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Alaska Department of Education & Early Development
Mathematics and Science

Chapter 5:Instruction


Mathematics and Science Instructional Practices to Reach All Students
Key Instructional Strategies for Mathematics and Science
Recommended Instructional Strategies for the Alaska Content Standards in Mathematics
Recommended Instructional Strategies for the Alaska Content Standards in Science
Science/Technology/Society Instructional Strategies

The Alaska Mathematics and Science Framework challenges teachers to support students as they develop the tools to become independent lifelong learners and contributors to society. The Framework also challenges teachers to be more aware of and responsive to the individual needs and goals of each student. These challenges require teachers to use a large repertoire of instructional strategies as they take their students into advanced levels of explorations and discoveries.

The first section describes the changing emphasis in instructional practices. It describes the shifting emphasis in what teachers are doing in the classroom to meet the standards.

The second section lists references which provide detailed information on how teachers can master recommended instructional strategies. These strategies will be particularly useful to teachers seeking to improve their instruction to meet specific Alaska Content Standards in Mathematics and Science. The Kentucky Framework and three other documents listed in this section are included in the Reference Kit.

The third and fourth sections suggest instructional strategies for reaching each of the specific Alaska Content Standards.

The final section provides information on how to involve students with local issues through the science/technology/society instructional strategy.


Mathematics and Science Instructional Practices to Reach All Students

The chart below is designed to assist curriculum committees as they develop district guidelines that move in the direction of student-centered instruction. These pairs of statements represent endpoints on a continuum of teaching and learning practices. Current trends are toward the strategies shown on the right hand side.

Shared Math-Science Instructional Practices
Decrease Emphasis On: Increase Emphasis On:
Math and science for some Math and science for all
Text based Experience and materials based
Single exposure to content Spiral curriculum
Teacher centeredTeacher as facilitator
Isolated topicsIntegrated topics and applications
Emphasis on facts and algorithms Emphasis on problem solving and concepts
One correct way to solve a problem More than one way to solve a problem
Competitive or individualized learning Cooperative learning
Limited use of technology Integration of appropriate technology
Passive learningActive learning
Paper and pencil assessments Multi-dimensional assessments

Mathematics-Specific Instructional Practices
Decrease Emphasis On: Increase Emphasis On:
Mastering prescribed algorithms Exploring, inventing, and comparing algorithms
Assessment focused on mastery of facts and algorithms Assessment exposes depth of understanding of concepts and processes
Exclusive use of paper, pencil, and blackboard Use of manipulatives, journals, computers, and calculators

Science-Specific Instructional Practices
Decrease Emphasis On: Increase Emphasis On:
Investigations with one correct outcome Problem solving investigations; students design questions; many possible outcomes
Teacher demonstrations Labs, field experiences, simulations
Science as a single subject with little relationship to mathematics, social studies, language arts, art or music Science as part of an interdisciplinary world; relating science to the students' world which is less compartmentalized
The teacher imparts knowledge and students learn it; one-way communication The teacher as a facilitator and a learner as well; students as both learners and teacher. Networks emerge instead of one-way channels of communication


Key Instructional Strategies for Mathematics and Science

The chart below lists key strategies that will support the Alaska Content Standards in Mathematics and Science. The strategies are referenced to books in the Reference Kit. (The citation (3)91 means to look at page 91 in the third reference in the end of this section, Transformations: Kentucky's Curriculum Framework.)

Key Teaching and Assessment Strategies

I. Foundation Strategies
Activating Prior Knowledge (3)91
Learning Cycle Model (4)
Metacognition (3)91
Modeling (3)92

II. Collaborative Process
Cooperative Learning (3)93
Peer or Cross-Age Tutoring (3)95
Reciprocal teaching (3)96

III. Community-Based Instruction
Field Studies (3)97
Mentoring/Apprenticeship/Co-op (3)97
Networking (3)98
Newspaper and Magazine Analysis
Service Learning (3)98
Shadowing (3)98
Science/Technology/Society Projects (1), (2)

