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Sarjana, Ketut, Laila Hayati, and Wahidaturrahmi Wahidaturrahmi. "Mathematical modelling and verbal abilities: How they determine students’ ability to solve mathematical word problems?" Beta: Jurnal Tadris Matematika 13, no. 2 (2020): 117–29. http://dx.doi.org/10.20414/betajtm.v13i2.390.
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 [English]: This study aims to determine the level of lower secondary school students’ ability in solving mathematical word problems and how much both mathematical modelling ability and verbal ability influence the ability to solve word problems in the implementation of Kurikulum 2013 (Curriculum 2013). This study involved 411 students as samples determined by stratified proportional random sampling technique. The test used was declared valid through construct validity and reliability with Cronbach's alpha. Data were analyzed descriptively and inferentially. Descriptively, the students' ability in solving mathematical word problems was classified as medium. Meanwhile, inferentially, results were obtained indicating that: (1) students' verbal ability is significantly influential on the ability to solve word problems by 47.6%; (2) the students’ ability in mathematical modelling is significantly influential on the ability to solve word problems by 84.6%; and (3) students' verbal and mathematical modelling abilities are significantly influential on the ability to solve word problems by 87.8%. This indicates that the increase in students' ability to solve mathematical word problems will be more optimal if the verbal ability and the mathematical modelling ability are considered simultaneously, rather than focusing on one ability only.
 Keywords: Verbal ability, Mathematical modelling, word problems, Curriculum 2013
 [Bahasa]: Penelitian ini bertujuan menentukan tingkat kemampuan siswa SMP menyelesaikan soal cerita matematika dan seberapa besar pengaruh kemampuan membuat model matematika dan verbal terhadap kemampuan menyelesaikan soal cerita pada pelaksaaan kurikulum 2013. Penelitian ini melibatkan 411 siswa sebagai sampel yang ditentukan melalui teknik stratified porposional random sampling. Tes yang digunakan dinyatakan valid melalui uji validitas konstruk dan reliabel dengan Alpha Cronbach. Data dianalisis secara deskriptif dan inferensial. Secara deskriptif, kemampuan siswa dalam menyelesaikan soal cerita matematika masih tergolong sedang. Sedangkan secara inferensial diperoleh hasil bahwa (1) kemampuan verbal siswa berpengaruh secara signifikan terhadap kemampuan menyelesaikan soal cerita, dengan kemampuan verbal 47,6%; 2) kemampuan siswa dalam membuat model matematika berpengaruh secara signifikan terhadap kemampuan menyelesaikan soal cerita, dengan kemampuan membuat model matematika 84,6%; 3) kemampuan verbal dan membuat model matematika siswa berpengaruh secara signifikan terhadap kemampuan menyelesaikan soal cerita, dengan kemampuan verbal dan membuat model matematika sebesar 87,8%. Hal ini mengindikasikan bahwa peningkatan kemampuan siswa dalam menyelesaikan soal cerita matematika akan lebih optimal jika kemampuan verbal dan kemampuan membuat model matematika diperhatikan secara bersamaan dibandingkan hanya fokus pada salah satu kemampuan saja.
 Kata kunci : Kemampuan verbal, Model matematika, Soal cerita, Kurikulum 2013
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Giordano, Gerard. "Strategies That Help Learning-Disabled Students Solve Verbal Mathematical Problems." Preventing School Failure: Alternative Education for Children and Youth 35, no. 1 (1990): 24–28. http://dx.doi.org/10.1080/1045988x.1990.9944245.
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Tasni, Nurfaidah, and Elly Susanti. "Membangun Koneksi Matematis Siswa dalam Pemecahan Masalah Verbal." Beta Jurnal Tadris Matematika 10, no. 1 (2017): 103. http://dx.doi.org/10.20414/betajtm.v10i1.108.
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[Bahasa]: Penelitian ini mendeskripsikan proses membangun koneksi matematis dalam pemecahan masalah verbal atau soal cerita. Pada proses penyelesaian masalah verbal, diidentifikasi beberapa jenis koneksi yang dibangun siswa. Jenis soal dikembangkan berdasarkan karakteristik koneksi matematis menurut NCTM, yaitu koneksi antar topik matematika, koneksi dengan disiplin ilmu lain, dan koneksi dalam kehidupan sehari-hari. Pengumpulan data dilakukan melalui proses wawancara semi terstruktur terhadap 2 orang subjek yang dipilih dengan tehnik purposive sampling. Penelitian ini mengunkap ada tujuh jenis koneksi yang dibangun oleh siswa pada saat menyelesaikan masalah verbal, yaitu: koneksi pemahaman, koneksi jika maka, koneksi representasi yang setara, koneksi hirarki, koneksi perbandingan melalui bentuk umum, koneksi prosedur, dan koneksi justifikasi dan representasi. 
 Kata kunci: Koneksi Matematis; Pemecahan Masalah; Soal Verbal
 [English]: The current research aims to describe the process of developing mathematical connection in solving verbal or word mathematics problems. In solving problems, the mathematical connections developed by the subjects are identified. The mathematics problems refer to the characteristics of mathematical connections by NCTM, i.e. connections within mathematics topics, connection with other fileds, and connections with daily life. Data collection is conducted through students’ work and semi-structure interview with two subjects. The subjects are selected through purposive sampling. This research reveals seven kinds of mathematical connections developed by the subjects in solving verbal mathematics problems, i.e. connection in understanding, if then connection, equal representation connection, hierarchy connection, proportion connection through general form, procedure connection, and justification and representation connection. 
 Keywords: Mathematical Connection; Problem Solving; Verbal Problems
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Silviana, Dewi, and Arnasari Merdekawati Hadi. "Profil Kemampuan Komunikasi Visual-Verbal Dalam Pemecahan Masalah Matematika." MANDALIKA Mathematics and Educations Journal 1, no. 2 (2019): 87. http://dx.doi.org/10.29303/mandalika.v1i2.1570.
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This research aim to discusses the profile of visual-verbal communication ability in mathematical problem solving from students' mathematics learning achievement. The instruments in this study were the researchers themselves, visual-verbal communication mathematics problem solving test and interview guidelines. Subjects in this study were 2 students with high learning achievement (PBT), 2 students with moderate learning achievement (PBS), and 2 students with low learning achievement (PBR). The results showed that students with high learning achievement improve verbal communication and mathematical communication skills that are more complicated than students with learning achievement who are solving mathematical problems. Meanwhile, students with low learning achievement solve problems by communicating verbal mathematical symbol. AbstrakPenelitian ini bertujuan mengungkap profil kemampuan komunikasi visual-verbal dalam pemecahan masalah matematika dilihat dari prestasi belajar matematika siswa. Instrumen dalam penelitian ini adalah peneliti sendiri, tes pemecahan masalah matematika komunikasi visual-verbal dan pedoman wawancara. Subjek penelitian terdiri dari 2 orang siswa prestasi belajar tinggi (PBT), 2 orang siswa prestasi belajar sedang (PBS), dan 2 orang siswa prestasi belajar rendah (PBR). Hasil penelitian menunjukkan bahwa siswa dengan prestasi belajar tinggi meningkatkan kemampuan komunikasi visual dan matematis verbal yang lebih rumit dari siswa dengan prestasi belajar sedang memecahkan masalah matematika. Sementara, siswa dengan prestasi belajar rendah memecahkan masalah dengan komunikasi simbol matematis verbal. Siswa prestasi belajar rendah memecahkan masalah dengan komunikasi simbol matematis verbal.
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Moskofoglou-Chionidou, Maria. "The effect of verbal and illustrative representation on solving statistical problems by students in elementary school." New Trends and Issues Proceedings on Humanities and Social Sciences 6, no. 7 (2019): 130–37. http://dx.doi.org/10.18844/prosoc.v6i7.4523.
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The purpose of this study was to examine the effect of verbal and illustrative representation of the same statistical problems experienced by 56 elementary school students. Students were evaluated on problem-solving skills through six statistical problems as presented in school textbooks. One week later, the students were re-evaluated on problem-solving skills using the same problems that had been illustratively and verbally represented by the researchers. At the same time, we examined the correlation of students' performance to the six given problems in relation to their reading comprehension, verbal and mathematical competence (based on teachers' grade assignment). From the results of the quantitative research method that was used, there was a statistically significant correlation between the verbal representations in a) two out of six problems related to the mean value calculation using α representational table format and b) a bar graph construction based on a representational table format. However, an important finding of the research was the high correlation between students' performance and their reading comprehension, verbal and mathematical competence.
 Keywords: Verbal representation of a problem, illustrative representation of a problem, statistics.
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Amaliyah AR, Rezki, and Nurfadilah Mahmud. "Analisis Kemampuan Representasi Matematis dalam Pemecahan Masalah Geometri serta Faktor-Faktor yang Mempengaruhinya." Jurnal Review Pembelajaran Matematika 3, no. 2 (2018): 146–60. http://dx.doi.org/10.15642/jrpm.2018.3.2.146-160.
