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