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Preceding Pages
- Looking Ahead
- Part A: Beliefs About Best Practices for Teaching and Learning Mathematics and Science
- Part B: Beyond Beliefs: The Guiding Principles
- Structure for the Discussion of Guiding Principles
- Guiding Principles
Current Page
- Guiding Principle #2. Students communicate effectively in mathematics and science.
- Instructional Implications
- Content Standards
- A.Students use clear and accurate communication in sharing their knowledge.
- B. Students construct knowledge through reflection, evaluation and refocusing.
- C. Students use models to communicate in mathematics and science.
- D. Students demonstrate competency in using multiple media to communicate in mathematics and science.
- E. Students critically analyze information from a variety of sources.
- F. Individually and collaboratively, students use effective communication techniques.
Following Pages
- Guiding Principles
- 3. Students reason effectively in mathematics and science.
- 4. Students are problem-solvers in mathematics and science.
- 5. Students understand their roles in the natural world.
- 6. Students understand historical and societal implications of mathematics and science.
- 7. Students attain and apply essential knowledge and skills of mathematics and science.
- References
Communication is an essential skill in learning, knowing and applying mathematics and science. It is a two-way process; receiving information accurately is as important as disseminating information clearly. Because scientifically and mathematically competent people understand the importance of accurate communication, they must possess certain skills related to the transfer of information in mathematics and science. Effective communication requires fluency with mathematics and science vocabulary and the ability to reflect on one's thinking. In addition, students construct knowledge through their own and others' communications. Just as young children learn the structure of language by listening to and talking with
others, so do students learn mathematics and science through communication.
Instructional ImplicationsNot only can educators effectively transmit ideas in mathematics and science by helping students improve communication skills, teachers can also gain useful insights about learning and make appropriate instructional decisions when they attend to learners' communications about thinking. Students construct knowledge of mathematics and science by communicating with each other as they involve themselves with subject matter and discoveries.
Teachers should help students practice a broad range of communication skills, including listening, speaking, reading, representing and writing in mathematics and science classes. Students need many opportunities to discuss, question, listen, reflect and summarize ideas. These ideas may come from self, other students, the teacher, or sources outside the classroom.
Teachers need to create an environment in which students are encouraged to communicate openly and reflect genuinely on their developing notions about the subject matter. Providing instruction in and opportunities for cooperative group work can be an important instructional tool for helping students improve their communication skills.
Familiarizing students with technological tools, in addition to traditional resources, can help them choose the most appropriate medium for both collecting information and communicating to a particular audience. Computers, graphing calculators and video/audio devices can enhance visual display of information. Electronic databases and the Internet can provide additional resources for in-depth research.
Teachers can help students reflect on their own and others' learning by providing opportunities for reflection and assessment in the classroom. Teachers should familiarize students with self-assessment tools such as rubrics, reflective journals and placements on a continuum.
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SNAPSHOT
In fourth-grade classrooms across the state, children are studying the Maine environment. The students work in groups to select a community-identified problem or concern and electronically communicate their problem to the students from other schools. The groups decide how they will share their information, research their topic, and develop a clear and detailed presentation for the class. With teachers' help, classes have worked to establish rules for student participation within the groups so that each group can function effectively. Before the presentations are shared, the class designs a rubric for grading the presentations, and each student completes a self-assessment on contributions within the group. Students also communicate their findings with the other classrooms participating in the unit.
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Content Standard A. Students use clear and accurate communication in sharing their knowledge.
______________________________________________________In order to gain and share knowledge effectively, students must develop scientific and mathematical language and use that language daily in classroom interactions. Reasoning and logic skills develop along with skill in proper language use. Sharing is done through a variety of methods including reading, writing, listening and speaking.
Learning to question appropriately leads to enhanced knowledge and understanding. Skillful questioning must be modeled by the teacher and practiced by the students.
