Montecito Union School District Philosophy of Mathematics

Math as a Learning Subject

Introduction
The teachers at Montecito Union School District believe strongly in the idea that we don’t simply cover a math curriculum, but instead we uncover it.  Each day, our classrooms become a place where students develop and practice the dispositions of inquiry, questioning, curiosity, confidence, and the value of seeing mistakes as opportunity for growth. Teachers plan and implement a program through a Thinking Curriculum where students are encouraged to solve real world tasks using multiple methods and strategies, engage in peer interaction, while also critiquing the reasoning and thinking of others. Students learn to think quantitatively and abstractly and develop an inquiry relationship with math as they build a foundation for rewarding work, and a means for comprehending and influencing the world in which they live.  Simply put, it is about learning, not performing.

Content
The teaching of mathematics is complex. It begins with teachers that have a deep mathematical understanding of the content and strategies that they teach. Teachers place strong emphasis on developing lessons where the Standards of Mathematical Practice are at the forefront of math instruction, in order to guide and enrich students’ learning experiences. Rich problems and tasks with room for learning allows for students to apply their mathematical knowledge to new and interesting situations, and to learn from their trials and errors. By conducting first hand investigations, working with physical materials, and expanding opportunities to interact with students and peers, students learn to solve real-world and complex problems. Daily Number Talks develops and strengthens mental computation with conceptual understanding and fluency. Technology is utilized to enhance and deepen the level of instruction and creates opportunities that may have been previously inaccessible. Instructional minutes are designed to ensure a minimum of 300 minutes per week.

Cognitive Demands
Complex lessons which present problems for students to experience “Productive Struggle”, fosters persistence, exploration, and that the idea of taking responsible risks allows for growth. Teachers pose purposeful questions that promote rich discourse and deeper thinking, asking students to make connections to prior learning and to the bigger world. Students make their thinking visible in order to learn from the thinking of others, and to discover diverse ways of solving tasks. Seeking the development of broader understanding and “sense-making” is valued over rote memorization of procedures. Ample opportunities are provided for students to routinely make and test conjectures in order to find more effective strategies. The adage of “less is more” comes to life as we ask our students to explore the Why? Why do we do this? Why does this work? Why does this make sense?

Reaching All Learners

Access
Every child can and should learn challenging mathematics. Differentiation is achieved through a thoughtfully rigorous and diverse program that allows for easy access to a wide range of abilities. We see math as a creative subject where a variety of approaches, tools and strategies, and thinking is encouraged and welcomed. Routines such as Notice and Wondering, Same Same But Different, and Claim Support Question uncovers students individual thinking, and invites students to see themselves as a valuable member of mathematical learning community.  All students develop the confidence, persistence, skills, and strategies to approach novel and rigorous problems.

Homework
Math homework serves at least one of the following purposes

• Review or practice known skills through student pages or games.  Known skills may be from the day’s lesson or from past learning.
• Engage in problem solving tasks.  Emphasis is placed on strategies, communication of thinking, and persistence. 
• Reflect on classroom learning.
• Connect to the real world outside the classroom.

 
Assessment
Assessment is used to drive instruction. Formative Assessments such as math journals, questioning, observation, math congresses, Number Talks, and discourse help teachers monitor growth and proficiency, while also determining next steps in instruction. In addition, Summative Assessment is used in the same capacity and allows for the evaluation and consideration of the overall strengths and needs of our school-wide program. Students take active roles in self-assessment by reflecting on their use of strategies, understanding of key concepts and math reasoning in order to move their thinking forward in new and enriching ways.