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This is qualitative research with a descriptive-explorative approach that aims to determine students' mathematical representation skills in solving Geometry problems. The population is all students in the mathematics education department who study Basic Geometry. The main subject was chosen by stratified technique and purposive sampling. The instruments are placement tests, diagnostic tests, and guided interviews. Data collection uses a triangulation method that aims to examine legitimate data. The results showed that 1) subjects with high skills always present visual representations and mathematical expressions, 2) subjects with intermediate skills present visual representations and mathematical expressions, and verbal but less representative representations, 3) subjects with low skills don’t present visual representations and mathematical expressions and verbal representations of problem-solving steps; and 4) there are several factors that influence the ability of mathematical representation to solve geometric problems, among others, subjects are less able to present problems in geometric patterns, because the subject does not understand the problem.
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Wulandari, Elis Dwi, Erry Hidayanto, and Rustanto Rahardi. "Representasi Matematis Siswa Tuna Rungu dalam Menyelesaikan Soal Cerita Matematika." Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan 4, no. 7 (2019): 971. http://dx.doi.org/10.17977/jptpp.v4i7.12644.
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<p><strong>Abstract:</strong> Mathematical representation is the way of communicating mathematical ideas and problems solutions. Communicating mathematical ideas requires external representation in the form of actions, verbal, symbolic, visual and real objects. This study aims to describe the form of representation of Deaf Students in solving mathematical story problems. The research was conducted by giving types of text questions as well as text and image questions to three DS at Banyuwangi State of Special Need High School. The results of student work analysis found that there are two types of mathematical representations that appear in solving story problems, namely verbal representation indicated by writing words, numbers, letters, sentences and oral and representation of mathematical expressions in the form of symbols and numbers. DS are able to representing, make mathematical symbols, explain in writing or sign language what they think are.</p><strong>Abstrak:</strong><em> </em>Representasi matematis adalah cara mengomunikasikan ide-ide matematis maupun solusi permasalahan. Mengomunikasikan ide-ide matematis diperlukan representasi eksternal berbentuk tindakan, verbal, simbolik, visual dan objek nyata. Studi ini bertujuan untuk mendeskripsikan bentuk representasi siswa Tuna Rungu dalam menyelesaikan soal cerita matematika. Penelitian dilakukan dengan memberikan jenis soal teks serta soal teks dan gambar kepada tiga siswa TR di SMALBN Banyuwangi. Hasil analisis pekerjaan siswa ditemukan terdapat dua tipe bentuk representasi matematis yang muncul dalam menyelesaikan soal cerita, yaitu representasi verbal yang ditunjukkan dengan tulisan kata, angka, huruf, kalimat serta lisan dan representasi ekspresi matematis berupa simbol dan angka. Siswa TR mampu merepresentasikan, membuat simbol matematis, menjelaskan dengan tulisan maupun bahasa isyarat apa yang mereka pikirkan.
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Rowan, Thomas E., and Josepha Robles. "Using Questions to Help Children Build Mathematical Power." Teaching Children Mathematics 4, no. 9 (1998): 504–9. http://dx.doi.org/10.5951/tcm.4.9.0504.
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This verbal exchange occurred in a fifth-grade classroom where the students were doing a simple warm-up activity in which they selected problems from a given set, solved them mentally, and shared their solution strategies. After listening to the strategies used by Tina, Dan, and Maria, their classmates looked to see if they could solve other problems in the same interesting ways. Asking children to share their strategies for solving problems is a simple but powerful learning tool for promoting understanding and flexibility in doing mathematics.
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Nizaruddin, Nizaruddin, Muhtarom Muhtarom, and Yanuar Hery Murtianto. "EXPLORING OF MULTI MATHEMATICAL REPRESENTATION CAPABILITY IN PROBLEM SOLVING ON SENIOR HIGH SCHOOL STUDENTS." Problems of Education in the 21st Century 75, no. 6 (2017): 591–98. http://dx.doi.org/10.33225/pec/17.75.591.
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The students’ multi-mathematical representation capability in problem solving is very important and interesting to discuss, specifically for problems in the two-variable linear equation system. Data was collected from 48 students using written tests and in-depth interviews with selected participants. The research findings showed that few students are using three representations namely symbolic - verbal - table representation, and symbolic representation, however most of the students are using three representations namely symbolic - verbal - images representation, and two representations namely symbolic – verbal representations, and the rest used symbolic representation. In the use of verbal representation, some students had difficulty composing words and all students encountered difficulties in the translational process from symbolic representation and verbal representation to other types of representation. The ability to understand concepts and relationships between mathematical concepts was found to be a necessary condition for the achievement of multi-mathematical representation capability. It is therefore recommended that teachers use a variety of different types of representation, such as verbal, tables and images, to enhance students' understanding of the material. Keywords: multiple representations, problem solving, two-variable linear equation system.
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Nizaruddin, Nizaruddin, Muhtarom Muhtarom, and Yanuar Hery Murtianto. "EXPLORING OF MULTI MATHEMATICAL REPRESENTATION CAPABILITY IN PROBLEM SOLVING ON SENIOR HIGH SCHOOL STUDENTS." Problems of Education in the 21st Century 75, no. 6 (2017): 591–98. http://dx.doi.org/10.33225/17.75.591.
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The students’ multi-mathematical representation capability in problem solving is very important and interesting to discuss, specifically for problems in the two-variable linear equation system. Data was collected from 48 students using written tests and in-depth interviews with selected participants. The research findings showed that few students are using three representations namely symbolic - verbal - table representation, and symbolic representation, however most of the students are using three representations namely symbolic - verbal - images representation, and two representations namely symbolic – verbal representations, and the rest used symbolic representation. In the use of verbal representation, some students had difficulty composing words and all students encountered difficulties in the translational process from symbolic representation and verbal representation to other types of representation. The ability to understand concepts and relationships between mathematical concepts was found to be a necessary condition for the achievement of multi-mathematical representation capability. It is therefore recommended that teachers use a variety of different types of representation, such as verbal, tables and images, to enhance students' understanding of the material. Keywords: multiple representations, problem solving, two-variable linear equation system.
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Islam, Muhammad Ainul Yaqin Fiddinil, Sunardi Sunardi, Reza Ambarwati, and Siti Alfiah. "Representasi Matematis Siswa Bina Prestasi MTsN 1 Jember dalam Menyelesaikan Masalah Segiempat Ditinjau dari Level van Hiele." Journal of Mathematics Education and Learning 1, no. 1 (2021): 27. http://dx.doi.org/10.19184/jomeal.v1i1.24373.
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This study aims to determine mathematical representation of Students’ Ability in Solving Quadrilateral Problems Based on Van Hiele’s Levels at an Enrichment Program in MTsN 1 Jember.. This research is a descriptive qualitative research. The subjects of this study were 17 students of class IXA at MTsN 1 Jember. The data collection method on this research are using test and interview methods. The test instrument on this research were a test of ability to think geometry and a test of mathematical representation on rectangular material. The results of data analysis were carried out by comparing the results of the mathematical representation test with interviews, then categorized based on Van Hiele's level of thinking from the results of the geometric thinking ability test. The results showed that students with a visual thinking level had a tendency to use symbolic and verbal representations in solving problems. Students with the analytical thinking level tend to use verbal, visual, and symbolic representations in solving problems. 
 Keyword: Mathematical Representation, Quadrilateral, High Achiever Student, Van Hiele levels
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Harra Hau, Rambu Ririnsia, Paulina Nelce Mole, Agustina Elizabeth, Yohanes Sudarmo Dua, and Maria Yani Leonarda. "Students' Multirepresentation Ability in Completing Physics Evaluation Problems." JIPF (Jurnal Ilmu Pendidikan Fisika) 5, no. 3 (2020): 187. http://dx.doi.org/10.26737/jipf.v5i3.1893.
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This study aims to describe students' multi-representation ability in solving physics evaluation questions carried out by the qualitative description method in class X MIA 1 SMA Katolik St. Gabriel Maumere for the 2019/2020 school year. The data were obtained from the matter of physics evaluation on Newton's law material about the force of gravity. Data analysis is based on student work steps in solving evaluation questions. Data analysis results show that the ability of multi-representation in solving physics problems on Newton's law material about the force of gravity in the high category. The number of mathematical representations of 100%, image representation of 10%, then in the medium type only uses a mathematical description of 100% and in the low category using a mathematical representation of 100% and a verbal representation of 40%.
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Johar, Rahmah, and Khairiyah Rahma Lubis. "The analysis of students’ mathematical representation errors in solving word problem related to graph." Jurnal Riset Pendidikan Matematika 5, no. 1 (2018): 96. http://dx.doi.org/10.21831/jrpm.v5i1.17277.
