Relevant bibliographies by topics / Mathematical thinking

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Mathematical thinking'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Mathematical thinking"

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Moiseienko, Lidiia, and Liubov Shehda. "Dependence of Mathematical Errors on Mathematical Thinking Style." Collection of Research Papers "Problems of Modern Psychology", no. 54 (December 3, 2021): 116–36. http://dx.doi.org/10.32626/2227-6246.2021-54.116-136.

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Knuth, Donald E. "Algorithmic Thinking and Mathematical Thinking." American Mathematical Monthly 92, no. 3 (1985): 170. http://dx.doi.org/10.2307/2322871.

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Knuth, Donald E. "Algorithmic Thinking and Mathematical Thinking." American Mathematical Monthly 92, no. 3 (1985): 170–81. http://dx.doi.org/10.1080/00029890.1985.11971572.

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Tonra, Wilda Syam, Talisadika S. Maifa, Willy Abdul Ghany, and Siti Fatimah. "MATHEMATICAL THINKING DAN KAITANNYA DENGAN WAYS OF UNDERSTANDING, WAYS OF THINKING: SEBUAH KAJIAN PUSTAKA." SIGMA 9, no. 1 (2023): 17. http://dx.doi.org/10.53712/sigma.v9i1.1970.

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Abstrak:Awal munculnya istilah “Mathematical Thinking” merujuk kepada istilah dari buku yang sangat terkenal berjudul Thinking Mathematically dengan jumlah sitasi saat ini mencapai 1781. Buku ini ditulis oleh John Mason dengan Leone Burton dan Kaye Stacey tahun 1982. Buku ini menjadi rujukan dari beberapa peneliti lainnya. Di buku ini, Mathematical Thinking proses dibagi menjadi 2 pasang proses yaitu Specialising and Generalising kemudian Conjecturing and Convincing. Namun, istilah “Mathematical Thinking”memiliki beberapa pergeseran makna sesuai dengan perkembangan dari tahun ke tahun. Selain
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Selden, Annie, Tommy Dreyfus, In P. Nesher, and J. Kilpatrick. "Advanced Mathematical Thinking." College Mathematics Journal 22, no. 3 (1991): 268. http://dx.doi.org/10.2307/2686656.

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Griffiths, H. B., and David Tall. "Advanced Mathematical Thinking." Mathematical Gazette 79, no. 484 (1995): 159. http://dx.doi.org/10.2307/3620036.

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Manouchehri, Azita, Pingping Zhang, and Jenna Tague. "Nurturing Mathematical Thinking." Mathematics Teacher 111, no. 4 (2018): 300–303. http://dx.doi.org/10.5951/mathteacher.111.4.0300.

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With the publication of the National Council of Teachers of Mathematics' Curriculum Standards document in 1989, nurturing students' mathematical thinking secure a prominent place in the discourse surrounding school curriculum and instructional redesign. Although the standards document did not provide a definition for mathematical thinking, the authors highlighted processes that could support its development, including problem solving, communicating ideas, building and justifying arguments, and reasoning formally and informally about potential mathematical relationships. Less articulated were w
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Edwards, Barbara S., Ed Dubinsky, and Michael A. McDonald. "Advanced Mathematical Thinking." Mathematical Thinking and Learning 7, no. 1 (2005): 15–25. http://dx.doi.org/10.1207/s15327833mtl0701_2.

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Turner, Julianne C., Karen Rossman Styers, and Debra G. Daggs. "Encouraging Mathematical Thinking." Mathematics Teaching in the Middle School 3, no. 1 (1997): 66–72. http://dx.doi.org/10.5951/mtms.3.1.0066.

