Success in Mathematics

1) Summary Statement

In order to be a successful learner in the discipline of mathematics, a student must possess various skills, dispositions and areas of knowledge. A student must be able to solve varying problems, communicate their reasoning and explanation, make connections to previous knowledge and real-life experience, use logic and reasoning in the disciplinary activities, use and create symbolic mathematical representations to support ideas and effectively utilize technology to enhance mathematical applications.

In addition to possessing certain skills, successful students must also have the right attitude towards math to gain the most relevant and valuable experience with work in the discipline. These attitudes and dispositions are also reflective of teaching practices and therefore directly apply to both learner and instructor. The students must feel a genuine excitement or interest in activities that help them to learn the mathematical concepts, rather than memorize procedures. These activities should evoke interest and engagement based on meaningful and life relevant problems. Students must possess attitudes that will lend themselves easily towards the necessary collaborative and cooperative nature of maximizing learning in math. Dispositions such as respect, high self expectations and motivation to advance are also valuable, but in summation it should be noted that these attitudes and dispositions are not intrinsic in all students of mathematics and therefore depend a lot on the teacher’s influence.

Finally, and at the core of the discipline, students must acquire knowledge principles from their career as pupils of mathematics. Essentially, the students must know number sense and operations, principles of estimation, geometry, measurement, patterns, relationships, procedures, probabilities, statistics and discrete mathematics.

With that, the knowledge, skills and dispositions that make up the components of a successful learner of mathematics depend on a highly qualified and enthusiastic teacher who shares the same qualities and characteristics as the standards envision for the student who will study from them.

2) How do the NJCCCS meet diverse student populations?

- Ethnicity
o Math is cross-cultural and multi-lingual in nature
- Special Needs
o Math is recursive, representative, symbolic and uses algorithms
- Multiple Intelligences
o Math is collaborative, individual, visual, concrete, abstract, creative and found everywhere in daily life

3) How do the NJCCCS not meet diverse student populations?

Since mathematical concepts build upon one another, if the student does not actually learn previous skills it is difficult for them to advance

The NJCCCS do not take into account teacher fallibility or external factors that might prevent their embracing and progress in mathematics

There is an inherent assumption that all areas of math from the previous year were taught and mastered by the student, which is not always true because of time constraints, absences or other struggles – forcing students to play a constant game of ‘catch up’ that would hinder the growth of necessary attitudes and dispositions towards the discipline of mathematics

4) What do they imply is of value? (in reaction to teaching and learning)

The implicit value necessary in the teaching and learning of this discipline, mathematics, is essentially the enthusiasm, excitement, engagement and relevance of math to the life experience. Logic and reason, two tenets of philosophy and the basis of all coherent thinking, are the ultimate goal of mathematical studies.