Developing a model for problem-solving in a Grade 4 mathematics classroom

The teaching of problem-solving through the development of a problem-solving model was investigated in a Grade 4 mathematics classroom. Learners completed a questionnaire regarding their knowledge of mathematical problem-solving, their attitudes towards problem-solving, as well as their experiences in solving problems. Learners’ responses revealed overall negative beliefs towards problem-solving as well as a lack of knowledge about what problem-solving in mathematics entails. The teacher then involved the learners in a structured learning programme where they worked in cooperative groups of six on different kinds of mathematical problems to solve. The groups regularly engaged in discussions about the different strategies they were using to solve a specific problem and eventually succeeded in formulating a generic problem-solving model they could call their own. The model was effectively used by the learners to solve various mathematical problems, reflecting their levels of cognitive development to a certain extent.

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Examining Mathematical Problem-Solving Beliefs among Rwandan Secondary School Teachers

International Journal of Learning Teaching and Educational Research ◽

10.26803/ijlter.20.7.13 ◽

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.

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Students’ Reflections on Dispositions in a Mathematics Classroom

Journal of ASIAN Behavioural Studies ◽

10.21834/jabs.v6i18.384 ◽

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

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

Educational Studies in Mathematics ◽

10.1007/s10649-021-10051-2 ◽

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.

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Students’ suspension of sense making in problem solving

ZDM ◽

10.1007/s11858-020-01215-0 ◽

2021 ◽

Author(s):

Gemma Carotenuto ◽

Pietro Di Martino ◽

Marta Lemmi

Keyword(s):

Problem Solving ◽

Qualitative Study ◽

Word Problem ◽

Word Problems ◽

Mathematical Problem ◽

Critical Issue ◽

Mathematical Problem Solving ◽

Sense Making ◽

Mathematical Problems

AbstractResearch on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms ‘realistic’ and ‘modeling’ associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students’ suspension of sense making when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students’ approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activation of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem.

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Teaching Personal Finance Mathematical Problem Solving to Individuals With Moderate Intellectual Disability

Career Development and Transition for Exceptional Individuals ◽

10.1177/2165143416681288 ◽

2016 ◽

Vol 40 (1) ◽

pp. 5-14 ◽

Cited By ~ 13

Author(s):

Jenny Root ◽

Alicia Saunders ◽

Fred Spooner ◽

Chelsi Brosh

Keyword(s):

Problem Solving ◽

Mathematical Problem ◽

Functional Relation ◽

Personal Finance ◽

Future Research ◽

School Students ◽

Problem Solving Skills ◽

Mathematical Problems ◽

Based Instruction ◽

Multiple Probe

The ability to solve mathematical problems related to purchasing and personal finance is important in promoting skill generalization and increasing independence for individuals with moderate intellectual disabilities (IDs). Using a multiple probe across participant design, this study investigated the effects of modified schema-based instruction (MSBI) on personal finance problem solving skills, purchasing an item on sale or leaving a tip, and using a calculator or iDevice (i.e., iPhone or iPad) for three middle school students diagnosed with a moderate ID. The results showed a functional relation between MSBI using a calculator on the participant’s ability to solve addition and subtraction personal finance word problems and generalize to iDevices. The findings of this study provide several implications for practice and offer suggestions for future research.

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PENDEKATAN MATEMATIKA REALISTIK UNTUK MEMBANGUN KEMAMPUAN PEMECAHAN MASALAH MATEMATIS SISWA KELAS XI IPS PADA MATERI PELUANG [REALISTIC MATHEMATICS EDUCATION IN BUILDING THE MATHEMATICS PROBLEM-SOLVING ABILITIES OF GRADE 11 SOCIAL SCIENCE TRACK STUDENTS STUDYING PROBABILITY]

JOHME Journal of Holistic Mathematics Education ◽

10.19166/johme.v2i2.1691 ◽

2019 ◽

Vol 2 (2) ◽

pp. 119

Author(s):

Susiana Juseria Tambunan ◽

Debora Suryani Sitinjak ◽

Kimura Patar Tamba

Keyword(s):

