As a future teacher, it is extremely important that I am familiar with and understand all that The National Council of Teachers of Mathematics (NCTM) has to offer, in order to maximize my students’ learning experiences. Chapter one of our textbook, “Elementary and Middle School Mathematics,” introduces the NCTM as a U.S. based organization of teachers and mathematics educators from both the United States and Canada. Since it is probable that I will be teaching in Canada, I must take advantage of the knowledge, resources and research that the NCTM provides. The NCTM mission statement is as follows, “The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.” In order to become the best teacher I am capable of becoming, I must embrace the NCTM.

 

Content Standards, Process Standards, and Teaching Standards have been developed by the NCTM and are all fundamental to the instruction of mathematics.

 

Content Standards

 

There are currently five content standards (Number and Operations, Algebra, Geometry, Measurement and Data Analysis, and Probability). Each content standard includes goals that apply to all grade bands (the grade bands being, pre-K-2, 3-5, 6-8 and 9-12). Rather than having a different set of mathematical topics for each grade band, the NCTM have formed a common set of content standards that are taught throughout all grade levels. Instead of learning solely about one of the content standards in a particular grade and then moving on to another the following year, students are able to use their prior knowledge concerning each set of mathematical topics in order to expand on what they have already learned (spiral curriculum), which I believe is effective in producing learning that is long term.

 

Process Standards

 

There are also five process standards highlighted by the NCTM, and they are, Problem Solving, Reasoning and Proof, Communication, Connections, and Representations. As a future teacher of mathematics, it is essential that I am familiar with all five of these processes. It is our job as teachers, to promote mathematical understanding and critical thinking, and in order to do this we must encourage our students to learn mathematics through doing mathematics. We must provide our students with opportunities to engage in all five process standards, but in order to be effective facilitators, we ourselves must practice these process standards.

 

Teaching Standards

 

The teaching standards developed by the NCTM, are the standards that teachers are required to follow when teaching math education. As future teachers, we must abide by these standards if we want to enhance student learning. These teaching standards include, Knowledge of Mathematics and General Pedagogy, Knowledge of Student’s Mathematical Learning, Worthwhile Mathematical Tasks, Learning Environment, Discourse, Reflection on Student’s Learning, Reflection on Teaching Practice. I believe that all seven teaching standards are important and that it is necessary for all teachers to familiarize themselves with them before teaching mathematics at any grade level.

 

            The NCTM is designed to provide guidance and direction for teachers of mathematics education from pre-kindergarten to grade 12. The NCTM states that the “six principles fundamental to high-quality mathematics education,” that teachers should be aware of are Equity, Curriculum, Teaching, Learning, Assessment and Technology:

 

The Equity Principle: “All students must have the opportunity and adequate support to learn mathematics.” In other words teachers must have high expectations for all students. This is extremely important, for not all students learn at the same rate or in the same way. We as future teachers must treat all students fairly and continuously motivate them to reach their maximum learning potentials.

 

The Curriculum Principle: Curriculum “must be coherent, focused on important mathematics, and well articulated across the grades.” In order to effectively teach mathematics or any subject area, teachers must be experts on the curriculum.

 

The Teaching Principle: “Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.” If we want to provide our students with the best possible learning experience, we as future teachers must familiarize ourselves with the learning needs of each student and provide learning opportunities that cater to these needs, allowing for success.

 

The Learning Principle: “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.” As future teachers we must recognize that all of our students come to class with different schemas, experiences and levels of knowledge. It is our job to take all of it into account when planning for and assessing student learning.  

 

The Assessment Principle: “Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.” Students should not be assessed solely on if they arrive at a particular answer or not, but rather on how they arrived at the particular answer, for mathematics encourages higher level thinking and creativity, which often results in a number of justifiable solutions and processes. We must not inhibit our student’s creative thinking when assessing mathematics.

 

The Technology Principle: “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” I believe that integrating technology (calculators, computerized games, etc.) into mathematics shows students that mathematics can, in fact have real world application.

 

            In order to be the best teacher possible, I hope to take advantage of everything offered by the NCTM. I have learned that it is necessary to approach mathematics with an open mind, for the more evident it is that you care about mathematics education, the more likely your students will deem it as important and this is essential for their future success. As future teachers, we should care about equity in mathematics, so that ALL students, regardless of their abilities, have the opportunity to learn without the fear of failure.