Appealing to Creativity Through Solving and Posing Problems in Mathematics Class

Abstract

Background: Creativity should be a key issue in mathematics learning. However, mathematics class rarely provides opportunities for students to experience it. Problem solving and posing can play a leading role in promoting creative thinking in mathematics. Objectives: This study aims to have an insight into 6 th -graders understanding of problem solving and posing, analyse their solving strategies, their ability to pose problems, and their difficulties when doing so. Design: Qualitative methods were used in a case study approach. An intervention of five sessions comprising five problem-solving and four problem-posing tasks was implemented in mathematics class. Setting and Participants: Participants were thirty 6 th -graders (11-12-year-olds) from a public supported school in Braga (Portugal). Data collection and analysis: Data collection used photographs, audio recordings, students' written productions, and researcher field notes. Results: Students conceptualised strategies such as building schemas and tables, solving from the end to the beginning, making attempts, and reducing to a simpler problem. Students faced problem posing positively, creating problems adjusted to the requirements, with a wide variety of creative contexts. Students' difficulties in problem solving rely on the interpretation of statements, recognition of previous similar problems, and mathematical communication; on problem posing, difficulties regarding the complexity of the formulated problems and a weak diversity of problems were identified. Conclusions: Problem solving and posing tasks can promote mathematical creativity and knowledge, therefore should be used more often in mathematics class, allowing the construction of solid mathematical skills and enthusiasm.

Significados e sentidos sobre pensamento criativo e criatividade em Matemática

“…A partir do corpus de análise temática dos dados da pesquisa compartilhados no Quadro 2, salientamos que o pensamento criativo e a criatividade em Matemática estão relacionados uns aos outros, pois se tecem de elementos como fluência (capacidade de criar muitas ideias nos processos de formulação e resolução de problemas), flexibilidade (variedade de ideias diferentes e soluções inovadoras para resolver um mesmo problema), originalidade (habilidade para criar ideias novas e únicas a partir da busca de resolução divergente e/ou formas diferentes para solucionar o problema) e elaboração (capacidade e desenvolvimento de uma ideia) (Ayllón Blanco et al, 2016;Costa et al, 2021;Fonseca & Gontijo, 2020;Gilat & Amit, 2014;Miranda & Mamede, 2022;Llorente Aguilera et al, 2014;Nadjafikhah & Yaftian, 2013;Panaoura & Panaoura, 2014;Santos & Santana, 2019).…”

“…Os problemas matemáticos (Figura 2) criados pelos(as) professores(as) participantes da formação continuada indicam alguns significados e sentidos teórico-práticos do pensamento criativo e da criatividade em Matemática, referentes aos processos dinâmicos utilizados ao formular e resolver diferentes problemas através de estratégias e recursos diversificados (Costa et al, 2021;Fonseca & Gontijo, 2020;Gilat & Amit, 2014;Llorente Aguilera et al, 2014;Miranda & Mamede, 2022;Nadjafikhah & Yaftian, 2013;Santos & Santana, 2019).…”

“…Nesse contexto, a abertura a ideias, estratégias e processos inovadores (Araya, 2021;Costa et al, 2021;Fonseca & Gontijo, 2020;Khalid et al, 2020;Miranda & Mamede, 2022;Nadjafikhah & Yaftian, 2013) requer a vivência do pensamento criativo e da criatividade em Matemática. Dessa forma, como estimular, nos encontros formativos e dialógicos na formação e na prática pedagógica de professores(as) que ensinam (ou ensinarão) esse componente curricular na educação básica, o que propõem esses(essas) autores(as) nos processos de ensino-aprendizagem de Matemática?…”

Eksperimentasi Model Pembelajaran Problem Posing Terhadap Kemampuan Berfikir Kreatif Pada Materi Lingkaran Berbantu Video Animasi

“…Model problem posing merupakan model pembelajaran yang menitikberatkan peserta didik untuk membuat soal berdasarkan informasi serta kondisi yang ditujukan kepada mereka (Miranda, 2022;Setiyani, 2020). Pertanyaan sederhana yang mereka ajukan kemudian ditukarkan dengan kelompok lain untuk dicari jawabanya secara individu maupun berdiskusi dengan teman kelompok (Isnani, 2020;Rochaminah, 2022).…”

Ethnomathematical and Mathematical Connections Activated by a Teacher in Mathematical Problems Posing and Solving

“…The literature on mathematics education recognises that establishing mathematical connections is essential for problem solving and understanding real-life concepts and phenomena (Ministry of National Education [MEN], 2006;Rodríguez-Nieto et al, 2021). In fact, posing contextualised problems is fundamental to favour the understanding and application of mathematics (Miranda & Mamede, 2022;Silber & Cai, 2016). In turn, ethnomathematics focuses on assessing the several kinds of mathematics practised by cultural groups and connecting them with school environments (D'Ambrosio, 2001;Rosa & Orey, 2021a, 2021b.…”