Abstract
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.
Highlights
The possibilities of a modelling perspective for school mathematics The findings of the international Trends in International Mathematics and Science Study (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
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 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
Summary
Daar is vandag ’n soeke na beter wiskundeonderwys op alle vlakke van die skoolwese. Min of meer dieselfde verhaal word by al die wiskundeonderwyskongresse oor die hele wêreld gerapporteer. Daar word onder meer gekyk na enkele voorbeelde van modellering in (leerders se) navorsing, asook na enkele groot projekte in die VSA wat modellering as uitgangspunt gebruik het. Dit is ’n wêreldwye verskynsel met ’n bepaalde siening oor die samehang tussen teorie en praktyk wat beteken dat die teoretiese beginsels van die positivistiese epistemologie direk op vakinhoudelike metodologiese kursusse deur onderwysers in daardie velde toegepas word (Cobb 2007: 4-5). Gelukkig word die gees van hierdie beginsels en standaarde sterk beklemtoon in die Suid-Afrikaanse Nasionale Kurrikulumverklaring wat tans in Graad R-12 in ons skole in werking is. Wanneer die kurrikulum bestudeer word, is dit duidelik dat die gees en toon daarvan ’n ryk bedding bied vir deurslaggewende rigtingbepalers in die onderrig daarvan, soos integrasie, gekonnekteerdheid, modellering, die takel van egtewêreldprobleme, en ryk kontekste. Die aard van die kurrikulum en die soort navorsing wat leerders daaroor doen, bevestig dat al die moontlikhede van modellering na vore gebring kan word
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