Abstract
Background: In science, posing problems is considered as important as solving them, however, school has explored little this type of activity. Objective: To examine the features of mathematical problems posed by elementary school teachers, analysing aspects related to the statement of the problems and the types of problems formulated. Design: Descriptive, qualitative research. Setting and participants: Eighty-seven teachers (45 teaching 1st and 2nd grades, and 42 teaching 3rd, 4th, and 5th grades of elementary school) attending a teacher education course promoted by the Municipal Secretary of Education of Curitiba. Data collection and analysis: The teachers were asked to formulate four problems involving addition, subtraction, multiplication, and division. The types of the quantities involved, the necessary information, the number of steps required for solving the problems, and the types of problems from the theory of conceptual fields were analysed. Results: The problems presented a clear language, sufficient information, required a single operation for their solution, involved discrete quantities, and presented few challenges. The problems of addition and subtraction involved situations of composition and transformation, those of multiplication were of simple proportion, and those of division were of partitive problems. Conclusions: The results suggest that the teachers have a limited conception about the formulation of problems, emphasising the need to promote teacher training courses that develop a greater understanding of the properties of the mathematical concept involved in the problems to be formulated and about resolution procedures to be adopted
Highlights
Problem posing is an old subject in science
They encounter practical difficulties in introducing problem posing in the classroom. Discussions about those results point to the little familiarity that teachers and prospective teachers have with this activity, since this theme is little addressed in initial and continuing education courses. Faced with this scenario and considering the relevance of this topic for mathematics education, this research aims to examine the characteristics of mathematical problems posed by elementary school teachers, analysing aspects related to the verbal statement and the types of problems they formulate
The participants 1 were divided into two groups: Group 1formed by 45 teachers who teach in the 1st and 2nd grades, and Group 2 formed by 42 teachers who teach in the 3rd, 4th, and 5th grades.Considering the objectives of this study, the groups were constituted because in the first two grades of elementary school there is a greater emphasis on the teaching of additive concepts, while from the third year onwards the focus is on the teaching of multiplicative concepts
Summary
Problem posing is an old subject in science. Singer, Ellerton and Cai (2013) comment that, back in 1938, Einstein and Infeld had already stated that formulating a problem could be more essential than solving it, because it is a process that makes it possible to raise new issues, new alternatives, face old problems from a new angle, and marking real advances in science. Its didactic value for learning mathematical concepts and problem solving strategies is emphasised, as well as providing the development of logical reasoning (Kilpatrick, 1987; Bonotto, 2013; Singer, Ellerton, & Cai, 2013). It stimulates the students’ creativity, motivation, and autonomy when learning in general (Bonotto, 2013; Brown & Walter, 2005; Sengul & Katranci, 2014). This theme has interested scholars in mathematics education and psychology (Freudenthal, 1973; Polya, 1995; Silver, 1994; Singer, Ellerton, & Cai, 2013; Spinillo, Lautert, Borba, Santos, & Silva, 2017; Stoyanova & Ellerton, 1996). Conclusions: The results suggest that the teachers have a limited conception about the formulation of problems, emphasising the need to promote teacher training courses that develop a greater understanding of the properties of the mathematical concept involved in the problems to be formulated and about resolution procedures to be adopted Key words: Problem posing; Mathematical problems; Teachers; Problem characteristics; Problem types
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