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.
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.
