Academic literature on the topic 'Mathematical word problems'

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Journal articles on the topic "Mathematical word problems"

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Croft, Sue. "Solving mathematical word problems." 5 to 7 Educator 2010, no. 66 (2010): xii—xiii. http://dx.doi.org/10.12968/ftse.2010.9.6.79488.

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Caligari, Laura, Eva Norén, and Paola Valero. "Collaging illustrated mathematical word problems." Prometeica - Revista de Filosofía y Ciencias 31 (November 29, 2024): 336–46. https://doi.org/10.34024/prometeica.2024.31.16413.

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In a mathematical educational context, mathematical word problems are an established practice with the aim to connect to students’ everyday life. Drawing on Neo-material perspectives and art based research methods we explore collage as a way to critically engage with illustrated mathematical word problems. We challenge the view of mathematical knowledge production as an objective, value-neutral and disembodied process by performing agential cuts with(in) illustrated mathematical word problems from two Swedish mathematical textbooks. The perspectives and methods mobilize sensibilities that advance new points of views. Hence, contributing to broaden the range of qualitative research methods and paradigms studying mathematical word problems.
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Hasemann, Klaus. "Word problems and mathematical understanding." Zentralblatt für Didaktik der Mathematik 37, no. 3 (2005): 208–11. http://dx.doi.org/10.1007/s11858-005-0010-8.

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Reyes, Joseph, and Zenaida Reyes. "Metacognitive Learning in Solving Mathematical Word Problems." Psychology and Education: A Multidisciplinary Journal 22, no. 2 (2024): 217–53. https://doi.org/10.5281/zenodo.12751160.

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The metacognition in mathematics learning on solving word problems, explicitly described the solving strategies using metacognition anchored from the two metacognitive components. The students’ knowledge of cognition in mathematics learning in terms of declarative knowledge utilized specific metacognitive strategies such as activating concepts on the problem and identifying and determining concepts and information techniques which include specific implication of strategies that elaborate concepts such as reading and recalling, translating, identifying mathematical concepts, determining the needed information, and understanding the leading question. Students’ procedural knowledge in mathematics learning utilized specific metacognitive strategies such as substituting, representing, and organizing process, which include specific implication of strategies that elaborate concepts to the substitution process, use of representation while solving, and organizing solution coherently and logically. Substituting, representing, and organizing process is the execution of plan, strategy, model, idea, decision, or method and the realization of an application of the subject. Students’ conditional knowledge in mathematics learning utilized specific metacognitive strategies such as questioning the problem and their own practices, which include specific implication of strategies that elaborate concepts to question the problem, consistent practice to develop familiarity, solution appropriateness, exploring possible solutions, and thinking of ways to approach the problem. Students’ regulation of cognition in mathematics learning in terms of planning utilized specific metacognitive strategies such as breaking down, illustrating, and labelling and thinking about the information, formula, and steps which include specific implication of strategies that elaborate concepts to write down the information in the problem, determine the required formula, think about the steps before solving, breakdown the problem, draw illustration, and put labelling. Students’ monitoring regulation in mathematics learning utilized specific metacognitive strategies such as making sense of their own work and verifying solutions, which include specific implication of strategies that elaborate concepts to second thoughts during and after solving, recognizing errors in the solution, familiarity towards the problem, checking of works step by step, reflecting from time to time, and use of scratch to draft solutions. Students’ evaluating regulation in mathematics learning utilized specific metacognitive strategies such as reviewing and revising which include specific implication of strategies that elaborate concepts to review calculations and procedures, use strategies to check answers, draw conclusions, think of alternative ways after completing a task, and revising solutions if not correct.
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Phaladi, Mabuse, Mmushetji Petrus Rankhumise, and Willy Mwakapenda. "The Role of Language in Solving Mathematical Word Problems among Grade 9 Learners." Dirasat: Human and Social Sciences 51, no. 3 (2024): 310–22. http://dx.doi.org/10.35516/hum.v51i3.650.

