• District Curriculum Overview
  • Introduction to Curriculum Guides
  • Professional Teaching Standards
  • Professional Development Guiding Principles
  • Social Justice Commitment
  • Curriculum Guide Glossary of Terms
• Teaching Standards
  • Knowledge of Students
  • Planning and Teaching for Learning
  • A Culture and Environment for Learning
  • Monitoring Progress
  • Professional Growth
• Subject Areas
  • English/Language Arts
  • Mathematics
  • Science
  • Social Studies

Mathematics Curriculum
Kindergarten Through Grade 12

Vision

Our goal is that all students both understand¹ and can do mathematics—that at all grade levels they develop both conceptual understanding and procedural fluency. We are committed to ensuring that our students all gain thorough competence in problem-solving, reasoning and proof, communication, connections, and representation with regard to whatever mathematical content they are studying. Students will understand that mathematics is both a tool and a way of thinking that can be used to address problems in the world. For every mathematical process they learn, students must have a deep understanding of that process and why that process works.

We have established the following benchmarks to measure student progress in attaining math proficiency:

• By the end of sixth grade students should understand the relationships among numbers and number operations and understand how mathematics can be used to solve problems in the real world. In addition, they should be able to use concrete materials to represent algebraic equations.
• By the end of eighth grade, we envision that all students will have a solid understanding of ratio and proportion. In addition, we envision that all students will have had exposure to the Algebra I curriculum. For some, this will lead to mastery of the Algebra I curriculum in eighth grade. For other students, it will be an introduction that will prepare them to be ready for Algebra I in high school.
• By the end of tenth grade, we strive to have all students complete the study of Algebra 1 (or its IMP equivalent). By graduation, our goal is to see all students achieve proficiency with Algebra 1 and Geometry (or their IMP equivalents) which will prepare them to continue their education at the college level if they choose. We see these as ‘gatekeeper courses’ which are essential for students to master, whether for entering the work force or continuing their education. At the same time, we envision the majority of students taking four years of high school mathematics while some will complete the high school math offerings and further their study of mathematics by enrolling in math classes at one of the area colleges.

¹Wiggins and McTighe (ASCD 1998) Understanding by Design, especially Chapter 4 contains an excellent description of what we mean by “understand”. The other major resources upon which this document is based are the Principles and Standards for School Mathematics, (NCTM 2000) and the Massachusetts Mathematics Curriculum Framework.

Philosophy

1. Equity—Excellence in mathematics education requires equity—high expectations and strong support for all students.
   1. All aspects of the program will include a focus on eliminating disparities in achievement related to race, class, and gender.
   2. Conceptual understanding and procedural fluency will be expected of all students.
   3. Every student will be expected to complete courses in high school algebra and geometry.
2. Curriculum—A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.
   1. “Big ideas” will be identified, the key enduring conceptual understandings that we want students to acquire at each grade span.
   2. Topics will be identified in accordance with state as well as national standards [The Massachusetts Curriculum Frameworks for Mathematics and NCTM standards.]
   3. The curriculum will include topics that adequately prepare students to transition smoothly from one level to the next, i.e. from grade to grade, course to course, school to school.
3. Assessment—Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.
1. Assessments will be designed to provide acceptable evidence of enduring understanding.
2. Assessment will be used to guide instruction.
3. Ongoing and individualized assessments will be developed with rubrics to assess achievement.
4. Multiple assessment strategies and tools will be aligned with the curriculum. 
5. Formal assessments will be developed for grades 3, 6, 8, and 10 which identify the key conceptual understandings and procedural skills expected in transitioning to the next level.
4. Instruction—Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.
   1. Teachers will provide instruction designed to teach for understanding.
   2. Teachers will use a variety of instructional strategies and modalities.
   3. Instruction will be differentiated so that the needs of learners who take more time than most of their peers to learn mathematics and those who demonstrate understanding in other ways than most of their peers will be successful.
   4. Math concepts will be taught in depth, with focused re-teaching as needed.
   5. Time allotted to the teaching and learning of mathematics will be established to provide consistency among grades and across schools.
   6. Both content and process skills will be taught and assessed.
   7. Math vocabulary in context will be explicitly taught.
   8. Mathematics will increasingly be taught in context—ranging across all disciplines
   9. The NCTM process standards will not be limited to mathematics, but will be applied in curriculum and instruction in many subject areas.
5. Professional Development—Effective, ongoing professional development in mathematics education deepens teachers’ knowledge of mathematics, their abilities to implement the pedagogy of the program, and their skill in assessing student development of both conceptual understanding and procedural fluency.
   1. Professional development focused on “teaching for understanding” will be provided.
   2. Professional development will be provided so that teachers at all levels acquire the in-depth understanding of mathematics needed in order to teach math effectively.
   3. Professional development will be provided to equip all teachers of mathematics to use current pedagogy consistent with the NCTM Standards.
   4. Professional development will include review of materials and how to use them to implement the philosophy of our revised mathematics program.
6. Supervision and Evaluation of Staff—Effective supervision and evaluation provide high expectations and strong support for all teachers and administrators.
   1. Professional development will be provided to administrators so that they acquire proficiency in supervision of the teaching of mathematics.
   2. Professional development for administrators will include sharing ways to spread successful practices.
   3. Through the district’s teacher evaluation process, teachers will be expected to demonstrate their competencies in the teaching of mathematics.
   4. Through the district’s evaluation process administrators will be expected to demonstrate their competencies in the supervision of mathematics instruction.
7. Program Evaluation—Effective evaluation uses multiple sources of data to furnish evidence of the extent to which the K-12 mathematics program enables students to develop conceptual understanding and procedural fluency.
   1. We will examine student learning through multiple sources of information with regard to eliminating disparities in achievement related to race, class, and gender.
   2. We will regularly examine the curriculum for its articulation from grade to grade, course to course, and school to school; its consistency with NCTM and state standards; and the extent to which it supports the development of conceptual understanding and procedural fluency.
   3. We will regularly evaluate instruction and assessment with regard to meeting the goal of mathematical proficiency for all students.
   4. We will develop effective evaluative methods in order to determine if our mathematics program is meeting its goals.

Pedagogy

The Principles and Standards for School Mathematics (NCTM 2000) describes the agreed upon pedagogy for mathematics in our district. The kinds of experiences teachers provide in the classroom play a major role in determining the extent and quality of student learning. Student understanding of mathematical ideas can be built throughout their school years if teachers present students with tasks and experiences designed to deepen and connect their knowledge. Learning with understanding is enhanced by classroom interactions as students propose mathematical ideas and conjectures, learn to evaluate their own thinking and that of others, and develop their mathematical reasoning skills. The teacher is responsible for creating an intellectual environment where serious engagement in mathematical thinking is the norm. Effective teaching requires deciding what aspects of a task to highlight, how to organize and orchestrate the work of students, what questions to ask students having varied levels of expertise, and how to support students without taking over the process of thinking for them. The Mathematics Process Standards provide a guideline to help teachers design learning activities that will foster student’s mathematical understanding.

We welcome your feedback to the Mathematics Curriculum Guide. Please send comments to Mathematics@arps.org.