Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving

Jäder, Jonas; Sidenvall, Johan; Sumpter, Lovisa

doi:10.1007/s10763-016-9712-3

Cited by 41 publications

(30 citation statements)

References 24 publications

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“…Even though the newspaper task is taken from an everyday life context and-we expect-recognisable and meaningful, students still fulfil a task for which they expect that there should be one correct answer, as is common in mathematics tasks (e.g. Jäder, Sidenvall, & Sumpter, 2017). The doubt students express is in line with Galotti's (1989) description for everyday reasoning tasks, because she states that "it is often unclear whether the current 'best' solution is good enough" (p. 335) in contrast to formal reasoning tasks where "it is typically unambiguous when the problem is solved" (p. 335).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Logical Reasoning in Formal and Everyday Reasoning Tasks

Bronkhorst

Roorda

Suhre

et al. 2019

Int J of Sci and Math Educ

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Logical reasoning is of great societal importance and, as stressed by the twenty-first century skills framework, also seen as a key aspect for the development of critical thinking. This study aims at exploring secondary school students' logical reasoning strategies in formal reasoning and everyday reasoning tasks. With task-based interviews among 4 16-and 17-year-old pre-university students, we explored their reasoning strategies and the reasoning difficulties they encounter. In this article, we present results from linear ordering tasks, tasks with invalid syllogisms and a task with implicit reasoning in a newspaper article. The linear ordering tasks and the tasks with invalid syllogisms are presented formally (with symbols) and non-formally in ordinary language (without symbols). In tasks that were familiar to our students, they used rulebased reasoning strategies and provided correct answers although their initial interpretation differed. In tasks that were unfamiliar to our students, they almost always used informal interpretations and their answers were influenced by their own knowledge. When working on the newspaper article task, the students did not use strong formal schemes, which could have provided a clear overview. At the end of the article, we present a scheme showing which reasoning strategies are used by students in different types of tasks. This scheme might increase teachers' awareness of the variety in reasoning strategies and can guide classroom discourse during courses on logical reasoning. We suggest that using suitable formalisations and visualisations might structure and improve students' reasoning as well.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Logical Reasoning in Formal and Everyday Reasoning Tasks

Bronkhorst

Roorda

Suhre

et al. 2019

Int J of Sci and Math Educ

View full text Add to dashboard Cite

show abstract

“…Likewise, McLeod (1992) had same opinion that mathematics beliefs enhance or weaken individual's mathematical and problem solving ability. Other researchers also supported these studies (Ahmed, Van der Werf, Kuyper, & Minnaert, 2013;Ayebo & Mrutu, 2019;Jäder, Sidenvall, & Sumpter, 2017).…”

Section: Introductionmentioning

confidence: 54%

An Evolving Research to Tackle Teaching and Learning Challenges during Differential Equations Course: A Combination of Non-routine Problems and Teacher Training

Bibi

Ahmad

Shahid

et al. 2019

Int Elect J Math Ed

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Teaching and learning of differential equations (DEs) have a prominent role in all the fields of education. In spite of its prominence and frequent applications, teaching and learning of DEs is still considered as one of the most difficult, particularly at pre-university level. This is because, the topic of differential equation along with differentiation and integration is only introduced first time at the 12th year of study or at pre-university level, and the students have no previous knowledge and understandings of this topic. Therefore, the aim of current study is to determine whether teaching and learning of DEs is a challenging task and also, to find out the ways these challenges can be tackled to develop a better understanding for differential equations problem solving. Results showed that teaching and learning of differential equation is not only a difficult part of the mathematics as compared to algebra, trigonometry but also demand high level of conceptual understanding and special efforts for solving differential equation problem. Addition of non-routine problems has been found major factor to enhance teaching and learning. Teacher should also be properly equipped and trained, so that they may educate both routine and nonroutine differential equation problem.

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“…It was influenced by the previously solved problems while the fourth problem was in the non-routine form of problem that could be solved directly without going through mathematical calculation procedures. Students tend to prefer assignments in the form of routine questions and there is a possibility of a student interpreting non-routine questions as the routine one, besides, they are confident that non-routine tasks are more suitable to be completed using the routine assignment approach (Jäder et al, 2017). Other research results state that the provision of non-routine tasks can be a trigger for the emergence of students' creative thinking and actions while routine tasks can hinder students' creative thinking processes (Beghetto, 2017).…”

Section: Table 4 Answer Confirmationmentioning

confidence: 99%

Students’ Cognitive Barrier in Problem Solving: Picture-based Problem-solving

Nanna

Pratiwi

2020

ajpm

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Pre-service teachers in primary education often have difficulty in solving mathematical problems, specifically fractions that are presented with a picture. In solving problems, some thought processes are needed by the teacher to reduce students' cognitive barriers. Therefore, this study aimed to reveal the cognitive barriers experienced by students in solving fraction problems. The cognitive barriers referred to in this study are ways of thinking about structures or mathematical objects that are appropriate in one situation and not appropriate in another situation. This study employed a descriptive-qualitative method. Furthermore, participants were followed up with in-depth semi-structured interviews to find out the cognitive barriers that occurred in solving fraction problems. This study discovers that the participants, in solving fraction problems, experienced all indicators of cognitive barrier and two cognitive obstacles are found as new findings that tend to involve mathematical calculations and violates the rules in dividing images into equal parts in the problem-solving procedure.

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Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving

Cited by 41 publications

References 24 publications

Logical Reasoning in Formal and Everyday Reasoning Tasks

Logical Reasoning in Formal and Everyday Reasoning Tasks

An Evolving Research to Tackle Teaching and Learning Challenges during Differential Equations Course: A Combination of Non-routine Problems and Teacher Training

Students’ Cognitive Barrier in Problem Solving: Picture-based Problem-solving

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