Rippling: Meta-Level Guidance for Mathematical Reasoning

2005 ◽  
Author(s):  
Alan Bundy ◽  
David Basin ◽  
Dieter Hutter ◽  
Andrew Ireland
Keyword(s):  
Mathematical Reasoning ◽  
Meta Level

scholarly journals University Mathematics Lecturing as Modelling Mathematical Discourse

2021 ◽  
Author(s):  
Olov Viirman
Keyword(s):  
Mathematics Teaching ◽  
Mathematical Reasoning ◽  
Empirical Support ◽  
Mathematical Discourse ◽  
Function Concept ◽  
First Semester ◽  
University Mathematics ◽  
Meta Level ◽  
General Rules ◽  
Lecture Format

AbstractThe lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching.

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.

Importance of the Intersection of Library and Information Sciences with Systems Theory

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
Hannah Lee
Keyword(s):  
System Theory ◽  
General System ◽  
General System Theory ◽  
Von Bertalanffy ◽  
Meta Level ◽  
Professional Field ◽  
The Subject ◽  
Critical Insight ◽  
Insight Into ◽  
Information Sciences

This paper is the attempt to show how system theory could provide critical insight into the transdisciplinary field of library and information sciences (LIS). It begins with a discussion on the categorization of library and information sciences as an academic and professional field (or rather, the lack of evidence on the subject) and what is exactly meant by system theory, drawing upon the general system theory established by Ludwig von Bertalanffy. The main conversation of this paper focuses on the inadequacies of current meta-level discussions of LIS and the benefits of general system theory (particularly when considering the exponential rapidity in which information travels) with LIS.

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.

Habitability: a process versus a state variable framework with observational tests and theoretical implications

2021 ◽  
pp. 1-8
Author(s):  
A. Lenardic ◽  
J. Seales
Keyword(s):  
Process Variable ◽  
State Variable ◽  
Modelling Framework ◽  
Meta Level ◽  
Planetary Habitability

The term habitable is used to describe planets that can harbour life. Debate exists as to specific conditions that allow for habitability but the use of the term as a planetary variable has become ubiquitous. This paper poses a meta-level question: What type of variable is habitability? Is it akin to temperature, in that it is something that characterizes a planet, or is something that flows through a planet, akin to heat? That is, is habitability a state or a process variable? Forth coming observations can be used to discriminate between these end-member hypotheses. Each has different implications for the factors that lead to differences between planets (e.g. the differences between Earth and Venus). Observational tests can proceed independent of any new modelling of planetary habitability. However, the viability of habitability as a process can influence future modelling. We discuss a specific modelling framework based on anticipating observations that can discriminate between different views of habitability.

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.

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