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The skills of reading, interpreting and constructing graphs are important for students. These skills are related to mathematical representation. The purpose of this study is to analyze Grade 8 students’ representation errors in solving word problems related to graphs in one of junior high schools in Banda Aceh, Indonesia. The data were obtained based on a mathematics test administered to 36 students and a short interview conducted for five selected students. The test consisted of eight problems adapted from four contexts of PISA problems related to graph. Students’ representation errors were classified based on the errors of changing one representation to another representation, such as visual to verbal, visual to symbolic, visual to visual and verbal to visual. The results reveal that representation errors are not solely influenced by the types of representation. It is indicated by the questions with similar representation resulted in a different percentage of students committing representation errors. In general, the students’ representation errors are due to the fact that students not being familiar with the problems requiring representation; students not being used to solve PISA context problems and word problems; as well as the teachers’ time constraint in teaching non-routine problems.
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Mateus-Nieves, Enrique, and Harold Randolph Devia Díaz. "Development of Mathematical Thinking Skill from the Formulation and Resolution of Verbal Arithmetic Problems." Acta Scientiae 23, no. 1 (2021): 30–52. http://dx.doi.org/10.17648/acta.scientiae.5845.
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Kristanto, Herman Yosep Wisnu, and Janet Trineke Manoy. "Representasi Matematis Siswa SMA dalam Menyelesaikan Masalah Matematika Ditinjau dari Gaya Kognitif Sistematis dan Intuitif." JURNAL PENELITIAN PENDIDIKAN MATEMATIKA DAN SAINS 4, no. 2 (2021): 50. http://dx.doi.org/10.26740/jppms.v4n2.p50-59.
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Penelitian ini merupakan penelitian deskriptif kualitatif dengan tujuan untuk mendeskripsikan representasi matematis siswa SMA dalam menyelesaiakan masalah matematika ditinjau dari gaya kognitif sistematis dan intuitif. Subjek dalam penelitian ini, yaitu dua siswa kelas XI yang terdiri dari satu siswa bergaya kognitif sistematis dan satu siswa bergaya kognitif intuitif. Instrumen penelitian yang digunakan dalam penelitian ini, yaitu tes gaya kognitif dan tes representasi matematis. Penelitian diawali dengan pemilihan subjek melalui tes gaya kognitif, kemudian subjek yang telah terpilih diberikan tes representasi matematis dan dilakukan wawancara tertulis. Data yang telah diperoleh dianalisis dengan teknik analisis data yang melalui tahapan, yaitu kondensasi data, penyajian data, serta penarikan kesimpulan dan verifikasi. Hasil penelitian yang diperoleh menunjukkan representasi matematis siswa bergaya kognitif sistematis dalam menyelesaikan masalah matematika, yaitu pada tahap memahami masalah menggunakan representasi verbal, pada tahap menyusun rencana penyelesaian menggunakan kombinasi antara representasi simbolik dan representasi verbal, pada tahap melaksanakan rencana penyelesaian menggunakan representasi simbolik dan representasi verbal, dan pada tahap memeriksa kembali penyelesaian menggunakan representasi verbal. Sedangkan representasi matematis siswa bergaya kognitif intuitif dalam menyelesaikan masalah matematika, yaitu pada tahap memahami masalah menggunakan representasi visual, pada tahap menyusun rencana penyelesaian menggunakan representasi simbolik, pada tahap melaksanakan rencana penyelesaian menggunakan representasi simbolik, dan tidak menunjukkan representasi matematis pada tahap memeriksa kembali penyelesaian. This research is descriptive-qualitative research that aimed to describe the mathematical representation of high school students in solving mathematical problems in terms of systematic and intuitive cognitive style. The subject of this research is two eleventh grade students, consists of one student with systematic cognitive style and one student with intuitive cognitive style. The research instruments used in this research are cognitive style test and mathematical representation test. Research starts by choosing the subject by cognitive style test, and then the subjects that have been chosen were given mathematical representation test and did written interview. The data obtained were analyzed with data analysis techniques, namely data condensation, data display, and drawing and verifying conclusions. Results of this research show the mathematical representation of student with systematic cognitive style on solving problems are verbal representation when understanding the problem, combination of symbolic and verbal representation when devising a plan, symbolic representation and verbal representation when carrying out the plan, and verbal representation when looking back. While the mathematical representation of student with intuitive cognitive style on solving problem are visual representation when understanding the problem, symbolic representation when devising a plan, symbolic representation when carrying out the plan, and not show mathematical representation when looking back.
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Duque de Blas, Gonzalo, Isabel Gómez-Veiga, and Juan A. García-Madruga. "Arithmetic Word Problems Revisited: Cognitive Processes and Academic Performance in Secondary School." Education Sciences 11, no. 4 (2021): 155. http://dx.doi.org/10.3390/educsci11040155.
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Solving arithmetic word problems is a complex task that requires individuals to activate their working memory resources, as well as the correct performance of the underlying executive processes involved in order to inhibit semantic biases or superficial responses caused by the problem’s statement. This paper describes a study carried out with 135 students of Secondary Obligatory Education, each of whom solved 5 verbal arithmetic problems: 2 consistent problems, whose mathematical operation (add/subtract) and the verbal statement of the problem coincide, and 3 inconsistent problems, whose required operation is the inverse of the one suggested by the verbal term(s). Measures of reading comprehension, visual–spatial reasoning and deductive reasoning were also obtained. The results show the relationship between arithmetic problems and cognitive measures, as well as the ability of these problems to predict academic performance. Regression analyses confirmed that arithmetic word problems were the only measure with significant power of association with academic achievement in both History/Geography (β = 0.25) and Mathematics (β = 0.23).
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Raghubar, Kimberly P., Marcia A. Barnes, Mary Prasad, Chad P. Johnson, and Linda Ewing-Cobbs. "Mathematical Outcomes and Working Memory in Children With TBI and Orthopedic Injury." Journal of the International Neuropsychological Society 19, no. 3 (2012): 254–63. http://dx.doi.org/10.1017/s1355617712001312.
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AbstractThis study compared mathematical outcomes in children with predominantly moderate to severe traumatic brain injury (TBI;n= 50) or orthopedic injury (OI;n=47) at 2 and 24 months post-injury. Working memory and its contribution to math outcomes at 24 months post-injury was also examined. Participants were administered an experimental cognitive addition task and standardized measures of calculation, math fluency, and applied problems; as well as experimental measures of verbal and visual-spatial working memory. Although children with TBI did not have deficits in foundational math fact retrieval, they performed more poorly than OIs on standardized measures of math. In the TBI group, performance on standardized measures was predicted by age at injury, socioeconomic status, and the duration of impaired consciousness. Children with TBI showed impairments on verbal, but not visual working memory relative to children with OI. Verbal working memory mediated group differences on math calculations and applied problems at 24 months post-injury. Children with TBI have difficulties in mathematics, but do not have deficits in math fact retrieval, a signature deficit of math disabilities. Results are discussed with reference to models of mathematical cognition and disability and the role of working memory in math learning and performance for children with TBI. (JINS, 2013,19, 1–10)
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Mahardika, I. Ketut, Zulfi Anggraini, Aris Doyan, and I. Wayan Sugiartana. "Approach to Representation of CRI Integrated Mathematics and Verbal (R-MV) to Analyze Misconception of Momentum and Impuls Materials." Jurnal Penelitian Pendidikan IPA 6, no. 2 (2020): 232. http://dx.doi.org/10.29303/jppipa.v6i2.437.
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Misconception is a misconception that refers to a concept that is not in accordance with scientific understanding or understanding received by experts in that field. This study aims to identify students' misconceptions in solving momentum and impulse problems through the R-MV approach (mathematical representation and verbal representation) integrated CRI (Certainly of Response Index). This research included in the type of qualitative descriptive analysis research. The subject of the research was tenth-grade students of Jember Regency Senior High School. Data collection techniques in this research use method of observation, tests, and interviews. The data analysis technique used was the mathematical representation approach integrated CRI. Based on the results of the research that has been done, the students' misconceptions percentage in Jember Senior High School of science tenth grade on material momentum and impulse through mathematical representation approach integrated CRI of 20.07% and through verbal representation approach integrated CRI of 32.94%. This is included in the category (Almost Very Confident) for mathematical representation and (Sure) for verbal representation, meaning the value that students get as truthful based on understanding material with correct
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Silwana, Amalia, Subanji Subanji, Muhamatsakree Manyunu, and Arifah Adlina Rashahan. "Students’ Responses Leveling in Solving Mathematical Problem Based on SOLO Taxonomy Viewed from Multiple Intelligences." Indonesian Journal on Learning and Advanced Education (IJOLAE) 3, no. 1 (2020): 1–16. http://dx.doi.org/10.23917/ijolae.v3i1.10528.
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This research aimed to determine the level of student response with logical-mathematical, verbal-linguistic, and visual-spatial intelligence tendency in solving mathematical problems of linear programming material based on SOLO taxonomy. The level of students’ responses as the output in this research is expected to be used as a reference by mathematics teachers to determine the appropriate learning methods and strategies in accordance with the tendency of students' multiple intelligence types. It can be useful in realizing the effectiveness of mathematics learning about what needs to improved and emphasized in learning so that all students can achieve optimal responses in solving mathematical problem and can develop their multiple intelligences. This research is descriptive qualitative research with six students in the 11th Grade of SMAN 1 Gondanglegi as research subjects: two students with logical-mathematical intelligence tendency, two students with verbal-linguistic intelligence tendency, and two students with visual-spatial intelligence tendency. Data collection was done by providing multiple intelligence classification tests, linear programming problem tests, and interviews. The result of the research showed the students’ response level in solving the mathematical problem of linear programming material based on SOLO taxonomy is that students with logical-mathematical intelligence tendency reached extended abstract response level, students with verbal-linguistic intelligence tendency reached multistructural response level, and students with visual-spatial intelligence tendency reached multistructural and relational response level.
