Learning mathematics for personal understanding and productions: A viewpoint

David Mtetwa,Lazarus Mudehwe,Sheunesu Munyira

doi:10.4102/pythagoras.v0i72.57

Abstract

In this paper we reflect on what makes mathematics more meaningful and more easily understood and thus enabling the learner to apply it to everyday situations in his/her life world. We identify personal – in relation to ‘collective’ or ‘public’ – mathematising as one key component towards real understanding of mathematics. We observe that today’s mathematics learner is often typified by such orientations as approaching the subject with timidity and in a cookbook fashion, adopting a re‐productive rather than a productive mode, and showing lack of intrinsic interest in the subject. Debilitating effects of some of these characteristics in relation to learning mathematics for personal development, include learner’s failure to exploit the subject’s natural features for developing own mental orientations such as algorithmic, stochastic, reflective, and creative thinking so essential in coping with modern life environments. We propose that, for inspirational effects, learners should have closer contact with and appreciation for the activities and practices of the professional mathematician. The mathematics teacher could enhance the learner’s mathematical learning experience by orienting instructional designs in ways that make the learning processes and outcomes more personal to the learner.

Highlights

I set myself the task of constructing all these functions
Notable proponents of this theory are the Dutch mathematician-cum-educator, Hans. Freudenthal, and his followers in the Realistic Mathematics movement, whose work has contributed to an increased focus in learning processes in mathematics education. According to this school of thought, mathematising is the crucial skill or knowledge required in order for one to learn mathematics with understanding, and at the heart of mathematisation lies the idea of what they call the ‘reinvention principle’ that is partially captured in the following statement: Children should repeat the learning process of mankind, not as factually took place but rather as it would have done if people in the past had known a bit more of what we know now. (Freudenthal, 1991, p. 48)
Considering the changing times and the pervasiveness of modern technology in our daily lives, we see the notion of personal mathematising as both compelling and promising as a strategy to explore and exploit in the learning of mathematics

Summary

Introduction

I set myself the task of constructing all these functions. I conducted a systematic siege and one after another, carried all the outworks; there was one which still held out and whose fall would bring about that of the whole position. All my efforts served only to make me better acquainted with the difficulty, which in itself was something. At this point I left for Mont-Valerin, where I was to discharge my military service. Each person needs to develop some mathematical concepts and methods for understanding and better managing of everyday activities in our modern world (Davis & Hersh, 1980). For one to communicate effectively, one needs some basic mathematical concepts. Fuller understanding of mathematical concepts and methods is achieved through personal mathematising by the learner her/himself. By personal mathematising we mean that each individual learner is involved in mathematical activities associated with the formation of a mathematical concept or method

Some theoretical considerations

From the fact that we can write m for

Teaching and learning

Concluding remarks