Mathematical Reasoning, Proof Principles, and Logic

2011 ◽  
pp. 1-100
Author(s):  
Jean Gallier
Keyword(s):  
Mathematical Reasoning

Distinct neural substrates recruited for logical and mathematical reasoning

2001 ◽  
Author(s):  
James K. Kroger ◽  
Jonathan D. Cohen ◽  
Philip N. Johnson-Laird
Keyword(s):  
Mathematical Reasoning ◽  
Neural Substrates

Analisis Kemampuan Penalaran Matematis Mahasiswa Calon Guru Matematika Sebagai Kajian Evaluasi

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Hanifah Nurus Sopiany
Keyword(s):  
High School Students ◽  
Secondary School ◽  
Mathematical Reasoning ◽  
Mathematics Learning ◽  
Good Reason ◽  
School Level ◽  
Real Analysis ◽  
Reasoning Ability ◽  
School Students ◽  
Secondary School Level

Penalaran matematis menggunakan pola pikir logis dalam menganalisa suatu masalah yang nanti pada akhirnya akan ditandai dengan aktivitas menyimpulkan atas masalah tersebut. Seseorang yang memiliki penalaran yang baik, tentunya akan berhati-hati dalam bertindak dan memutuskan sesuatu. Materi-materi pada kalkulus merupakan materi yang ada pada tingkat sekolah menengah yang nantinya menjadi lahan mengajar mahasiswa calon guru matematika S-1. Kemampuan penalaran yang dikaji mempengaruhi pembelajaran mahasiswa kedepannya karena berlaku pada matakuliah lanjut, contohnya pada kemampuan pembuktian akan selalu digunakan pada matakuliah persamaan diferensial, struktur aljabar, analisis  vektor, analisis real, dll. Sedangkan sebagai calon guru yang nantinya mengajar pada tingkat sekolah menengah, maka kemampuan penalaran ini menjadi salah satu capaian pembelajaran matematika bagi siswa sekolah menengah, maka oleh karena itu guru yang mengajarnya haruslah memiliki kemampuan penalaran yang baik. Analisis kesalahan sangat penting untuk melakukan evaluasi dan refleksi pada struktur soal maupun pada perlakuan dalam pembelajaran dalam upaya memperbaiki kemampuan penalarannya.   Mathematical reasoning uses a logical mindset in analyzing a problem that will eventually be marked by concluding activity on the problem. Someone who has good reason, will certainly be careful in acting and deciding something. The material content on the calculus is the material that exists at the secondary school level which will become the field of teaching the prospective master of math teacher bachelor. The reasoning ability studied influences student learning in the future as it applies to advanced courses, for example in the ability of proof will always be used in the course of differential equations, algebraic structure, vector analysis, real analysis, etc. While as a teacher candidate who will teach at the secondary school level, then this reasoning ability becomes one of the achievements of mathematics learning for high school students, therefore teachers who teach it must have good reasoning ability. Error analysis is very important to evaluate and reflect on the problem structure as well as on the treatment in learning in order to improve the reasoning ability.

A Priority and Application: Philosophy of Mathematics in the Modern Period

2009 ◽  
Author(s):  
Lisa Shabel
Keyword(s):  
Early Modern ◽  
Mathematical Reasoning ◽  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Natural World ◽  
Pure Mathematics ◽  
Philosophical Account ◽  
Mathematical Ontology ◽  
To Come ◽  
Modern Mathematics

The state of modern mathematical practice called for a modern philosopher of mathematics to answer two interrelated questions. Given that mathematical ontology includes quantifiable empirical objects, how to explain the paradigmatic features of pure mathematical reasoning: universality, certainty, necessity. And, without giving up the special status of pure mathematical reasoning, how to explain the ability of pure mathematics to come into contact with and describe the empirically accessible natural world. The first question comes to a demand for apriority: a viable philosophical account of early modern mathematics must explain the apriority of mathematical reasoning. The second question comes to a demand for applicability: a viable philosophical account of early modern mathematics must explain the applicability of mathematical reasoning. This article begins by providing a brief account of a relevant aspect of early modern mathematical practice, in order to situate philosophers in their historical and mathematical context.

scholarly journals Students’ agency, creative reasoning, and collaboration in mathematical problem solving

