Mathematics Curriculum Framework
Achieving Mathematical Power - January 1996
Partnerships Advancing the Learning of Mathematics and Science (PALMS)
The following criteria -- Evaluating Instructional Materials and Programs in Science, Technology and Mathematics -- are recommended for use by Massachusetts educators.
These criteria are designed to help districts, schools and teachers to first, reassess the strengths and weaknesses of the programs and materials they have in place, and second, to assess the strengths and weaknesses of new programs and materials being considered for implementation.
The Massachusetts Department of Elementary and Secondary Education does not choose to mandate specific programs, but rather to provide tools that will help professionals to select programs that best match the specific needs of their students.
While the criteria are primarily for district leaders, they also provide a useful guide for teachers as they reshape specific curriculum activities to align with the Curriculum Frameworks for Mathematics and for Science and Technology. These Frameworks, which are based upon the goals set forth in the Massachusetts Common Core of Learning, present a vision for the reform of science, technology and mathematics in the Commonwealth schools. The Frameworks also provide Guiding Principles, Habits of Mind and Content Standards, which are organized according to Core Concepts, Strands, Learning Standards, and Examples of Student Learning.
The Curriculum Frameworks in Mathematics and in Science and Technology should be used in conjunction with the criteria. It is unlikely that a program will satisfy all components of the criteria. Reviewing published programs critically and becoming familiar with their particular strengths and weaknesses will help teachers and districts to make informed decisions about program selection, program modification and the use of supplementary materials.
These criteria are organized into six categories. These categories should be considered as overlapping rather than distinct. In evaluating programs and materials, it is recommended that the evaluating committee give special consideration to how all the components of the materials and programs work together to ensure that students' experiences in science, technology and mathematics are of the highest possible quality.
All Categories reflect the Vision, Guiding Principles, and Habits of Mind described in the Content Chapters of the Mathematics and/or the Science and Technology Curriculum Frameworks.
1. Science, Technology and Mathematics Content
- Reflects the Learning Standards in the Content Chapters of the Mathematics and/or Science and Technology Curriculum Frameworks.
- Is scientifically and mathematically correct and current.
- Incorporates real-world science technology and/or mathematics.
- Provides opportunities to show how a scientist, mathematician or technologist thinks.
- Reflects the diversity of our society through activities, use of language, and illustrations.
2. Organization and Structure
- Provides cohesive units, multi-day in length, that build conceptual understanding.
- Provides for in-depth, inquiry-based investigations of major scientific and mathematical concepts.
- Emphasizes connections among science domains technology and within mathematics.
- Emphasizes interdisciplinary connections.
- Incorporates appropriate instructional technology.
- Incorporates materials that are appropriate and engaging for students of the community.
- Includes a master source of materials and resources.
- Includes safety precautions where needed, and clear instructions on using tools, equipment and materials.
3. Student Experiences
- Emphasize students doing science technology or mathematics.
- Involve students in active, inquiry-based, open-ended learning, and problem solving.
- Involve use of manipulatives to explore, model and analyze.
- Involve use of instructional technology to visualize complex phenomena or concepts, acquire and analyze information, and communicate solutions.
- Provide multiple routes for students to explore concepts and communicate ideas and solutions.
- Are developmentally appropriate and provide for diverse cultural backgrounds, abilities and learning styles.
- Encourage collaboration and reflection.
- Have relevance to the students' day-to-day experiences.
- Use a variety of resources (e.g., trade books, measuring tools, information technology, manipulatives, primary sources and electronic networks).
- Teacher Support Materials
- Provide background about the content.
- Offer ideas for how parents and community could be involved and kept informed about the program.
- Give suggestions for creating a variety of learning environments, such as cooperative learning, independent research, grouping strategies, student as teacher, learning centers, and field trips.
- Reference resource materials such as appropriate videos, file clips, reference books, software, video laser disk, long-distance learning, CD ROM, and electronic bulletin boards.
- Suggest how to adapt materials for different developmental levels of students.
- Incorporate strategies for engaging all students such as open-ended questions to stimulate student thinking, journals, manipulatives, explorations, and visual, auditory, and kinesthetic approaches.
- Include suggestions for teacher use of a variety of assessment approaches such as portfolios, journals, projects, tests, and performance assessments.
5. Student Assessment Materials
- Are free of racial, cultural, ethnic, linguistic, gender, and physical bias.
- Are oriented toward problem solving and real-world applications.
- Are embedded in the instructional program, occurring throughout the unit, not just at the end.
- Incorporate multiple forms of assessment such as: student demonstrations; oral and written work; student self-assessment; technology; teacher observations; individual and group assessments, and journals.
- Focus on the process of learning such as: predicting; modeling; making inferences; and reasoning (not just the product).
6. Program Development and Implementation
- Was designed using a research base.
- Has evidence of effectiveness, such as field test data regarding impact on student learning, behavior, and attitudes, including underrepresented student populations.
- Is flexible and adaptable to local curriculum and/or school.
- Offers training, sustained technical assistance, and long-term follow-up for teachers.
Peg Bondorew, Massachusetts Department of Elementary and Secondary Education
Marilyn Decker, CESAME, Northeastern University
Sue Doubler, TERC
Eileen Ferrance, Regional Alliance for Mathematics and Science Education Reform
Nancy Love, The Network, Inc.
William Masalski, University of Massachusetts, Amherst
Katherine Frome Paget, TERC
Tom Plati, Wellesley Public Schools
Gisele Charron Zangari, Massachusetts Department of Elementary and Secondary Education/Mansfield Public Schools
Mike Zapantis, Massachusetts Department of Elementary and Secondary Education