scholarly journals The Interplay between Individual and Collective Activity: an Analysis of Classroom Discussions about the Sierpinski Triangle

2021 ◽  
Author(s):  
Geoffrey B. Saxe ◽  
Amelia M. Farid
Keyword(s):  
Common Ground ◽  
Mathematical Reasoning ◽  
Inductive Reasoning ◽  
Mathematical Object ◽  
Cultural Analysis ◽  
Active Listening ◽  
Classroom Norms ◽  
Sierpinski Triangle ◽  
Word Forms ◽  
Area And Perimeter

AbstractThis article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area and perimeter of the Sierpinski triangle, a unique mathematical object with zero area and infinite perimeter. As participants conceptualize and communicate about the Sierpinski problem, they unwittingly generate a linguistic register of action word forms (e.g., fencing, zooming) and object word forms (e.g., area, infinity) to serve Sierpinski-linked mathematical reasoning functions, a register that we document in the first analytic section of the article. In the second analytic section, we report a developmental analysis of microgenetic, ontogenetic, and sociogenetic shifts in the word forms constitutive of the register and their varied functions in participants’ activities. In the third analytic section, we provide a cultural analysis of the classroom’s collective practices, practices that enable and constrain participants’ constructions of form-function relations constituting the register. We examine the ways in which participants work to establish a common ground of talk in their communicative exchanges, exchanges supported by classroom norms for public displays of reasoning and active listening to one another’s ideas. We show that it is as participants work to establish a common ground that the register emerges and is reproduced and altered. We conclude by pointing to ways that the analytic framework can be extended to illuminate learning processes in other classroom settings.

Context-dependency and impoliteness in intercultural communication

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Istvan Kecskes
Keyword(s):  
Intercultural Communication ◽  
Common Ground ◽  
Native Speakers ◽  
Cultural Analysis ◽  
Cross Cultural ◽  
Context Dependency ◽  
Shared Knowledge ◽  
Cross Cultural Differences ◽  
Actual Meaning ◽  
Interpretation Process

AbstractThere has been a great deal of research on impoliteness focusing on one particular language or cross-cultural differences between languages (e.g. Bousfield 2008; Bousfield and Locher 2008; Culpeper 2005, 2009; Haugh 2007, 2011; Kienpointner 1997). However, much less attention has been paid to impoliteness in intercultural communication in which all or some speakers communicate in a language other than their native tongue.On the basis of research on L1s and cross-cultural analysis of impoliteness, most of the researchers (e.g. Culpeper 2005, 2009, Haugh 2011; Watts 2003) in the field seem to agree that no act is inherently impolite, and that such an interpretation depends on the context or speech situation that affects interpretation (see Culpeper 2009). The paper will examine this context-dependency in intercultural communication where interlocutors cannot always rely on much existing common ground, shared knowledge and conventionalized context but need to co-construct most of those in the communicative process. It will be argued that limited shared knowledge and common ground may restrict the interpretation process to the propositional content of utterances, which may result in an increase in the actual situational context-creating power of utterances. Recent research (e.g. Abel 2003; Bortfeld 2002, 2003; Cieślicka 2004, 2006; House 2002, 2003; Kecskes 2007) demonstrated that in intercultural communication the most salient interpretation for non-native speakers is usually the propositional meaning of an utterance. So interpretation generally depends on what the utterance says rather than on what it actually communicates. As a consequence of their taking propositional meaning for the actual meaning of an utterance, interlocutors are sometimes unaware of impoliteness conveyed implicitly or through paralinguistic means.

scholarly journals A multimodal analysis of lexical explanation sequences in webconferencing-supported language teaching

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Ciara R. Wigham
Keyword(s):  
Foreign Language ◽  
Language Learning ◽  
Teaching And Learning ◽  
Sequential Analysis ◽  
Common Ground ◽  
Target Item ◽  
Business Students ◽  
Foreign Language Learning ◽  
Active Listening ◽  
Semiotic Resources