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Objectives: The study aimed to explore mathematical word problem solving abilities among Grade 9 learners in Tshwane North District Schools. It highlighted how language plays a pivotal role in learning mathematics and understanding mathematical word problems. Moreover, it showed how language inadequecy and incorrect translation affect Grade 9 learners’ solutions to mathmatical word problems in schools around Tshwane North District. Methods: The study used both qualitative and quantitative methods. It also made use of contextual, exploratory, and descriptive statistical data. The study involved 26 nineth-grade learners in Tshwane North District secondary schools in Gauteng Province. Data collection was based on learners’ written work (a questionnaire) and analysing the results of the administered test. Data was analysed to detect the language difficulties that learners’ face when translating and solving mathematical word problems. The analysis process involved developing initial insights, coding, interpreting, and drawing conclusions to determine whether there is a connection between language proficiency and solving mathematical word problems. Results: The study showed that learners face difficulties in mathematical processes such as inadequate language comprehension when translating words into mathmatical symbols. It also revealed that there is a strong connection between vocabulary knowledge and word problem solving, resulting in learning challenges related to understanding the meaning associated with mathmatical word problems. Conclusions: Evidence from the word problem test for Grade 9 learners revealed that mathematical vocabulary and syntactic features are the main factors causing difficulties in understanding and solving mathmatical word problems.
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Gallagher, Melissa A., Laura Ellis, and Travis Weiland. "Making Word Problems Meaningful." Mathematics Teacher: Learning and Teaching PK-12 114, no. 8 (2021): 580–90. http://dx.doi.org/10.5951/mtlt.2020.0247.

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Czocher, Jennifer A., Diana L. Moss, and Luz A. Maldonado. "Revitalizing and Repurposing Conventional Word Problems." Mathematics Teacher: Learning and Teaching PK-12 113, no. 5 (2020): 404–10. http://dx.doi.org/10.5951/mtlt.2019.0031.

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Conventional word problems can't help students build mathematical modeling skills. on their own. But they can be leveraged! We examined how middle and high school students made sense of word problems and offer strategies to question and extend word problems to promote mathematical reasoning.
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KHATIB, Suzan, Liliana CIASCAI, and Ioana MAGDAŞ. "Future teachers’ opinions regarding the mathematical word problems." Acta Didactica Napocensia 17, no. 2 (2024): 125–36. https://doi.org/10.24193/adn.17.2.10.

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This study examines the attitudes and opinions of 161 students, future primary school teachers, in Romania towards mathematical word problems during the 2023-2024 academic year. The investigation aimed at identifying their views on the importance, utility, and challenges of word problems. The results indicate that most students recognize the educational benefits of word problems, particularly in enhancing logical thinking and applying math to real-life scenarios. Feelings towards word problems vary: many students find them interesting and feel more confident after solving difficult problems, while most are neutral, and some need extra training to boost confidence and reduce anxiety. The study shows that many future teachers handle word problems well, but some experience difficulties. While most students have skills for solving word problems, there is notable variation in proficiency and practices. Some students lack adequate training and struggle with self-organization and attention to detail. Students support the increased educational efforts made in university courses to teach them to apply various strategies for solving word problems and recognize their importance. Overall, students are confident in their ability to solve and teach mathematical word problems, which suggests a strong commitment to improving their future teaching skills.
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Bednorz, David, and Michael Kleine. "Unsupervised machine learning to classify language dimensions to constitute the linguistic complexity of mathematical word problems." International Electronic Journal of Mathematics Education 18, no. 1 (2023): em0719. http://dx.doi.org/10.29333/iejme/12588.

