Planning mathematical modelling tasks from neurobiological data and principles

Abstract

The background of the article is the discourse on the application of neuroscience principles, protocols and tools to education. In this paper, we discuss how theory from neuroscience was used to plan learning tasks in mathematical modelling environments. It prompts the question, “How should we structure mathematical modelling lessons if we can pinpoint the functional and structural vulnerabilities, and the subsequent lack of neural integration, in an individual’s brain?” The article aims to illustrate via a case study how educators can use neurobiological data to plan mathematical modelling tasks for middle school students with disabilities who are performing at a very early level in mathematics. The original research (Scott-Wilson, 2014) was conducted in Central Australia with a classroom of students with disabilities (SWD) participating in mathematical modelling tasks. The intervention consisted of replacing their typical and more traditional instructivist-oriented mathematical lessons with mathematical modelling tasks for one month. The tasks were designed specifically for the SWD using data from their psycho-educational profile and their neurobiological data. The former was kept in their school records and the latter, showing the structural and functional vulnerabilities of the brain, was obtained through a clinical brain mapping assessment conducted by a trained professional. The primary research methodology was design-based research (DBR). DBR was used to plan, implement and evaluate the effectiveness and suitability of the modelling tasks for the SWD. The secondary research methodology was a case study analysis. This was used to record the progress, and specific barriers to learning, that emerged while working through the DBR cycles. The education philosophy of the researcher-teacher is based on the Christian curriculum-approach by Harro Van Brummelen (1988).

The outcomes suggest that neurobiological data are useful in designing mathematical modelling tasks that will support students with multiple barriers to learning. Future research on a much larger sample is needed to support the discourse on the meaning of current neuroscience and its application and relevance to the field of teaching and learning.

Die akademiese gesprek oor die toepassing van neurologiese beginsels, protokolle en werktuie wat gerig is op opvoeding, met die doel die beplanning van leergerigte take in wiskundige modelleringomgewings, vorm die agtergrond van hierdie artikel. Dit vra die vraag: “Hoe moet ons wiskundige modelleringslesse struktureer sodat ons presies kan vasstel waar die funksionele en strukturele swakplekke en die gevolglike gebrek aan neurologiese integrasie in ?n individu se brein is?” Die doel van die artikel is om in ?n gevallestudie te illustreer hoe opvoeders neurobiologiese data kan gebruik om wiskundige modelleringstake vir middelskool leerders met leergebreke, wat slegs in staat is om op ?n baie vroee? wiskundige vlak te funksioneer, te beplan. Die oorspronklike navorsing (Scott-Wilson, 2014) was uitgevoer in Sentraal-Australie? in ?n klaskamer met leerders met leergebreke (LMG) – ?n reeks van wiskundige modelleringslesse is gebruik. Die onderwyssessie het bestaan uit die vervanging van hul tipiese en meer tradisionele-onderrig gerigte wiskundelesse met ?n reeks wiskundige modelleringstake wat oor ?n maand gestrek het. Die take was spesifiek ontwikkel vir LMG leerders waartydens die data van hul psigo-opvoedkundige profiele wat in die skool se rekords te vinde was, gebruik is. Hierby is data gevoeg wat uit kritiese assessering tydens die sessie verkry is. Die prime?re navorsingsmetodologie was die ontwerpgebaseerde navorsingsbenadering (OGNB) wat die effektiwiteit en geskiktheid van die beplanning, implementering en evaluering van die modelleringstake vir die LMGs bepaal het. Die sekonde?re navorsingsmetodologie was gevallestudie analises om die vordering, en spesifiek die leergrensversperrings wat gedurende die implementering van die leertrajek ontstaan het toe deur siklusse van OGNB gewerk is, te ondersoek. Die opvoedingsfilosofie van die navorser-onderwyser is gebaseer op die christelike kurrikulumbenadering soos beskryf deur Harro Van Brummelen (1988).

Die uitkomste van die studie suggereer dat die neurologiese data baie handig en geskik is in die ontwerp van modelleringstake waartydens leerders met gestremdhede wat veelvuldige leerversperrings beleef, in hierdie proses versterk kan word. Verdere navorsing op ?n groter skaal is nodig om die akademiese gesprek in huidige neuro-wetenskap in sy toepassings en relevansie vir die veld van (wiskundige) onderrig en leer, te ondersteun.