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Alaska Department of Education & Early Development
Mathematics and Science Education

Chapter 3: Context

References for the Curriculum Development Process in Mathematics and Science
Preservice Education and Professional Development
Learning Partners and School to Work
Equity
Early Childhood Education
Technology
Other Resources: Staff, Time, Materials, Supplies, Equipment, Facilities

The Getting Started and Starting Points chapters discuss many issues and strategies for creating an overall educational plan that helps all students attain the Alaska student standards. This chapter describes specific issues, strategies, and references for science and mathematics education.

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References for the Curriculum Development Process in Mathematics and Science

Additional Considerations for Math and Science:

A curriculum development process guide is included in the Getting Started chapter of this document. That guide is appropriate for any content area. This section provides specific references addressing science and mathematics curriculum development.

For More Science and Mathematics Information:

Association of State Supervisors of Mathematics. (1993). Guide to Selecting Instructional Materials for Mathematical Education. ASSM. This publication provides guidelines for choosing instructional materials and is helpful if a district wants to adopt a textbook. It is included in the Resource Notebook of the Reference Kit.

Preservice Education and Professional Development

Additional Considerations for Math and Science:

The Alaska Department of Education & Early Development is now working on recommended guidelines for teacher preparation and certification to support the standards. See Results of Survey.

Most teachers were taught science as a set of facts. In science labs they followed "recipes" for lab work in which one predetermined outcome was expected. They were taught the basic skills in math, and they were taught to solve more difficult computations by applying memorized algorithms. They will continue to rely on these methods until they experience for themselves instruction that asks them to

• look for patterns in order to solve problems,
• invent algorithms to represent those patterns and provide short-cuts for mathematical solutions,
• develop and apply their mathematical reasoning in interdisciplinary contexts,
• construct conceptual understanding in science by resolving discrepancies between their experiences, their observations, and their explanations, and
• apply the process skills of science to these inquiries.

These personal educational experiences must be provided through preservice education and professional development opportunities. They should provide appropriate modeling in content, instruction, and assessment, and they should reference developmentally appropriate practice for students of all ages. This requires collaboration between the science, math, and education departments within teacher preparation institutions and K-12 schools.

In addition, teachers learning these constructive approaches to teaching need support as they develop

• images of effective practices from field placements in restructured schools,
• collegial relationships with master teachers, scientists, mathematicians, teacher educators, and community members who understand their needs,
• a knowledge of the potential projects and applications through which they can develop the skills and concepts of mathematics and science, and
• critical analysis of the Alaska Mathematics and Science Framework, the philosophies and assumptions on which it is based, and the alternative instruction and assessment strategies to prepare students to meet the Alaska Content Standards in Mathematics and Science.

For More Science and Mathematics Information:

Learning Partners and School to Work

Additional Considerations for Math and Science:

Alaska has a wealth of potential learning partners to strengthen the science and mathematical experiences of our students. Consider some of the following partnerships:

• Many Alaskans have excellent first hand knowledge and experiences with Alaska's natural environment. Ask dog mushers, subsistence fishermen and women, hunters, trappers, photographers, gardeners, and nature artists to create opportunities for your students to experience natural phenomena and to solve small survival or creativity challenges. These experiences will engage and motivate students to investigate phenomena from a more detailed and quantitative perspective later.
• Create Internet connections between students and mentor scientists, mathematicians, natural resource managers, and interest groups around specific projects. Provide mentor relationships in other tech prep areas by emphasizing the engineering, design technology, and society-oriented decisions associated with the professions. Encourage students to explore mentorships in fields that are not typically accessible to their gender.
• Ask local businesses to support the development of innovative tech prep academic courses by providing mentorships, materials, technology, and advice.
• Provide assistance to parents and guardians as they help their children with these new types of homework. Provide opportunities for parent leaders to obtain education in Family Math and Family Science programs and let them run parent training and support groups. Ask families to conduct long-term inquiries at home and to report the results in journals that are later discussed in class. Create e-mail or voice-mail information lines to remind students and parents of homework assignments and to provide examples of the type of work required. Emphasize the contributions to science and math from the cultures of your students. Help students to understand that different people look at phenomena with different perspectives. Remember to include qualitative understandings of phenomena, living within ecosystem limits, low tech inventions and innovations, and creative and practical uses of patterns as well as the more quantitative applications and discoveries.
• Emphasize the many ways of knowing about phenomena. Allow students to interact with learning partners at sights chosen by the learning partners. Don't require all learning partners to provide information through a lecture format; they may convey their perspective and skills more effectively in a context that is familiar and natural to them.

For More Science and Mathematics Information:

Stenmark, J., Thompson, V., and Cossey, R. (1986). Family Math. Berkeley, CA: Lawrence Hall of Science.