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The study examines language dimensions of mathematical word problems and the classification of mathematical word problems according to these dimensions with unsupervised machine learning (ML) techniques. Previous research suggests that the language dimensions are important for mathematical word problems because it has an influence on the linguistic complexity of word problems. Depending on the linguistic complexity students can have language obstacles to solve mathematical word problems. A lot of research in mathematics education research focus on the analysis on the linguistic complexity based on theoretical build language dimensions. To date, however it has been unclear what empirical relationship between the linguistic features exist for mathematical word problems. To address this issue, we used unsupervised ML techniques to reveal latent linguistic structures of 17 linguistic features for 342 mathematical word problems and classify them. The models showed that three- and five-dimensional linguistic structures have the highest explanatory power. Additionally, the authors consider a four-dimensional solution. Mathematical word problem from the three-dimensional solution can be classify in two groups, three- and five-dimensional solutions in three groups. The findings revealed latent linguistic structures and groups that could have an implication of the linguistic complexity of mathematical word problems and differ from language dimensions, which are considered theoretically. Therefore, the results indicate for new design principles for interventions and materials for language education in mathematics learning and teaching.
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Abdullah, Abdul Halim, Nurain Nadhirah Mohamad, Sitti Fithriani Saleh, and Mutmainnah. "Unlocking mathematics' power: interpreting content and context within word problems." International Journal of Evaluation and Research in Education (IJERE) 13, no. 4 (2024): 2288–95. https://doi.org/10.11591/ijere.v13i4.28658.

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Mathematics is a fundamental subject with wide-reaching importance in education, providing students with the tools to apply mathematical principles in diverse contexts. This study examines the abilities of 60 pre-service mathematics teachers (PSTs) in identifying content and context within mathematical word problems. Utilizing a case study approach, the study employed the mathematics word problems test and the content and context questionnaire. The findings reveal that PSTs generally struggle with error detection and content comprehension in mathematical word problems, as demonstrated by their inability to recognize inaccuracies in two of three test questions. The failure of PSTs to identify errors in mathematical word problems often stems from their tendency to rely solely on the solutions they obtain, without first understanding the entire question presented. In essence, they may focus on finding a solution rather than critically evaluating the problem, which can lead to the oversight of errors or inaccuracies within the problem statement itself. This study emphasizes the need for PSTs to grasp mathematical concepts and contextualize them in everyday life scenarios. Challenges were observed in linking computational results to real-world contexts. Thus, the study calls for future research in pre-service teacher education to explore strategies for enhancing critical thinking, error detection, and the integration of practical context in mathematical problem-solving. Furthermore, the study suggests that assessing the ability of PSTs to formulate problem-solving questions evaluates their capacity to answer questions and their ability to construct questions that can enhance students’ cognitive abilities.
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Dissertations / Theses on the topic "Mathematical word problems"

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Conley, Michele E. "UTILIZING TECHNOLOGY TO ENHANCE READING COMPREHENSION WITHIN MATHEMATICAL WORD PROBLEMS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/121.

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Many students who are proficient with basic math facts struggle for understanding when it comes to word problems. Teachers time and time again teach and re-teach problem solving strategies in hope that their students will one day acquire all the skills necessary to become proficient in this area. Unfortunately understanding problem solving skills is not the only answer to solving word problems. There has been a significant amount of evidence linking reading comprehension to mathematical reasoning. The development of a website to assist teachers and students who are having difficulties with mathematical word problems is extremely beneficial. The website is designed with links, power points, and examples that enhance reading comprehension within mathematical word problems. Through this project, it has been determined that students who are exposed to an additional mathematical program related to breaking apart word problems show evidence of a greater understanding and mastery of solving mathematical word problems.
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Kanevsky, Inna Glaz. "Role of rules in transfer of mathematical word problems." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3223010.

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Thesis (Ph. D.)--University of California, San Diego, 2006.<br>Title from first page of PDF file (viewed September 21, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 86-90).
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Bernadette, Elizabeth. "Third grade students' challenges and strategies to solving mathematical word problems." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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Muoneke, Ada Felicitas. "The effects of a question and action strategy on the mathematical word problem-solving skills of students with learning problems in mathematics /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008402.

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Tan, Li-hua, and 陳麗華. "Primary school students' thinking processes when posing mathematical word problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31962592.

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Tan, Li-hua. "Primary school students' thinking processes when posing mathematical word problems." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk:8888/cgi-bin/hkuto%5Ftoc%5Fpdf?B23425155.

