Mathematics
Sylvania Schools
Mathematics Course of Study
Introduction
The Sylvania Schools Mathematics Course of Study provides the focus and
structure for all mathematics teaching in grades K-12. Consistency from
classroom to classroom and building to building is essential in assuring
student success. In order to insure that students receive the balanced and
complete mathematics education essential for their success in life, it is
important that every teacher of mathematics focus on the concepts, applications,
and skills appropriate for his/her grade level.
When concepts from a previous grade level have not
been mastered by some students, the remedy is intervention for the students who
need assistance—not a change in the content of the curriculum for all students.
It is the nature of much learning that, once a concept or skill has been
learned, it needs to be used and reviewed in order to be maintained. However,
reviewing skills and concepts does not mean re-teaching them. Rather they
should be reviewed and maintained through use in new areas of learning. For
example, students should have mastered multi-digit addition and subtraction by
the end of fourth grade. In later grades, instruction in addition and
subtraction of whole numbers is inappropriate. Rather, these skills should be
practiced in the context of problems in data analysis, measurement, geometry,
and other new content.
The learning and performance objectives in this
course of study are complete and represent the content of the mathematics
program adopted by the Sylvania Schools Board of Education. They will not be
changed. However, the other elements of this course of study document (such as
related assessments, connections, teacher notes) will be updated periodically
as new materials become available and as the Mathematics Curriculum and
Alignment Team continue to research and identify best practice in the teaching
of mathematics.
Philosophy
The mathematics that is taught and learned is shaped by the beliefs and values
of the learning community. The mathematics philosophy that forms the foundation
for this course of study is based on the following beliefs.
- We believe
that mathematics is the study and understanding of quantitative and
spatial relationships and the use of these concepts in solving problems
and that problem solving is not limited to the use of standard processes
and procedures.
- We believe
that a strongly developed number sense, fluency with mathematical
computation and vocabulary, and well-developed strategies for estimation
and judgment of reasonableness are essential features of mathematical
literacy.
- We believe
that, in today’s society with increased use of mathematical data in
decision-making, every student must have a curriculum that includes the
study of algebraic thinking, spatial visualization and geometric
reasoning, data analysis and statistics, the
mathematics of chance (probability), and discrete mathematics.
- We believe
that students of any age and ability are capable of higher order thinking
and reasoning about mathematical concepts regardless of past achievement
and level of computational mastery.
- We believe
that the development of mathematical concepts must be connected to past
learning and that mathematics is only learned when it becomes part of the
learner’s conception of the world. We believe that correct conceptions
will replace misconceptions when students are provided with information
that challenges their misconceptions and offers opportunities to formulate
their own ideas.
- We believe
that instructional materials, teaching strategies, and classroom groupings
should provide an environment in which all students learn and work
together on the same concepts regardless of their present level of
achievement. Appropriate activities will challenge all students to further
their understanding and knowledge of mathematics.
- We believe
that the role of the teacher is to present concepts that are organized and
integrated so that the learner will see how they relate to each other.
Effective mathematics teaching requires an understanding of what students
know and what they need to learn then challenges them and supports them in
their learning and instills confidence within the learner.
- We believe
that teachers of mathematics should be provided with ongoing professional
development to promote professional growth in the areas of mathematical
methods, concepts and instructional practices.
- We believe
that assessment is a tool to help make instructional decisions and that
students should be assessed in ways compatible with methods of instruction.
Formal and informal assessment should take place in a variety of formats
in order to evaluate the student’s conceptual understanding as well as to
provide guidance for growth.
- We believe
that, because technology is an integral part of today’s world, regular use
of technology is essential in today’s classroom to enhance both
theoretical and real-world understanding of mathematics.
- We believe
that the use of technology in mathematics outside the classroom should
influence the content of the mathematics taught in the classroom. Some
mathematics becomes more important because technology requires it; some
mathematics becomes possible because technology allows it.
Therefore, the mathematics program must ensure that
every student is provided access to a wide range of mathematical topics and
appropriate technological support to investigate them. Ann appropriate
mathematics curriculum includes, at every grade level, investigation of the
connections and interplay among various mathematical topics so that students
can apply those topics in real life situations. Students can learn to use
models, diagrams, and symbols to represent concepts and translate from one mode
of representation to another. They can recognize when alternative mathematical
procedures are appropriate and reliable and efficiently execute these
procedures with confidence and competence