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Ester, Pilar, Isabel Morales, Álvaro Moraleda, and Vicente Bermejo. "The Verbal Component of Mathematical Problem Solving in Bilingual Contexts by Early Elementary Schoolers." Mathematics 9, no. 5 (2021): 564. http://dx.doi.org/10.3390/math9050564.
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The main aim of the present study is to analyze the differences that may exist when students address the resolution of verbal problems in their mother tongue and in the language of instruction when these are different. We understand that knowing the type of verbal problems and their semantic structure can be helpful for students’ contextual and mathematical understanding and will allow teachers to improve instruction during the first years of elementary education in bilingual schools specialized in the area of second language acquisition as well as in CLIL (Content and Language Integrated Learning). This study shows how children, as they are acquiring a greater command of the second language, show similar effectiveness to those students who work on mathematics in their mother tongue. This transversal study was conducted on 169 bilinguals studying in international schools. The sample was made up of 80 1st grade students (39 girls, mean age of 7.1 years and 41 boys, mean age of 7.3 years); and 89 2nd grade students (38 girls, mean age 8.2 years, and 51 boys, mean age 8.2 years). The exploratory analyses let us show how 1st grade students demonstrate lower effectiveness in solving problems when they do it in a second language, compared to 2nd grade students whose effectiveness is higher in carrying them out. It is also relevant that in first graders, the largest number of errors are found in the simplest tasks as students’ effectiveness is less when they are taught in a second language, since it takes them longer to create effective resolution models. This fact will allow us to reconsider appropriate strategies and interventions when teaching mathematics in bilingual contexts.
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Suaedy, Nurjayanty. "CHARACTERISTICS OF MATHEMATICAL REASONING IN SOLVING MATHEMATICAL PROBLEMS IN TERMS OF THE COGNITIVE STYLE OF THE ELEVENTH GRADE STUDENTS OF SMA NEGERI 3 WAJO." Global Science Education Journal 1, no. 1 (2019): 65–72. http://dx.doi.org/10.35458/gse.v1i1.6.
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This research aims at describing characteristics of students mathematical reasoning in solving mathematical problem regarded from cognitive style. Based on data analysis, it can be concluded that (1) The ways of the subject reasoning of visualizer cognitive style are analyzing, synthesizing, analyzing, then generalizing. While the ways of the subject reasoning who are verbalizer cognitive are synthesizing, analyzing, then generalizing. (2) The sub indicators of subject reasoning of visualizer cognitive style are presenting mathematical statement through picture specifically and obviously, conducting a beginning asumption specifically, explaining the concept relevancy used through picture, giving reason logically in solving problem and using other alternatives with different strategies, rechecking every steps of completion, tending to conclude the result of completion with picture and tending to conclude generally based on the specific case from mathematical symptom. While the subjects who are verbalizer cognitive are presenting mathematical statement through verbal symbol specifically and obviously, less specific in doing assumption, relating the concept but ordering based on the sequences known and asked with the writing of symbol in modelling the problem, giving the relevant argument to the steps of completion with the same strategies, rechecking every steps of completion, tending to conclude the result of completion with verbal symbol, and tending to conclude generally based on the specific case and mathematical symptom.
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Imangaliyevа, S. D., B. Zh Bekzhanova, and A. S. Akhmetovа. "PROBLEMS OF STUDYING VERBAL-LOGICAL THINKING AND ANXIETY OF YOUNGER PUPILS." BULLETIN Series of Pedagogical Sciences 67, no. 3 (2020): 144–51. http://dx.doi.org/10.51889/2020-3.1728-5496.19.
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This article deals with the problems of using the Kazakh version of the method of E.F. Zambatsevichene, modified by L.I. Peresleni, "Verbal subtests" and the anxiety scale (the Children's Form of Manifest Anxiety Scale – CMAS), modified by A.M. Prikhozhan. To analyze the dynamics of vocabulary and logical thinking of children of preschool and primary school age, the pre-profile school version of the methodology was translated into Kazakh and applied to the study of vocabulary and logical thinking of primary school children. А psychological and pedagogical experiment was carried out with primary school students using variants of the Verbal Subtests methodology and the Children's Form of Manifest Anxiety Scale (CMAS) modified by A.M. Prikhozhan, and respondents who were fluent in Kazakh Russian languages. The experiment was carried out in two stages, at the first stage, the study of the development of verbal-logical thinking and anxiety in children of 9-10 years old was carried out according to the methodology in the Kazakh language, and at the second stage the methods were carried out in Russian with children of this age. The experiment carried out methods in both versions, and the results of the Russian-Kazakh version of the method were analyzed using mathematical and statistical research methods.
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Huda, Ummul, Edwin Musdi, and Nola Nari. "ANALISIS KEMAMPUAN REPRESENTASI MATEMATIS SISWA DALAM MENYELESAIKAN SOAL PEMECAHAN MASALAH MATEMATIKA." Ta'dib 22, no. 1 (2019): 19. http://dx.doi.org/10.31958/jt.v22i1.1226.
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This research is motivated by the low mathematical representation ability of students in solving mathematical problem solving questions based on TIMSS data and facts in the field. The study aims to analyze the mathematical representation ability of MTsN Batusangkar students visually, verbally and symbolically in solving mathematical problem solving problems. This field research uses descriptive method. The instrument used is a description question and interview guide. Quantitative data based on test results were analyzed to determine the predicate of mathematical representation ability, while Miles and Huberman model wwas used to analyze qualitative data from interviews. The results show that students' mathematical visual and symbolic abilities are satisfactory, while verbal mathematical representations are less satisfactory.
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Sanwidi, Ardhi. "STUDENTS' REPRESENTATION IN SOLVING WORD PROBLEM." Infinity Journal 7, no. 2 (2018): 147. http://dx.doi.org/10.22460/infinity.v7i2.p147-154.
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The purpose of this research is to describe the representation of sixth grade students in solving mathematics word problems. The focus of the representation of this research is an external representation which is viewed from students with high mathematical abilities. The method used in this research is task-based interview, by giving a problem test of word problems. Students who have a high level of abilities, he makes pictures of all problems and successfully solve the problems. Students whose level of abilities is lacking, he only makes incomplete symbol / verbal representations, he has wrong when solving the problems. Various kinds of representations and increasing abilities in many problems such as multiplying exercises and solve the word pronlem. Applying various representations to students are very important to be improved by students in order to succeed in solving various mathematical word problems.
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Hernawati, Faridah. "PENGEMBANGAN PERANGKAT PEMBELAJARAN MATEMATIKA DENGAN PENDEKATAN PMRI BERORIENTASI PADA KEMAMPUAN REPRESENTASI MATEMATIS." Jurnal Riset Pendidikan Matematika 3, no. 1 (2016): 34. http://dx.doi.org/10.21831/jrpm.v3i1.9685.
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Penelitian pengembangan ini bertujuan untuk menghasilkan Rencana Pelaksanaan Pembelajaran (RPP) dan Lembar Kegiatan Siswa (LKS) yang valid, praktis dan efektif. RPP yang dikembangkan memuat sintaks PMRI, yaitu memahami masalah kontekstual, mendeskripsikan masalah kontekstual, menyelesaikan masalah kontekstual, membandingkan dan mendiskusikan jawaban, dan menyimpulkan. LKS yang dikembangkan memfasilitasi kemampuan representasi matematis siswa, yaitu kemampuan mengungkapkan verbal ke simbol, simbol ke visual, dan verbal ke visual. Hasil validasi para ahli menyatakan bahwa produk yang dikembangkan mencapai kategori valid. Hasil pengisian angket penilaian kepraktisan oleh guru menunjukkan bahwa produk yang dikembangkan mencapai kategori praktis, hasil pengisian angket penilaian kepraktisan oleh siswa menunjukkan bahwa produk yang dikembangkan mencapai kategori praktis, dan hasil observasi keterlaksanaan pembelajaran menunjukkan bahwa persentase keterlaksanaan pembelajaran adalah 88,89%. Keefektifan produk terlihat dari hasil kemampuan representasi matematis (KRM). Hasil KRM menunjukkan persentase siswa yang mencapai KKM adalah 76,67% dengan nilai rata-sata 77,67% Secara keseluruhan hasil penelitian menunjukkan bahwa perangkat pembelajaran yang dikembangkan adalah layak untuk digunakan.Kata Kunci: pengembangan, perangkat pembelajaran, PMRI, kemampuan representasi matematis. DEVELOPING A MATHEMATIC LEARNING DEVICE WITH PMRI APPROACH ORIENTED ON MATHEMATICAL REPRESENTATION ABILITY AbstractThis development research was aimed to produce the lesson plan (RPP) and the worksheet (LKS) are valid, practical , and effective. RPP was developed contain PMRI syntax, ie understanding the contextual problems, describing the contextual problems, solving the contextual problems, comparing and discussing the answers, and concluding. LKS was developed facilitate the mathematical representation ability, ie expressing the verbal to symbol, the symbol to the visual, and the verbal to visual. The validaty of product can be seen from the results of experts validation which demonstrates that the product is valid. The practicality of product can be seen from the result of the teacher practicality assessment sheet which shows that the product is in a practical category, the result of the students assessment sheet shows that the product is in a practical categories, learning implementation observation shows that the minimum implementation percentage is 88.89% and maximum is 100%. The effectiveness of the product can be seen from the results of mathematical representation ability test. The result of mathematical representation test shows that percentage of students who reach the KKM is 76.67% with a mean value of 77.67%. Overall the results of this study show that the developed learning tools are feasibel to use.Keywords: development, learning tool, PMRI, mathematical representation ability.