AbstractHigher education institutions are increasingly interested in offering more flexible teaching and learning delivery methods that are often independent of place. Where foreign language learning is concerned, telecollaboration is gaining ground. This paper focuses on synchronous webconferencing-supported teaching and examines how different semiotic resources are used during lexical explanation sequences. The context is a telecollaborative exchange between Business students learning French and trainee teachers on a Master’s programme in Teaching French as a Foreign Language. Using multimodal transcriptions of interaction data from two sessions, the sequential analysis provides access to different combinations of semiotic resources. These include using the visual mode to project active listening strategies and the complementary role of the text chat to secure common ground concerning the target item. The analysis sheds light on a ‘thinking break’ strategy employed by the trainees. Descriptive examples demonstrate how verbal explanations were accompanied, firstly, by deictic and iconic gestures and, secondly, by metaphoric gestures used to help forefront different properties of the target item. Finally, changes in gaze and proximity were observed as playing a role in interaction management and in signalling which verbal modality was forefronted. The study illustrates emerging pedagogical and multimodal communication strategies for ‘doing vocabulary teaching’.

scholarly journals Mathematical Reasoning Analysis in Solving Limit Functions Problems of Students in Mathematics Education of Pare-pare Muhammadiyah University

2018 ◽  
Vol 2 (1) ◽  
pp. 59
Author(s):  
Asdar Dollo
Keyword(s):  
Mathematics Education ◽  
Deductive Reasoning ◽  
Mathematical Reasoning ◽  
Inductive Reasoning ◽  
Research Process ◽  
Limit Problem ◽  
Limit Function ◽  
Research Subject ◽  
High Ability ◽  
Main Instrument

This research aimed to describe the students‘ reason in solving theproblem of limit function and comparation between high-ability subject(HS) and medium-ability subject (MS). The instrument in this research wasthe researcher himself as the main instrument guided by the task limitfunction and valid interview guidelines. Data collection was done by taskbasedinterviews. The subjects of the study were V-semester studentsconsisting of 2 students (1 subject is having high ability and 1 subject ishaving medium ability). The research process followed the steps of: (a)formulating the mathematical reasoning indicator in solving the problem oflimit function based on theory, (b) formulating the supporting instrument(task limit function and interviewing guide), (c) taking the research subject,(d) taking the data to tell the students‘ reasoning in solving the limit functiontests (f) conducting analysis of mathematical reasoning data of the studentsin solving the problem of function limit, (g) conducting discussion ofanalysis result, (h) concluding the research results. The result of the researchshowed that 1) the reasoning equation of the high-ability subject (HS) andthe medium ability subject (MS) in solving the function limit problem wasto do inductive reasoning first then perform deductive reasoning, 2)difference of reasoning subject with high ability (HS) medium ability (MS)in solving the problem of function limit was only in terms of mathematicalreasoning process.

scholarly journals Thinking and Scientific Language in the Primary Classes

2020 ◽  
Author(s):  
Anggi Cecilia Safaningrum
Keyword(s):  
Elementary School ◽  
Mathematical Reasoning ◽  
Fourth Graders ◽  
Inductive Reasoning ◽  
Sixth Graders ◽  
Scientific Language ◽  
Research Findings ◽  
Reasoning Tasks ◽  
Math Reasoning ◽  
Practical Implications

According to psychological and cognitive development theories, the preferences of pupils in elementary school toward inductive versus deductive and general types of reasoning when asked to prove or review mathematical claims, changes along the school years. This study examines this hypothesis through a survey in which 267 pupils from the Arabic sector in three different elementary schools in Israel, in grades 4 to 6 participated. The survey, based on the math reasoning tasks by Healy and Hoyles (1998), is comprised of Algebra and Geometry reasoning tasks. Additionally, 12 of these pupils’ teachers were interviewed in order to explore their attitudes toward mathematical reasoning and math proving tasks. Findings show that: 1) There is a difference in students’ preferences towards types of reasoning, between grades 4 and 6; 2) Sixth graders will be less likely to accept tautologic and inductive reasoning than fourth graders; 3) Elementary school pupils tend to prefer empirical arguments (such as inductive and example-based) as their approach in contrast to the arguments that they believe will receive the highest scores from their teachers. However, findings do not support the hypothesis that there will be a difference in teachers’ preferences towards different types of thinking. The research findings and their practical implications are discussed.

