Developing children’s abilities for mathematisation is the main goal of mathematics education. The twin concerns of the Mathematics curriculum are: What can mathematics education do to engage the mind of every student and develop the student’s inner resources to make them critical and creative?
It is at this stage that Mathematics comes to the students as an academic discipline and they begin to perceive the structure of mathematics. For this, the notions of argumentation and proof become central to curriculum. Mathematical terminology is highly stylised, self conscious and rigorous. The student appreciates how an edifice is built up, arguments constructed using propositions justified earlier, to prove a theorem, which in turn is used in proving further theorems.
At the secondary stage, a special emphasis on experimentation and exploration may be worthwhile. Mathematics laboratories are a recent phenomenon, which hopefully will expand considerably in future. Activities in practical mathematics help students immensely in visualisation.
It is therefore, essential at this stage that the curriculum should focus on development of higher levels of learning mathematics through opportunities to explore, experiment, verify and prove conjectures that are obtained from patterns. Visualising relationships among various topics of mathematics and among other subjects is expected from the students. Thus the learning outcomes of mathematics should be seen integrated with other subjects at this stage like numbers related with geometry (points on a number line and real numbers), with usage in Science and Social Science and later with problem solving skills.