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With these words, the NCTM (1989, 65) portrays a dilemma familiar to many middle-grades teachers. Although many teachers strive to involve their students in active and challenging problem-solving activities, students' past experiences may have instilled preconceptions that mathematics is mechanical, uninteresting, or unattainable. In addition, many teachers lack models and examples of how to design mathematics instruction so that it fosters students' engagement. Because the middle grades are crucial years for developing students' future interest in mathematics, middle-grades teachers must take
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Yusrina, Siti Laiyinun, and Masriyah Masriyah. "Profil Berpikir Aljabar Siswa SMP dalam Memecahkan Masalah Matematika Kontekstual Ditinjau dari Kemampuan Matematika." MATHEdunesa 8, no. 3 (2019): 477–84. http://dx.doi.org/10.26740/mathedunesa.v8n3.p477-484.

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Algebra is one of the important concepts in mathematics and began to be taught in class VII of junior high school. One way to find out students' thinking and reasoning abilities algebraically is to algebraic thinking. Algebraic thinking is a mental activity consisting of generalization, abstraction, dynamic thinking, modeling, analytic thinking, and organization. The means that can be used to explore students' algebraic thinking is problem solving. The problem used in this research is contextual mathematical problems. Algebraic thinking in each student in solving contextual mathematical proble
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Dissertations / Theses on the topic "Mathematical thinking"

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Hart, Hilary. "Mathematics Vocabulary and English Learners: A Study of Students' Mathematical Thinking." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2573.

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This study examined the mathematical thinking of English learners as they were taught mathematics vocabulary through research-based methods. Four English learners served as focus students. After administering a pre-performance assessment, I taught a 10-lesson unit on fractions. I taught mathematics vocabulary through the use of a mathematics word wall, think-pair-shares, graphic organizers, journal entries, and picture dictionaries. The four focus students were audio recorded to capture their spoken discourse. Student work was collected to capture written discourse. Over the course of the unit
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Hannula, Markku. "Affect in mathematical thinking and learning /." Turku : University of Turku, 2004. http://kirjasto2.utu.fi/julkaisupalvelut/b/annaalit/B273.html.

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Monteleone, Chrissoula. "Critical mathematical thinking in young students." Phd thesis, Australian Catholic University, 2021. https://acuresearchbank.acu.edu.au/download/cb06753760247f43b88bfde14ea04bc78463c1734aa47d3ca60129d4d5e7c8ec/2879980/Monteleone_2021_Critical_mathematical_thinking_in_young_students.pdf.

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The aims of the study were to investigate critical mathematical thinking in young students, and teaching actions/questions that help these young students exhibit their critical mathematical thinking. A key finding was the conceptualisation of a Critical Mathematical Thinking Framework for Young Students. This framework (a) articulates the key characteristics young students exhibit as they engage in critical mathematical thinking, and (b) can be used by teachers to help them identify critical mathematical thinking within the classroom context. Additionally, specific teacher questions that suppo
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Argyle, Sean Francis. "Mathematical thinking: From cacophony to consensus." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1337696397.

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Lane, Catherine Pullin. "Mathematical Thinking and the Process of Specializing." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1307441324.

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Stillman, Gloria Ann. "Assessing higher order mathematical thinking through applications /." St. Lucia, Qld, 2001. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe16747.pdf.

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Cardella, Monica E. "Engineering mathematics : an investigation of students' mathematical thinking from a cognitive engineering perspective /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/10692.

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Tanner, H. F. R. "Using and applying mathematics : developing mathematical thinking through practical problem solving and modelling." Thesis, Swansea University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639162.

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Using and Applying Mathematics in the National Curriculum focuses on the development of reasoning skills through problem solving, and links the processes involved in learning new mathematics with the application of existing knowledge to new situations. This thesis begins by examining how mathematical knowledge is constructed and how children make sense of it. The nature of practical problem solving and modelling is considered and the literature on teaching and learning problem solving and modelling is reviewed with particular emphasis on metacognition and social practices. The research reports
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Reyes-Santander, Pamela, David Aceituno, and Pablo Cáceres. "Mathematical Thinking Styles of Students with Academic Talent." Pontificia Universidad Católica del Perú, 2017. http://repositorio.pucp.edu.pe/index/handle/123456789/123827.