scholarly journals ANALISIS KEMAMPUAN PENALARAN INDUKTIF MATEMATIS MAHASISWA PENDIDIKAN MATEMATIKA UNIVERSITAS PAPUA

2018 ◽  
Vol 1 (2) ◽  
pp. 113
Author(s):  
Septian Woro Drupadi ◽  
Jeinne Mumu
Keyword(s):  
Mathematics Education ◽  
Qualitative Methods ◽  
Mathematical Reasoning ◽  
Inductive Reasoning ◽  
Reasoning Ability ◽  
Education Students ◽  
Reasoning Abilities ◽  
Reasoning Skills

This research was conducted to analyze the mathematical Inductive reasoning abilities of students’ mathematics education UNIPA. Research on inductive mathematical reasoning skills using qualitative methods using observation techniques, tests and interviews. The results showed that the mathematical inductive reasoning abilities of mathematics education students UNIPA were mostly in the moderate category. Students' inductive reasoning ability on each indicator is the ability to present mathematical statements in writing or drawings of 66.66%, the ability to submit suspicions by 26.66%, mathematical manipulation ability of 29.44%, ability to compile evidence, provide reasons or evidence for some solutions of 5.82%, finding patterns or traits of mathematical symptoms to generalize of 30.27%, examining validity of arguments 11.32% and drawing conclusions from statements of 5.27%.

scholarly journals PROFIL KEMAMPUAN PENALARAN INDUKTIF MATEMATIKA MAHASISWA PENDIDIKAN MATEMATIKA UNIPA DITINJAU DARI GAYA BELAJAR

2018 ◽  
Vol 1 (2) ◽  
pp. 127
Author(s):  
Agus Haryono ◽  
Benidiktus Tanujaya
Keyword(s):  
Mathematics Education ◽  
Learning Styles ◽  
Learning Style ◽  
Mathematical Reasoning ◽  
Visual Learning ◽  
Inductive Reasoning ◽  
Education Students ◽  
Reasoning Abilities ◽  
Kinesthetic Learning ◽  
Mathematical Problems

<p>The purpose of this research was to study the profile of students' mathematical inductive reasoning abilities regarding visual, auditory and kinesthetic learning styles in solving mathematical problems. The research method used is qualitative with a descriptive approach. The results of the study showed that UNIPA mathematics education students tended to study with Visual Learning Styles. Students with this learning style tend to have inductive mathematical reasoning abilities that are better than inductive mathematical reasoning abilities of students learning with auditorial learning styles and those who learn with the kinesthetic learning style. Also, Mathematics Education students of the University of Papua do not have the ability to examine the validity of an argument and find patterns or characteristics of mathematical symptoms to generalize.</p>

scholarly journals Acquiring Indonesian for 3-5 Year Olds in the Children Study Group of Wolosoko Village, Wolowaru District, Ende Regency

2021 ◽  
Vol 2 (2) ◽  
pp. 199-208
Author(s):  
Yosef Demon ◽  
Veronika Genua
Keyword(s):  
Theoretical Basis ◽  
Inductive Reasoning ◽  
Qualitative Approach ◽  
Study Group ◽  
Face To Face ◽  
Word Forms

This study aims to objectively find and describe the acquisition of Indonesian for children aged 3-5 years in the Wolosoko Village Children Study Group, Wolowaru District, Ende Regency (abbreviated as WVCSG). This paper elaborates on the acquisition and the factors that influence the acquisition of Indonesian for children aged 3-5 years at the WVCSG. This research uses a qualitative approach. An approach that emphasizes the originality of the data natural, the researcher acts as a key instrument, the data is collected using the technique of engaging, face-to-face, record and documentation. The data were analyzed using an inductive reasoning model. The theoretical basis of this paper uses Psycholinguistic theory. The results of the study prove that phonologically, children aged 3-5 years are not able to pronounce the sounds [r], [ng], [ny], [y] and [k] perfectly, while children aged 5 years are already able to pronounce these two sounds. perfectly. Morphologically, children aged 3-5 years are able to use basic words and rephrases, while children aged 5 years are able to use three word forms (basic words, rephrases and affix words). Syntactically, children aged 3-5 are able to communicate using 2-3 words while children aged 5 years are able to use 2-5 words in communicating.