IV. Continuous Progress Assessment
Anecdotal Records (3)99
Checklist (3)100
Conferencing (3)103
Interviewing (3)103
Math Journaling
Observation (3)104
Performance Tasks/Events/Exhibitions (3)105, (5)
Portfolio Development (3)106
Self-assessment/Reflection (3)107

V. Graphic Organizers
Advance Organizers (3)109
Compare/Contrast Structures, Venn Diagrams, Matrices (3)110-111
Flowcharts, Sequence Chains, Time Lines (3)112
Graphic Representation (3)114
KWL: Know, Want to know, Learned Chart (3)114
Mapping/Webbing (3)115
Notetaking, Storyboard, Story Map (3)117

VI. Problem Solving
A. Process
Brainstorming (3)119
Discussion (3)119
Heuristics (3)120
Inquiry/Investigation/Experimentation (3)121
Questioning (3)122

B. Product
Case Studies (3)123
Creative Problem Solving (3)123
Debate (3)125
Formulating Models (3)125
Interviews/Surveys/Polls (3)126
Oral History (3)126
Research (3)126
Role-play, Simulations (3)127
Simulations (3)127

VII. Technology/Tools
Adaptive Devices (digitized audio, video) (3)128
Calculators
Computer Utility (databases, spreadsheets, graphics, word-processing)
Data Collection Tools (lab probes, digital cameras) (2)255-273
Design (e.g., CAD-CAM)
Distance Learning
Teleconferencing Games
Interactive Video
Manipulatives (3)150
Multimedia (Videodisk, CD-ROM) (2)325
Puppets
Telecommunications
Video/Audio Production/Videotaping (2)325

Detailed information on how to master these recommended instructional strategies are referenced and are available in the Toolkit. (The citation (3)91 means to look at page 91 in the third reference in the end of this section, Transformations: Kentucky's Curriculum Framework.)

For More Information:

(1) Cheek, D. (1992). Thinking Constructively about Science, Technology, and Society. Albany: State University of New York Press. This book looks at and suggests the constructivist approaches that are facilitated through an S/T/S curriculum.

(2) Cheek, D., Briggs, R, and Yager, R, eds. (1992). Science Curriculum Resource handbook: A Practical Guide for K-12 Science Curriculum. Millwood, NY: Kraus International Publications. This book contains thorough and annotated references for trends and topics in curriculum design, sample curriculum guides, textbooks, classroom activity guides, software, and publishers of science education materials.

(3) Kentucky Department of Education. (1993). Transformations: Kentucky's Curriculum Framework. Frankfort, Kentucky: Kentucky Department of Education. The second volume of this document provides detailed information on most of the specific instructional strategies listed in the preceding chart.

(4) Schafer, L (ed). (1994). Behind The Methods Class Door: Educating Elementary And Middle School Science Teachers. Columbus Ohio: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. This document provides a number of perspectives on the use of Learning Cycle Model. It suggests approaches that provide an effective sequence of engagement, exploration, and extension in the science classroom.

(5) Shavelson , R. J. (1994). Laboratory Notebook: Performance Assessment in Science. Santa Barbara, CA: University of California. This document provides examples of clearly defined tasks for students to complete individually or in small groups.


Recommended Instructional Strategies for the Alaska Content Standards in Mathematics

The key elements of the Alaska Content Standards contain concepts and skills that students should master. Teachers will design integrated instructional units that address many of these key elements in an integrated fashion. As teachers design their units they should refer to the key elements, taking every opportunity to develop these new skills and concepts. The following charts suggest appropriate instructional strategies for each of the key elements of the Alaska Content Standards. References to detailed information on how to master these strategies are identified later in this chapter.
Math Content Standard A

All Alaska students will understand mathematical facts, concepts, principles, and theories.