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Maluleka, Bondo Kenneth. "Improving grade 9 learners' Mathematical processes of solving word problems." Thesis, University of Limpopo (Turfloop Campus), 2013. http://hdl.handle.net/10386/965.

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Thesis (M.A. (Mathematics Education)) --University of Limpopo, 2013<br>This study intended to improve Grade 9 learners’ mathematical processes of solving word problems. It was an action research study in my own classroom consisting of 64 Grade 9 learners. Learners were given learning activities on word problems to carry out as part of their normal classroom mathematics’ lessons. Data were collected in two stages: first, through passive observation, that is, without my intervention, and later through participant observation thus provoking their thinking as they attempt the given questions. The learners’ responses were analyzed through checking the mathematical processes they used without my intervention. Learners also submitted their post-intervention responses for analysis of progress after interventions. The scripts were reviewed based on four problem- solving stages adopted from George Polya (1945). Those stages are, namely understanding the problem, devising the plan, carrying out the plan and looking back. It became evident from the findings that learners attempt solving word problems with no understanding. Communication, reasoning and recording processes appear to be key factors in assisting learners to make sense of word problems and, finally, proceeding towards an adequate solution.
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Brook, Ellen. "INVESTIGATING THE ADULT LEARNERS’ EXPRERIENCE WHEN SOLVING MATHEMATICAL WORD PROBLEMS." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1394513871.

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Borchert, Katja. "Disassociation between arithmetic and algebraic knowledge in mathematical modeling /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/9141.

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Guthormsen, Amy. "Conceptual integration of mathematical and semantic knowledge /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/8995.

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Books on the topic "Mathematical word problems"

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Long, Lynette. Wacky Word Problems. John Wiley & Sons, Ltd., 2005.

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Kessler, Colleen. Math problem solvers: Using word problems to enhance mathematical problem-solving skills. Prufrock Press, 2005.

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Swetz, Frank. Mathematical expeditions: Exploring word problems across the ages. Johns Hopkins University Press, 2012.

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Virginia, Brown. Test of mathematical abilities. 2nd ed. Pro-Ed, 1994.

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Wingard-Nelson, Rebecca. Algebra word problems: No problem! Enslow Publishers, 2011.

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Wingard-Nelson, Rebecca. Geometry word problems: No problem! Enslow Publishers, 2012.

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Harry, Briggs, ed. The Grapes of Math: Mind-Stretching Math Riddles. Scholastic, 2004.

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Wingard-Nelson, Rebecca. Geometry word problems: No problem! Enslow Publishers, 2011.

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Wingard-Nelson, Rebecca. Algebra word problems: No problem! Enslow Publishers, 2011.

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Wingard-Nelson, Rebecca. Math measurement word problems: No problem! Enslow Publishers, 2011.

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Book chapters on the topic "Mathematical word problems"

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Amado, Nélia, Susana Carreira, and Sandra Nobre. "The Spreadsheet Affordances in Solving Complex Word Problems." In Mathematical Problem Solving. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10472-6_5.

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Lohrey, Markus. "Compressed Word Problems for Inverse Monoids." In Mathematical Foundations of Computer Science 2011. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22993-0_41.

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Novotna, Jarmila. "Student’s Levels of Understanding Word Problems." In Proceedings of the Ninth International Congress on Mathematical Education. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-010-9046-9_43.

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Shalev, Aner. "Some Results and Problems in the Theory of Word Maps." In Bolyai Society Mathematical Studies. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39286-3_22.

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Degrande, Tine, Lieven Verschaffel, and Wim Van Dooren. "Proportional Word Problem Solving Through a Modeling Lens: A Half-Empty or Half-Full Glass?" In Posing and Solving Mathematical Problems. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28023-3_13.

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Verschaffel, Lieven, Brian Greer, and Erik de Corte. "Everyday Knowledge and Mathematical Modeling of School Word Problems." In Symbolizing, Modeling and Tool Use in Mathematics Education. Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-3194-2_16.

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Ayabe, Hiroaki, Emmanuel Manalo, Mari Fukuda, and Norihiro Sadato. "What Diagrams Are Considered Useful for Solving Mathematical Word Problems in Japan?" In Diagrammatic Representation and Inference. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86062-2_8.

