Supporting Mathematical Learning Processes by Means of Mathematics Conferences and Mathematics Language Tools

Abstract

In recent decades, the instructional theory of Realistic Mathematics Education has exerted a powerful influence on mathematics education around the world. The idea of progressive mathematisation has gained international acceptance. In this chapter, we will illustrate the way in which we benefited from the idea of organising the teaching and learning of mathematics in keeping with this guiding principle. After some personal memories of the first author, we start by describing what we consider to be the central elements of the principle of progressive mathematisation. This is followed by a description of two methods, the mathematics conferences and mathematics language tools, for rendering the learning and teaching concepts entailed by the principle of progressive mathematisation-especially its vertical component-even more expedient and fruitful. The contribution concludes with an explanation of how we understand the term 'realistic' in Realistic Mathematics Education. KeywordsProgressive schematisation • Mathematics conferences • Language and mathematics • Individual learning processes • Co-operative learning • Mathematics language tools The Santa Claus ProblemIt must have been at the end of 1983 that the first author-at the time studying to become a primary school teacher-became aware of Adri Treffers' paper "Fortschreitende Schematisierung -ein natürlicher Weg zur schriftlichen Multiplikation und Division im 3. und 4. Schuljahr" (Treffers, 1983). Taking the multiplication of large

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“…According to Selter and Walter (2020), learning is a consequence of mathematization. This process leads to the development of formal thinking based on several principles.…”

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“…1) Production in small groups, 2) Reflection in large groups, 3) Discussion in plenary (Selter & Walter, 2020).…”

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