Key Element Instructional Strategies
1. Understand and use the concept of numbers, number systems and numeration including: counting numbers, whole numbers, integers, rational, irrational and complex numbers. Manipulatives
Performance Tasks/Centers
Modeling
2. Select and use appropriate systems, units and tools of measurement, including estimation. Manipulatives
Performance Tasks/Centers
Inquiry/Investigation/Experimentation
3. Perform basic arithmetic functions and make reasoned estimates. Select and use appropriate methods or tools for computation or estimation such as mental arithmetic, paper and pencil, calculator, computer. Computer
Data Collection Tools
Peer or Cross-Age Tutoring
Reciprocal Teaching
4. Represent, analyze, and use mathematical patterns, relation, and functions, using methods such as tables, equations, and graphs. Computer
Manipulatives
Cooperative Learning
5. Construct, draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures. Venn Diagrams
Computer
Manipulatives
6. Collect, organize, analyze, interpret, represent, and formulate questions about data. Make reasonable and useful predictions about the certainty, uncertainty, or impossibility of an event. Computer Inquiry/Investigation/Experimentation

Math Content Standard B

All Alaska students will understand, select and use a variety of problem solving strategies.

Key Element Instructional Strategies
1. Use computational methods and appropriate technology as problem-solving tools. Computer
Calculators
2. Use problem-solving to investigate and understand mathematical content. Brainstorming
Discussion
Open Ended Questioning
Manipulatives
3. Formulate mathematical problems that arise from everyday situations. Field Studies
Formulating Models
Newspapers and magazines
4. Develop and apply strategies to solve a variety of problems. Heuristics
5. Check the results against mathematical rules. Reciprocal Teaching
6. Use common sense to interpret results. Computer
7. Apply what was learned to new situations. S/T/S
Learning Cycle Model
Field Studies
8. Be able to use mathematics with confidence. S/T/S

Math Content Standard C:

All Alaska students will understand, form and use appropriate methods to define and explain mathematical relationships.

Key Element Instructional Strategies
1. Express and represent mathematical ideas using oral and written representations, physical materials, pictures, graphs, charts, and algebraic expressions. Compare/Contrast Structures, Venn Diagrams, Matrices
Open Ended Questions
2. Relate mathematical terms to everyday language. Peer or Cross-Age Tutoring
Math Journaling
3. Develop, test and defend mathematical hypotheses. Reciprocal Teaching
Research
Formulating Models
Math Journaling
4. Clarify mathematical ideas through discussion with others. Discussions
Open Ended Questions

Math Content Standard D:

All Alaska Students will use logic and reason to solve problems.

Key Elements Instructional Strategies
Strategies apply to all key elements:

1. Analyze situations;
2. Draw logical conclusions;
3. Use models, known facts, and relationships to explain their reasoning;
4. Verify conclusions, judge the validity of arguments, and construct valid arguments (deductive reasoning); and
5. Recognize patterns and form mathematical propositions (inductive reasoning).
Brainstorming
Discussion
Inquiry/Investigation/Experimentation
Questioning
Graphic Organizers

Math Content Standard E:

All Alaska students will apply mathematical concepts and processes to situations within and outside of school.

Key Elements Instructional Strategies
1. Explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations. Newspaper and magazine math
2. Use mathematics in daily life. Science/Technology/Society Investigations (Cheek)
Service Learning
Learning Cycle Model
Field Studies
3. Use mathematics in other curriculum areas. Learning Cycle Model
S/T/S
Interviews/Surveys/Polls
Graphic Organizers
Problem Solving (all strategies)
Computer Utility


Recommended Instructional Strategies for the Alaska Content Standards in Science

The key elements of the Alaska Content Standards identify the concepts and skills that students should master. Teachers will design integrated instructional units that address many of these key elements. As teachers design their units they should refer to the key elements, taking every opportunity to develop new skills and concepts. The following charts suggest appropriate instructional strategies for each of the key elements of the Alaska Content Standards. References to detailed information on how to master these strategies are identified later in this chapter.

Science Content Standard A:

All Alaska students will understand scientific facts, concepts, principles, and theories.