Equity

Additional Considerations for Math and Science:

Less than ten percent of all high school students have had access to four years of college preparatory science and mathematics courses. All students are capable of understanding and applying advanced concepts in these fields if instruction is developmentally and culturally appropriate. Schools have reduced the equity gap in science and mathematics by:

• eliminating tracking, increasing expectations and course requirements, and changing course content sequences;
• utilizing technology to customize instruction, address multiple learning modalities, facilitate complex reasoning, and provide visual models of concepts;
• enhancing life skills through math and science literacy;
• capitalizing on cultural learning styles and culturally relevant curriculum;
• addressing staffing needs;
• engaging parents as active partners; and
• increasing affective and academic support for students.

Creative science and math instruction can produce more equitable learning environments by using the powers of scientific inquiry, mathematical reasoning, and culturally-inquisitive investigations and applications to foster cooperation and social justice within schools. Consider some of the following suggestions:

• Content Integration: Broaden content to include contributions from all cultures. Place an emphasis on the contributions of Alaska Native traditional knowledge about local resources.
• Knowledge Construction: Acknowledge the various ways of knowing and validating knowledge in different cultures. Help students investigate how traditional knowledge about local resources and patterns was accumulated and validated. Compare this with current methods of scientific and mathematical reasoning. Emphasize the similarities, compatibilities, and complimentary processes.
• Prejudice Reduction: Use math and science instruction to reduce prejudice; include multicultural literature, use cooperative groupings of diverse students, use statistics to investigate inequities, review and critique studies about physiological, metabolic, cognitive, and other differences between cultural populations.
• Equitable Pedagogy: Develop effective teaching practices, questioning strategies, and curriculum development processes that promote academic success for underserved populations. Design instruction that meets and expands the diverse learning styles of all students.
• Empowering School Culture and Social Structure: Work creatively to increase the visibility and status of diverse employees and students in your schools. Involve students and staff as learning partners to share the contributions of their cultures to math and science. Create opportunities for parents of all cultures to understand the math and science curriculum approaches that their children experience. Highlight guest speakers from math and science professions who represent the cultures of the students to emphasize that all students have equal career opportunities in these fields.

See Equity Issues in Science and Math Bibliography.

For More Science and Mathematics Information:

Early Childhood Education

Additional Considerations for Math and Science:

Young children need ample opportunities to express their ideas with real items (concrete objects or manipulatives) before expressing those ideas with symbols. Make sure that each early childhood classroom (K-3) has flexible combinations of manipulatives for students to use at all times. Curriculum options such as "Math Their Way" and "Box It and Bag It" provide appropriate experiences with easily made manipulatives and provide bridges for more abstract representation of mathematical ideas and problem-solving with symbols. Projects in art, music, and other disciplines that allow students to recognize cause and effect relationships, classify objects and create categories, compare and contrast, predict and interpret results, and test their own theories while working and playing with real objects promote developmentally appropriate inquiry behaviors for young children.

All young children should be expected and allowed to solve challenging problems even if they have not yet mastered their basic math facts. Make sure that manipulatives are available for children to use to help solve problems that otherwise would require abstract reasoning or recalling facts.

Older learners also benefit from instruction that first provides hands-on experiences with simple models of the phenomena before expanding into symbolic representations and abstract ideas. Teachers of older students should provide both instruction and assessment with concrete manipulatives if the content is confusing to the students.

An effective model for helping young children construct their own scientific theories is "Look, Guess, Test, Tell." Children should be encouraged to construct their own unique explanations of phenomena and to describe how their theories explain their observations and experiences. They should struggle to identify the reasoning behind their beliefs. This process of inquiry is more important during these years than developing accurate knowledge of how things work.

For More Science and Mathematics Information:

Technology

Additional Considerations for Math and Science:

Technology can provide science and math experiences for students that otherwise would not be possible. It can provide linkages into the home, community, university, and workplace to increase students' contact with learning partners. Interactive media models experiences that are not possible through the limited science lab facilities at most schools. Computer based labs and probeware allow students to collect and analyze technical data with accuracy and ease. Simulations stimulate students to use mathematical and scientific reasoning to solve realistic problems of urban renewal, overpopulation, and other social issues. Software tools such as databases and spreadsheets allow students to focus on defining the problem and comparing alternative solutions while simplifying the redundant computations that would otherwise be involved. Graphing calculators make it financially possible for the entire class to simultaneously utilize technology for many of these purposes.