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Alshaya, Fahad S. "Students’ Difficulties in Solving Physics Problems in Introductory College PhysicsCourses at King Saud University." Journal of Educational and Psychological Studies [JEPS] 8, no. 2 (2014): 272. http://dx.doi.org/10.24200/jeps.vol8iss2pp272-289.
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The purpose of this study was to identify the difficulties facing students in introductory college physics courses at King Saud University in solving physics problems, by exploring faculty members' perceptions of these difficulties, and through analyzing students' answers to physics problems in final exams. The study mainly focused on four themes of difficulties, including: the problems verbal context, physics laws, mathematical skills and graphs or diagrams. The study also sought to learn about faculty's perception towards the degree of influence of the proposed solutions. The study sample consisted of 27 physics faculty members, in addition to 391 students. The study showed consistency between the faculty members' perception towards the difficulties of solving problems and the analysis of student answers in final exams. The difficulties related to the verbal context were the most common among students, whereas difficulties related to mathematical skills were the least common. In addition, the results revealed that there were also difficulties related to physical laws, and knowledge of graphs or diagrams. The findings showed that the perceptions of faculty members towards proposed solutions as being as a “high effect”on fourteen suggested techniques, while their perception towards the rest of the techniques were as “medium effect”. Finally, their perception towards only one technique was being of “low effect".
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Wibawa, Kadek Adi. "Fragmentation of the Thinking Structure of Translation in Solving Mathematical Modelling Problems." Southeast Asian Mathematics Education Journal 9, no. 1 (2019): 25–36. http://dx.doi.org/10.46517/seamej.v9i1.71.
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Fragmentation of the thinking structure is the process of construction of information in the brain that is inefficient, incomplete, and not interconnected, and hinders the process of mathematical problem solving. In solving mathematical modeling problems, students need to do translation thinking which is useful for changing the initial representation (source representation) into a new representation (target representation). This study aims to discover how the occurrence of the fragmentation of the thinking structure of translation within students in their solving of mathematical modeling problems. The method used is descriptive qualitative with the instrument in the form of one question for the mathematical modeling of necklace pendants and semi-structured interview sheets. The results showed that there were three errors that occurred in solving mathematical modeling problems. First, the error in changing a verbal representation to a graph. Secondly, errors in changing a graphical representation to symbols (algebraic form). Thirdly, errors in changing graphical representation and symbols into mathematical models. The three errors that occur are described based on the four categories of Bosse frameworks (Bosse, et al., 2014), namely: (1) unpacking the source (UtS), (2) preliminary coordination (PC), (3) constructing the target (CtT), and (4) determining equivalence (DE). In this study, there were 3 subjects who experienced fragmentation of the thinking structure in solving mathematical modeling problems. One of the highlights is the fragmentation of the structure of translation thinking often starts from the process of unpacking of the source due to the incompleteness of considering all the available source details.
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Nurrahmawati, Nurrahmawati, Cholis Sa'dijah, Sudirman Sudirman, and Makbul Muksar. "Assessing students’ errors in mathematical translation: From symbolic to verbal and graphic representations." International Journal of Evaluation and Research in Education (IJERE) 10, no. 1 (2021): 115. http://dx.doi.org/10.11591/ijere.v10i1.20819.
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Translation skills are very important possessed by students, but currently, there are still many students who have difficulty in translating between representations. The purpose of this study is to analyze students' errors in translating from symbolic representations to verbal and graphic representations. This research was descriptive study with qualitative approach. Tests are given to junior high school students. From the results of data analysis, it is obtained that in translating from symbolic to verbal forms (problems in daily life) that are following the given system of equations, students are still unable to make representations correctly. When students are asked to translate into graphical form, students are still unable to draw complete graphs and errors made by students are misinterpretation and implementation errors, so they cannot maintain the semantic congruence between source representation and target representation. Based on this, it is necessary to make a learning plan that can improve students’ ability to translate between representations.
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Grabauskienė, Vaiva, and Ada Zabulionytė. "The Employment of Verbal and Visual Information for 3rd Grade Deaf Students in Arithmetic Story Problem Solving." Pedagogika 129, no. 1 (2018): 171–86. http://dx.doi.org/10.15823/p.2018.12.
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The scientific studies have shown that deaf students in comparison to their hearing peers find mathematical word tasks much more difficult to solve. Following this finding, in our article we are discussing how Lithuanian oral/written and Sign languages (LSL) supported by illustrations might assist deaf students solving mathematical word problems.
 The analytical part of this article is based on results from a small field survey – deaf students were asked to take math word problems followed by discussions with the same students (performed in LSL) about their (un)success. The following methods have been applied: instrumental case study, written survey, observation, and qualitative content analysis. Due to the specifics of schools for deaf children we have chosen a small sample group consisting of six deaf 3rd grade students.
 Study results show that it was quite difficult for deaf students to understand what exactly the mathematical word problem has been asking for. This observation leads to the assumption that it would be useful making wording of math problems shorter and at the same time more friendly to the mindset of the deaf students. On top of that, the wording and written language constructions used in mathematical word tasks should be at the level of overall language comprehension of deaf students at that age level. This approach would lead to more rational teaching strategies to be used for deaf students - enabling them to recognize the key message in the task by separating it from the less important secondary information. The results also show that deaf students very rarely use illustrations as a supporting tool while resolving mathematical word tasks (though it might be some exceptions if students are asked to solve tasks that are more complex). This observation supports the idea, that it would be useful to apply proper illustrations helping to enhance the understanding and strengthen the ability to overcome the low comprehension of verbal information. In that case, the key objective in teaching deaf students would be in how to extract the required mathematical information from the illustrations presented and connect it with the word task itself. It has been noticed also that deaf students usually ask for help and support in Lithuanian Sign language. This underlines the importance of having the teacher able to communicate in their preferable way (using LSL) on a constant basis.
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Rofiki, Imam, and Ika Santia. "Describing the phenomena of students’ representation in solving ill-posed and well-posed problems." International Journal on Teaching and Learning Mathematics 1, no. 1 (2018): 39. http://dx.doi.org/10.18860/ijtlm.v1i1.5713.
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<p>Mathematical representation is an essential aspect of mathematical problem-solving. But students’ ability of an accurate representation in ill-posed problem-solving is still very minimal compared to that in well-posed problem-solving. However, ill-posed problem supported mathematical abstraction used in mathematical concept understanding. This study described the representations used by mathematics education students in solving ill-posed and well-posed problems. Thirty Indonesian matematics education students have solved ill-well posed problems by using think-aloud. Researchers also collected data using a video recorder and a field note. Data were analyzed by a constant comparative method so that it was obtained the different characteristics of representations between solving ill-posed and well-posed problems. The finding of the study showed that verbal and symbolic representations were used by subjects to compute, detect, and correct error. They also justified their answers in ill-posed problem-solving. However, the visual representation was only used by first subject to identify and correct error. The subjects lacked to expose necessary information to solve the ill-posed problem compared to the well-posed problem.</p>
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Mariyati, Yuni, Sintayana Muhardini, and Sukron Fujiaturrahman. "IDENTIFIKASI KESULITAN SISWA SD DALAM MEMAHAMI KEMAMPUAN VERBAL DAN NUMERIK BERBASIS MASALAH MATEMATIKA TAHUN PELAJARAN 2018/2019." Jurnal Ulul Albab 23, no. 1 (2019): 8. http://dx.doi.org/10.31764/jua.v23i1.644.
