# Mathematical Reasoning

Our innovative math courses focus on problem-based mathematical modeling and statistics, integrated with science and social studies courses.

The overall goals of the mathematics curriculum are to provide a strong mathematical foundation and appreciation of mathematics to serve its graduates as citizens, in the workplace, and in future studies, and to insure that students are prepared for the required Regents exams. These goals will be driven by contexts, problems, and issues drawn from the disciplines of environmental studies, social justice, and sustainability.

All students are required to complete four years of mathematics coursework. Students who have not completed algebra successfully prior to enrolling at New Roots Charter School will begin with Mathematical Reasoning I. Students who have successfully completed an algebra course prior to enrolling at NRCS will enroll in Mathematical Reasoning II.

Recognizing that mathematical development proceeds at different rates for different students, the New Roots Charter School mathematics curriculum allows students up to two years to prepare for the Regents Algebra exam. Such pacing will also permit students to develop the mathematical knowledge and skills needed for this assessment in the context of meaningful realistic problems related to the environment. Such a focus on applied problem solving is consistent with the five process standards articulated by NYS, and will insure the development of conceptual understanding, procedural fluency, and problem solving skills as expected by the NYS Standards.

Mathematical Reasoning I and II will provide a foundation in algebra and geometry, that in addition to raising students’ level of quantitative literacy and improving their problem-solving ability, will also provide a foundation for the upper two mathematical courses in New Roots Charter School’s curriculum.

In spreading the development of the mathematical fundamentals out over two years, we will create three important opportunities: i) a chance for all students to mature and succeed at their own pace, ii) time in which to pursue some topics in more depth in response to student interest, and iii) time to enhance students’ appreciation of mathematics and its role in culture and society by balancing the emphasis on the skills and concepts required for the NYS Regents exam with attention to the historical and cultural aspects of mathematics as a human activity and to contemporary developments in the mathematical sciences.

**Mathematical Reasoning II**

This course is a continuation of Mathematical Reasoning I and extends the students’ knowledge and skills to additional topics in geometry including some topics in three-dimensional geometry and transformations. Additional work in coordinate geometry will focus on inequalities and solving systems of equalities and inequalities that will also extend the students’ algebraic understanding of quadratic functions. All topics will be developed to the level of Assessment (NYS benchmark level) by the end of the course. Students will hone their problem-solving skills using meaningful and realistic contexts. All students will have the option to take the Geometry Regents exam at the end of the course.

The next two courses in the sequence will emphasize the role of mathematical modeling as both a means of representing “real-world” problems and a means of solving these problems through use of the mathematical reasoning skills developed in the two previous courses. The first upper-level course, Probability, Statistics, and Discrete Mathematics for Sustainability, will develop further the ideas about probability and statistics first encountered in Mathematical Reasoning I and II. In addition, students will study topics drawn from financial mathematics, operations research, and discrete mathematics. The fourth course in the mathematics curriculum will be a capstone course for students to further develop their mathematical reasoning and problem-solving skills.

**Mathematical Reasoning I**

This course is primarily the study of algebra as the grammar of mathematics. All of the strands of New York’s math Skills Standards are introduced. The concepts and skills associated with variables and variable expressions, algebraic transformation and simplification, functions, generalizations, and proofs are introduced, developed, and assessed. Students’ prior understanding of integers and rational numbers is extended to the Real number system. Graphing on the Cartesian coordinate system lays the foundation for coordinate geometry that in turn leads to an introduction to geometry emphasizing properties of shapes, symmetry, transformations, and proofs related to two-dimensional geometry. As needed by some real-world problems, some elementary trigonometry, probability, and statistical ideas are also developed. The overall emphases are on developing mathematical fluency with variable expressions, equations, and formulas, and on honing students’ problem-solving skills in the context of meaningful realistic contexts. Students will prepare for and take the Algebra Regents exam at the end of their 9th grade year.

The following 11th and 12th grade course(s) are currently under construction, but here's a preview of what to expect for one of the upperclassmen math core:

- Probability, Statistics, and Discrete Mathematics for Sustainability:

This 11th grade course introduces advanced concepts and skills required for understanding the roles played by chance, data, and discrete relationships in understanding and solving realistic problems in the fields of environmental studies, politics, business, industry, and science. All five Mathematical Process Standards will guide all work done in this course. Some of the Performance Indicators from previous courses will be deepened by advanced work in these areas as needed in the context of issues of sustainability. This course will be structured around a text such as Discrete Mathematics Through Applications 3rd Edition, by Crisler and Froelich and published by W.H. Freeman.

For a more in-depth look into these courses, please click on the PDF file listed below.