Mathematics is an underlying element within the world around us. It is sometimes obvious and sometimes concealed. As members of society, we are required to use and incorporate mathematics into our daily lives, regardless of whether or not we are directly aware of it. Every person of every age is exposed to mathematics, and it is through education that each individual is formally introduced to and taught the foundations of it. These educations influence not only our knowledge but also our disposition and desire to learn more about mathematics.
A particular stage in which the influences are more immediate is post-secondary education. As individuals choosing to move beyond the basic K-12 education, college students are seeking to expand their knowledge in hopes of opening their doors to more opportunities for future careers. These careers, themselves, vary for each student. Some students strive to enter into mathematics-intensive programs such as engineering, others venture into other realms such as architecture or communications that are not as mathematically focused, and yet there are those college students who are undecided on what they want to pursue. With such an array of objectives, these students require an educational experience that caters to their needs, provides them with stimulating ideas, and encourages their progress.
This is not a task that is easily achieved. It requires diversity in the curriculum tracks that address both the necessary basics and the mathematical connection with other fields and with real life. It also demands the coherent and encouraging delivery of the material, which is, of course, the role of the effective teacher. In collaboration with the curriculum, the teacher and the students create a representation of mathematics that is relevant, achievable, and challenging. At the root of this process is the teacher’s pedagogical knowledge, or the knowledge of teaching.
The National Council of Teachers of Mathematics, the Mathematics Achievement Partnership, and the American Mathematical Association of Two-Year Colleges all share similar views in terms of curriculum and teaching principles. All value the significance of a well-prepared curriculum and a well-prepared teacher that implement the constructivist approach of learning.
This document addresses this suggested approach in detail, focusing on the curriculum for students – math-focused, non-math-focused, undecided, and possible future educators – and the pedagogical strategies that teachers can implement to foster an educational environment that each individual can benefit from.