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AbstractPrevious studies have shown that diagram use is effective in mathematical word problem solving. However, they have also revealed that students manifest many problems in using diagrams for such purposes. A possible reason is an inadequacy in students’ understanding of variations in types of problems and the corresponding kinds of diagrams appropriate to use. In the present study, a preliminary investigation was undertaken of how such correspondences between problem types and kinds of diagrams are represented in textbooks. One government-approved textbook series for elementary school level in Japan was examined for the types of mathematical word problems, and the kinds of diagrams presented with those problems. The analyses revealed significant differences in association between kinds of diagrams and types of problems. More concrete diagrams were included with problems involving change, combination, variation, and visualization of quantities; while number lines were more often used with comparison and variation problems. Tables and graphs corresponded to problems requiring organization of quantities; and more concrete diagrams and graphs to problems involving quantity visualization. These findings are considered in relation to the crucial role of textbooks and other teaching materials in facilitating strategy knowledge acquisition in students.
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Verschaffel, Lieven. "Real-World Knowledge and the Modeling of School Word Problems." In Proceedings of the Ninth International Congress on Mathematical Education. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-010-9046-9_52.

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Lohrey, Markus. "Word Problems for 2-Homogeneous Monoids and Symmetric Logspace." In Mathematical Foundations of Computer Science 2001. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44683-4_44.

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Mandal, Sourav, and Sudip Kumar Naskar. "Solving Arithmetic Mathematical Word Problems: A Review and Recent Advancements." In Advances in Intelligent Systems and Computing. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7590-2_7.

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Conference papers on the topic "Mathematical word problems"

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Luik, Piret, Carmen Keivabu, and Kerli Orav-Puurand. "Using ChatGPT 3.5 to Reformulate Word Problems for State Exam in Mathematics." In 17th International Conference on Computer Supported Education. SCITEPRESS - Science and Technology Publications, 2025. https://doi.org/10.5220/0013152200003932.

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He, Xin, and Chao Sun. "Enhanced Graph-Based Model with Mathematical Knowledge Embedding for Math Word Problem Solving." In 2024 International Conference on Intelligent Education and Intelligent Research (IEIR). IEEE, 2024. https://doi.org/10.1109/ieir62538.2024.10959951.

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Liang, Zhenwen, Jipeng Zhang, Kehan Guo, Xiaodong Wu, Jie Shao, and Xiangliang Zhang. "Compositional Mathematical Encoding for Math Word Problems." In Findings of the Association for Computational Linguistics: ACL 2023. Association for Computational Linguistics, 2023. http://dx.doi.org/10.18653/v1/2023.findings-acl.635.

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Hayyulbathin, Isfa, Retno Winarni, and Tri Murwaningsih. "Analysing students’ errors in solving mathematical word problems." In INTERNATIONAL CONFERENCE ON APPLIED COMPUTATIONAL INTELLIGENCE AND ANALYTICS (ACIA-2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0126624.

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Ahmad, Azlina, Halimah Badioze Zaman, Siti Salwah Salim, and Roziati Zainuddin. "MINDA: A cognitive tool for solving mathematical word problems." In 2010 International Symposium on Information Technology (ITSim 2010). IEEE, 2010. http://dx.doi.org/10.1109/itsim.2010.5561328.

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Kadupitiya, J. C. S., Surangika Ranathunga, and Gihan Dias. "Automated assessment of multi-step answers for mathematical word problems." In 2016 Sixteenth International Conference on Advances in ICT for Emerging Regions (ICTer). IEEE, 2016. http://dx.doi.org/10.1109/icter.2016.7829900.

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Kadupitiya, J. C. S., Surangika Ranathunga, and Gihan Dias. "Assessment and Error Identification of Answers to Mathematical Word Problems." In 2017 IEEE 17th International Conference on Advanced Learning Technologies (ICALT). IEEE, 2017. http://dx.doi.org/10.1109/icalt.2017.48.