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Penelitian ini bertujuan untuk mengetahui faktor–faktor yang mempengaruhi kesulitan siswa dilihat dari kemampuan verbal dan numerik siswa dalam memecahkan masalah matematika pada materi KPK. Penelitian ini menggunakan pendekatan kualitatif yang bersifat deskriptif dengan menggambarkan proses penelitian secara benar sesuai dengan fakta yang di dapatkan. Dalam penelitian ini subjek penelitian sebanyak 30 peserta. Siswa yang terpilih sebagai subjek penelitian tersebut adalah siswa kelas IV. Data dikumpulkan dengan pemberian tes soal dan wawancara. Tes soal yang digunakan berbentuk soal cerita. Hasil penelitian menunjukkan bahwa faktor-faktor yang mempengaruhi kesulitan peserta didik dalam kemampuan verbal adalah peserta didik kurang mampu memahami permasalahan atau soal yang diberikan, selain itu siswa sulit dalam membahasakan hasil perhitungannya sebagai jawaban akhir atas permasalahan matematika yang diberikan, sedangkan faktor-faktor yang mempengaruhi kesulitan peserta didik dalam kemampuan numerik adalah peserta didik tidak memahami rumus yaitu salah dalam menentukan kelipatan dan salah dalam menentukan KPK dengan menggunakan pohon factor Abstract : This study aims to determine the factors that influence student difficulties seen from the verbal and numerical abilities of students in solving mathematical problems in the KPK material. This study uses a qualitative approach that is descriptive by describing the research process correctly in accordance with the facts obtained. In this study, the subject of the study were 30 students grade IV students. Data was collected by giving question tests and interviews. The test questions used are in the form of story problems. The results showed that the factors that influence the difficulties of students in verbal abilities were students were less able to understand the problems or questions given, other than that the students find it difficult to express the results of their calculations as the final answer to the mathematical problems given, while the factors that influence the difficulty of students in numerical abilities are students who do not understand the formula which is wrong in determining multiples and wrong in determining the KPK by using a tree factor.
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Özgül, İlhan, and Lütfi İncikabı. "Prospective Teachers’ Representations for Teaching Note Values: An Analysis in the Context of Mathematics and Music." Journal of Education and Training Studies 5, no. 11 (2017): 129. http://dx.doi.org/10.11114/jets.v5i11.2654.
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In this study, the representations preferred by prospective teachers in the teaching of note values were determined and the accuracy of these representations was analyzed in the context of mathematics and music. The case study, one of the qualitative research designs, was used in the study. Study group of the research consisted of 113 pre-school teachers. According to the findings of the research, prospective teachers preferred verbal (92%), note and (80%) real life representations in defining the note values in general terms. On the other hand, geometrical and algebraic representations were preferred at lower rates. The mathematical expressions of the vast majority were found to be correct when the accuracy of representations chosen by the teacher candidates were analyzed. Problems experienced in relation to mathematical expressions in teaching note values include disproportionate fragmentation, modeling error, and algebraic error. On the other hand, representations used in the teaching of note values have generally been unsuccessful in musical expressions; the problems faced in articulation were determined as not (being able to) showing note values, incorrectly showing quarter note values and incorrectly defining note values. The accuracy rates of mathematical expressions are higher than those of musical expressions, regardless of the representation used (note, real life, geometric, verbal, algebraic). In addition, research findings show that prospective teachers who use four types of representation in the teaching of note values are more successful in mathematical and musical context than those who use two and three representations.
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Santia, Ika, Purwanto Purwanto, Akbar Sutawidjadja, Sudirman Sudirman, and Subanji Subanji. "EXPLORING MATHEMATICAL REPRESENTATIONS IN SOLVING ILL-STRUCTURED PROBLEMS: THE CASE OF QUADRATIC FUNCTION." Journal on Mathematics Education 10, no. 3 (2019): 365–78. http://dx.doi.org/10.22342/jme.10.3.7600.365-378.
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Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and meaningfulness of what they learn, they also are connected with their prior knowledge. The focus of this research is exploring the used of mathematical representations in solving ill-structured problems involving quadratic functions. The topic of quadratic functions is considered necessary in mathematics teaching and learning in higher education. It's because many mathematics education students have difficulty in understanding these matters, and they also didn’t appreciate their advantage and application in daily life. The researchers' explored mathematical representation as used by two subjects from fifty-four mathematics education students at the University of Nusantara PGRI Kediri by using a qualitative approach. We were selected due to their completed all steps for solving the ill-structured problem, and there have different ways of solving these problems. Mathematical representation explored through an analytical framework of solving ill-structured issues such as representing problems, developing alternative solutions, creating solution justifications, monitoring, and evaluating. The data analysis used technique triangulation. The results show that verbal and symbolic representations used both subjects to calculate, detect, correct errors, and justify their answers. However, the visual representation used only by the first subject to detect and correct errors.
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Proboretno, Setyaning, and Pradnyo Wijayanti. "Representasi Matematis Siswa SMP dalam Meyelesaikan Masalah Segiempat Ditinjau dari Perbedaan Jenis Kelamin." MATHEdunesa 8, no. 3 (2019): 472–76. http://dx.doi.org/10.26740/mathedunesa.v8n3.p472-476.
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Mathematical representation has an important role to help students understand and solve quadrilateral problems in mathematics learning. Students will use different forms of mathematical representation to solve a quadrilateral problem. This allows that the form of mathematical representation used by male and female students is different. The purpose of this study was to describe the mathematical representation of male and female junior high school students in solving quadrilateral problems. This research is classified into descriptive qualitative research using test and interview methods. The results of this study indicate that male students use visual-spatial representations in the form of images to represent an object that is in the problem solving test. In addition, they use visual-spatial representations and formal-notational representations to reveal information about a problem. During the problem solving process, dominant male students use formal-notational representation. They also explained verbally each step of the completion in detail and in order. Dominant female students use formal-notational representation to write information and solve a problem. To represent an object in a problem solving test, they use visual-spatial representations. Female students also use verbal representations to explain each step of solving problems.Keywords: mathematical representation, quadrilateral problems, gender
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Sopamena, Patma, Toto Nusantara, Eddy Bambang Irawan, and Sisworo. "Students’ thinking path in mathematics problem-solving referring to the construction of reflective abstraction." Beta: Jurnal Tadris Matematika 11, no. 2 (2018): 155–66. http://dx.doi.org/10.20414/betajtm.v11i2.230.
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[English]: This research aims to reveal the path of student thinking in solving mathematical problems referring to the construction of reflective abstraction. Reflective abstraction is the process of thinking in constructing logical structures (logico-mathematical structures) by individuals through interiorization, coordination, encapsulation, and generalization. It is an explorative research with the qualitative descriptive approach which involve fourteen undergraduate students enrolled in Calculus course. Data was analyzed through (1) transcribing verbal data (results of think aloud, interviews, observations, field notes, and results of construction of student mathematical concepts), (2) conducting data reduction (coding, drawing thinking structures), (3) analyzing thought processes, and (4) drawing conclusions. We found that the thinking process of students in solving mathematical problems based on the construction of reflective abstraction can occur through the path of interiorization - coordination - encapsulation - generalization then to coordination - encapsulation - generalization. Thus, student’s thinking path in solving mathematical problems is categorized as a simple closed path.
 Keywords: Thinking path, Limit problem, Reflective abstraction, Simple closed path
 [Bahasa]: Penelitian ini bertujuan untuk mendeskripsikan terjadinya jalur berpikir mahasiswa dalam menyelesaikan masalah matematika berdasarkan konstruksi abstraksi reflektif. Abstraksi reflektif adalah proses berpikir dalam membangun struktur logis oleh individu melalui interiorisasi, koordinasi, enkapsulasi, dan generalisasi. Penelitian ini tergolong penelitian eksploratif dengan pendekatan deskriptif kualitatif melibatkan empat belas mahasiswa yang mengikuti matakuliah Kalkulus. Proses analisis data dalam penelitian ini dilakukan melalui langkah-langkah: (1) mentranskrip data verbal (hasil thinkalouds, wawancara, pengamatan, catatan lapangan, dan hasil konstruksi konsep matematika mahasiswa), (2) melakukan reduksi data (membuat coding, menggambar struktur berpikir), (3) analisis proses berpikir, dan (4) penarikan kesimpulan. Hasil penelitian menunjukkan bahwa proses berpikir mahasiswa dalam menyelesaikan masalah matematika berdasarkan konstruksi abstraksi reflektif dapat terjadi melalui jalur interiorisasi – koordinasi – enkapsulasi – generalisasi kemudian ke koordinasi – enkapsulasi – generalisasi. Dengan demikian, jalur berpikir mahasiswa dalam menyelesaikan masalah matematika dikategorikan sebagai jalur berpikir tipe lintasan tertutup sederhana.
 Kata kunci: Jalur berpikir, Masalah limit, Abstraksi reflektif, Jalur tertutup sederhana
 NB: PDF version of this article will be available in maximum two weeks after this publication
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Zentall, Sydney S., and Mary Ann Ferkis. "Mathematical Problem Solving for Youth with ADHD, with and without Learning Disabilities." Learning Disability Quarterly 16, no. 1 (1993): 6–18. http://dx.doi.org/10.2307/1511156.
