Mathematically Connected Communities

NSF ESI 9714999

The Show-Me Center, in partnership with five NSF-sponsored middle grades curriculum development satellites (University of Wisconsin, Michigan State University, University of Montana, Institute for Research on Learning, Educational Development Center) and publishers (Dale Prentice Hall Publications, Creative Publications, Voyager Expanded Learning, Encyclopedia Brittanica, and McDougal-Littell) provides information and resources needed to support selection and implementation of standards-based middle grades mathematics curricula.

The phrase "standards-based" is used here to refer to implementation of recommendations regarding mathematics curriculum and instructional practice outlined in the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989) and the Professional Standards for Teaching Mathematics (1991). The Standards documents call for curriculum and instruction that engages, challenges, and prepares students for continued study and growth in mathematical skills and understandings, causes them to develop mathematical habits of mind and to understand and appreciate the role of mathematics in human affairs. The intent of the Standards is that students become mathematically literate, including being able to explore, conjecture, reason logically and use a variety of mathematical methods to solve problems.

Five curriculum projects were funded in 1992 by the National Science Foundation to develop comprehensive "standard-based" curricula. The phrase "standards-based" is used here to refer to implementation of recommendations regarding mathematics curriculum and instructional practice as described in the NCTM Standards. These Standards call for curriculum and instruction that engages, challenges, and prepares students for continued study and growth in mathematical skills and understandings, causes them to develop mathematical habits of mind and to understand and appreciate the role of mathematics in human affairs. The intent of the Standards is that students become mathematically literate, including being able to explore, conjecture, to reason logically and to use a variety of mathematical methods to solve problems.

Each curricula represents a comprehensive (not supplementary or ancillary) program based on the premise that the mathematics content and teaching methodology of the middle grades should:

be designed to reach ALL students;
focus on investigations that interest, challenge and motivate students;
identify and explore "significant" mathematical concepts that will prepare students for continuing to learn mathematics in high school;
engage students as active learners of mathematics;
require teachers and students to assume different roles, including coach and co-investigator;
illustrate use of alternative forms of evaluation such as portfolios.

Each curricula is unique and should be explored by those considering implementing a standards-based curriculum.

Connected Math Project (CMP)

The title Connected Mathematics Project (CMP) reflects the author team's interest in developing student knowledge of mathematics that is rich in connections--connections among the various topic strands of the subject, connections between mathematics and its applications in other disciplines, connections between the planned teaching/learning activities and the special aptitudes and interests of middle school students, and connections between the preparation developed by elementary school mathematics and the goals of secondary school mathematics.

In each strand the fundamental concern is to make sure students have a confident understanding of the most important concepts, principles, and techniques required to apply mathematics to the solution of significant problems. Themes and situations are used to develop mathematics and to engage the interest of students. That is, the mathematics and processes are motivated by the applied situation. Skilled performance of routine procedures is not useful unless those skills are accompanied by a clear sense of when and how they should be applied. The intention is to make maximum use of relations and connections between strands and between grade levels.

Publisher:: Prentice Hall
Phone #: 1-800-848-9500
Web Site: http://phschool.com/
NM Sales Representatives: http://www.k12pearson.com/rep_finder/index.cfm
Satellite:: Michigan State University
email: cmp@math.msu.edu
Web Site: http://www.math.msu.edu/cmp/

Mathematics in Context (MiC)

Mathematics in Context represents a comprehensive mathematics curriculum for the middle grades consistent with the content and pedagogy suggested by the NCTM Curriculum and Evaluation Standards for School Mathematics, and Professional Standards for Teaching Mathematics. The development of the curriculum units reflects a collaboration between research and development teams at the Freudenthal Institute at the University of Utrecht, The Netherlands, research teams at the University of Wisconsin, and a group of middle school teachers.

