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n Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie - Die moontlikhede van 'n modelleringsperspektief vir skoolwiskunde - : navorsings- en oorsigartikel
Source : Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, Volume 28, Issue 1, Dec 2009, p. 319 - 339
Keyword(s) : Attitudes and beliefs in mathematics, Bevoegdhede, Competencies, Connectedness, Gekonnekteerdheid, Houdings en geloof in wiskunde, Matematisering, Mathematising, Modellering, Modelling, Probleemgesentreerde onderrig en leer, Probleemoplossing, Problem solving, Problem-centred teaching and learning, Representations, Tradisionele wiskundeonderwys, Traditional mathematics teaching and Voorstellinge
Die resultate van die Trends in International Mathematics and Science Study (TIMSS) se ondersoeke na die stand van probleemoplossing en die toepassing van probleemoplossingstrategieë in skoolwiskunde in ongeveer 50 lande 'n paar jaar gelede het die wêreld geskud. Suid-Afrika het elke keer onder die laastes van die deelnemende lande geëindig. Uitkomsgebaseerde onderwys, wat in die Westerse wêreld al hoe meer algemeen word, laat al die deelnemers in daardie stelsels beter voel oor wiskunde, maar verbeter nie noodwendig wiskunde-prestasie nie. Modellering in die wiskundeklaskamer blyk 'n belangrike middel te wees om die leer van wiskunde meer effektief te maak. Die bemeestering van probleemoplossing en modelleringstrategieë en vaardighede sal beslis die oriëntasie, bevoegdhede en prestasies van leerders op elke skoolvlak verbeter. Dit blyk uit die navorsing dat leerders daarvan hou om wiskunde se toepassingskant te sien en te beleef. Egte probleme behoort gekies te word en daarom is 'n modelleringsperspektief in die onderrig en leer van wiskunde noodsaaklik. Modellering wat ook integrerend aangebied word in die wiskundekurrikulum het ook die vermoë om leerders op alle skoolvlakke ten volle betrokke te kry, om hulle beter toegang tot matematisering te gee, die wiskundige taal meer vloeiend te laat gebruik, probleemoplossings te doen, argumente te kritiseer, bewyse te vind en wiskundige konsepte te herken en te abstraheer uit 'n realistiese situasie. Modellering behoort 'n volle kans gegun te word in wiskundeonderwysersopleiding en in indiensopleiding sodat die leerders die volle voordeel daarvan kan beleef. Dit sal die wiskunde-prestasies van ons land se jeug op 'n stewiger grondslag plaas en hulle so hopelik meer mededingend in die toekoms maak.
The possibilities of a modelling perspective for school mathematics
The findings of the international TIMSS investigations of a few years ago into the position and application of problem solving strategies in school mathematics in about 50 countries caused serious concern globally. During each survey South Africa was found to be among the poorest performers of the participating countries. The main problem was that the majority of school learners in South Africa do not have the ability to solve mathematical problems; in fact, it would appear that they lack the total spectrum of mathematical problem solving competencies. The present school system does not develop their mathematical abilities or competencies. While Outcomes-based education, which became very popular in the Western world, has the ability to improve participants' affective values of mathematics, it proved to be inadequate in improving the quality of their mathematical performances.
Mathematics teachers are unsuccessful in teaching in a manner that will make a difference with respect to the way learners do, learn or perform in mathematics. The pedagogical and mathematics content knowledge of the teachers are lacking in conceptual depth, clarity and connectedness (integration). The language proficiency of the learners is poor, which means that they do not understand what they should do with a problem and how to interpret, present and verify their findings. Learners still do not know how to handle mathematics and how to utilise mathematics in order to solve problems. They seriously lack the ability to approach problems in a meaningful and constructive way. Real-life and open-ended problems are being perceived as huge obstacles to most learners. Teachers are not trained and educated to assist their learners in bridging this gap.
The teaching methodology that will make a difference in the classroom falls in the broad category of problem solving. The day-to-day teaching method should be the problem-centred teaching and learning approach. This rather complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem.
Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has definitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to finding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full benefit of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.
Persistent Link : https://hdl.handle.net/10520/EJC20463