Teaching mathematics has always been a challenging task for all mathematics teachers as the subject fundamental basis is on numerical logic. Thus in expounding this intricate subject to the very young pre-schoolers, primary, secondary, junior college and tertiary level have undergone much study and research to make teaching of this subject systematic and comprehensible even in the teaching of complex mathematical theories.
One of the most important features of principles and standards for school mathematics is the articulation of six principles fundamental to high-quality mathematics education:
The equity principle is that all students must have the opportunity and adequate support to learn mathematics regardless of background, physical challenges or characteristics.
The curriculum should be more than just a collection of activities, it must be coherent and focused on important mathematics and well articulate to the students. It may not be far from the truth that one can study to be a mathematics genius but one may not be a genius in teaching mathematics. In summary, not all mathematics teachers make good teachers.
To provide high quality mathematics teaching, teachers must deeply understand the content they are teaching; understand how students learn mathematics and the awareness each student’s mathematical development; select meaningful instructional and strategies that will enhance learning.
The learning principle is that students must learn with understanding and be able to build knowledge from experience and prior knowledge. Students must be taught to think and reason mathematically to solve new problem as “scaffolding of mathematical knowledge” can be said to be the a good measure of successful teaching.
Assessment is an important tool in the teaching of mathematics as from the data collected, teachers are able to have solid gauge of the students’ progress and to make decisions and necessary strategic changes to support learning.
The application of mathematics can be seen where the generating of strategies for solving problems in the classroom can be translated to the application to real life situations.
Two theories, namely constructivism and sociocultural theory are most commonly used by researchers in mathematics education to understand how students learn. The aforementioned learning theories are not teaching tools in the education of mathematics but rather they provide an understanding on how learning takes place and this form a reliable framework for the teaching of mathematics. For example, constructivism might explain explicitly how a student internalize an idea while sociocultural theory would be a better tool for analyzing influence of the social/cultural aspects of the classroom.