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This study explores the predominant mathematical thinking style that students with academic talent used in solving mathematical problems. Thinking styles are preferences by subjects in the way of expressing mathematical skills against a task, in this case, visual, formal and integrated. We assessed 99 students from an academic support talent program, in a retrospective ex post facto study with only one group. We administered the questionnaire mathematical thinking styles of Borromeo-Ferri and determined that these students exhibited mostly an integrated style of thinking, which involves the us
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Coetzee, Carla. "Mathematical thinking skills needed by first year programming students." Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/60991.

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The aim of this qualitative study is to explore and describe the mathematical thinking skills that students require for a first level programming subject that forms part of the National Diploma in Information Communication Technology (ICT) at a University of Technology (UoT). Mathematics is an entry requirement for many tertiary programmes, including ICT courses, unfortunately the poor quality of schooling in South Africa limits learners' access to higher education. From the literature it is evident that students lack fluency in fundamental mathematical and problem-solving skills when t
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Books on the topic "Mathematical thinking"

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Karloff, Howard. Mathematical Thinking. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33203-6.

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Tall, David, ed. Advanced Mathematical Thinking. Springer Netherlands, 1991. http://dx.doi.org/10.1007/0-306-47203-1.

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Patras, Frédéric. Contemporary Mathematical Thinking. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27548-7.

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Orme, Tall David, ed. Advanced mathematical thinking. Kluwer Academic Publishers, 1991.

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1948-, Watson Anne, Houssart Jenny, Roaf Caroline, and National Association for Special Educational Needs (Great Britain), eds. Supporting mathematical thinking. David Fulton, 2005.

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H, Schoenfeld Alan, ed. Mathematical thinking and problem solving. L. Erlbaum Associates, 1994.

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J, Sternberg Robert, and Ben-Zeev Talia, eds. The nature of mathematical thinking. L. Erlbaum Associates, 1996.

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university, Open. Using mathematical thinking: Course guide. OU., 1996.

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D'Angelo, John P. Mathematical thinking: Problem-solving and proofs. Prentice Hall, 1997.

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Alex, Kozulin, ed. Rigorous mathematical thinking: Conceptual formation in the mathematics classroom. Cambridge University Press, 2008.

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Book chapters on the topic "Mathematical thinking"

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Shipton, Eva, Michael Kenwood, Cyril Moss, and Charles Plumpton. "Mathematical thinking." In Examinations in Mathematics. Macmillan Education UK, 1985. http://dx.doi.org/10.1007/978-1-349-08089-2_2.

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Müller-Stach, Stefan. "Mathematical Thinking." In Mathematics Study Resources. Springer Berlin Heidelberg, 2024. http://dx.doi.org/10.1007/978-3-662-69483-1_3.

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Ervynck, Gontran. "Mathematical Creativity." In Advanced Mathematical Thinking. Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47203-1_3.

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Hanna, Gila. "Mathematical Proof." In Advanced Mathematical Thinking. Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47203-1_4.

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Krzywacki, Heidi, Leila Pehkonen, and Anu Laine. "Promoting Mathematical Thinking." In Miracle of Education. SensePublishers, 2012. http://dx.doi.org/10.1007/978-94-6091-811-7_8.

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Neri, Ferrante. "Basic Mathematical Thinking." In Linear Algebra for Computational Sciences and Engineering. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40341-0_1.

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Neri, Ferrante. "Basic Mathematical Thinking." In Linear Algebra for Computational Sciences and Engineering. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21321-3_1.

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Gattuso, Linda, and Maria Gabriella Ottaviani. "Complementing Mathematical Thinking and Statistical Thinking in School Mathematics." In Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education. Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-1131-0_15.

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Alibert, Daniel, and Michael Thomas. "Research on Mathematical Proof." In Advanced Mathematical Thinking. Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47203-1_13.

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Dreyfus, Tommy. "Advanced Mathematical Thinking Processes." In Advanced Mathematical Thinking. Springer Netherlands, 2002. http://dx.doi.org/10.1007/0-306-47203-1_2.

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Conference papers on the topic "Mathematical thinking"

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McMaster, Kirby, Brian Rague, and Nicole Anderson. "Integrating Mathematical Thinking, Abstract Thinking, and Computational Thinking." In 2010 IEEE Frontiers in Education Conference (FIE). IEEE, 2010. http://dx.doi.org/10.1109/fie.2010.5673139.