Problem Solving ◽

Social Science ◽

Mathematical Problem ◽

Mathematical Problem Solving ◽

Mathematics Problem Solving ◽

Realistic Mathematics ◽

Mathematical Problems ◽

Mathematic Education ◽

Realistic Mathematic ◽

Grade 11

This research aims to build students’ abilities in mathematical problem-solving and to explain the uniqueness of the steps of realistic mathematic education in building the problem-solving abilities of a grade 11 (social science track) class in the study of probability at one of the schools in Kupang. The observation results found that every student was having difficulties to solving the mathematical problems, particularly the narrative questions. The research method is Kemmis and Taggart model of Classroom Action Research which was conducted in three cycles, from October 4 to November 3 with twenty-four students. Triangulation had been done to every instrument of variable. The data of mathematical problem-solving was obtained from the students by using test sheets, questionnaires, and student’s discussion sheets. Meanwhile, the data of realistic mathematic education’s variable was obtained from three sources: mentors, two colleagues, and students that were using test sheets, questionnaires, and student’s discussion sheets. The results showed that the fourteen-steps of Realistic Mathematic Education that had been done were able to build mathematical problem-solving abilities of the students. This was evidenced through the increase of three indicators of mathematical problem-solving in every cycle. The average increase of indicators of mathematical problem-solving of the grade 11 students from the first to the third cycle was 10%. Therefore, it can be concluded that the Realistic Mathematics Approach can build the ability of problem-solving of grade 11 students in a social science track studying probability at one of the schools in Kupang.BAHASA INDONESIA ABSTRACT: Penelitian ini bertujuan untuk membangun kemampuan pemecahan masalah matematis siswa dan menjelaskan kekhasan langkah-langkah pendekatan matematika realistik untuk membangun kemampuan tersebut di salah satu sekolah di Kupang kelas XI IPS pada materi peluang topik kaidah pencacahan. Pada hasil pengamatan ditemukan bahwa setiap siswa kesulitan dalam memecahkan masalah matematis khususnya soal berbentuk cerita. Metode penelitian yang digunakan adalah Penelitian Tindakan Kelas model Kemmis dan Taggart yang berlangsung selama tiga siklus, yaitu 04 Oktober – 03 November kepada 24 orang siswa. Triangulasi dilakukan pada setiap instrumen variabel. Data variabel kemampuan pemecahan masalah matematis diperoleh dari siswa menggunakan lembar tes, lembar angket, dan lembar diskusi siswa. Sedangkan data variabel tingkat pelaksanaan pendekatan matematika realistik diperoleh dari tiga sumber, yaitu mentor, dua orang rekan sejawat, dan siswa menggunakan lembar observasi, lembar angket, dan lembar wawancara. Hasil penelitian menunjukkan bahwa keempat belas langkah-langkah pendekatan matematika realistik yang terlaksana dengan baik sekali mampu membangun kemampuan pemecahan masalah matematis setiap siswa kelas XI IPS di salah satu sekolah di Kupang. Hal ini dinyatakan melalui peningkatan ketiga indikator pemecahan masalah matematis di setiap siklus. Peningkatan rata-rata indikator pemecahan masalah matematis siswa kelas XI IPS dari siklus pertama sampai ketiga adalah sebesar 10%. Oleh karena itu, dapat disimpulkan bahwa pendekatan matematika realistik dapat membangun kemampuan pemecahan masalah matematis siswa kelas XI IPS di salah satu sekolah di Kupang pada materi peluang topik kaidah pencacahan.

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Pengaruh Model Pembelajaran E-learning Berbantuan Media Pembelajaran Edmodo Terhadap Kemampuan Pemecahan Masalah Matematis Peserta Didik

NUMERICAL Jurnal Matematika dan Pendidikan Matematika ◽

10.25217/numerical.v3i1.453 ◽

2019 ◽

pp. 31-42

Author(s):

Hanifah Hanifah ◽

Nanang Supriadi ◽

Rany Widyastuti

Keyword(s):

Problem Solving ◽

Quantitative Research ◽

Mathematical Problem ◽

Learning Model ◽

Mathematical Problem Solving ◽

Learning Material ◽

Learning Models ◽

Mathematical Problems ◽

E Learning ◽

Initial Knowledge

Mathematical problem solving is a problem solving that uses mathematical problem solving. Students in the problem solving did not use the polya method so that students succeeded in difficulties. Educators still use conventional learning models so that students become bored, passive and reluctant to ask whether going forward working on the questions given by the educator, so that new learning models need to be applied. The e-learning learning model assisted with Edmodo learning media is an online presentation material on an Edmodo account using the mobile phone of students. PAM is the knowledge learned by students before getting learning material. This study aims to study the interaction of e-learning learning models assisted by Edmodo learning media to solve mathematical problems. This study is quantitative research. Data collection used with tests, interviews, collection and collection. The data analysis technique uses two-way anava test with cells that are not the same. From the results of the analysis, the influence of the e-learning learning model on mathematical problem solving abilities. It is necessary to question the high, medium, and low mathematical initial knowledge of Great mathematical problem solving ability, then there is no difference between assisted e-learning learning models edmodo, mathematical initial knowledge of mathematical problem solving abilities.

