{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:28:45Z","timestamp":1773656925277,"version":"3.50.1"},"reference-count":51,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T00:00:00Z","timestamp":1755129600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Assisted Learning"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title><jats:sec><jats:title>Background<\/jats:title><jats:p>Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming\u2010based mathematical problem\u2010solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes. However, implementing programming\u2010based mathematics instruction requires teachers to have sufficient knowledge about learners' thinking processes in such a context, while very little is known about multifaceted solution development from a learner\u2010centred perspective.<\/jats:p><\/jats:sec><jats:sec><jats:title>Objectives<\/jats:title><jats:p>Viewing CT and MT as processes that go beyond specific skills or concepts, we conducted a qualitative study to investigate how participants develop computational solutions to mathematical problems and construct meaningful understandings of these solutions.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>We adopted an interpretive approach to participants' solution pathways to reveal their diverse thinking processes underlying solution development. A constant comparative analysis approach was undertaken to guide the data analysis.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results and Conclusions<\/jats:title><jats:p>We identified multiple solution pathways in developing programming\u2010based mathematical solutions (PMS) and characterised four significant pathways comprising seven distinct sub\u2010situations: (1) transition between personal MT and invalid PMS, (2) evolution from invalid PMS to valid PMS, (3) construction from non\u2010meaningful PMS to meaningful PMS and (4) revision from suboptimal PMS to optimal PMS. The findings contribute to a deeper understanding of problem solvers' learning in programming\u2010based mathematical problem\u2010solving and offer implications for theory and practice in programming\u2010rich mathematics education.<\/jats:p><\/jats:sec>","DOI":"10.1111\/jcal.70102","type":"journal-article","created":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T05:06:26Z","timestamp":1755234386000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Learner\u2010Centred Exploration of Teachers' Solution Pathways in K\u201012 Programming\u2010Based Mathematical Problem\u2010Solving"],"prefix":"10.1111","volume":"41","author":[{"given":"Huiyan","family":"Ye","sequence":"first","affiliation":[{"name":"Department of Curriculum and Instruction, Faculty of Education The Chinese University of Hong Kong  Hong Kong China"}]},{"given":"Biyao","family":"Liang","sequence":"additional","affiliation":[{"name":"Faculty of Education The University of Hong Kong  Hong Kong China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3736-7845","authenticated-orcid":false,"given":"Oi\u2010Lam","family":"Ng","sequence":"additional","affiliation":[{"name":"Department of Curriculum and Instruction, Faculty of Education The Chinese University of Hong Kong  Hong Kong China"}]}],"member":"311","published-online":{"date-parts":[[2025,8,14]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/bxs074"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.12973\/eu-jer.11.3.1495"},{"key":"e_1_2_12_4_1","unstructured":"Bhattacherjee A.2012.\u201cSocial Science Research: Principles Methods and Practices.\u201d USF Tampa Bay Open Access Textbooks Collection. 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