scholarly journals Advanced Mathematical Thinking and Students’ Mathematical Learning: Reflection from Students’ Problem-Solving in Mathematics Classroom

2016 ◽  
Vol 5 (3) ◽  
pp. 72 ◽  
Author(s):  
Wasukree Sangpom ◽  
Nisara Suthisung ◽  
Yanin Kongthip ◽  
Maitree Inprasitha
Keyword(s):  
Problem Solving ◽  
Undergraduate Students ◽  
Tertiary Education ◽  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Advanced Mathematical Thinking ◽  
Mathematical Learning ◽  
Teaching Concept ◽  
Calculus I

<p>Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students’ inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In order to overcome this learning deficit, it is necessary that the concept of “reflection” be implemented in the teaching of this subject. It is believed that the adoption of this teaching concept will allow students to learn mathematics by themselves. This article is aimed at presenting mathematical problem-solving of undergraduate students on Calculus I. Concrete problems were assigned to students to participate, to improve students’ way of mathematical thinking, and to encourage the students’ mathematical learning and advanced mathematical thinking. The study was a qualitative research project conducted with first-year undergraduate students of Rajamangala University of Technology Phra Nakhon who had enrolled for Calculus I. Data were collected from interviews and field notes, along with video recordings. Findings showed that students succeeded in solving mathematical problems from simple to complex levels and using the subject fundamentals to connect to several methods of higher levels of thinking. Students also created effective means of problem-solving and applied these concepts to solve new problems.</p>

scholarly journals “I am part of the group, the others listen to me”: theorising productive listening in mathematical group work

2021 ◽  
Author(s):  
Marie Sjöblom ◽  
Tamsin Meaney
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Design Research ◽  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Sufficient Information ◽  
Educational Design ◽  
Mathematical Problems ◽  
Communication Frameworks

AbstractAlthough group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students’ listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, “productive listening,” is described which focuses on observable features connected to students’ ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker’s contribution as being valuable and feeling that one’s own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others’ mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework

2020 ◽  
Vol 13 (2) ◽  
pp. 130-151
Author(s):  
Kadek Adi Wibawa ◽  
I Putu Ade Andre Payadnya ◽  
I Made Dharma Atmaja ◽  
Marius Derick Simons
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Undergraduate Students ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Graph Representations ◽  
Symbolic Representations ◽  
Mathematics Educators ◽  
Three Stages ◽  
Algebraic Forms

 [English]: The fragmentation of thinking structure is a failed construction existing in students’ memory due to disconnections on what they have learned. It makes students undergo difficulties and errors in solving mathematical modeling problems. There is a need to prevent permanent fragmentations. The problem-solving involving modeling problems requires translational thinking, changing from source representations to targeted representations. This research aimed to formulate undergraduate students’ effort in restructuring their fragmented translational thinking (defragmentation of translational thinking structure). The defragmentation was mapped through the CRA framework (checking, repairing, ascertaining). The subjects were three of eighty-five 4th and 6th-semester students. Data were analyzed through three stages; categorization, reduction, and conclusion. The analysis resulted in three types of defragmentation of translational thinking structure: from verbal representations to graph representations, from graph representations to symbolic representations (algebraic forms), and from the graph and symbolic representations to mathematical models. The finding shows that it is essential for mathematics educators to allow students to manage their thinking structures while experiencing difficulties and errors in mathematical problem-solving. Keywords: Thinking structure, Fragmentation, Defragmentation, Translational thinking, CRA framework  [Bahasa]: Fragmentasi struktur berpikir merupakan kegagalan konstruksi yang terjadi di dalam memori akibat dari konsep-konsep yang dipelajari tidak terkoneksi dengan baik. Hal ini membuat mahasiswa sering mengalami kesulitan dan kesalahan dalam memecahkan masalah pemodelan matematika. Untuk itu, perlu dilakukan upaya agar tidak terjadi fragmentasi struktur berpikir yang permanen. Dalam memecahkan masalah pemodelan matematika, mahasiswa perlu melakukan berpikir translasi, yaitu mengubah representasi sumber menjadi representasi yang ditargetkan. Penelitian ini bertujuan untuk merumuskan upaya mahasiswa dalam melakukan penataan fragmentasi struktur berpikir translasi yang terjadi (defragmentasi struktur berpikir translasi) dalam memecahkan masalah pemodelan matematika. Defragmentasi yang dilakukan mahasiswa dipetakan melalui kerangka CRA (checking, repairing, dan ascertaining). Subjek penelitian adalah mahasiswa semester 4 dan 6 yang terdiri dari 3 orang dipilih dari 85 mahasiswa. Analisis data dilakukan melalui tiga tahap, yaitu pengategorian data, reduksi data, dan penarikan kesimpulan. Penelitian ini menemukan tiga jenis defragmentasi struktur berpikir translasi: defragmentasi dari representasi verbal ke grafik, dari representasi grafik ke simbol (bentuk aljabar), dan representasi grafik dan simbol (bentuk aljabar) ke model matematika. Penelitian ini menunjukkan pentingnya pengajar matematika memberikan kesempatan kepada mahasiswa dalam menata struktur berpikirnya ketika mengalami kesulitan dan kesalahan dalam memecahkan masalah matematika. Kata kunci: Struktur berpikir, Fragmentasi, Defragmentasi, Berpikir translasi, Kerangka CRA

scholarly journals Examining Mathematical Problem-Solving Beliefs among Rwandan Secondary School Teachers

