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Showing 1 to 20 of 38 for “"Mathematical Reasoning"”.
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Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity
… reciprocity, in order to study the critical reasoning process that drives discovery in mathematics. We begin with an examination of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric …
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Investigating Middle School Students’ Mathematical Reasoning in a Connected In-school and Out-of-School Context
… Specifically, the study explores the forms of mathematical reasoning that the students used while engaged in such contexts and also the influence of collaboration on the forms of mathematical reasoning used. Since the term mathematical reasoning is often used in mathematics education research …
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Secondary students' proof schemes during the first encounters with formal mathematical reasoning: appreciation, fluency and readiness.
The topic of the thesis is proof. At Year 9 Greek students encounter proof for the first time in Algebra and Geometry. Thus the principal research question of the thesis is: How do students’ perceive proof when they first encounter it? The analysis tool in order to obtain an image of students’ …
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A Study of the Performance of Deaf/Hard of Hearing Students in High School Mathematics on Conceptual Understanding, Procedural Fluency, and Mathematical Reasoning Tasks
… understanding, procedural fluency, and mathematical reasoning on an assessment with New York State Regents Algebra I questions.
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Spatial Skills Activities in the Middle School Mathematics Teachers' Toolkit: The Impact of Spatial Skill Activities on Mathematical Thinking
… by middle school mathematics teachers on the mathematical reasoning of their students. Current research suggests that success in spatial reasoning is a strong predictor of success in STEM fields, and is known to be strong in successful mathematicians (Newcombe, 2013; Tepylo Moss, 2013; Uttal …
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Teaching a Geometry Unit on Solids Incorporating Blending Learning
… develop student’s conceptual understanding and mathematical reasoning. The materials are aligned with the Common Core State Standards (CCSS) and intended for a Non-Regents Geometry course.
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Towards AI Safety via Interpretability and Oversight
… oversight methodologies across three key areas: mathematical reasoning in large language models (LLMs), the validity of sparse autoencoders, and scalable oversight. First, we reverse-engineer addition within mid-sized LLMs and discover that LLMs represent numbers as helices. We demonstrate that …
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Using Contrasting Pedagogical Approaches to Detect Differential Item Functioning in the Third International Mathematics and Science Study
… based on whether an item could be solved using mathematical reasoning abilities or whether it required the use of some memorized fact or skill. In addition, the issue of what types of conditioning scores, total test score or latent ability estimate, was explored.
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Language models for verifiable mathematical automation: Interaction, integration, and autoformalization
Stronger automation in formal mathematical reasoning provides scalability, trust-worthiness, and accessibility: it enables efficient verification of complex proofs, reduces the likelihood of errors in intricate calculations, allows non-experts to engage with mathematical concepts, and potentially …
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Deployable structures inspired by the origami art
… materials and structural analysis, mathematical reasoning, manipulating space and form, parametric modeling, fabrication, and finite element testing. Parting from conventional, figural forms, mathematicians developed open-surface forms together with theorems that governed the ability …
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Finding meaning in mathematics through its philosophy: An empirical study with 17-year-old Greek students
… were: whether mathematics exists; whether mathematical knowledge is certain, objective, true and immutable; whether mathematics consists of rules; and whether mathematical knowledge is based on logic or on experience. A thematic analysis helped me to move within the hermeneutical circle of …
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Utilizing Backwards Design Instruction to Incorporate Real World Applications in Algebra 1 Linear Equations Unit
… their own real-world applications in relation to mathematical reasoning will enhance their understanding of the Algebra skills necessary for NYS Next Generation Mathematics Standards
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Second Graders' Solution Strategies and Understanding of a Combination Problem
… the classroom helped students learn to propose mathematical ideas, make conjectures, evaluate their own and others' thinking, and develop mathematical reasoning skills.</p>
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A Curriculum Project on Project-based Learning Supported by Scaffolding and Collaboration in an Algebra I Classroom.
… the world issue of pollution to design multiple mathematical representations of this issue and theorize practical solutions. This experience is meant to be collaborative, and student driven using scaffolding, reciprocal learning, and a project-based learning approach. The curriculum presents …
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UTILIZING TECHNOLOGY TO ENHANCE READING COMPREHENSION WITHIN MATHEMATICAL WORD PROBLEMS
… of evidence linking reading comprehension to mathematical reasoning. The development of a website to assist teachers and students who are having difficulties with mathematical word problems is extremely beneficial. The website is designed with links, power points, and examples that enhance …
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Mathematics, cognition, and you!
… of actions performed in the pursuit of mathematical understanding. The actions are the processes of proving claims that come in such forms as lemmas, theorems, or conjectures. These proofs can be accomplished through a variety of means including (though not limited to) logical deduction, …
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Robust portfolio construction controlling the alpha-weight angle
… the theory of the authors with focus on both mathematical reasoning and practical application. We show that the distortions of the mean-variance optimization process can be quantified by considering the angle between the vector of expected returns and the vector of optimized portfolio …
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Matemaattinen minäkäsitys ja ahdistuneisuus nuorten matematiikka-aikomuksia ennustavina tekijöinä
… the study examined whether the students' mathematical performance and gender contribute to their mathematics intentions. Self-concept is the image that people have of themselves. Mathematics anxiety is a feeling of discomfort that arises when a person comes into situations that require …
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Teachers' Positioning of Students as Math Doers and its Influence on their Teaching Moves in Ghanaian Elementary Schools
… dynamics teachers use to construct students’ mathematical competence during instruction. Data were drawn from semi-structured interviews and three classroom observations for each of five elementary school teachers. The analysis focused on communication acts, positioning practices, teaching …
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Positioning of Fifth Grade Students in Small-Group Settings: Naming Participation in Discussion-Based Mathematics
… students as they learned to talk about academic mathematical reasoning over the course of a school year using Freeze Frame Analysis (Leander & Rowe, 2006) to help map ¨Dtalking spaces¡¬ and Critical Discourse Analysis to understand the discursive turns that helped students to become more …
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