Each of the units uses a theme that is based on a problem situation that should be of interest to students. These themes are the "living contexts" from which negotiated meanings can be developed and sense-making can be demonstrated. Over the course of the four-year curriculum, students will explore in-depth the mathematical themes of number, common fractions, ratio, decimal fractions, integers, measurement, synthetic geometry, coordinate and transformation geometry, statistics, probability, algebra, and patterns and functions. Although many units may emphasize the principles within a particular mathematical domain, most will involve ideas from several domains, emphasizing the interconnectedness of mathematical ideas. These units are designed to be a set of materials that can be used flexibly by teachers, who tailor activities to fit the individual needs of their classes.

Students working individually and in flexible group situations, which include paired work and cooperative groups. We believe that the shared reality of doing mathematics in cooperation with others develops a richer set of experiences than students working in isolation.

Publisher:: Encyclopaedia Britannica
Phone: 800-HRW-9799
Email: holtinfo@hrw.com
Web Site: http://www.britannica.com/

Satellite:: University of Wisconsin-Madison
Contact: Meg Meyer
email: mrmeyer2@wisc.edu
Website: http://www.wcer.wisc.edu/

MathScape

The MathScape curriculum builds upon the central theme of mathematics in the human experience. Throughout the curriculum, students experience mathematics as it is used for planning, predicting, designing, exploring, explaining, coordinating, comparing, deciding and for other activities fundamental to human endeavors throughout the world and throughout history. The content of the curriculum includes processes of mathematical investigation (e.g., abstracting, representing, generalizing, proving, creating, applying, and communicating); four central mathematical ideas (proportional reasoning, multiple representations, patterns/functional relationships, and modeling); and specific concepts, skills, and language in the areas of algebra, estimation/computation, discrete mathematics, functions, geometry/visual reasoning, measurement, number, probability, and statistics.

The pedagogy of the curriculum reflects a view of learning as a process of constructing one's own knowledge and emphasizes the importance of the social context of learning for middle school students. Technology is integrated throughout the curriculum. In addition to working with calculators, students use a set of general-purpose software tools such as spreadsheet software and dynamic geometry software. They also use software designed to accompany specific units (e.g., a probability lab).

Publisher:: Glencoe/McGraw-Hill
Phone #: 1-800-334-7344
Web Site: http://www.glencoe.com/sec/math/mathscape/index.php/
Satellite:: Education Development Center, Inc.
email: mathscape@edc.org
Web Site: http://www2.edc.org/mathscape/

MathThematics

Middle Grades Math Thematics (STEM) is designed to provide teachers with curricular materials that are mathematically accurate, utilize technology, and provide students with bridges to science and other mathematical fields. The materials are designed to integrate communication into mathematics by providing opportunities for students to use reading, writing, and speaking as tools for learning mathematics. MathThematics materials are problem-centered, application based, and use technology where appropriate. Many lessons are designed to be project oriented and have students work cooperatively. New assessment techniques are used throughout the materials.

Students who complete the MathThematics curriculum will have acquired the mathematical skills necessary to solve problems, to reason inductively and deductively, and to apply the numerical and spatial concepts necessary to function according to their needs in a technologica society. Students will be independent learners, well prepared for both work and further experiences in mathematics. They will have the knowledge, ability, and confidence to explore mathematics at the secondary level. They will be experienced in working with extended projects, cooperative learning activities, technology, hands-on materials, applications, modeling, and new assessment techniques. MathThematics students learn to think mathematically, to become decision makers, and to view mathematics as relevant to their lives and connected to other areas.

Publisher:: McDougal Littell
Phone #: 800 323-5435
Web Site: http://www.classzone.com/math_middle.cfm and
http://classzone.com/math_hs.cfm
Satellite:: University of Montana
Contact: Rick Billstein
email: rickb@mso.umt.edu