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Liyanage, Vijini, and Surangika Ranathunga. "A Multi-language Platform for Generating Algebraic Mathematical Word Problems." In 2019 IEEE 14th Conference on Industrial and Information Systems (ICIIS). IEEE, 2019. http://dx.doi.org/10.1109/iciis47346.2019.9063354.

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Zeng, Jing, James D. Tan, and Kenneth Y. T. Lim. "UTILISING DEEP LEARNING IN SINGAPORE PRIMARY SCHOOL MATHEMATICAL WORD PROBLEMS." In 15th International Conference on Education and New Learning Technologies. IATED, 2023. http://dx.doi.org/10.21125/edulearn.2023.0679.

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Tan, Minghuan, Lei Wang, Lingxiao Jiang, and Jing Jiang. "Investigating Math Word Problems using Pretrained Multilingual Language Models." In Proceedings of the 1st Workshop on Mathematical Natural Language Processing (MathNLP). Association for Computational Linguistics, 2022. http://dx.doi.org/10.18653/v1/2022.mathnlp-1.2.

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Reports on the topic "Mathematical word problems"

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Wei, Xin, Amanda Wortman, Cristina Heffernan, et al. Language and Mathematics Learning: A Comparative Study of Digital Learning Platforms. SEERNet, Digital Promise, 2024. http://dx.doi.org/10.51388/20.500.12265/206.

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This paper presents a conceptual exploration of how Digital Learning Platforms (DLPs) can be utilized to investigate the impact of language clarity, precision, engagement, and contextual relevance on mathematics learning from word problems. Focusing on three distinct DLPs—ASSISTments/E-TRIALS, MATHia/UpGrade, and Canvas/Terracotta—we propose hypothetical studies aimed at uncovering how nuanced language modifications can enhance mathematical understanding and engagement. While these studies are illustrative in nature, they provide a blueprint for researchers interested in leveraging DLPs for empirical investigation so that future investigators gain a better understanding of the emerging infrastructure for research in DLPs and the opportunities provided by them. In highlighting three distinct implementations of the same core research question, we reveal both commonalities as well as differences in how different educational technologies might build evidence, offering a unique opportunity to advance the field of math education and other education research fields.
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De Bortoli, Lisa, and Catherine Underwood. PISA 2022. A closer look at mathematics in Australia. Australian Council for Educational Research, 2025. https://doi.org/10.37517/978-1-74286-786-1.

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The Programme for International Student Assessment (PISA) is an international comparative study that assesses how well 15-year-olds, who have nearly completed compulsory schooling in most participating educational systems, can use their knowledge and skills to meet real-world opportunities and challenges. In each cycle of PISA, students are assessed in the domains of reading, mathematics and science. Each cycle has a domain that is the major focus and for which there is a higher proportion of questions than from the others. Mathematics was the major focus in the 2022 cycle. The mathematics assessment framework includes 2 mathematics subscales that reflect the complexity of mathematics. The content subscales (Change and relationships; Quantity; Space and shape; and Uncertainty and data) represent the core areas of mathematics knowledge that students encounter in educational curricula worldwide. The process subscales (Formulating situations mathematically; Employing mathematical concepts, facts and procedures; Interpreting, applying and evaluating mathematical outcomes; and, Mathematical reasoning) reflect the mental actions required for effective problem-solving in mathematics. This report presents the mathematics results on the content and process subscales for Australia as a whole, for the Australian states and territories and for the other groups in PISA 2022. This report also presents the results from the teacher questionnaire about the teaching of mathematics and explores the perspectives of teachers on the constructs of: goals and views about teaching mathematics; encouraging mathematical thinking; fostering reasoning; and, teaching of mathematical reasoning and 21st-century mathematics topics. Each construct examines the similarities and differences in teachers teaching of mathematics between countries, the Australian jurisdictions and different demographic groups. Similarly, the student questionnaire ascertains student perspectives about the constructs of: effort and persistence in mathematics; mathematics self-efficacy in mathematical reasoning and 21st-century mathematics topics; and, mathematics anxiety. The constructs present the similarities and differences in students' attitudes and behaviours toward learning mathematics between countries, the Australian jurisdictions and different demographic groups.
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Bilous, Vladyslav V., Volodymyr V. Proshkin, and Oksana S. Lytvyn. Development of AR-applications as a promising area of research for students. [б. в.], 2020. http://dx.doi.org/10.31812/123456789/4409.