scholarly journals Social semiotics analysis of Palestinian mathematics textbooks for eighth grade

2020 ◽  
Vol 5 (1) ◽  
pp. 1-12
Author(s):  
Wajeeh Daher ◽  
Ijteyad Abu Thabet
Keyword(s):  
Teaching And Learning ◽  
Mathematics Classroom ◽  
Mathematical Reasoning ◽  
Mathematical Object ◽  
Social Semiotics ◽  
Second Person ◽  
Mathematics Textbook ◽  
Mathematical Objects ◽  
Person Pronoun ◽  
Inverse Theorems

Mathematics textbook analysis can serve to understand the teaching and learning processes in the mathematics classroom. The present study utilizes a social semiotics framework to analyze the triangle unit of the Palestinian mathematics book for grade 8. The results of the study indicate that the authors utilized the representational aspect of the mathematical object to introduce those objects to the reader. Moreover, the nature of mathematics resulting from this unit is that of a subject that learners do not need material processes to discover, so it is enough to reason about it mentally to arrive at the mathematical objects and relations. The authors used a plural first-person pronoun to describe the need to engage with theorems and inverse theorems. They used the singular second-person pronoun to attract the attention of the reader to specific features of the mathematical objects. The authors did not use any pronoun when stating the theorem. Some of the connectors were verbs, nouns, and sentences, where the most used connector was the sentence, especially in reasoning. This use of the sentence in mathematical reasoning indicates that the authors wanted to advance the mathematical reasoning as a narrative to facilitate it for the reader.

scholarly journals SECONDARY SCHOOL MATHEMATICS TEACHERS’ PERCEPTIONS ABOUT INDUCTIVE REASONING AND THEIR INTERPRETATION IN TEACHING

2021 ◽  
Vol 12 (2) ◽  
pp. 239-256
Author(s):  
Landy Elena Sosa-Moguel ◽  
Eddie Aparicio-Landa
Keyword(s):  
Secondary School ◽  
Professional Learning ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Inductive Reasoning ◽  
Quadratic Equation ◽  
Analysis Method ◽  
School Teachers ◽  
Mathematical Concepts ◽  
Teachers Perceptions

Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers’ perceptions of inductive reasoning and interprets this mathematical reasoning type in teaching the quadratic equation. The data were collected from a questionnaire administered to 22 teachers and an interview conducted to expand their answers. Through the thematic analysis method, it was found that more than half the teachers perceived inductive reasoning as a process for moving from the particular to the general and as a way to acquire mathematical knowledge through questioning. Because teachers have little clarity about inductive phases and processes, they expressed confusion about teaching the quadratic equation inductively. Results indicate that secondary school teachers need professional learning experiences geared towards using inductive reasoning processes and tasks to form concepts and generalizations in mathematics.

scholarly journals Conception and development of inductive reasoning and mathematical induction in the context of written argumentations

2020 ◽  
Vol 13 (2) ◽  
pp. 65-79
Author(s):  
Tugba UYGUN-ERYURT
Keyword(s):  
Elementary Education ◽  
Mathematical Reasoning ◽  
Inductive Reasoning ◽  
Mathematical Induction ◽  
Teacher Education Programs ◽  
Factors Affecting ◽  
Grade Levels ◽  
Proof Construction ◽  
Reasoning Strategy ◽  
Multiple Case

Abstract: Nowadays, mathematical reasoning and making proof have taken importance for all students from the grade level of elementary education to university. More specifically, mathematical induction (MI) is a kind of proof and reasoning strategy taking place nearly all grade levels. Moreover, teachers are important factors affecting student learning and they can acquire necessary knowledge and skills developmentally in their teacher education programs. This paper makes contributions to domain of research by investigating the development of PMT’s conception of MI in the context of written argumentations encouraging MI. In other words, the purpose of this multiple case study is to explore how PMT’s conception of mathematical induction develop through their written argumentations. These cases show that there exist improvements in PMT’s written argumentations, conception of MI and proof construction activities related to MI. In other words, the more organized and structured they produced written argumentation, the more successfully they use and make mathematical induction.

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