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Burazin, Andrijana; Kajander, Ann; Lovric, Miroslav – International Journal of Mathematical Education in Science and Technology, 2021
Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…
Descriptors: Mathematical Formulas, Mathematics Instruction, Teaching Methods, Geometry
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Harel, Guershon; Soto, Osvaldo – International Journal of Research in Undergraduate Mathematics Education, 2017
In this paper we give a general definition of structural reasoning, followed by a typology that instantiates the definition in mathematical practices. Five major categories of structural reasoning, some with subcategories, are offered: (a) pattern generalization, (b) reduction of an unfamiliar structure into a familiar one, (c) recognizing and…
Descriptors: Abstract Reasoning, Classification, Secondary School Teachers, Mathematics
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Owens, Kay – Australian Primary Mathematics Classroom, 2020
In this article Kay Owens explains how a real-world context can be used to encourage student noticing and deeper analysis of geometric structures when students are asked to draw what they saw. Kay presents examples of students' drawings made during a school trip to the zoo which followed a series of inquiry learning experiences in geometry.
Descriptors: Spatial Ability, Logical Thinking, Elementary School Mathematics, Visualization
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Wackerly, Jay Wm. – Journal of Chemical Education, 2021
This commentary provides an overview of abduction, also known as Inference to the Best Explanation, and argues that the term and relevant problem-solving methods should be adopted by chemistry educators. Abductive reasoning, especially within the context of science and medicine, continues to be an active area of exploration for philosophers and…
Descriptors: Organic Chemistry, Science Instruction, Teaching Methods, Logical Thinking
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Bronkhorst, Hugo; Roorda, Gerrit; Suhre, Cor; Goedhart, Martin – International Journal of Science and Mathematics Education, 2020
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…
Descriptors: Secondary School Students, Logical Thinking, Thinking Skills, Task Analysis
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Carreira, Susana; Amado, Nélia; Jacinto, Hélia – Education Sciences, 2020
The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and…
Descriptors: Logical Thinking, Thinking Skills, Problem Solving, Mathematical Logic
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Lee, Hyung Sook; Yim, Jaehoon; Coomes, Jacqueline – Mathematics Teacher: Learning and Teaching PK-12, 2020
Children see and describe patterns in the primary grades when they develop the meaning of numbers by composing and decomposing. During their early years, they use patterns to learn properties of operations (Common Core Standards Writing Team 2011). While describing the intent of the third-grade standards for multiplication, the CCSS writers…
Descriptors: Mathematics Instruction, Mathematical Logic, Teaching Methods, Elementary School Mathematics
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Yee, Sean P.; Roy, George J.; Graul, LuAnn – Mathematics Teacher: Learning and Teaching PK-12, 2020
As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.
Descriptors: Mathematical Concepts, Logical Thinking, Computer Games, Mathematics Activities
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Jones, Ryan Seth; Jia, Zhigang; Bezaire, Joel – Mathematics Teacher: Learning and Teaching PK-12, 2020
Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.
Descriptors: Statistical Inference, Probability, Mathematics Instruction, Mathematical Models
Herbert, Sandra – Mathematics Education Research Group of Australasia, 2019
Mathematical reasoning is foundational to making sense of mathematics. Yet assessing mathematical reasoning can be challenging for teachers. This paper reports on a project where teachers taught two lessons with a specific focus on reasoning and came together with other teachers at their school to attempt to assess the reasoning of their students.…
Descriptors: Mathematics, Logical Thinking, Student Evaluation, Elementary School Mathematics
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Anderson, Nancy – Mathematics Teacher: Learning and Teaching PK-12, 2021
The questions that teachers ask to elicit student reasoning are among the most important aspects of productive mathematics talk. These questions--often referred to as "press for reasoning"--offer teachers an effective tool for helping students explicate the concepts and principles that undergird their strategies (Kazemi and Stipek 2009).…
Descriptors: Mathematics Teachers, Mathematics Instruction, Mathematical Logic, Thinking Skills
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Kollosche, David – Educational Studies in Mathematics, 2021
Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in…
Descriptors: Cognitive Style, Thinking Skills, Mathematics Education, Mathematical Models
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Hawthorne, Casey; Druken, Bridget K. – Mathematics Teacher, 2019
Both the Common Core State Standards (CCSSI 2010) and the NCTM Process and Content Standards distinguish between Standards for Mathematical Practice (SMP) and standards for mathematical content. We believe this distinction is important and note that students often acquire knowledge of mathematical content without necessarily developing the related…
Descriptors: Mathematics Skills, Mathematical Logic, Mathematics Instruction, Problem Solving
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Brakoniecki, Aaron; Amador, Julie M.; Glassmeyer, David M. – Mathematics Teacher: Learning and Teaching PK-12, 2021
This article examines a common proportional reasoning problem used in schools, often referred to as the Orange Juice task. The authors show how these six strategies described by Nikula (e.g., Unitizing, Norming, etc.) and one additional strategy can be used to either solve or make progress in the Orange Juice task. The article presents work from…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Mathematical Logic
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Berkovich, Izhak; Eyal, Ori – Leadership and Policy in Schools, 2021
Despite the centrality of research concerning both ethics and leadership styles in education administration, our knowledge of the relations between them is limited. The present study closes this gap by investigating the relations of transformational and transactional leadership with multiple ethical paradigms that have been suggested as relevant…
Descriptors: Ethics, Transformational Leadership, Leadership Styles, Correlation
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