Performance Indicators Primary
1.Describe and compare things in terms of number, shape, texture, size, weight, color and behavior. (S-L1)
2. Read and write instructions to be followed or instructions which explain procedures. (S-L2)
3. Use numerals and symbols to report numerical relationships and data (M-K1)
4. Explain problem-solving processes using verbal, pictorial and written methods. (S-L4)
5. Create mathematical problems for others to solve.
6. Share and support mathematical and scientific understanding orally and in writing
Intermediate
1. Record results of experiments or activities (e.g. interviews, discussions, field work) and summarize and communicate what they have learned. (S-L1)
Middle
1. Discuss mathematical, scientific, and technological ideas and make conjectures and convincing arguments. (S-L1)
2. Describe how mathematical formulas are generated and used.
Secondary
1. Analyze research or other literature for accuracy in the design and findings of experiments (S-L1)
2. Use families of functions, displayed in graphical, tabular and symbolic form, to communicate and support findings and ideas.
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SNAPSHOT
Seventh-grade students are studying the Maine environment. The students work in groups to select a community-identified local problem or concern. The groups decide how they will research their topic, exchange information, and develop a clear and detailed presentation for the class.
After contacting area local scientists to gain more background knowledge, students go into the field to gather information about their local environment. Using library and computer resources to investigate similar situations in other geographical areas, learners compile this information in an attempt to formulate a solution to their problems. They share their solutions with each other and with other groups of students outside the school, submitting the solutions to criticism and defending positions with logical arguments.
With the teacher's help, the whole class has worked to establish rules for participation within the groups. Before the presentations are shared, the class designs a presentation rubric focusing on good communication skills. In addition, students complete a self-assessment of their participation within the group.
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Content Standard B. Students construct knowledge through reflection, evaluation and refocusing.
_______________________________________________________Knowledge is constructed by relating the new to the known. When students are given time to reflect on what they have experienced and observed, they are assisted in clarifying their thinking and building upon their previous knowledge. They should be given opportunities to reflect orally and in writing, individually and in groups.
Performance Indicators Primary
1. Ask clarifying questions (What do you mean? What would you do? Could you tell me more?) about their own work as well as the work of others. (S-L2)
Intermediate
1. Ask clarifying and extending questions (S-L2)
2. Reflect on work in science, technology, and mathematics using such activities as discussions, journals, and self-assessment. (S-L3)
3. Extend self-assessment to include work in groups and individual work.
Middle
1. Defend problem-solving strategies and solutions. (S-L2)
2. Evaluate individual and group communication for its clarity, and work to improve communication (S-L3)
3. Generate and use self-assessment tools.
Secondary
1. Use journals and self-assessment to describe and analyze mathematical, scientific, and technological experiences and to reflect on problem-solving processes. (S-L2)
2. Refine and extend the use of self-assessment tools.
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SNAPSHOT High school seniors are asked to design and complete a science and mathematics research project to demonstrate expertise in a mathematical or scientific area of their interest. The project audience may include teachers, fellow students, parents and outside experts. Topics may range from the use of probability in medical research, to a detailed analysis of the depletion of fishing stocks, to the influence of crystal structure on various artists.
The students are expected to conduct significant research, searching through professional journals and various electronic resources and interviewing experts, compiling their findings into a comprehensive paper worthy of publication. Students also prepare an oral presentation to be made to a specified audience.
Earlier in the year, students have worked with the teacher to develop guidelines for acceptable and outstanding research, writing and presentations. During their school career, students have been given many opportunities to research, write and present, so the process is not new to them. Throughout the process, the teacher is available as a guide, helping the students to narrow their topics, find the appropriate resources, organize their data and make reasonable conclusions.
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Content Standard C. Students use models to communicate in mathematics and science.
_______________________________________________________Constructing models involves representing a problem or idea in a visual or symbolic form to help others understand it. Modeling, an essential component of mathematics and science, is one of the most powerful tools for communicating in these disciplines.