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Susanti, Elsa, and Hartono. "Mathematical Critical Thinking and Creative Thinking Skills." In the 2019 International Conference. ACM Press, 2019. http://dx.doi.org/10.1145/3348400.3348408.

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Henderson, Peter B., Will Lloyd, Bill Marion, et al. "Striving for mathematical thinking." In Working group reports from ITiCSE. ACM Press, 2001. http://dx.doi.org/10.1145/572133.572136.

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Deng, Jixia. "Improve the students' mathematical thinking." In 2016 International Conference on Economy, Management and Education Technology. Atlantis Press, 2016. http://dx.doi.org/10.2991/icemet-16.2016.7.

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Nakamura, Takayasu, and Tetsushi Kawasaki. "Computer Science Unplugged for Developing Computational Thinking and Mathematical Thinking." In 2019 International Joint Conference on Information, Media and Engineering (IJCIME). IEEE, 2019. http://dx.doi.org/10.1109/ijcime49369.2019.00108.

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Desmayanasari, Dwi, Desrina Hardianti, Fitria Lestari, Tia Agnesa, and Pujia Siti Balkist. "Designing mathematical creative thinking skill instrument." In IWOSP 2021, INTERNATIONAL WORKSHOP ON STATISTICAL PHYSICS. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0123718.

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Riskon, Muhammad, Rochmad, and Nuriana Rachmani Dewi’. "Mathematical Disposition in Algebraic Thinking Skills." In 6th International Conference on Science, Education and Technology (ISET 2020). Atlantis Press, 2022. http://dx.doi.org/10.2991/assehr.k.211125.011.

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Marsitin, Retno, and Nyamik Rahayu Sesanti. "Student Worksheet in Mathematical Creative Thinking." In Annual Conference on Social Sciences and Humanities. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0007419803210325.

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Jiang, Minghong. "Cultivation of Excellent Mathematical Quality Integrating Multilevel Mathematical Thinking Model." In 2019 International Conference on Robots & Intelligent System (ICRIS). IEEE, 2019. http://dx.doi.org/10.1109/icris.2019.00127.

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Risnanosanti. "Mathematical thinking styles of undergraduate students and their achievement in mathematics." In THE 4TH INTERNATIONAL CONFERENCE ON RESEARCH, IMPLEMENTATION, AND EDUCATION OF MATHEMATICS AND SCIENCE (4TH ICRIEMS): Research and Education for Developing Scientific Attitude in Sciences And Mathematics. Author(s), 2017. http://dx.doi.org/10.1063/1.4995145.

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Reports on the topic "Mathematical thinking"

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Duden, Mary. Teacher Learning in the Context of Students’ Mathematical Thinking. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.7367.

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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 ass
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Näslund-Hadley, Emma. IDB Briefly Noted: No. 9 : June, 2011: Less Talk, More Play: Bolstering Math Learning in Argentina. Inter-American Development Bank, 2011. http://dx.doi.org/10.18235/0008215.

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Argentina and the Inter-American Development Bank (IDB) joined forces to test a new math education model called Mathematics for All (MAT). After just one academic year, learning increased in schools using the model, with particularly dramatic improvements among underperforming students. This brief describes how MAT improved learning by focusing on the development of mathematical thinking rather than on the memorization of formulas.
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Vroom, Kristen. Guided Reinvention as a Context for Investigating Students' Thinking about Mathematical Language and for Supporting Students in Gaining Fluency. Portland State University Library, 2000. http://dx.doi.org/10.15760/etd.7420.

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Modlo, Yevhenii O., Serhiy O. Semerikov, Ruslan P. Shajda, Stanislav T. Tolmachev, and Oksana M. Markova. Methods of using mobile Internet devices in the formation of the general professional component of bachelor in electromechanics competency in modeling of technical objects. [б. в.], 2020. http://dx.doi.org/10.31812/123456789/3878.

