Mathematics Educators’ Views on the Role of Mathematics Learning in Developing Deductive Reasoning

Ayalon, Michal; Even, Ruhama

doi:10.1007/s10763-010-9238-z

Cited by 11 publications

(8 citation statements)

References 22 publications

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“…[III] Secondary 1 and 3 Starts with intuitive considerations, then 4 , confined to rectilinear figures.…”

Section: Modern Mathematicsmentioning

confidence: 99%

“…One of the main goals of teaching geometry has been to help students acquire deductive reasoning as part of human culture [1][2][3]. According to commonly accepted notions, deductive reasoning is the process of inferring conclusions from known information (premises) based on formal logic rules, where conclusions are necessarily derived from the given information, and there is no need to validate them by experiments [4]. Even though deductive reasoning plays a central position in school geometry, how to teach deductive reasoning does not always have a clear process.…”

Section: Introductionmentioning

confidence: 99%

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The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

Zhang

Wong

2021

Mathematics

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The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed.

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“…[III] Secondary 1 and 3 Starts with intuitive considerations, then 4 , confined to rectilinear figures.…”

Section: Modern Mathematicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

Zhang

Wong

2021

Mathematics

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“…Polya (1945) defines inductive reasoning as the process of conjecturing a general rule through observation and analysis of specific examples. Ayalon and Even (2010) define deductive reasoning in mathematics as the process of inferring conclusions from known information (premises) based on formal logic rules in mathematics.…”

Section: Background Literaturementioning

confidence: 99%

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Patel

McCombs

Zollman

2014

School Sci & Mathematics

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Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student metaphorical reasoning, we examined 11 college instructors' metaphorical reasoning on limit concepts. This paper focused on previous research of metaphor clusters observed among students to answer the following: (a) Do college instructors use metaphorical reasoning to conceptualize the meaning of a limit? (b) Can we characterize instructor metaphorical reasoning similar to those observed among students? (c) Will an instructor's self‐identification of metaphor clusters be consistent with our metaphor coding? We found that college instructors' perspectives vary, either graphical or algebraic, in their explanations of limit items. All the instructors used metaphors, and instructor metaphorical reasoning aligned with student metaphor clusters. Instructors tended to change their metaphors with respect to the limit item. Instructors were not aware of their use of metaphors, nor were they aware of their inconsistency in their choice of metaphor. We believe that instructor awareness of their own distinct perspectives and metaphors would assist students' understanding of limit concepts.

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“…Math equipped students to deal with world challenge, which was more growing, and as one tool used was reasoning. This matter was suitable with the statement of Ayalon & Even (2010), namely math served students a group of unique powerful tool to comprehend and to change the world. These tools scoped logically reasoning, problem solving ability and abstract thinking ability.…”

Section: Introductionmentioning

confidence: 99%

Abilities of Reasoning and Mathematics Representation on Guided Inquiry Learning

Yumiati

Noviyanti

2017

EduLearn

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This research initiated by some research result regarding the lower Reasoning and Mathematics Representation of student on the math learning. In order to upgrade the abilities is passing through the guided inquiry learning. The aim of the reasearch is to analyze comprehensively on accomplishment reasoning and math representation of student who gain the guided inquiry learning and conventional learning. The research is applying experiment method by design of one group pretest-posttest. The result of research indicates the guided inquiry learning is more effective in accomplishment and improvement of student representation capabilities and student comprehend compared with the conventional learning. Reasoning and Mathematics Representation of group student or guided inquiry learning is higher from the group student of conventional learning. The improvement of Mathematics Reasoning of Group Student of guided inquiry learning values 0.33 on the medium category, while the improvement of Mathematics Representation of group student of conventional learning values 0.19 on the low category. The amount of improvement on Mathematics Representation of group student of the guided inquiry learning is 0.41 on the medium category, and the improvement on Mathematics Representation of group student of conventional learning is 0.26 is on the low category.

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Mathematics Educators’ Views on the Role of Mathematics Learning in Developing Deductive Reasoning

Cited by 11 publications

References 22 publications

The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Abilities of Reasoning and Mathematics Representation on Guided Inquiry Learning

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