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PENERAPAN I-SPRING SUITE 8 PADA MODEL PEMBELAJARAN IMPROVE UNTUK MENINGKATKAN KEMAMPUAN PEMAHAMAN DAN PEMECAHAN MASALAH MATEMATIS PESERTA DIDIK PADA POKOK BAHASAN PROGRAM LINEAR DI TINGKAT SEKOLAH MENENGAH

Gunahumas ◽

10.17509/ghm.v2i2.23026 ◽

2020 ◽

Vol 2 (2) ◽

pp. 357-386

Author(s):

Yomi Chaeroni ◽

Nizar Alam Hamdani ◽

Akhmad Margana ◽

Dian Rahadian

Keyword(s):

Problem Solving ◽

Direct Instruction ◽

Mathematics Learning ◽

Mathematical Problem ◽

Learning Model ◽

Mathematical Understanding ◽

Learning Models ◽

Research Subjects ◽

Purposive Sampling ◽

Mathematical Problems

ABSTRAK Penelitian ini dilatarbelakangi oleh fakta bahwa kemampuan pemahaman dan kemampuan pemecahan masalah matematis merupakan salah satu kemampuan matematika tingkat tinggi yang harus dimiliki oleh setiap peserta didik. Selain itu kemampuan pemahaman dan kemampuan pemecahan masalah matematis jarang diterapkan dalam pembelajaran matematika di sekolah. Salah satu model pembelajaran yang dapat menjadi alternatif bagi pembelajaran matematika dan kemampuan pemahaman dan pemecahan masalah matematis adalah model pembelajaran IMPROVE. Penelitian ini bertujuan untuk mengetahui penerapan i-spring suite 8 pada model pembelajaran IMPROVE untuk meningkatkan kemampuan pemahaman dan pemecahan masalah matematis peserta didik. Metode penelitian yang digunakan adalah quasi eksperimen karena penelitian ini menggunakan satu kelas eksperimen dan satu kelas kontrol sebagai subyek penelitian. Cara pengambilan subjek penelitian yang digunakan adalah purposive sampling. Subjek penelitian dipilih sebanyak dua kelas dari keseluruhan peserta didik kelas XI SMA Muhammadiyah Banyuresmi tahun pelajaran 2019/2020. Dari hasil penelitian dan perhitungan statistik diperoleh kesimpulan: 1) Terdapat peningkatan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan i-spring suite 8 pada model pembelajaran IMPROVE; 2) Terdapat peningkatan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan model pembelajaran konvensional/direct instruction; 3) Terdapat peningkatan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan i-spring suite 8 pada model pembelajaran IMPROVE dibandingkan dengan peserta didik yang dalam pembelajarannya menggunakan model pembelajaran konvensional/direct instruction; 4) Tidak terdapat perbedaan kemampuan pemahaman dan pemecahan masalah matematis peserta didik yang dalam pembelajarannya menggunakan i-spring suite 8 pada model pembelajaran IMPROVE dan yang menggunakan model konvensional/direct instruction.Kata kunci: Kemampuan Pemahaman Matematis, Kemampuan Pemecahan Masalah Matematis, Model IMPROVEABSTRACT This research is motivated by the fact that the ability to understand and the ability to solve mathematical problems is one of the high-level mathematical abilities that must be possessed by every student. In addition, the ability to understand and the ability to solve mathematical problems are rarely applied in mathematics learning in schools. One learning model that can be an alternative for mathematics learning and mathematical understanding and problem solving abilities is the IMPROVE learning model. This study aims to determine the application of ispring suite 8 on the IMPROVE learning model to improve students' mathematical understanding and problem solving abilities. The research method used is quasi-experimental because this study uses one experimental class and one control class as research subjects. The method of taking the research subject used was purposive sampling. The research subjects were selected as many as two classes from all grade XI students of SMA Muhammadiyah Banyuresmi in the 2019/2020 academic year. From the results of research and statistical calculations conclusions: 1) There is an increase in the ability to understand and solve mathematical problems of students who in learning use the i-spring suite 8 on the IMPROVE learning model; 2) There is an increase in the ability of understanding and solving mathematical problems of students who in learning use conventional learning models / direct instruction; 3) There is an increase in students' mathematical understanding and problem solving abilities in learning using i-spring suite 8 in the IMPROVE learning model compared to students in learning using conventional learning models / direct instruction; 4) There is no difference in the ability to understand and solve mathematical problems of students who in learning use the i-spring suite 8 on the IMPROVE learning model and who use the conventional model / direct instruction.Keywords: Mathematical Understanding Ability, Mathematical Problem Solving Ability, IMPROVE Model

