Examination of 7th-grade students’ mathematical reasoning and argumentation process during problem-solving

2021 ◽  
pp. 1-28
Author(s):  
Sevilay Tavşan ◽  
Alaattin Pusmaz
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning

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 ANALISIS KEMAMPUAN PEMECAHAN MASALAH PADA SOAL CERITA MATEMATIKA BERDASARKAN TEORI POLYA DITINJAU DARI ADVERSITY QUOTIENT

2020 ◽  
Vol 2 (1) ◽  
pp. 105-128
Author(s):  
Novita Nurul Aini ◽  
Mohammad Mukhlis
Keyword(s):  
Problem Solving ◽  
Data Collection ◽  
Mathematical Reasoning ◽  
Linear Equations ◽  
Learning Goals ◽  
Problem Solving Skills ◽  
Data Presentation ◽  
Validity Test ◽  
Descriptive Research ◽  
Qualitative Descriptive

One of the studen learning goals mathematics is mathematical reasoning for outcomes training student to solve the problems. One of the problems faced by students is word questions. There are several students responses in dealing with word question which is known as Adversity Quotient. This research aims to describe the students' problem solving skills in system of three-variable linear equations subject based on Polya's theory in terms of Adversity Quotient. This is a qualitative descriptive research with three subjects of students class X IPA 1 SMAN Arjasa Jember, there are one climber student, one camper student and one quitter student. These subjects took purposive sampling with consideration according to the results of questionnaire scores that meet each of the criteria of Adversity Quotient. Data collection techniques used were questionnaires, tests, interviews and observations. The validity test used is technical triangulation. Data analyzed through data condensation, data presentation and conclusion drawing. The results showed that student with the type of climber was able to meet all the indicators of problem solving in the problem of the word questions which included indicators of understanding the problem, planning the solution, carrying out the plan of solving and re-checking. Camper type student met all indicators of problem solving except at the re-checking stage. Quitter type student in completing word questions met the stage of understanding the problem and planning the solution, while the stage of carrying out the plan and re-checking is not fulfilled by the quitter student.

scholarly journals Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

Assessing Self-regulation Development through Sharing Feedback in Online Mathematical Problem Solving Discussion

2010 ◽  
pp. 232-247 ◽  
Author(s):  
Bracha Kramarski
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Self Regulation ◽  
Sixth Grade ◽  
Mathematical Problem Solving ◽  
Social Feedback ◽  
Self Regulated Learning ◽  
Metacognitive Teaching ◽  
Online Feedback

This study examined the relative efficacies of two different metacognitive teaching methods – problem solving (M_PS) and sharing knowledge (M_SK). Seventy-two Israeli sixth-grade students engaged in online mathematical problem solving and were each supported using one of the two aforementioned methods. M_PS students used a problem-solving and feedback process based on the IMPROVE model (Kramarski & Mevarech, 2003). In contrast, M_SK participants were instructed to reflect and provide feedback on the solution without an explicit model. This study evaluated each method‘s impact on the students’ mathematical online problem solving. It also examined self-regulated learning (SRL) processes by assessing students‘ online feedback using a rubric scheme. Findings indicated that M_PS students outperformed the M_SK students in algebraic knowledge and mathematical reasoning, as well as on various measures of sharing cognitive and metacognitive feedback. The M_SK students outperformed the M_PS students on measures of sharing motivational and social feedback.

Brief Report: Gender Differences in Mathematics: An International Perspective

1990 ◽  
Vol 21 (1) ◽  
pp. 74-80
Author(s):  
Corinna A. Ethington
Keyword(s):  
Gender Differences ◽  
Elementary School ◽  
Problem Solving ◽  
Mathematical Reasoning ◽  
International Perspective ◽  
School Level ◽  
Spatial Problem ◽  
National Assessment ◽  
Factors Associated ◽  
Quantitative Performance

Gender-related differences on measures of quantitative performance and problem-solving abilities consistently appear in national assessments (e.g., Dossey, Mullis, Lindquist, & Chambers, 1988; Fennema & Carpenter, 1981; National Assessment of Educational Progress, 1975, 1983; Wilson, 1972). Using a variety of performance measures, investigators have examined the nature of these differences and the factors associated with them for subjects varying in age from elementary school to undergraduates in college. From these studies, it is generally concluded that no gender differences are evidenced at the elementary school level, but beginning at approximately the seventh grade, any differences that appear, such as those found in spatial problem-solving tasks and tasks requiring mathematical reasoning, favor males. (See Fennema, 1974, 1980 and Leder, 1985, for a review of this literature.)

scholarly journals PROFIL PENALARAN MATEMATIS SISWA SMP DALAM PEMECAHAN MASALAH ARITMETIKA SOSIAL BERDASARKAN KEMAMPUAN MATEMATIKA

