K-12 PHILOSOPHY
The Groton Public Schools (GPS) Mathematics curriculum is based on the belief that the knowledge of mathematics is essential for
students to become productive members of an ever-changing technological and information-based society.
General Beliefs: Mathematics instruction must provide experiences for students that are consistent with well-established theories of
cognitive development. Children progress through stages of learning from concrete to pictorial to abstract. Understanding of
mathematical concepts comes only through ample opportunity for developmental learning. High expectations are important for all
students, regardless of gender, race, handicapping condition or socioeconomic status.
Mathematics instruction must include higher level thinking processes. These are transferable to a variety of problem solving activities
involving number sense, logic, real life problems, graphing, measurement, geometry, probability and statistics, algebra, and discrete
mathematics.
Teachers and administrators will help students to achieve the greatest possible success by:
* holding students accountable for their learning;
* developing partnerships with parents and community members;
* actively involving students in the learning process.
Reasons for Learning Content: Mathematics Education helps prepare students for:
* applying mathematical skills and concepts to subsequent math instruction and other disciplines;
* using logical processes in problem solving and decision-making;
* everyday life, vocations, and careers.
Teaching Strategies: Good mathematics instruction involves visual, auditory, and kinesthetic modalities. Teaching strategies include:
* developing concepts from concrete to pictorial to abstract;
* linking prior knowledge to new ideas, concepts, and situations;
* guiding students to use manipulatives and technology appropriately;
* communicating mathematical ideas through examples, demonstrations, models, drawings, and logical arguments;
* promoting student use of inquiry and creativity;
* guiding students to self-monitor their learning;
* connecting with other disciplines and real-life experiences;
* working cooperatively to explore concepts and solve problems;
* exploring multiple approaches to solving problems;
* presenting problems with multiple solutions;
* challenging students to defend and support their solutions;
* asking guided questions that foster the development of conceptual understanding and higher level thinking skills;
* guiding students to determine the reasonableness of answers;
* addressing various learning styles;
* using precise math vocabulary.
Teaching strategies and methods may include individualization, flexible grouping, collaborative learning, lateral expansion, and
acceleration as deemed appropriate.
Assessment is an ongoing process of monitoring student learning, guiding further instruction, and improving the program.
Effective assessment:
* aligns with instructional strategies, national standards, state frameworks, and curriculum content;
* incorporates a variety of formal and informal methods, providing feedback to students, parents, and teachers. Examples: journals,
projects, teacher observations, self-evaluations, quizzes, tests, and other types of student work;
* includes the use of rubrics to evaluate open-ended items;
* provides success for students with different learning styles.
Technology: the ability to utilize technology as a tool is an essential life skill. Technology allows the student to:
* focus on learning concepts;
* develop ability to use logical processes;
* develop higher order thinking skills;
* learn how to solve problems and make rational decisions;
* learn how to manipulate data;
* make connections between mathematics disciplines;
* visualize abstract concepts concretely.
Additionally, technology provides up-to-date content and variety in instructional strategies and assessment techniques in order to
prepare students for their future in the world community.
THE CONNECTICUT COMMON CORE OF LEARNING
The Groton Public Schools Mathematics curriculum aligns with the Connecticut Common Core of Learning. The Common Core
provides a set of high expectations for all Connecticut students. It recognizes that while students enter school with varying levels of
readiness, interests, and aspirations, the creation of one Common Core sets no limits on any student and allows each one to attain his
or her dreams.
Accordingly, Connecticut's Common Core of Learning establishes a vision of what Connecticut's high school graduates should know
and be able to do as a result of participating in the entire K-12 school experience. The Common Core articulates Connecticut's
expectations for all its schools and all its youth by describing abilities that are necessary not just for employment and for future
education, but also for becoming a productive member of society. The Common Core is not meant to define a minimum set of
competencies; rather, it is designed to set and define the high standards required for students to become fully educated citizens.
In addition to foundational skills, competencies, and discipline-based applications, Connecticut's Common Core outlines the attitudes
and attributes necessary for learning. It emphasizes an interdisciplinary approach in which students work both independently and
collaboratively. The Common Core reflects a commitment to excellence in public education and will help develop young people who
can think and act independently and work with others, leading our students into the future with confidence and clear direction.
LEARNING ENVIRONMENT
To learn the essential mathematics for the 21st century, students need a non-threatening environment in which they are encouraged to
ask questions and take risks. Students need to explore mathematics using manipulatives, measuring devices, models, calculators and
computers. They need opportunities to talk to each other and to write about mathematics. Instruction should emphasize problem
solving, applications and higher-order thinking skills. Students need to work together to pose questions, analyze solutions, try
alternative strategies and check for reasonableness of results.
PROGRAM GOALS
It is the goal of the Groton Public School's Mathematics Program that our graduates have the mathematical skills to succeed in
meeting the challenges of our ever-changing world. To meet this goal, students will:
1. Recognize and value the interaction and impact of mathematics and logical reasoning in the world around them from a historical
and contemporary perspective.
2. Solve real-world problems, both independently and collaboratively by appropriately using a variety of mathematical strategies
including technology.
3. Effectively communicate mathematical ideas orally and in written form.
4. Be confident in their ability to solve increasingly complex problems by making connections to prior math knowledge.
5. Reason mathematically by making conjectures, gathering evidence, and building an argument in order to draw valid conclusions
about real problem situations.