Affine Functions and Mixed Problems in Elementary School

Resumo

Background: The understanding of the concept of function is complex for students of Basic Education to. The National Common Curriculum Base (BNCC) recommends that ideas of function, such as regularity, pattern generalisation and proportionality, be studied from the initial years of elementary school. Objectives: We aim to analyse function ideas mobilised by 5^th-grade students when solving mixed problems, that is, problems involving operations of addition or subtraction and multiplication or division. Design: This study used a qualitative participant approach. Setting and participants: Thirteen elementary school 5^th graders attending a rural school participated in the research. Data collection and analysis: The six groups of students solved four mixed problems implemented by the researcher during class time. The analyses were based on the conceptual fields theory, from audio recordings of the groups’ dialogues, their written productions and through the researcher’s notes. Results: The analyses show that the six groups of students expressed the ideas of function correspondence, dependence, regularity, variable, proportionality, and affine function modelling, and two groups expressed the idea of generalisation. Mixed problems can be associated with affine function ideas and can be solved by students since the initial years. Conclusions: Based on the results and on the conceptual fields theory, we argue that mixed problems should be proposed from the initial years so that ideas of function are appropriated and deepened by students during the school process.