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.