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Analytic program derivation in type theory

Twenty Five Years of Constructive Type Theory ◽

10.1093/oso/9780198501275.003.0009 ◽

1998 ◽

Author(s):

Petri Mäenpää

Keyword(s):

Mathematical Method ◽

Problem Solving ◽

Type Theory ◽

Mathematical Problem ◽

Geometric Analysis ◽

Algebraic Method ◽

Point Of View ◽

Program Derivation ◽

Mathematical Problems ◽

The Given

This work proposes a new method of deriving programs from their specifications in constructive type theory: the method of analysis-synthesis. It is new as a mathematical method only in the area of programming methodology, as it is modelled upon the most successful and widespread method in the history of exact sciences. The method of analysis-synthesis, also known as the method of analysis, was devised by Ancient Greek mathematicians for solving geometric construction problems with ruler and compass. Its most important subsequent elaboration is Descartes’s algebraic method of analysis, which pervades all exact sciences today. The present work expands this method further into one that aims at systematizing program derivation in a heuristically useful way, analogously to the way Descartes’s method systematized the solution of geometric and arithmetical problems. To illustrate the method, we derive the Boyer-Moore algorithm for finding an element that has a majority of occurrences in a given list. It turns out that solving programming problems need not be too different from solving mathematical problems in general. This point of view has been emphasized in particular by Martin-Löf (1982) and Dijkstra (1986). The idea of a logic of problem solving originates in Kolmogorov (1932). We aim to refine the analogy between programming and mathematical problem solving by investigating the mathematical method of analysis in the context of programming. The central idea of the analytic method, in modern terms, is to analyze the functional dependencies between the constituents of a geometric configuration. The aim is to determine how the sought constituents depend on the given ones. A Greek analysis starts by drawing a diagram with the sought constructions drawn on the given ones, in the relation required by the problem specification. Then the sought constituents of the configuration are determined in terms of the given ones. Analysis was the Greeks’ method of discovering solutions to problems. Their method of justification was synthesis, which cast analysis into standard deductive form. First it constructed the sought objects from the given ones, and then demonstrated that they relate as required to the given ones. In his Geometry, Descartes developed Greek geometric analysis-synthesis into the modern algebraic method of analysis.

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Pre-Service Class Teacher’ Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

Higher Education Studies ◽

10.5539/hes.v6n3p32 ◽

2016 ◽

Vol 6 (3) ◽

pp. 32 ◽

Cited By ~ 2

Author(s):

Nahil M. Aljaberi ◽

Eman Gheith

Keyword(s):

High School ◽

Problem Solving ◽

Daily Life ◽

Mathematical Problem ◽

Service Class ◽

Problem Solving Skills ◽

Life Issues ◽

Mathematical Problems ◽

Academic Year ◽

Class Teacher

This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya’s Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving skills in daily-life issues. The study sample consisted of 65 female students majoring in class teacher. Data were collected using two questionnaires: the mathematical problem solving test which was developed by the researchers and daily life problem solving scale which was developed by (Hamdi, 1998). The findings indicate that students had high level skills in solving daily problems; there are no statistically significant differences in daily problem solving in relation to their academic year or high-school stream. Conversely, the findings also indicate weaknesses in students’ skills in solving mathematical problems, with no statistically significant differences among students in solving mathematical problems according to Polya’s problem solving steps. However, there were statistically significant differences in students’ performance in solving mathematical problems in relation to the mathematical topic, and in favor of measurements and algebra; in addition to statistically significant differences in students’ ability to solve mathematical problems in relation to academic year and high-school stream, but no correlation between students’ abilities in solving mathematical problems and those in solving daily problems.

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