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The article substantiates the importance of using augmented reality in the educational process, in particular, in the study of natural and mathematical disciplines. The essence of AR (augmented reality), characteristics of AR hardware and software, directions and advantages of using AR in the educational process are outlined. It has proven that AR is a unique tool that allows educators to teach the new digital generation in a readable, comprehensible, memorable and memorable format, which is the basis for developing a strong interest in learning. Presented the results of the international study on the quality of education PISA (Programme for International Student Assessment) which stimulated the development of the problem of using AR in mathematics teaching. Within the limits of realization of research work of students of the Borys Grinchenko Kyiv University the AR-application on mathematics is developed. To create it used tools: Android Studio, SDK, ARCore, QR Generator, Math pattern. A number of markers of mathematical objects have been developed that correspond to the school mathematics course (topic: “Polyhedra and Functions, their properties and graphs”). The developed AR tools were introduced into the process of teaching students of the specialty “Mathematics”. Prospects of research in development of a technique of training of separate mathematics themes with use of AR have been defined.
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4

Zinonos, Natalya O., Elena V. Vihrova, and Andrey V. Pikilnyak. Prospects of Using the Augmented Reality for Training Foreign Students at the Preparatory Departments of Universities in Ukraine. CEUR-WS.org, 2018. http://dx.doi.org/10.31812/123456789/2657.

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The purpose of the study is to highlight the potential and the prospects of using the augmented reality in the mathematical education for foreign students at the preparatory departments of universities. Objectives of the study: to determine the peculiarities of the virtualization of the training of foreign students at the preparatory departments of universities, as well as the possibilities of using the technology of complementary reality in the teaching of mathematics. Object of research: a virtually oriented educational environment of foreign students at the preparatory departments of universities. Subject of research: virtualization of learning with the augmented reality of mathematical education of foreign students at the preparatory departments of universities. Used research methods: theoretical – analysis of scientific and methodological literature; empirical-study, observation of the educational process. Results of the research: on the basis of the analysis of scientific publications, the notion of virtualization of education and the virtually oriented educational environment of foreign students at the preparatory departments of higher educational institutions is described. The main conclusions and recommendations: 1) the article outlines the possibilities and prospects of using the augmented reality in the mathematical education for foreign students at the preparatory departments of universities; 2) the considering the various targets of mobile applications, which are used in solving mathematical problems, as well as analysis of the characteristics of various practical achievements of using the augmented reality in the mathematical preparation for foreign students at the preparatory departments of universities, it is planned to devote a separate work.
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5

Perdigão, Rui A. P. Earth System Dynamic Intelligence - ESDI. Meteoceanics, 2021. http://dx.doi.org/10.46337/esdi.210414.

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Earth System Dynamic Intelligence (ESDI) entails developing and making innovative use of emerging concepts and pathways in mathematical geophysics, Earth System Dynamics, and information technologies to sense, monitor, harness, analyze, model and fundamentally unveil dynamic understanding across the natural, social and technical geosciences, including the associated manifold multiscale multidomain processes, interactions and complexity, along with the associated predictability and uncertainty dynamics. The ESDI Flagship initiative ignites the development, discussion and cross-fertilization of novel theoretical insights, methodological developments and geophysical applications across interdisciplinary mathematical, geophysical and information technological approaches towards a cross-cutting, mathematically sound, physically consistent, socially conscious and operationally effective Earth System Dynamic Intelligence. Going beyond the well established stochastic-dynamic, information-theoretic, artificial intelligence, mechanistic and hybrid techniques, ESDI paves the way to exploratory and disruptive developments along emerging information physical intelligence pathways, and bridges fundamental and operational complex problem solving across frontier natural, social and technical geosciences. Overall, the ESDI Flagship breeds a nascent field and community where methodological ingenuity and natural process understanding come together to shed light onto fundamental theoretical aspects to build innovative methodologies, products and services to tackle real-world challenges facing our planet.
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Kuropiatnyk, D. I. Actuality of the problem of parametric identification of a mathematical model. [б. в.], 2018. http://dx.doi.org/10.31812/123456789/2885.

