proposicions, processos i argumentacions.…”

Class teachers’ attitudes towards the importance of the activity of setting up the problem in teaching mathematics to beginners

“…Барлоу и Кејтс (Barlow & Cates, 2006) су показали да постављање проблема у разредној настави позитивно утиче и на веровања наставника о природи саме математике и настави математике (у вези са учењем, поучавањем, улогама наставника и ученика, решавањем проблема итд.). Нажалост, наставници не користе у довољној мери постављање проблема у свом наставном раду зато што сматрају да је тешко применити ове активности и зато што не поседују потребне вештине и способности (Leung & Silver, 1997;Leung, 2013;Mallart, Font & Diez, 2018;Rosli, Capraro & Capraro, 2014). Од способности наставника да припреме и примене активности постављања проблема на часу зависи колико ће и како ученици разумети одговарајуће математичке идеје и садржаје (Stoyanova, 2003).…”