The above information was excerpted from the Show-Me Center


a Parents Teachers Administrators	Creating Mathematically Connected Communities
	The Show-Me Project Created under Mathstar
Standards Based Resources Assessments Instructional Materials Math Resources NCTM Standards NM Standards and Benchmarks Recursos en Español Research Textbook Adoption Textbook Evaluation Resources Connecting Our Communities Administrators For Parents Maps Math Discussion Boards NM Public Education Department Partners Regional Facilitators Toolkits Curriculum Matrix Implementing CMP MC² Academies General Information Past Academy Resources Upcoming Academies Our Project Contact Information Focus Areas Facilitators » Calendar Workshops Maps Mission News Briefs on Summer Academies Project Reports Regional Facilitators Student Achievement Data Lesson Study SiteMap		NSF ESI 9714999 The Show-Me Center, in partnership with five NSF-sponsored middle grades curriculum development satellites (University of Wisconsin, Michigan State University, University of Montana, Institute for Research on Learning, Educational Development Center) and publishers (Dale Prentice Hall Publications, Creative Publications, Voyager Expanded Learning, Encyclopedia Brittanica, and McDougal-Littell) provides information and resources needed to support selection and implementation of standards-based middle grades mathematics curricula. The phrase "standards-based" is used here to refer to implementation of recommendations regarding mathematics curriculum and instructional practice outlined in the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics (1989) and the Professional Standards for Teaching Mathematics (1991). The Standards documents call for curriculum and instruction that engages, challenges, and prepares students for continued study and growth in mathematical skills and understandings, causes them to develop mathematical habits of mind and to understand and appreciate the role of mathematics in human affairs. The intent of the Standards is that students become mathematically literate, including being able to explore, conjecture, reason logically and use a variety of mathematical methods to solve problems. Five curriculum projects were funded in 1992 by the National Science Foundation to develop comprehensive "standard-based" curricula. The phrase "standards-based" is used here to refer to implementation of recommendations regarding mathematics curriculum and instructional practice as described in the NCTM Standards. These Standards call for curriculum and instruction that engages, challenges, and prepares students for continued study and growth in mathematical skills and understandings, causes them to develop mathematical habits of mind and to understand and appreciate the role of mathematics in human affairs. The intent of the Standards is that students become mathematically literate, including being able to explore, conjecture, to reason logically and to use a variety of mathematical methods to solve problems. Each curricula represents a comprehensive (not supplementary or ancillary) program based on the premise that the mathematics content and teaching methodology of the middle grades should: be designed to reach ALL students; focus on investigations that interest, challenge and motivate students; identify and explore "significant" mathematical concepts that will prepare students for continuing to learn mathematics in high school; engage students as active learners of mathematics; require teachers and students to assume different roles, including coach and co-investigator; illustrate use of alternative forms of evaluation such as portfolios. Each curricula is unique and should be explored by those considering implementing a standards-based curriculum. Connected Math Project (CMP) The title Connected Mathematics Project (CMP) reflects the author team's interest in developing student knowledge of mathematics that is rich in connections--connections among the various topic strands of the subject, connections between mathematics and its applications in other disciplines, connections between the planned teaching/learning activities and the special aptitudes and interests of middle school students, and connections between the preparation developed by elementary school mathematics and the goals of secondary school mathematics. In each strand the fundamental concern is to make sure students have a confident understanding of the most important concepts, principles, and techniques required to apply mathematics to the solution of significant problems. Themes and situations are used to develop mathematics and to engage the interest of students. That is, the mathematics and processes are motivated by the applied situation. Skilled performance of routine procedures is not useful unless those skills are accompanied by a clear sense of when and how they should be applied. The intention is to make maximum use of relations and connections between strands and between grade levels. Publisher: Prentice Hall Phone #: 1-800-848-9500 Web Site: http://phschool.com/ NM Sales Representatives: http://www.k12pearson.com/rep_finder/index.cfm Satellite: Michigan State University email: cmp@math.msu.edu Web Site: http://www.math.msu.edu/cmp/ Mathematics in Context (MiC) Mathematics