At a minimum, each school should have a well-maintained computer lab with integrated word processing, database, spreadsheet, and graphing software, software that develops the visual-spatial abilities of all students, software that supports pattern awareness and sequencing, software that supports any drill and practice needs for math facts with connections to the concrete concepts of addition, subtraction, multiplication and addition, interactive software for discovery learning in geometry, algebra, and calculus, CD-ROM disks that support the major content areas in science with excellent graphics, and simulations of a variety of issues-oriented science topics with integrated math applications. Each elementary school should have several classroom sets of calculators. Each middle school and high school should have classroom sets of graphing calculators and accompanying probeware or the equivalent computer-based software and hardware. Ideally each classroom should have at least six computer workstations to allow teachers to integrate technology centers into the day and to allow students to analyze and display data for ongoing projects. Each teacher should have a networked computer with audiovisual capabilities to allow the students to interact with mentors, learning partners, and potential employers.

See Useful Software for Science and Mathematics Education for lists of useful science and math software.

For More Science and Mathematics Information:

Other Resources: Staff, Time, Materials, Supplies, Equipment, Facilities

Additional Considerations for Math and Science:

Staff Resources

The district must recruit highly qualified math and science teachers who have specific science and math endorsements or coursework and specific training in a variety of instructional strategies and methodologies.

It is imperative that districts make teaching assignments based on the needs of the students and the qualifications and strengths of teachers, not what is most convenient for the schedule, the other teachers, or the administration.

It is essential that a district provide a support system for beginning math and science teachers to ensure continuous professional growth and commitment. (This may involve a mentor teacher, time to observe others, coursework, and involvement in the Alaska Science and Math Consortia.)

At the elementary level, if science or math specialists are not available, people within the building or district who have special expertise in certain facets of science or math need to be identified and utilized as peer coaches and leadership support teams.

Time Resources

The amount of time spent on an instructional topic directly affects the students' learning. Although time alone will not improve student learning (adequate staff development, materials, and facilities are necessary as well), student learning will not improve if adequate time is not provided. The National Science Teachers Association recommends the minimum amount of time spent on science instruction per week as two and one-half hours for primary grades and four hours for intermediate grades. The National Center for Improving Science Education recommends twice that much. The Scope Sequence and Coordination agenda for secondary science reform suggests that all secondary students take courses in each of the science disciplines every year of their secondary school experience (rather than starting with the biological sciences and advancing into the physical sciences only if they are successful in the earlier courses).

The NCTM Standards do not specify minimum time allotments for mathematics instruction, but they do recommend that all students be exposed to the major strands of mathematics throughout every year of their education. The Standards suggest that all students experience algebra, geometry, probability, statistics, and discrete mathematics repeatedly throughout their pre-college experience. This transition requires more time spent on significant conceptual development, rather than the traditional use of time mastering basic skills and facts.

It is essential that time also be provided for short and long term planning. To have successful classrooms, teachers need time to set up and take down labs. Schedules should take transition time into consideration. A teacher with multiple course preparation requirements and no prep time at the high school level teaches less effectively than a teacher with the time to adequately prepare.

Materials, Supplies, Equipment

Appropriate materials for math and science instruction promote the desired math and science outcomes. They must be in alignment with the goals and expectations of math and science curriculum, including the assessment component. The new demands of technology are expensive, and funding practices must be aligned with the needs. This requires strong advocates for school funding through private donations, local levies, state-wide initiatives, and grant work. Numerous resources offer detailed lists of appropriate science and math materials and equipment that should be part of a program. Check with the Alaska Department of Education & Early Development, your state and national organizations and their documents, commercial companies, your master teachers in science and math, other states' framework documents if this type of listing would be desirable. However, these lists will be more valuable if they are created by teachers in direct response to their instructional needs. Most often, by the time districts are to the stage of planning for materials, they find that a list made by someone else will not meet their needs.

Facility Resources

The Alaska Content Standards require an emphasis on connections and applications of science and math within other disciplines and real-life contexts. Science is no longer "lab dependent". Therefore, teachers must have an environment in which they can easily incorporate math and science into their other studies. Classrooms should have tables that promote small-group cooperative activities where students can easily decide to measure, construct, observe, and test objects and ideas. Students should have ready access to the world outside of the school building through telecommunications and doorways. Electrical outlets must be adequate and dependable to support the increased technology in the classroom. Windows should be designed to support instruction about light, reflection, and refraction. Mechanical spaces should be available for design and engineering studies. Buildings should be wired to support computer networking within the building, within the district, and through the Internet and World Wide Web.

Facilities need to be considered when developing curriculum. The Alaska Department of Education & Early Development, your state and national math and science organizations, your local health and safety inspector, your maintenance personnel, other state documents, school facility texts and manuals, and your master teachers in math and science are all good resources.

For More Science and Mathematics Information:

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