MATHEdunesa ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 110-120
Author(s):  
YULIANA DWI RAHMAWATI ◽  
Masriyah Masriyah
Keyword(s):  
Problem Solving ◽  
Qualitative Data ◽  
Mathematical Reasoning ◽  
Research Subjects ◽  
Ability Test ◽  
Reasoning Abilities ◽  
Mathematical Abilities ◽  
Reasoning Problem ◽  
Mathematical Problems ◽  
Problem Solving Strategies

Mathematical reasoning is the ability to think about mathematical problems, namely by thinking logically about mathematical problems to get conclusions about problem solutions. There are several factors that can affect students' mathematical reasoning, including mathematical abilities. Dissimilarity of students' mathematical abilities allows for dissimilarity in their mathematical reasoning abilities. So, this research intends to describe students' mathematical reasoning abilities in solving social arithmetic problems based on dissimilarity in mathematical abilities. The purpose of this research was to describe qualitative data about the mathematical reasoning abilities of students with high, medium, or low abilities in solving social arithmetic problems. The instrument used was the Mathematical Ability Test to determine the three research subjects, followed by a Problem Solving Test to get qualitative data about students' mathematical reasoning abilities, then interviews to get deeper data that was not obtained through written tests. Thus, the research data were analyzed using mathematical reasoning indicators. From the result of data analysis, it was found that all students understood the problem well. Students with high and medium mathematical abilities are determining and implementing problem solving strategies properly, namely writing down the step for solving them correctly and making accurate conclusions by giving logical argumens at aech step of the solution. However, students with low mathematical abillities have difficulty in determining and implementing problem solving strategies because they do not understand the concept, thus writing the steps to solve the problems incorrectly and not giving accurate conclusions about the correctness of the solution. Keywords: mathematical reasoning, problem solving, mathematical abilities

scholarly journals Perbandingan keefektifan pendekatan problem solving dan problem posing dalam pembelajaran matematika pada siswa SMP

2016 ◽  
Vol 11 (2) ◽  
pp. 136
Author(s):  
Harinda Nurril Falach
Keyword(s):  
High School ◽  
Problem Solving ◽  
Junior High School ◽  
Junior High ◽  
Mathematical Reasoning ◽  
Mathematical Understanding ◽  
T Test ◽  
Problem Posing ◽  
Reasoning Ability ◽  
Quasi Experiment

Penelitian ini bertujuan untuk mendeskripsikan: 1) keefektifan pendekatan problem solving terhadap kemampuan pemahaman dan penalaran matematis; 2) keefektifan pendekatan problem posing terhadap kemampuan pemahaman dan penalaran matematis; 3) perbandingan keefektifan antara pendekatan pembelajaran problem solving dan problem posing terhadap kemampuan pemahaman dan penalaran matematis siswa SMP pada pembelajaran bangun ruang sisi datar. Penelitian ini merupakan penelitian eksperimen semu (quasi experiment). Data dianalisis menggunakan one sample t test, uji MANOVA rumus T2 Hotteling, dan uji t kriteria Bonferroni. Hasil penelitian menunjukkan bahwa: 1) pendekatan problem solving  efektif terhadap kemampuan pemahaman dan penalaran matematis; 2) pendekatan problem posing efektif terhadap kemampuan pemahaman dan penalaran matematis; 3) pendekatan problem solving lebih efektif dibandingkan problem solving terhadap kemampuan pemahaman matematis tetapi pendekatan problem solving tidak lebih efektif dibandingkatn problem posingterhadap kemampuan penalaran matematis siswa SMP pada pembelajaran bangun ruang sisi datar.Kata kunci: pendekatan problem solving, pendekatan problem posing, kemampuan pemahaman matematis, dan kemampuan penalaran matematis. The effectiveness comparison of problem solving and problem posing approaches in mathematics learning towards junior high school students AbstractThe aim of this study is to describe: 1) the effectiveness of problem solving approach on mathematical understanding and reasoning ability; 2) the effectiveness of problem posing approach on mathematical understanding and reasoning ability; 3) the comparison effectiveness of polyhedral learning using problem solving approach and problem posing approach on mathematical understanding and reasoning ability of State Junior High School. This study was a quasi experiment. The data were analyzed using one-sample t test, MANOVA test with T2 Hotteling's formula, and t-test with Bonferroni criterion. The results of the study show that: 1) the problem solving approach has an effect on mathematical understanding and reasoning ability; 2) the problem posing approach has an effect on mathematical understanding and reasoning ability; and 3) the problem solving approach is more effective than the problem posing approach on mathematical understanding ability, but the problem solving approach is not more effective in polyhedral learning than the problem posing approach on mathematical reasoning ability of State Junior High.Keywords: problem solving approach, problem posing approach, mathematical understanding ability, and mathematical reasoning ability

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