The goal of Technology for Mathematical Argumentation (TMA) was to construct a computational environment in which elementary students could explore the behavior of arithmetic operations such as multiplication and division. It is based on the work of Russell, Schifter & Bastable (2011), who introduced the idea of representation-based proofs, a way for young students to demonstrate why a generalization is true using a representation rather than algebraic symbols. Our system, Classroom Learning Partner, provides two kinds of tools to support this process: Tools to construct and manipulate mathematical representations, such as arrays, and an animation system to record the transformation of a quantity through an operation. Here, we demonstrate how we designed a curriculum sequence to lead second-grade students to use CLP to explore the generalization: Nx4 = (Nx2)x2.<\/p>\n\n\n\n
TMA\u00a0is a collaboration between\u00a0AV巴士\u00a0and MIT\u2019s Center for Educational Computing Initiatives, now part of MIT\u2019s Office of Digital Learning. This material is based upon work supported by the National Science Foundation under Grant Numbers\u00a0DRL-1019841 and 1020152. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the\u00a0NSF.<\/p>\n\n\n\n
NSF Awards:\u00a01250362<\/a>,\u00a01250802<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":50,"featured_media":1626,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_eb_attr":""},"grade_level":[6],"keyword":[9,13,14],"funder":[37],"class_list":["post-1625","videos","type-videos","status-publish","has-post-thumbnail","hentry","grade_level-grades-k-6","keyword-mathematics","keyword-technology","keyword-emerging-technologies","funder-nsf-cyberlearning"],"acf":[],"yoast_head":"\n