2021 ◽  
Vol 20 (7) ◽  
pp. 227-240
Author(s):  
Aline Dorimana ◽  
Alphonse Uworwabayeho ◽  
Gabriel Nizeyimana
Keyword(s):  
Problem Solving ◽  
Secondary School Teachers ◽  
Mathematics Classroom ◽  
Mathematical Problem ◽  
Real Life ◽  
Mathematical Problem Solving ◽  
Teachers Beliefs ◽  
Mathematical Problems ◽  
Teacher Professional

This study explored teachers' beliefs about mathematical problem-solving. It involved 36 identified teachers of Kayonza District in Rwanda via an explanatory mixed-method approach. The findings indicate that most teachers show a positive attitude towards advancing problem-solving in the mathematics classroom. However, they expose different views on its implementation. Role of problem-solving, Mathematical problems, and Problem-solving in Mathematics were identified as main themes. Problem-solving was highlighted as an approach that helps teachers use time adequately and helps students develop critical thinking and reasoning that enable them to face challenges in real life. The study recommends teacher professional development initiatives with their capacity to bring problem-solving to standard.

scholarly journals Students’ Reflections on Dispositions in a Mathematics Classroom

2021 ◽  
Vol 6 (18) ◽  
pp. 61-78
Author(s):  
Teoh Sian Hoon ◽  
Parmjit Singh ◽  
Mazlini Adnan ◽  
Koo Ah Choo
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Publishing House ◽  
Mathematical Problem ◽  
Reflective Journal ◽  
Mathematics Classrooms ◽  
Mathematical Problems ◽  
International Publishing ◽  
Journal Entries ◽  
Open Access Article

This study investigated students' dispositions. It is a qualitative study that analyzes students' reflective journal entries. It captured students’ dispositions and described how the reflective activities influence their engagement mathematical problem-solving. The findings showed that the students considered the mathematical problems were challenging to them, but their positive dispositions kept them engaged in learning. Engagement through effort and thinking algebraically with teachers' guidance was the crucial first steps in problem-solving. Results from this study provide educators with a wealth of knowledge to develop learning dispositions that will encourage active thinking and engagement among students in mathematics classrooms.                                                                Keywords: reflection; disposition; mathematics; engagement eISSN 2514-7528 © 2021 The Authors. Published for AMER ABRA CE-Bs by E-International Publishing House, Ltd., UK. This is an open-access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians / Africans / Arabians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/jabs.v6i18.384

scholarly journals Peningkatan kemampuan pemecahan masalah matematis siswa melalui penerapan model pembelajaran missouri mathematic project

2021 ◽  
Vol 2 (1) ◽  
pp. 33-41
Author(s):  
Boni Harianda ◽  
Beni Junedi
Keyword(s):  
Data Analysis ◽  
Problem Solving ◽  
Learning Process ◽  
Mathematical Problem ◽  
Learning Model ◽  
Mathematical Problem Solving ◽  
Research Subjects ◽  
Mathematical Learning ◽  
Ability Test ◽  
Problem Solving Skills

Abstrak. Pemecahan masalah merupakan kemampuan dasar yang seharusnya dimiliki ole siswa. Kemampuan pemecahan masalah matematis berperan dalam menyelesaikan setiap permasalahan baik pelajaran lain maupun permasalahan dalam kehidupan sehari-hari. Melalui kegiatan pemecahan masalah matematis siswa diarahkan dalam membangun pengetahuan matematika, berpikir logis, sistematis dan terukur. Faktanya kemampuan pemecahan masalah matematis siswa masih rendah. Proses pembelajaran yang menitikberatkan pada latihan yang memberikan kesempatan pada siswa dalam mengembangkan kemampuan pemecahan masalah matematis menjadi model perbaikan dalam proses pembelajaran. Model pembelajaran missouri mathematic project merupakan model pembelajaran yang tepat memfasilitasi siswa dalam mengembangkan pemikirannya dalam menyelesaikan soal-soal pemecahan masalah matematis. Untuk itu penelitian ini bertujuan untuk meningkatkan kemampuan pemecahan masalah matematis siswa melalui penerapan model pembelajaran missouri mathematic project. Jenis penelitian merupkan penelitian tindakan kelas (PTK). Subjek penelitian siswa kelas V MIS Al Firdausy Pematang Reba. Teknik pengumpulan data yang digunakan tes kemampuan pemecahan masalah matematis. Teknik analisis data yang digunakan adalah analisis data kuantitatif. Berdasarkan hasil tes kemampuan pemecahan masalah matematis terjadi peningkatan pada setiap siklus dimulai dari tes awal pra tindakan, siklus I dan siklus II. Dapat disimpulkan bahwa terjadi peningkatan kemampuan pemecahan masalah matematis siswa melalui penerapan model pembelajaran missouri mathematic project. Abstract. Problem solving is a basic skill that should be possessed by students. Mathematical problem solving abilities play a role in solving every problem both other subjects and problems in everyday life. Through mathematical problem solving activities students are directed to build mathematical knowledge, think logically, systematically and measurably. The fact is that students' mathematical problem solving abilities are still low. The learning process that focuses on exercises that provide opportunities for students to develop mathematical problem solving skills to become a model for improvement in the learning process. The Missouri Mathematical Project learning model is an appropriate learning model to facilitate students in developing their thinking in solving mathematical problem solving problems. For this reason, this study aims to improve students' mathematical problem solving abilities through the application of the Missouri mathematical learning model. This type of research is a classroom action research (PTK). The research subjects were grade V students of MIS Al Firdausy Pematang Reba. The data collection technique used was a mathematical problem-solving ability test. The data analysis technique used is quantitative data analysis. Based on the results of the test of mathematical problem solving abilities, there was an increase in each cycle starting from the initial pre-action test, cycle I and cycle II. It can be concluded that there is an increase in students' mathematical problem solving abilities through the application of the Missouri mathematical learning model.

