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Mathematics
PK-12 Curriculum

Introduction	Grade Level Benchmarks:
Philosophy	Pre-Kindergarten Benchmarks
Table of Standards	Kindergarten Benchmarks
Content Standards:	First Grade Benchmarks
Number and Operations Standard	Second Grade Benchmarks
Algebra Standard	Third Grade Benchmarks
Geometry Standard	Fourth Grade Benchmarks
Measurement Standard	Fifth Grade Benchmarks
Data Analysis & Probability Standard	Sixth Grade Benchmarks
Process Standards:	Seventh Grade Benchmarks
Problem Solving Standard	Algebra Benchmarks
Reasoning and Proof Standard	Geometry Benchmarks
Communication Standard	Algebra II Benchmarks
Connections Standard	Precalculus Benchmarks
Representation Standard	Math Topics Benchmarks
	Calculus Benchmarks
Appendix: "Expose, Teach, and Reinforce" Explained Further Steps

Introduction

This Colegio Maya mathematics curriculum is largely based on the Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics in 2000. Using their document as a starting point and as a source for ideas, this curriculum outlines a vision of school mathematics appropriate for Colegio Maya. It includes descriptions of what mathematics instruction should enable students to know and do. The Principles and Standards document outlines five content and five process standards for mathematics. The Colegio Maya curriculum follows this basic organizational scheme. The content and process standards are inextricably linked and both are equally important to the vision of this curriculum.

Most mathematical content is highly sequential and this curriculum includes grade level benchmarks for each of the five content standards, indicating what topics should be taught in what classes. Realizing that most ideas are not mastered in a single year, the benchmarks show whether the teacher should expose (E), teach (T), or reinforce (R) a given topic at a given grade level. This E, T, and R structure is further explained in the appendix.

The five process standards are treated a bit differently than the content standards. Mathematical processes such as problem solving and communication are not as highly sequential as mathematical content, so grade level benchmarks for these standards are not included in this curriculum. Instead, there are lists of classroom examples that indicate the many ways that students can meet these standards. The lists are not exhaustive and are meant only to give readers an idea of how the process standards might look in Colegio Maya classrooms. More detailed discussion of this and other issues can be found in the NCTM's Principles and Standards document.

The curriculum concludes with a list outlining what steps are still needed to support the vision of school mathematics pictured here. Complete implementation of the mathematics curriculum will require further decisions regarding teacher training, student assessment, and purchase of classroom resources. Further review and revision of the curriculum will be an ongoing process. This document is only the first step in a longer process for improving mathematics education at Colegio Maya.

Philosophy

Mathematics is a language and science of patterns. As a language, mathematics is a means for describing with symbols and vocabulary the patterns and relationships in our world. As a science, mathematics is a mode of inquiry relying on logic, observation, simulation, and experimentation as a means of enhancing and extending our understanding of the world.

The vision of school mathematics outlined in this curriculum is based on students' learning mathematics with understanding. Unfortunately, learning mathematics without understanding has long been a common outcome of school mathematics instruction. An effective mathematics program will enable students to really understand the mathematics they are doing and to use what they learn to solve the new kinds of problems they will inevitably face in the future. Students will develop persistence, confidence, and ability to do mathematics and will develop the belief that math does have relevance and meaning.

Excellence in mathematics education also requires equity - a belief that mathematics can and must be learned by all students. A strong mathematics program includes both high expectations for all students and a means for providing further assistance and accommodation to those who need it.

Finally, a school mathematics program needs to find a balance regarding the use of calculators and computation. Pencil-and-paper computational methods that are over-practiced without understanding are often forgotten or remembered incorrectly. On the other hand, understanding without fluency can inhibit the problem-solving process. Teachers must help their students wisely use the technology available to them, balancing the need for conceptual understanding with the need for computational fluency.

Table of Standards

Content Standards Instructional programs from prekindergarten through grade 12 should enable all students to -
Number and Operation	Understand numbers, ways of representing numbers, relationships among numbers, and number systems Understand meanings of operations and how they relate to one another Compute fluently and make reasonable estimates
Algebra	Understand patterns, relations, and functions Represent and analyze mathematical situations and structures using algebraic symbols Use mathematical models to represent and understand quantitative relationships Analyze change in various contexts
Geometry	Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Specify locations and describe spatial relationships using coordinate geometry and other representational systems Apply transformations and use symmetry to analyze mathematical situations Use visualization, spatial reasoning, and geometric modeling to solve problems
Measurement	Understand measurable attributes of objects and the units, systems, and processes of measurement Apply appropriate techniques, tools, and formulas to determine measurement
Data Analysis and Probability	Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them Select and use appropriate statistical methods to analyze data Develop and evaluate inferences and predications that are based on data Understand and apply basic concepts of probability

Process Standards Instructional programs from prekindergarten through grade 12 should enable all students to -
Problem Solving	Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving
Reasoning and Proof	Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof
Communication	Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely
Connections	Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics
Representation	Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena

Mathematics PK-12 Curriculum

Mathematics
PK-12 Curriculum