2021 ◽  
Author(s):  
Ellen Kristine Solbrekke Hansen
Keyword(s):  
Problem Solving ◽  
Driving Forces ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Shared Understanding ◽  
Interaction Patterns ◽  
Collaborative Processes ◽  
Mathematical Properties ◽  
Shared Agency

AbstractThis paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

scholarly journals A comparison of dyadic and social network assessments of peer influence

2021 ◽  
Vol 45 (3) ◽  
pp. 275-288
Author(s):  
Dawn DeLay ◽  
Brett Laursen ◽  
Noona Kiuru ◽  
Adam Rogers ◽  
Thomas Kindermann ◽  
...  
Keyword(s):  
Social Network ◽  
Peer Influence ◽  
Mathematical Reasoning ◽  
Statistical Significance ◽  
Relative Strength ◽  
Third Grade Students ◽  
Social Network Influence ◽  
Influence Parameter ◽  
Math Reasoning ◽  
Peer Nominations

The present study compares two methods for assessing peer influence: the longitudinal actor–partner interdependence model (L-APIM) and the longitudinal social network analysis (L-SNA) Model. The data were drawn from 1,995 (49% girls and 51% boys) third grade students ( M age = 9.68 years). From this sample, L-APIM ( n = 206 indistinguishable dyads and n = 187 distinguishable dyads) and L-SNA ( n = 1,024 total network members) subsamples were created. Students completed peer nominations and objective assessments of mathematical reasoning in the spring of the third and fourth grades. Patterns of statistical significance differed across analyses. Stable distinguishable and indistinguishable L-APIM dyadic analyses identified reciprocated friend influence such that friends with similar levels of mathematical reasoning influenced one another and friends with higher math reasoning influenced friends with lower math reasoning. L-SNA models with an influence parameter (i.e., average reciprocated alter) comparable to that assessed in L-APIM analyses failed to detect influence effects. Influence effects did emerge, however, with the addition of another, different social network influence parameter (i.e., average alter influence effect). The diverging results may be attributed to differences in the sensitivity of the analyses, their ability to account for structural confounds with selection and influence, the samples included in the analyses, and the relative strength of influence in reciprocated best as opposed to other friendships.

Mathematical Issues Arising From the Directed Mutation Controversy

Genetics ◽  
2003 ◽  
Vol 164 (1) ◽  
pp. 373-379
Author(s):  
Qi Zheng
Keyword(s):  
Mathematical Reasoning ◽  
Large Body ◽  
Directed Mutation ◽  
The Past ◽  
New Evidence

Abstract During the past 14 years or so a large body of new evidence that supposedly supports the directed mutation hypothesis has accumulated. Interpretation of some of the evidence depends on mathematical reasoning, which can be subtler than it appears at first sight. This article attempts to clarify some of the mathematical issues arising from the directed mutation controversy, thereby offering alternative interpretations of some of the evidence.

Labirinto matemático a game to stimulate mathematical reasoning in children

2016 ◽  
Author(s):  
Raul T. do Prado ◽  
Willian Yudi Sirakawa ◽  
Joao Henrique da Silva Arruda ◽  
Beatriz A. Pacheco ◽  
Ilana A. Souza-Concilio
Keyword(s):  
Mathematical Reasoning

Theoretical Difficulties in the Study of Nationalism

1996 ◽  
Vol 22 ◽  
pp. 63-92 ◽  
Author(s):  
Yael Tamir
Keyword(s):  
Mathematical Reasoning ◽  
Philosophical Problem ◽  
Social Phenomenon ◽  
Isaiah Berlin ◽  
Nationalist Discourse ◽  
Mathematical Problems ◽  
Good And Evil ◽  
Philosophical Questions

Philosophical questions are not like empirical problems, which can be answered by observation or experiment or entitlements from them. Nor are they like mathematical problems which can be settled by deductive methods, like problems in chess or any other rule-governed game or procedure. But questions about the ends of life, about good and evil, about freedom and necessity, about objectivity and relativity, cannot be decided by looking into even the most sophisticated dictionary or the use of empirical or mathematical reasoning. Not to know where to look for the answer is the surest symptom of a philosophical problem.Isaiah BerlinCritics of recent philosophical analyses of nationalism suggest that nationalism is a unique social phenomenon that cannot, and need not, be theorized. Are there, indeed, some special features constitutive of nationalism that might defy theorization? Those answering this question in the affirmative point to the plurality and specificity of national experiences, as well as to the emotional and eclectic nature of nationalist discourse.

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