scholarly journals PENGARUH METODE THINKING ALOUD PAIR PROBLEM SOLVING TERHADAP PENINGKATAN KEMAMPUAN MENYELESAIKAN MASALAH MATEMATIKA MAHASISWA

2019 ◽  
Vol 7 (2) ◽  
pp. 48
Author(s):  
Yuntawati Yuntawati
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Average Score ◽  
Single Subject ◽  
Thinking Aloud ◽  
Baseline Phase ◽  
Ability Test ◽  
Group Design ◽  
Average Value ◽  
Calculus I

The purpose of this study was to determine the effect of the Thingking Aloud Pair Problem Solving (TAPPS) Method on the Mathematical Problem Solving Capabilities of Semester 1 Students in Mathematics Education Program FPMIPA IKIP Mataram on Calculus I Subjects. The research method used was a quasi single subject experiment with group design (group design). In this study comparisons between groups using the average score (mean) with AB design, namely measurement of target behavior in the baseline phase (A) before the application of the TAPPS method carried out in two sessions and the provision of intervention (B) or the application of the TAPPS method performed in two sessions anyway. The instrument used was a lecturer and student activity observation sheet, to collect data about developments in each session or stage, a student interview guide, used to dig deeper information about the application of the TAPPS learning method, and a problem solving ability test sheet. The results of this study indicate an increase in the average value of session 1 by 60.17 and session 2 by 60.67 in the baseline phase (A) to session 3 by 66.83 and session 4 by 71.5 in the intervention phase (B). Based on the results of the study it can be concluded that the application of the TAPPS method has a positive effect on the ability to solve calculus I problems.

scholarly journals Key Universal Activities of Mathematical Learning in Problem Solving Mathematics Classroom

2013 ◽  
Vol 04 (11) ◽  
pp. 700-704
Author(s):  
Saastra Laah-On ◽  
Pimpaka Intaros ◽  
Kiat Sangaroon
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Mathematical Learning

scholarly journals Undergraduate Students’ Difficulties in Solving Derivative and Integral Mathematical Problems

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Nourooz Hashemi ◽  
Mohd Salleh Abu ◽  
Hamidreza Kashefi
Keyword(s):  
Problem Solving ◽  
Qualitative Methods ◽  
Undergraduate Students ◽  
Mathematical Thinking ◽  
Previous Knowledge ◽  
Mathematical Problems ◽  
Symbolic World ◽  
Quantitative And Qualitative Methods ◽  
Experienced Difficulty

Undergraduate students often experienced difficulty in solving problem related to derivative and integral topics. The main goal of this study was to investigate the reasons of students’ difficulties in solving derivative and integral problems based on mathematical thinking approach. The participants of the study consisted of 63 undergraduate students. A test contained derivative and integral problems was given to students and the results was analyzed by quantitative and qualitative methods. Results revealed that the reasons of students’ difficulties in solving problems were inability to use suitable problem solving framework, weakness in recalling previous knowledge in entry and attack steps of specialization and generalization, weakness in making connection between embodied and symbolic worlds of mathematical thinking and using symbolic world rather than embodied world.

Teaching Mathematics With Technology: Using the Video Camera in Mathematical Problem Solving

1993 ◽  
Vol 41 (1) ◽  
pp. 41-43
Author(s):  
M. G. (Peggy) Kelly ◽  
James H. Wiebe
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Instructional Television ◽  
Video Camera ◽  
Video Technology ◽  
Evaluation Standards ◽  
Reasoning Abilities ◽  
Visual Element ◽  
Effective Use

In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), technology, including the use of video, is discussed as a way to develop mathematical thinking and reasoning abilities, promote problem solving, and apply mathematics in the classroom. Effective use of the video camera and instructional television may help students construct meaning in mathematical situations. Video technology brings in the outside world and adds excitement to the classroom by contributing a visual element that is often lacking in class discussions.

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