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Mathematics Common Core Guiding Principles

The following principles are philosophical statements that underlie the mathematics content and practice standards and resources in this curriculum framework. They should guide the construction and evaluation of mathematics programs in the schools and the broader community.

*These recommended Guiding Principles for Mathematics Programs are adapted from** the Massachusetts Curriculum Framework January 2011; **http://www.doe.mass.edu/frameworks/current.html** *

## Guiding Principle 1: Learning

*Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.*

Students need to understand mathematics deeply and use it effectively. The standards of mathematical practice describe ways in which students increasingly engage with the subject matter as they grow in mathematical maturity and expertise through the elementary, middle, and high school years.

## Guiding Principle 2: Teaching

*An effective mathematics program is based on a carefully designed set of content standards that are clear and specific, focused, and articulated over time as a coherent sequence*.

## Guiding Principle 3: Technology

*Technology is an essential tool that should be used strategically in mathematics education.*

Technology enables students to communicate ideas within the classroom or to search for information in external databases such as the Internet, an important supplement to a school’s internal library resources. Technology can be especially helpful in assisting students with special needs in regular and special classrooms, at home, and in the community.

## Guiding Principle 4: Equity

*All students should have a high quality mathematics program that prepares them for college and a career.*

All students should have high quality mathematics programs that meet the goals and expectations of these standards and address students’ individual interests and talents. The standards provide clear signposts along the way to the goal of college and career readiness for all students. The standards provide for a broad range of students, from those requiring tutorial support to those with talent in mathematics. To promote achievement of these standards, teachers should encourage classroom talk, reflection, use of multiple problem solving strategies, and a positive disposition toward mathematics. They should have high expectations for all students. At every level of the education system, teachers should act on the belief that every child should learn challenging mathematics. Teachers and guidance personnel should advise students and parents about why it is important to take advanced courses in mathematics and how this will prepare students for success in college and the workplace.

## Guiding Principle 5: Literacy Across the Content Areas

*An effective mathematics program builds upon and develops students’ literacy skills and knowledge*.

Reading, writing, and communication skills are necessary elements of learning and engaging in mathematics, as well as in other content areas. Supporting the development of students’ literacy skills will allow them to deepen their understanding of mathematics concepts and help them determine the meaning of symbols, key terms, and mathematics phrases as well as develop reasoning skills that apply across the disciplines. In reading, teachers should consistently support students’ ability to gain and deepen understanding of concepts from written material by acquiring comprehension skills and strategies, as well as specialized vocabulary and symbols. Mathematics classrooms should make use of a variety of text materials and formats, including textbooks, math journals, contextual math problems, and data presented in a variety of media.

## Guiding Principle 6: Assessment

*Assessment of student learning in mathematics should take many forms to inform instruction and learning.*

A comprehensive assessment program is an integral component of an instructional program. It provides students with frequent feedback on their performance, teachers with diagnostic tools for gauging students’ depth of understanding of mathematical concepts and skills, parents with information about their children’s performance in the context of program goals, and administrators with a means for measuring student achievement.

Assessments take a variety of forms, require varying amounts of time, and address different aspects of student learning. Having students “think aloud” or talk through their solutions to problems permits identification of gaps in knowledge and errors in reasoning. By observing students as they work, teachers can gain insight into students’ abilities to apply appropriate mathematical concepts and skills, make conjectures, and draw conclusions. Homework, mathematics journals, portfolios, oral performances, and group projects offer additional means for capturing students’ thinking, knowledge of mathematics, facility with the language of mathematics, and ability to communicate what they know to others. Tests and quizzes assess knowledge of mathematical facts, operations, concepts, and skills and their efficient application to problem solving. They can also pinpoint areas in need of more practice or teaching. Taken together, the results of these different forms of assessment provide rich profiles of students’ achievements in mathematics and serve as the basis for identifying curricula and instructional approaches to best develop their talents.

2 Milken, Lowell, A Matter of Quality: A Strategy for Answering the High Caliber of America’s Teachers, Santa Monica, California: Milken Family Foundation, 1999.

3 Ma, p. 147.

4 National Center for Education Statistics, Pursuing Excellence: A Study of U.S. Fourth-Grade Mathematics and Science Achievement in International Context. Accessed June 2000.