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The purpose of the article is to study the possibilities of increasing the efficiency of a mathematical model by identifying the parameters of an object. A key factor for parametrization can be called the consideration of properties of the values of the model at a specific time point, which allows a deeper analysis of data dependencies and correlation between them. However, such a technique does not always work, because in advance it is impossible to predict that the parameters can be substantially optimized. In addition, it is necessary to take into account the fact that minimization reduces the values of parameters without taking into account their real physical properties. The correctness of the final values will be based on dynamically selected parameters, which allows you to modify the terms of use of the system in real time. In the development process, the values of experimentally obtained data with the model are compared, which allows you to understand the accuracy of minimization. When choosing the most relevant parameters, various minimization functions are used, which provides an opportunity to cover a wide range of theoretical initial situations. Verification of the correctness of the decision is carried out with the help of a quality function, which can identify the accuracy and correctness of the optimized parameters. It is possible to choose different types of functional quality, depending on the characteristics of the initial data. The presence of such tools during parametrization allows for varied analysis of the model, testing it on various algorithms, data volumes and conditions of guaranteed convergence of functional methods.
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7

Saptsin, Vladimir, and Володимир Миколайович Соловйов. Relativistic quantum econophysics – new paradigms in complex systems modelling. [б.в.], 2009. http://dx.doi.org/10.31812/0564/1134.

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This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system’s state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondefinable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception(operator is a mathematical image of the procedure, the action), description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereffect i.e. the memory. In consideration of the analysis conducted in the work we suggest new paradigms of the economical-mathematical modeling.
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Pasupuleti, Murali Krishna. Mathematical Modeling for Machine Learning: Theory, Simulation, and Scientific Computing. National Education Services, 2025. https://doi.org/10.62311/nesx/rriv125.

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Abstract Mathematical modeling serves as a fundamental framework for advancing machine learning (ML) and artificial intelligence (AI) by integrating theoretical, computational, and simulation-based approaches. This research explores how numerical optimization, differential equations, variational inference, and scientific computing contribute to the development of scalable, interpretable, and efficient AI systems. Key topics include convex and non-convex optimization, physics-informed machine learning (PIML), partial differential equation (PDE)-constrained AI, and Bayesian modeling for uncertainty quantification. By leveraging finite element methods (FEM), computational fluid dynamics (CFD), and reinforcement learning (RL), this study demonstrates how mathematical modeling enhances AI-driven scientific discovery, engineering simulations, climate modeling, and drug discovery. The findings highlight the importance of high-performance computing (HPC), parallelized ML training, and hybrid AI approaches that integrate data-driven and model-based learning for solving complex real-world problems. Keywords Mathematical modeling, machine learning, scientific computing, numerical optimization, differential equations, PDE-constrained AI, variational inference, Bayesian modeling, convex optimization, non-convex optimization, reinforcement learning, high-performance computing, hybrid AI, physics-informed machine learning, finite element methods, computational fluid dynamics, uncertainty quantification, simulation-based AI, interpretable AI, scalable AI.
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Schoen, Robert C., Mark LaVenia, Charity Bauduin, and Kristy Farina. Elementary Mathematics Student Assessment: Measuring the Performance of Grade 1 and 2 Students in Counting, Word Problems, and Computation in Fall 2013. Florida State University, 2016. http://dx.doi.org/10.17125/fsu.1508170543.

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Schoen, Robert C., Mark LaVenia, Charity Bauduin, and Kristy Farina. Elementary Mathematics Student Assessment: Measuring the Performance of Grade 1 and 2 Students in Counting, Word Problems, and Computation in Fall 2014. Florida State University, 2016. http://dx.doi.org/10.17125/fsu.1508174887.

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