<p>A proposal of categorisation for analysing inductive reasoning</p>

Abstract

We present an analysis of the inductive reasoning of twelve Spanish secondary students in a mathematical problem-solving context. Students were interviewed while they worked on two different problems. Based on Polya´s steps and Reid’s stages for a process of inductive reasoning, we propose a more precise categorization for analyzing this kind of reasoning in our particular context. In this paper we present some results of a wider investigation (Cañadas, 2002). Una propuesta de categorización para analizar el razonamiento inductivo Presentamos un análisis del razonamiento inductivo de doce estudiantes de educación secundaria en un contexto de resolución de problemas matemáticos. Los estudiantes fueron entrevistados mientras trabajaban en dos problemas diferentes. Basándonos en los pasos considerados por Pólya y Reid para un proceso de razonamiento inductivo, proponemos una categorización más precisa para analizar este tipo de razonamiento en nuestro contexto particular. En este documento presentamos algunos resultados de una investigación más amplia (Cañadas, 2002).Handle: http://hdl.handle.net/10481/4717Nº de citas en WOS (2017): 7 (citas de 2º orden, 11)Nº de citas en SCOPUS (2017): 5 (citas de 2º orden, 9)

Strategies Employing Prospective Primary Education Teachers in a Functional Relationship Task

“…An example of the above is the answers of P3 (see Table 3) as, in Questions A, B, and C, he employed the arithmetic thinking strategy, while in Questions D and E, he employed the functional thinking strategy, which he generalised. In this way, we underscore the importance of the design of the task carried out in this study, in which we base ourselves on the inductive reasoning model of Cañadas and Castro (2007), which suggests that particular cases are intended for generalisation.…”

“…(p. 6) For his part, Kruteskii (1976) alludes to the fact that generalisation is the process of moving away from the concrete situation, or the process of abstraction from what is similar and relevant in the structure of objects, relationships, or operations. Cañadas and Castro (2007), based on Polya's works, point out that one way to achieve generalisation is through the work and organisation of different particular cases, and suggest that students reach generalisation when they can relate an identified pattern with a general rule and not only for some cases. However, Mason (1996) considers that it is also possible to reach generalisation through a single particular example or case with specific characteristics, which is known as a generic example.…”

“…The proposed problem was adapted from the work done by Carraher et al (2008), whose context addressed the functional relationship between the number of tables and the number of guests. To demonstrate the prospective teachers' functional relationship between the amounts involved in the problem, we formulated several questions based on the inductive reasoning model of Cañadas and Castro (2007). In other words, by employing questions for particular cases and a general question, we sought the generalisation of who solves the task (see Table 1).…”

Investigating Functional Thinking Processes that Impact on Function Composition Problems in Indonesia

“…Observing particular cases is one of the activities of the inductive reasoning process in solving problems. This is supported by Cañadas et al (2007), Ikram et al (2020), Canadas and Castro (2007), Pinto and Cañadas (2005), Polya (1973), Reid (2002), Yuniati (2018), andYuniati (2020), who states that observing cases is an activity of an inductive reasoning process that is carried out on certain cases of the proposed problem. Thus, the functional thinking process is an inductive reasoning process.…”

Penalaran Matematis Siswa dalam Menyelesaikan Masalah Pola Bilangan dan Scaffoldingnya

“…Pada langkah ini, RR sudah memenuhi tahap membuat dugaan dan generalisasi. Hal tersebut sesuai dengan pendapat(Cañadas & Castro, 2007) bahwa generalisasi dugaan termasuk salah satu indikator penalaran matematis. Pada langkah berikutnya, jawaban RR tidak menunjukkan adanya pembenaran dan argumen logis.…”