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The article describes the components of methods of using mobile Internet devices in the formation of the general professional component of bachelor in electromechanics competency in modeling of technical objects: using various methods of representing models; solving professional problems using ICT; competence in electric machines and critical thinking. On the content of learning academic disciplines “Higher mathematics”, “Automatic control theory”, “Modeling of electromechanical systems”, “Electrical machines” features of use are disclosed for Scilab, SageCell, Google Sheets, Xcos on Cloud in
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Peters, Vanessa, Deblina Pakhira, Latia White, Rita Fennelly-Atkinson, and Barbara Means. Designing Gateway Statistics and Chemistry Courses for Today’s Students: Case Studies of Postsecondary Course Innovations. Digital Promise, 2022. http://dx.doi.org/10.51388/20.500.12265/162.

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Scholars of teaching and learning examine the impacts of pedagogical decisions on students’ learning and course success. In this report, we describes findings from case studies of eight innovative postsecondary introductory statistics and general chemistry courses that have evidence of improving student completion rates for minoritized and low-income students. The goal of the case studies was to identify the course design elements and pedagogical practices that were implemented by faculty. To identify courses, Digital Promise sought nominations from experts in statistics and chemistry educatio
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Hernández Orellana, Marisol. Educating for the Future: Why Universities Must Lead the Way in Ethical and Digital Competence. Carver University; Universidad Autónoma de Chile, 2025. https://doi.org/10.32457/hernandez2202597.

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As artificial intelligence (AI) reshapes our world, higher education faces a pivotal decision: will it merely adopt these technologies or will it actively guide their integration in ways that preserve human judgment, ethics, and intellectual autonomy? This opinion article argues that universities must take a leadership role—not only to safeguard their institutional identity but also to contribute to a society populated by digitally competent, ethically grounded professionals. Recent studies show that AI tools like ChatGPT and Wolfram Alpha are increasingly used by students to automate complex
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Ivanova, Halyna I., Olena O. Lavrentieva, Larysa F. Eivas, Iuliia O. Zenkovych, and Aleksandr D. Uchitel. The students' brainwork intensification via the computer visualization of study materials. [б. в.], 2020. http://dx.doi.org/10.31812/123456789/3859.

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The paper the approaches to the intensification of the students’ brainwork by means of computer visualization of study material have been disclosed. In general, the content of students’ brainwork has been presented as a type of activity providing the cognitive process, mastering the techniques and ways of thinking, developing the capabilities and abilities of the individual, the product of which is a certain form of information, as a result of the brainwork the outlook of the subject of work is enriched. It is shown the visualization is the process of presenting data in the form of an image wi
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Koh, Teck Seng. Enhancing STEM education through improvisational tinkering and computational thinking: A professional development package for Singapore teachers. National Institute of Education, Nanyang Technological University, Singapore, 2023. https://doi.org/10.32658/10497/27371.

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IMprovisational Tinkering (MT) emphasizes the creative, improvisational nature of problem solving that is the hallmark of MT as an educative, inquiry-based practice in Science, Technology, Engineering and Mathematics (STEM) education. Broadly, Improvisational Tinkering refers to the skill involved in Computational Thinking (CT) refers to MT and CT align with the aspirations of the Singapore education system. The school Science curricula places, at the heart of its curricula framework, the learners to apply themselves meaningfully in the new digital age.
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Schoen, Robert C., Daniel Anderson, and Charity Bauduin. Elementary Mathematics Student Assessment: Measuring Grade 3, 4, and 5 Students’ Performace in Number (Whole Numbers and Fractions), Operations, and Algebraic Thinking in Spring 2016. Florida State University Library, 2018. http://dx.doi.org/10.33009/fsu.1653497279.

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This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades 3, 4, and 5 student abilities. The test was administered to 2,754 participating grade 3, 4, and 5 students in 55 schools located in 10 public school districts in Florida during spring 2016. Focused on number (including whole number and fractions), operations, and algebraic thinking, the student assessment was designed to serve as a baseline measure of student achievement in a randomized controlled trial evaluating the impact of a teac
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