in Context represents a comprehensive mathematics curriculum for the middle grades consistent with the content and pedagogy suggested by the NCTM Curriculum and Evaluation Standards for School Mathematics, and Professional Standards for Teaching Mathematics. The development of the curriculum units reflects a collaboration between research and development teams at the Freudenthal Institute at the University of Utrecht, The Netherlands, research teams at the University of Wisconsin, and a group of middle school teachers. Each of the units uses a theme that is based on a problem situation that should be of interest to students. These themes are the "living contexts" from which negotiated meanings can be developed and sense-making can be demonstrated. Over the course of the four-year curriculum, students will explore in-depth the mathematical themes of number, common fractions, ratio, decimal fractions, integers, measurement, synthetic geometry, coordinate and transformation geometry, statistics, probability, algebra, and patterns and functions. Although many units may emphasize the principles within a particular mathematical domain, most will involve ideas from several domains, emphasizing the interconnectedness of mathematical ideas. These units are designed to be a set of materials that can be used flexibly by teachers, who tailor activities to fit the individual needs of their classes. Students working individually and in flexible group situations, which include paired work and cooperative groups. We believe that the shared reality of doing mathematics in cooperation with others develops a richer set of experiences than students working in isolation. Publisher: Encyclopaedia Britannica Phone: 800-HRW-9799 Email: holtinfo@hrw.com Web Site: http://www.britannica.com/ Satellite: University of Wisconsin-Madison Contact: Meg Meyer email: mrmeyer2@wisc.edu Website: http://www.wcer.wisc.edu/ MathScape The MathScape curriculum builds upon the central theme of mathematics in the human experience. Throughout the curriculum, students experience mathematics as it is used for planning, predicting, designing, exploring, explaining, coordinating, comparing, deciding and for other activities fundamental to human endeavors throughout the world and throughout history. The content of the curriculum includes processes of mathematical investigation (e.g., abstracting, representing, generalizing, proving, creating, applying, and communicating); four central mathematical ideas (proportional reasoning, multiple representations, patterns/functional relationships, and modeling); and specific concepts, skills, and language in the areas of algebra, estimation/computation, discrete mathematics, functions, geometry/visual reasoning, measurement, number, probability, and statistics. The pedagogy of the curriculum reflects a view of learning as a process of constructing one's own knowledge and emphasizes the importance of the social context of learning for middle school students. Technology is integrated throughout the curriculum. In addition to working with calculators, students use a set of general-purpose software tools such as spreadsheet software and dynamic geometry software. They also use software designed to accompany specific units (e.g., a probability lab). Publisher: Glencoe/McGraw-Hill Phone #: 1-800-334-7344 Web Site: http://www.glencoe.com/sec/math/mathscape/index.php/ Satellite: Education Development Center, Inc. email: mathscape@edc.org Web Site: http://www2.edc.org/mathscape/ MathThematics Middle Grades Math Thematics (STEM) is designed to provide teachers with curricular materials that are mathematically accurate, utilize technology, and provide students with bridges to science and other mathematical fields. The materials are designed to integrate communication into mathematics by providing opportunities for students to use reading, writing, and speaking as tools for learning mathematics. MathThematics materials are problem-centered, application based, and use technology where appropriate. Many lessons are designed to be project oriented and have students work cooperatively. New assessment techniques are used throughout the materials. Students who complete the MathThematics curriculum will have acquired the mathematical skills necessary to solve problems, to reason inductively and deductively, and to apply the numerical and spatial concepts necessary to function according to their needs in a technologica society. Students will be independent learners, well prepared for both work and further experiences in mathematics. They will have the knowledge, ability, and confidence to explore mathematics at the secondary level. They will be experienced in working with extended projects, cooperative learning activities, technology, hands-on materials, applications, modeling, and new assessment techniques. MathThematics students learn to think mathematically, to become decision makers, and to view mathematics as relevant to their lives and connected to other areas. Publisher: McDougal Littell Phone #: 800 323-5435 Web Site: http://www.classzone.com/math_middle.cfm and http://classzone.com/math_hs.cfm Satellite: University of Montana Contact: Rick Billstein email: rickb@mso.umt.edu The above information was excerpted from the Show-Me Center