eprintid: 10001748 rev_number: 29 eprint_status: archive userid: 587 source: pure dir: disk0/00/00/17/48 datestamp: 2010-03-18 14:55:07 lastmod: 2025-02-07 13:58:29 status_changed: 2010-03-18 14:55:07 type: book_section metadata_visibility: show item_issues_count: 0 creators_name: Noss, Richard creators_name: Hoyles, Celia title: Exploring Mathematics Through Construction and Collaboration ispublished: pub divisions: B14 note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. abstract: All learning environments are designed based on a set of assumptions about what knowledge should be learned. For example, most mathematics classrooms are designed to teach a certain kind of mathematical knowledge that comprises procedures that solve isolated problems quickly, and this implicitly devalues the importance of structural understanding or of developing an appreciation of underlying mathematical models (see Lehrer & Schauble, this volume). This means that all too often, students do not see the need for consistency or rigor, do not notice conflicting strategies or solutions, and therefore cannot learn from them. Based on our research in a variety of workplace situations, we are convinced that a crucial element of knowledge required by most, if not all, people, is precisely this appreciation of underlying models. A version of mathematics that emphasizes structures also has the potential to help students understand the computational systems that are increasingly critical in today's society, because computer systems are mathematical models – computer software is built out of variables and relationships. As technology becomes more and more advanced, and the underlying models more and more obscure and invisible, it becomes increasingly important that children learn awareness of models; how to build, revise, and evaluate them, and to develop some analytic understanding of how inputs relate to outputs. date: 2005 date_type: published publisher: Cambridge University Press official_url: https://doi.org/10.1017/CBO9780511816833.024 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual doi: 10.1017/CBO9780511816833.024 isbn_13: 9780511816833 full_text_status: public series: Handbooks in Psychology place_of_pub: Cambridge,UK pagerange: 389-406 pages: 17 refereed: FALSE book_title: The Cambridge Handbook of the Learning Sciences editors_name: Sawyer, R. Keith citation: Noss, Richard; Hoyles, Celia; (2005) Exploring Mathematics Through Construction and Collaboration. In: Sawyer, R. Keith, (ed.) The Cambridge Handbook of the Learning Sciences. (pp. 389-406). Cambridge University Press: Cambridge,UK. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10001748/1/Noss2006Exploring389.pdf