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The mathematical achievement of youth with learning disabilities, attention deficit disorders, and attention-deficit hyperactive disorders is lower than that of their peers. Cognitive ability (including memory) and reading contribute to the comprehension skills needed to eliminate extraneous information, handle multiple operations, and transform verbal information within problems. Further, slow computation affects problem solving by increasing attentional load. Through our work and a review of other studies, we have documented that when IQ and reading are controlled, “true” math deficits are specific to mathematical concepts and problem types. Implications for instruction are drawn from learner characteristics as these interact with the current mathematics curriculum.
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Francescoli, Gabriel. "Are Verbal-Narrative Models More Suitable than Mathematical Models as Information Processing Devices for Some Behavioral (Biosemiotic) Problems?" Biological Theory 14, no. 3 (2019): 171–76. http://dx.doi.org/10.1007/s13752-019-00323-9.
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Berteletti, Ilaria, Jérôme Prado, and James R. Booth. "Children with mathematical learning disability fail in recruiting verbal and numerical brain regions when solving simple multiplication problems." Cortex 57 (August 2014): 143–55. http://dx.doi.org/10.1016/j.cortex.2014.04.001.
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Wibawa, Kadek Adi, I. Putu Ade Andre Payadnya, I. Made Dharma Atmaja, and Marius Derick Simons. "Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework." Beta: Jurnal Tadris Matematika 13, no. 2 (2020): 130–51. http://dx.doi.org/10.20414/betajtm.v13i2.327.
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[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
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Nugroho, Aryo Andri, Nizaruddin Nizaruddin, Ida Dwijayanti, and Anggi Tristianti. "Exploring students' creative thinking in the use of representations in solving mathematical problems based on cognitive style." JRAMathEdu (Journal of Research and Advances in Mathematics Education) 5, no. 2 (2020): 202–17. http://dx.doi.org/10.23917/jramathedu.v5i2.9983.
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Creative thinking is the cognitive activities that process the received information to produce new representations. Therefore, it is necessary to develop creative thinking and represent a problem. This study aims to investigate the students' creative thinking processes based on representation in solving mathematical problems reviewed from cognitive style. Qualitative research was used as a procedure of the study. The data was collected through MFFT questionnaires, mathematics problem tests, and interviews. This research involved 31 eighth-grade students at one of junior high school in Kendal regency, Central Java. Those two subjects represented the reflective and impulsive cognitive styles that have been selected based on their mathematical abilities. The data was analyzed through iterative method. The results of the study showed that both subjects demonstrated a different performance in solving problem. In term of fluency, both subjects used visual representations in interpreting information. On the originality, the reflective subject used symbolic representations. while the impulsive one used symbolic and verbal representations in constructing the mathematical expressions. However, both of them have not yet created new ideas in solving problems. Moreover, on the flexibility, these both subjects used visual and symbolic representations that could solve the problems by utilizing the environment objects towards the interpret problems into mathematical expressions. However, the reflective subject made a mistake in elaborating the formula as well as the impulsive subject can do it. These results indicated that both subjects have used the representation of each indicator of creative thinking in solving problems.
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Kuzu, Okan. "Preservice mathematics teachers’ competencies in the process of transformation between representations for the concept of limit: A qualitative study." Pegem Eğitim ve Öğretim Dergisi 10, no. 4 (2020): 1037–66. http://dx.doi.org/10.14527/pegegog.2020.032.
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In this study, external representations and the problems encountered related transformation process between representations towards limit concept were investigated. "Limit Representation Conversion Test" was administered to 41 preservice mathematics teachers studying at a state university in central Turkey during 2018–2019 academic years. In this study, which was designed with the case study model, which is one of the qualitative research models, the data were analyzed by content analysis. Unstructured interviews were made with preservice mathematics teachers whose explanations were insufficient or differed and the problems encountered were determined. It was observed that preservice mathematics teachers had most difficulties in the verbal representation type questions. It was revealed that preservice mathematics teachers who gave the wrong answers mostly had deficiencies in the concept and the process and could not fully understand the limit problems. It was determined that preservice mathematics teachers had difficulties in knowing the concept of limit point, determining the function and interpreting verbal data. It was seen that preservice mathematics teachers who proceeded towards the concept and process answered wrong due to mathematical operations errors and carelessness. When the wrong answers were examined, it was observed that errors were gathered under the themes "lack of content knowledge" and "lack of reading comprehension" for verbal type input; under the theme "carelessness" for graphical type input; under the theme "lack of content knowledge" for algebraic and numerical type input.
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Presentación, M. J., Rebeca Siegenthaler, V. Pinto, et al. "MEMORIA DE TRABAJO EN NIÑOS DE EDUCACIÓN INFANTIL CON Y SIN BAJO RENDIMIENTO MATEMÁTICO." International Journal of Developmental and Educational Psychology. Revista INFAD de Psicología. 3, no. 1 (2016): 233. http://dx.doi.org/10.17060/ijodaep.2014.n1.v3.498.
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Abstract:This study aims to explore working memory in preschool children with and without low mathematical performance. The sample consisted of 255 children aged 5-6 years, to whom were administered neuropsychological tests of working memory and TEDI-MATH to estimate the mathematical performance. The results highlight the capacity of verbal working memory to significantly differentiate groups of children with and without problems in 8 of the 9 analyzed mathematical domains. This factor together with visuospatial working memory differentiate the group of children at risk for mathematical learning disabilities.Keywords: working memory, preschool, math performance, mathematics learning disabilitiesResumen:Este estudio se propone analizar la memoria de trabajo en niños de Educación Infantil con y sin bajo rendimiento matemático. La muestra estaba compuesta de 255 niños de 5 a 6 años, a los que se les aplicó pruebas neuropsicológicas de memoria de trabajo y el TEDI-MATH para estimar el rendimiento matemático. Los resultados destacan la capacidad de la memoria de trabajo verbal para diferenciar significativamente los grupos de niños con y sin dificultades en 8 de los 9 dominios matemáticos analizados. Este mismo factor junto con la memoria de trabajo viso-espacial estática diferencian al grupo de niños con riesgo de aprendizaje de las matemáticas.Palabras clave: memoria de trabajo, Educación Infantil, rendimiento matemático, dificultades de aprendizaje de las matemáticas.
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BAYDUZ, Serkan, and Mithat TAKUNYACI. "INVESTIGATION OF 8th GRADE STUDENTS' PROBLEM POSING TOWARDS DIFFERENT REPRESENTATIONS." IEDSR Association 6, no. 15 (2021): 435–53. http://dx.doi.org/10.46872/pj.390.
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In this study, it is aimed to examine and analyze the problems posed by eighth grade students for different forms of representation. In the study, it was also examined how the problems posed by the students differed according to their academic success. 54 eighth grade students selected by appropriate sampling participated in the study, which was designed as a case study, one of the qualitative research methods. The data of the research were obtained with the “Problem Posing Test” developed by the researcher and the “Mathematics Achievement Test” consisting of exam questions prepared by the Ministry of National Education. Silver and Cai’s (1996) analysis scheme was used to analyze the obtained data. According to the findings, it was seen that only 44% of the answers given by the students were solvable problems suitable for the given ones. While most of the problems posed in the desired direction were of “low” mathematical nature in terms of mathematical complexity, it was seen that they were in the “conditional” category in terms of linguistic complexity. It has been found that students are more successful in posing problems for table and verbal representation, compared to picture and symbolic representation. It has been observed that as students' mathematical achievements increase in representations other than symbolic representation, their rate of posing a problem suitable for the given ones also increases.
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Tushnova, Yulya. "Features of Social-Perceptual Properties of Mathematically Gifted Students." International Journal of Cognitive Research in Science, Engineering and Education 8, Special issue (2020): 103–12. http://dx.doi.org/10.23947/2334-8496-2020-8-si-103-112.
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The attention of modern society to intellectual potential makes the problem of studying mathematically gifted youth at the stage of self-determination in higher education relevant. Practical problems related to the psychological features of social adaptation of mathematically gifted youth require solving. The main goal of the research is to study the social and perceptual abilities of mathematically gifted students. The study sample consisted of 76 natural science students aged 17-23 years (M=19.8, SD=3.2 (58% men). The research methods were: testing (test of analytical mathematical abilities, test of the structure of intelligence (TSI) of R. Amthauer), expert assessment, survey (questionnaire of V. A. Krutetsky, questionnaires aimed at diagnosing socio-perceptual abilities), statistical methods. Self-assessment of intelligence, composite assessment, and some components of social intelligence and some components of empathy are significantly different. The ability of mathematical generalization and practical mathematical thinking have a greater number of relationships with social and perceptual properties. Here we found relationships not only with empathy, but also the ability to recognize verbal expression and the General ability to understand and manage their own and other people’s emotions. The ability to operate images in two-dimensional space is related only to the level and components of emotional intelligence. According to the results of the study, the features of socio-perceptual properties of students with different levels of analytical mathematical abilities are described. The conclusions can be used in the development of a program of psychological support for this category of students.
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Saleh, Sitti Fithriani, Purwanto Purwanto, Sudirman Sudirman, Erry Hidayanto, and Susiswo Susiswo. "Elementary School Teachers' Mathematical Connections in Solving Trigonometry Problem." Research in Social Sciences and Technology 3, no. 3 (2018): 32–41. http://dx.doi.org/10.46303/ressat.03.03.3.
