References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt160",{id:"formSmash:upper:j_idt160",widgetVar:"widget_formSmash_upper_j_idt160",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt161_j_idt163",{id:"formSmash:upper:j_idt161:j_idt163",widgetVar:"widget_formSmash_upper_j_idt161_j_idt163",target:"formSmash:upper:j_idt161:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Matematiska resonemang i en lärandemiljö med dynamiska matematikprogramPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (Swedish)Doctoral thesis, comprehensive summary (Other academic)Alternative title
##### Abstract [en]

##### Abstract [sv]

##### Place, publisher, year, edition, pages

Karlstad: Karlstads universitet, 2015. , 77 p.
##### Series

Karlstad University Studies, ISSN 1403-8099 ; 2015:12
##### Keyword [en]

Mathematical reasoning, Task design, Dynamic mathematics software
##### Keyword [sv]

matematiska resonemang, uppgiftsdesign, dynamiska matematikprogram
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kau:diva-35037ISBN: 978-91-7063-623-3OAI: oai:DiVA.org:kau-35037DiVA: diva2:784065
##### Public defence

2015-03-18, 21A 342 (Eva Erikssonsalen), Karlstad, 10:15 (Swedish)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt404",{id:"formSmash:j_idt404",widgetVar:"widget_formSmash_j_idt404",multiple:true});
##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt416",{id:"formSmash:j_idt416",widgetVar:"widget_formSmash_j_idt416",multiple:true});
Available from: 2015-03-04 Created: 2015-01-28 Last updated: 2015-03-04Bibliographically approved
##### List of papers

Mathematical Reasoning in a Dynamic Software Environment (English)

The overall problem that formed the basis for this thesis is that students get limited opportunity to develop their mathematical reasoning ability while, at the same time, there are dynamic mathematics software available which can be used to foster this ability. The aim of this thesis is to contribute to knowledge in this area by focusing on task design in a dynamic software environment and by studying the reasoning that emerges when students work on tasks in such an environment. To analyze students’ mathematical reasoning, a new analytical tool was developed in the form of an expanded version of Toulmin’s model.

Results from one of the studies in this thesis show that exploratory tasks in a dynamic software environment can promote mathematical reasoning in which claims are formulated, examined and refined in a cyclic process. However, this reasoning often displayed a lack of the more conceptual, analytic and explanatory reasoning normally associated with mathematics. This result was partly confirmed by another of the studies. Hence, one key question in the thesis has been how to design tasks that promote conceptual and explanatory reasoning. Two articles in the thesis deal with task design. One of them suggests a model for task design with a focus on exploration, explanation, and generalization. This model aims, first, to promote semantic proof production and then, after the proof has been constructed, to encourage further generalizations. The other article dealing with task design concerns the design of prediction tasks to foster student reasoning about exponential functions. The research process pinpointed key didactical variables that proved crucial in designing these tasks.

**Baksidestext**

Det övergripande problem som legat till grund för denna avhandling är att elever får begränsad möjlighet att utveckla sin resonemangsförmåga samtidigt som det finns dynamiska matematikprogram som kan utnyttjas för att stimulera denna förmåga. Syftet med avhandlingen är att bidra till den samlade kunskapen inom detta problemområde, dels genom att fokusera på design av uppgifter i en lärandemiljö med dynamiska matematikprogram och dels genom att studera och karakterisera de resonemang som utvecklas när elever jobbar med olika uppgifter i denna miljö. För att analysera elevernas resonemang utvecklades ett nytt analysverktyg i form av en utökad version av Toulmins modell.

Resultat från en av studierna i avhandlingen visar att dynamiska matematikprogram i kombination med utforskande uppgifter kan stimulera till matematiska resonemang där hypoteser formuleras, undersöks och förfinas i en cyklisk process. Samtidigt visar samma studie att de resonemang som utvecklas i stor utsträckning saknar matematiskt grundade förklaringar. Detta resultat bekräftas till viss del av ytterligare en studie. Frågan hur uppgifter bör designas för att främja matematiskt grundade resonemang har därför varit central i avhandlingen. Två av artiklarna behandlar uppgiftsdesign, men utifrån olika utgångspunkter.

1. A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment$(function(){PrimeFaces.cw("OverlayPanel","overlay749412",{id:"formSmash:j_idt454:0:j_idt458",widgetVar:"overlay749412",target:"formSmash:j_idt454:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. An Expanded Version of Toulmin’s Model to Analyze Students’ Mathematical Reasoning in a Dynamic Software Environment$(function(){PrimeFaces.cw("OverlayPanel","overlay784039",{id:"formSmash:j_idt454:1:j_idt458",widgetVar:"overlay784039",target:"formSmash:j_idt454:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Students’ Mathematical Reasoning in a Dynamic Software Environment$(function(){PrimeFaces.cw("OverlayPanel","overlay784030",{id:"formSmash:j_idt454:2:j_idt458",widgetVar:"overlay784030",target:"formSmash:j_idt454:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Designing Prediction Tasks in a Mathematics Software Environment$(function(){PrimeFaces.cw("OverlayPanel","overlay783985",{id:"formSmash:j_idt454:3:j_idt458",widgetVar:"overlay783985",target:"formSmash:j_idt454:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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