Performance Indicators Primary
1. Make and read simple graphs. (S-L5)
2. Use objects and pictures to represent scientific and mathematical ideas. (S-L6)
Intermediate
1. Make and/or use sketches, tables, graphs, physical representations, and manipulatives in presentations to explain procedures and ideas in a concise and clear manner. (S-L4 and M-K1 combined)
2. Use numerical data to describe and compare objects and events.
Middle
1. Translate relationships into algebraic notation. (M-K1)
2. Make and use scale drawings, maps, and three-dimensional models to represent real objects, find locations, and describe relationships. (S-L4)
3.Organize data in tables, charts and graphs to make claims and support arguments.
4. Use symbols to represent mathematical and scientific concepts.
5. Draw pictures and diagrams to solve some types of problems.
Secondary
1. Make and use appropriate mathematical and scientific symbols, pictures, diagrams, scale drawings, and models to represent and simplify real life situations and to solve problems. (S-L3)
2. Employ graphs, tables, and maps in making arguments and conclusions. (S-L4)
3. Critique models, stating how they do and do not effectively represent the real phenomenon. (S-L5)
=========================================Content Standard D. Students demonstrate competency in using multiple media to communicate in mathematics and science.
_______________________________________________________Multiple media are used as instructional tools to develop ideas, assimilate information, solve problems and communicate with others. Students at all levels should have equitable access to communication media, including computers, CD-ROMs, interactive video, telecommunications, and traditional sources such as books, magazines, encyclopedias and manipulatives.
Performance Indicators Primary
1. Use calculators, computers, and other tools in mathematics and science learning.
Intermediate
1. Gather and present information using a variety of media including computers (e.g., spreadsheets, word processing, programming, graphics, modeling). (S-L5)
Middle
1.Access information at a remote site using telecommunications. (S-L5)
2. Identify and use suitable media to collect information and to communicate a particular idea to a given audience.
Secondary
1. Evaluate the communication capabilities of new kinds of media (e.g., cameras with computer disks instead of film). (S-L6)
2. Use computers to organize data, generate models, and do research for problem solving. (S-L7)
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Content Standard E. Students critically analyze information from a variety of sources.
_______________________________________________________People are bombarded with mathematical and scientific information in various forms and from many sources. Much of this information is not analyzed for accuracy before it is transmitted. Students need to practice analyzing information for bias, consistency, logical connections and a sense of the author's intended effect.
Performance Indicators Primary
1. Explore connections between folklore and scientific principles.
2. Evaluate apprpriate sources of information.
Intermediate
1. Cite examples of bias in information sources and question the validity of information obtained from various sources. (S-L6)
Middle
1. Use statistics, tables, and graphs to communicate ideas and information in convincing presentations and analyze presentations of others for bias or deceptive presentation. (M-K2)
2. Communicate the same information in different ways to support diverse points of view.
3. Recognize that more evidence can change decisions, points of view and conclusions.
Secondary
1. Restate, create, and use definitions in mathematics to express understanding, classify figures, and determine the truth of a proposition or argument. (M-K1)
2. Read mathematical presentations of topics within the Learning Results with understanding. (M-K2)
3. Engage in a debate on a scientific issue, where both points of view are based on the same information.
=========================================Content Standard F. Individually and collaboratively, students use effective communication techniques.
_______________________________________________________Human beings generally live in groups, voluntarily cooperating with one another. In the workplace it is common for teams of people to be assigned projects where each individual is responsible for a piece of the project or where people must collaborate in the development of ideas. Therefore, educators need to help learners develop effective written and oral communication in both independent and collaborative settings.
Performance Indicators Primary
1. Assess one's own performance within a group.
2. Interact in groups of various sizes.
3. Listen carefully to each other.
Intermediate
1. Function effectively in groups within various assigned roles (e.g., reader, recorder). (S-L7)
1. Identify and fulfill roles necessary to accomplish group tasks. (S-L6)
Secondary
1. Identify tasks, formulate groups and assign roles to accomplish the tasks.