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This study aims to reveal mathematical connections of elementary school teachers in solving trigonometric problem. The subjects of this study were 22 elementary school teachers as the prospective participants of Professional Teacher Education and Training (PTET). They came from several districts of South Sulawesi Province. The teachers were given trigonometry problem. Trigonometry problems could encourage teachers to connect geometrical and algebraic concept, graphical representation and algebraic representation, as well as daily life context. The result shows that most of the subject teachers of this study solved the problem according to procedures they know without considering everyday life context. On the other hand, there were some subjects who connected problem with everyday life context using graphical, verbal, or numerical representation. Thus, subjects who were able to connect problem information with appropriate concepts and procedures are categorized as substantive connections. While the subjects who were able to connect problem information with mathematical concepts but less precise in using the procedure are categorized as classification connections.
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W, Goulart, Ailes E, Golden C, and Lashley L. "A-191 The Role of Memory in Mathematical Abilities." Archives of Clinical Neuropsychology 35, no. 6 (2020): 986. http://dx.doi.org/10.1093/arclin/acaa068.191.
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Abstract Objective To determine the contribution of different types of memory (Visual Memory, Auditory Memory and Visual Working Memory) to mathematical abilities. Method The participants were drawn from a deidentified adult clinical database. A multiple regression tested (n = 91, Mage = 29.9, Medu = 13.3, 49% Caucasian, 57% Female) the ability of the Wechsler Memory Scale Fourth edition (WMS-IV) Auditory Memory Index Score, Visual Memory Index Score, and Visual Working Memory Index Score to predict the Key Math-3rd edition (KM3) Total Test Standard Score. Results In a standard regression, Visual Memory, Auditory Memory, and Visual Working Memory indexes significantly predicted KM3 Total Test Standard Scores. The regression was statistically significant, F(3,87) = 17.1, p = &lt; .001, R2 = .370. In this model, WMS-IV Visual Working Memory (beta = .338, p = .004) and Auditory Memory (beta = .271, p = .007) added significantly to the prediction. Conclusion The results of this study suggest that memory is important in mathematical calculations and different types of memory make distinct contributions. Furthermore, the Visual Working Memory Index explained a greater percentage of variance than the Auditory Memory Index. This suggests that visual working memory skills play a greater role in mathematical abilities and highlights the importance of the ability to remember and manipulate figures in our minds when solving math problems. The significance of auditory memory to mathematics may be related to remembering how to solve problems, word problems, and verbal problem-solving strategies. The Visual Memory Index may not have contributed unique variance because this composite may overlap with the Visual Working Memory Index, and academic learning may be stored verbally.
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الكيلاني, حامد صالح زيد, та غازي إسماعيل المهر. "درجة تضمين الاختبارات المدرسية للمسائل الرياضية اللفظية / الحياتية = The Degree of including Mathematical Verbal / Life Problems in School Tests". مجلة جامعة القدس المفتوحة للأبحاث و الدراسات التربوية و النفسية 4, № 14 (2016): 335–66. http://dx.doi.org/10.12816/0027777.
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Widodo, An nur Ami, and Dedi Nur Aristiyo. "KEMAMPUAN REPRESENTASI MATEMATIS MAHASISWA DALAM MENYELESAIKAN MASALAH STATISTIKA BERDASARKAN LANGKAH KRULIK DAN RUDNICK." Jurnal Edukasi dan Sains Matematika (JES-MAT) 5, no. 2 (2019): 99. http://dx.doi.org/10.25134/jes-mat.v5i2.1988.
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This research intended to describe the mathematical representation of students in solving statistical problems based on the Krulik anf Rdunick steps. This research is a qualitative descriptive study. The subjects of this study were students of the second semester mathematic education study program. The procedure of subjects using purposive sampling techniques. Data collection techniques in this study were observation, interviews and documentation. Data validity used triangulation. Data analysis techniques using the Mile and Huberman step, namely data reduction, data presentations, drawing conclusions and verifyingconclusions. The results The results of this study are as follows: (1) subjects with high ability in the read and think and exploration and plan stages, using verbal and symbolic representations. The stage of select a strategy, using symbolic representation. The find and answer stage, uses symbolic and visual representations. In the reflect and extend step, the subject uses verbal representations. For students with moderate ability in the stage of read and think and explore and plan using verbal representation. The stage of finding an answer and select a strategy using verbal and symbolic representation. The reflect and extend stage of the subject uses symbolic representations. In students with low ability to read and think and explore and plan using verbal representation. Stage select a strategy subject using symbolic representation.
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Qomariyah, Nur, and Rini Setianingsih. "Kemampuan Komunikasi Matematis Siswa SMP dalam Menyelesaikan Masalah Matematika Berdasarkan Gaya Kognitif Reflektif dan Impulsif." JURNAL PENELITIAN PENDIDIKAN MATEMATIKA DAN SAINS 4, no. 1 (2021): 22. http://dx.doi.org/10.26740/jppms.v4n1.p22-32.
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Abstrak — Komunikasi matematis merupakan cara penyampaian ide, strategi, maupun solusi masalah matematika secara tertulis maupun lisan. Gaya kognitif yang berbeda memungkinkan terjadinya perbedaan komunikasi dalam menyelesaikan masalah matematika baik secara lisan maupun tulisan. Penelitian ini bertujuan untuk mendeskripsikan kemampuan komunikasi matematis siswa dengan gaya kognitif reflektif dan impulsif dalam menyelesaikan masalah matematika. Penelitian ini merupakan penelitian deskriptif kualitatif. Subjek penelitiannya yaitu satu siswa bergaya kognitif reflektif (SR) dan satu siswa bergaya kognitif impulsif (SI). Hasil penelitian ini menunjukkan bahwa kemampuan komunikasi matematis tulis siswa yang bergaya kognitif reflektif dapat dikatakan tidak akurat, tidak lengkap, dan lancar pada tahap memahami masalah. Kemampuan komunikasi lisan siswa yang bergaya kognitif reflektif dapat dikatakan akurat, lengkap, dan lancar disetiap tahap penyelesaian masalah. Kemampuan komunikasi matematis tulis siswa yang bergaya kognitif impulsif dapat dikatakan tidak akurat, tidak lengkap dan lancar pada tahap memahami masalah. Selain itu, di tahap memeriksa kembali dapat dikatakan tidak akurat, tidak lengkap, dan tidak lancar. Kemampuan komunikasi matematis lisan siswa bergaya kognitif impulsif dapat dikatakan tidak akurat, tidak lengkap dan tidak lancar di tahap memeriksa kembali.Kata Kunci: Komunikasi Matematis, Gaya Kognitif Reflektif, Gaya Kognitif Impulsif Abstract — Mathematical communication is a way to convey ideas of problem solving, strategies and mathematical solutions both in writing and verbally. The different cognitive styles allowing communication differences in solving mathematical problems both verbally and in writing. This study aims to describe the mathematical communication skills of students with reflective and impulsive cognitive styles in solving mathematical problems. This research is a qualitative descriptive study. The research subjects were one student with reflective cognitive style (SR) and one student with impulsive cognitive style (SI). The results of this study indicate that students' written mathematical communication skills with reflective cognitive style can be said to be inaccurate, incomplete, and fluent at the step of understanding the problem. The verbal communication skills of students who are reflective cognitive style can be said to be accurate, complete, and fluent at every step of problem solving. The students' written mathematical communication skills with impulsive cognitive style can be said to be inaccurate, incomplete and fluent at the stage of understanding the problem. In addition, the step of looking back can be said to be inaccurate, incomplete, and influent. The verbal mathematical communication skills of students with impulsive cognitive style can be said to be inaccurate, incomplete and influent at the step of looking back.Keywords: Mathematical Communication, Reflective Cognitive Style, Impulsive Cognitive Style
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Kuznetsova, Elena. "What Colors do Undergraduates Associate with Training Courses? Student Evaluations of the Applied Mathematics Educational Program through the Color Selection Method." Bolema: Boletim de Educação Matemática 34, no. 66 (2020): 314–31. http://dx.doi.org/10.1590/1980-4415v34n66a15.
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Abstract It is no doubt that today the role of mathematics is increasing and mathematical education requires constant attention. Nevertheless, there are not so many studies devoted to the problems of teaching university students who have chosen mathematics as their profession. The purpose of this article is to research the attitude of undergraduates towards the courses that make up the Applied Mathematics educational program, implemented in one of the technical universities in Russia. The survey was conducted using the Color Selection Method, based on Max Lüscher ideas. Students have associated each course with one of the eight proposed colors. The outcomes of the survey were investigated through correlation and cluster analysis and compared with the results of another survey conducted by a verbal evaluation tool. This research has revealed that the student's assessments obtained through two methods (verbal and imaginative) do not contradict each other. The use of the Color Selection Method helps identifying the problems that arise in the educational process and allows to outline ways of improving teaching quality.