• Research in Mathematical Education
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• v.27 no.1
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• pp.75-92
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• 2024

Mathematical argument has been given much attention in the research literature as a mediating construct between reasoning and proof. However, there have been relatively less efforts made in the research that examined the nature of empirical arguments represented in textbooks and how students perceive them as proofs. Cases of point include Intermediate Value Theorem [IVT] and Maximum-Minimum theorem [MMT] in grade 11 in Korea. In this study, using Toulmin's framework (1958), the author analyzed the substance of the empirical arguments provided for both MMT and IVT to draw comparisons between the nature of datum, claims, and warrants among empirical arguments offered in textbooks. Also, an online survey was administered to learn about how students view as proofs the empirical arguments provided for MMT and IVT. Results indicate that nearly half of students tended to accept the empirical arguments as proofs. Implications are discussed to suggest alternative approaches for teaching MMT and IVT.

• The Mathematical Education
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• v.63 no.2
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• pp.139-163
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• 2024

The purpose of this study is to examine the capabilities of ChatGPT as a tool for supporting students in generating mathematical arguments that can be considered proofs. To examine this, we engaged students enrolled in a mathematics pathways course in evaluating and revising their original arguments using ChatGPT feedback. Students attempted to find and prove a method for the area of a triangle given its side lengths. Instead of directly asking students to prove a formula, we asked them to explore a method to find the area of a triangle given the lengths of its sides and justify why their methods work. Students completed these ChatGPT-embedded proving activities as class homework. To investigate the capabilities of ChatGPT as a proof tutor, we used these student homework responses as data for this study. We analyzed and compared original and revised arguments students constructed with and without ChatGPT assistance. We also analyzed student-written responses about their perspectives on mathematical proof and proving and their thoughts on using ChatGPT as a proof assistant. Our analysis shows that our participants' approaches to constructing, evaluating, and revising their arguments aligned with their perspectives on proof and proving. They saw ChatGPT's evaluations of their arguments as similar to how they usually evaluate arguments of themselves and others. Mostly, they agreed with ChatGPT's suggestions to make their original arguments more proof-like. They, therefore, revised their original arguments following ChatGPT's suggestions, focusing on improving clarity, providing additional justifications, and showing the generality of their arguments. Further investigation is needed to explore how ChatGPT can be effectively used as a tool in teaching and learning mathematical proof and proof-writing.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.347-356
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• 2007

In this paper, we shall consider a class of hyperbolic nonlinear differential equations with continuous deviating arguments. Some new sufficient conditions for oscillation of all solutions with two kinds of boundary conditions are obtained.

• Research in Mathematical Education
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• v.25 no.1
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• pp.65-89
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• 2022

Despite its recognition in the field of mathematics education and mathematics, students' understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers' judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

• Journal of Science Education
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• v.34 no.1
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• pp.175-184
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• 2010

We agree with Hanna and Jahnke's assertion on the use of arguments from physics in mathematical proofs and analyze their educational example of the use of arguments from physics in the proof of the center of gravity of a triangle. Moreover, we suggest practical models for the center of gravity of a triangle for the demonstration in a classroom. Comparing with the traditional mathematical arguments, the role of concepts and models from physics in arguments from physics will be clearly pointed out. Also, the necessity for arguments from physics in the classroom will be discussed in this paper.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.355-367
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• 2006

In this paper, we consider the oscillation second order unstable neutral difference equations with continuous arguments $\Delta^2_{/tau}(\chi(t)-p\chi(t-\sigma))=f(t,\chi(g(t)))$ and obtain some criteria for the bounded solutions of this equation to be oscillatory.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.741-748
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• 2012

In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.191-202
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• 2019

The aim of this paper is to develop a monotone iterative technique by introducing upper and lower solutions to Riemann-Liouville fractional differential equations with deviating arguments and integral boundary conditions. As an application of this technique, existence and uniqueness results are obtained.

• Journal of The Korean Association For Science Education
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• v.35 no.2
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• pp.199-208
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• 2015

An enhanced understanding of the nature of scientific knowledge-what counts as a scientific argument and how scientists justify their claims with evidence-has been central in Korean science instruction. However, despite its importance, scholars are generally concerned about the difficulty of both addressing and improving students' epistemic understanding, especially for students of a young age. This study investigated Korean middle school students' epistemic ideas about claim, data, evidence, and argument when they engage in reading both text-based and data-inscription arguments. Compared to previous studies, Korean middle school students show a sophisticated understanding of the role of claim and evidence. Yet, these students think that there is only a single way of interpreting data. When comparing students' ideas from text-based and data-inscription arguments, the majority of Korean students barely perceive text description as evidence and recognize only measured data as evidence.

• Language and Information
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• v.20 no.1
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• pp.51-71
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• 2016

The status of the Korean morphological marker '-e ci' has been controversial whether it is a passive marker, an anticausative marker, or a passive/anticausative marker. However, the previous approaches that tried to classify '-e ci' constructions based on the syntactic verb classes (i.e. intransitive or transitive) were short of explaining the properties of the constructions. In this study, the '-e ci' constructions were distinguished based on agentivity, following Levin & Rappaport Hovav (1995) and Alexiadou et al. (2006). Moreover, how the verbal root meaning is associated with the passive/anticausative construction was investigated by means of Distributed Morphology (DM) (Embick 2010; Marantz 1997). I argued that the morphological marker '-e ci' is the instantiation of the absence of external arguments. With respect to the behavior of the Korean '-e ci' constructions with the semantics of each verbal root class, I found out that the '-e ci' constructions can form passives with the verbal roots that require the external arguments; whereas, the anticausatives cannot be formed with the roots that necessarily require the agentive arguments. However, contrary to the previous arguments that '-e ci' passives can be only formed with transitive verbs, it is discovered that non-agentive transitive roots do form anticausatives. Moreover, I argued that there are two types of the anticausatives - zero and '-e ci' anticausatives. Since the valency reduction is marked by the non-active voice morphology, the zero anticausatives appear only with the roots that do not require external arguments. The different '-e ci' constructions (passives, '-e ci', and zero anticausatives) are represented by the distinct syntactic structures. I proposed that the morphological similarity between the passives and the '-e ci' anticausatives is due to the presence of VoiceP, which introduces the external arguments. Moreover, the lack of the voice morphology in the zero anticausatives is explained by the absence of the VoiceP.