Key Elements Instructional Strategies
Strategies apply to all 16 key elements.
1. (Structure of Matter);
2. (Changes and Interactions of Matter);
3. (Universe);
4. (Earth);
5. (Forces of Nature);'
6. (Motion);
7. (Processes that Shape the Earth);
8. (Energy Transformations);
9. (Flow of Matter and Energy);
10. (Cells);
11. (Heredity)
12. (Diversity);
13. (Evolution and Natural Selection);
14. (Interdependence);
15. (Local Knowledge)
16. (Relativity)
Learning Cycle Models
Activating Prior Knowledge
Mapping/Webbing
KWL
Videodisc/CD ROM

Science Content Standard B

All Alaska students will develop the skills of scientific inquiry.

Key Elements Instructional Strategies
1. Use the processes of science including observing, classifying, measuring, interpreting data, inferring, communicating, controlling variables, developing models and theories, hypothesizing, predicting and experimenting. Modeling
Performance Tasks/Centers
Inquiry/Investigation/Experimentation
Computer Utility
Learning Cycle Models
S/T/S
2. Design and carry out investigations using appropriate instruments Performance Tasks Centers
Inquiry/Investigation/Experimentation
Learning Cycle Models, STS
3. Understand that scientific inquiry often involves different ways of thinking, curiosity and the exploration of multiple paths. Cooperative Learning
Mentoring/Apprenticeship/Co-op
Simulations (Computer or role play)
Inquiry/Investigation/Experimentation
Learning Cycle Models
S/T/S, Case Studies
4. Understand that personal integrity, skepticism, openness to new ideas, creativity, collaborative effort and logical reasoning are all aspects of scientific inquiry. Mentoring/Apprenticeship/Co-op
Cooperative Learning
Inquiry/Investigation/Experimentation
Case Studies
Simulations
Learning Cycle Models
S/T/S
5. Employ ethical standards, such as unbiased data collection, honest reporting of results, and respect for living things. Modeling
Discussion
Data Collection Tools
Debate
Learning Cycle Models
S/T/S
6. Employ strict adherence to safety procedures in conducting scientific investigations. Modeling
Performance Tasks

Science Content Standard C

All Alaska students will understand the nature and history of science.

Key Elements Instructional Strategies
Strategies apply to all 8 key elements.
1. Understand how the terms fact, observation, concept, principle, law, and theory are generally used in the scientific community;
2. Know that scientific knowledge is validated by repeating specific experiments which may conclude in similar results;
3. Understand that society, culture, history and environment affect the development of scientific knowledge;
4. Understand that some personal and societal beliefs accept non-scientific methods for validating knowledge;
5. Know that the sharing of scientific discoveries is important in influencing individuals and society and in advancing scientific knowledge;
6. Understand that scientific discovery is often a combination of an accidental happening and observation by a knowledgeable person with an open mind;
7. Understand that major scientific "breakthroughs" link large amounts of knowledge, often building upon the contributions of many scientists and crossing different lines of study; and
8. Understand that acceptance of a new idea depends upon supporting evidence and that new ideas that conflict with beliefs or common sense are often resisted.
Mentoring/Apprenticeship/Co-op
Shadowing
Inquiry/Investigation/
Experimentation
Oral History
Multimedia
Case Studies
Oral History
Interviews/Surveys/Polls
Discussion
Simulations
I Search. We Search

Science Content Standard D

All Alaska students will apply scientific knowledge and skills to make reasoned decisions about the use of science and scientific innovations.

Key Elements Instructional Strategies
1. Apply scientific knowledge and skills to understand issues and everyday events. Field Studies
Service Learning
S/T/S
Learning Cycle Models
2. Understand that scientific innovations may affect our economy, safety, environment, health and society. These effects may be long or short term, positive or negative, expected or unexpected. Science/Technology/Society Projects
Oral History
Case Studies
3. Recommend solutions to everyday problems by applying scientific skills and knowledge. S/T/S
Brainstorming
Heuristics
Case Studies
Simulations (Computer or Role Play )
Formulating Models
4. Evaluate the scientific and social merits of solutions to everyday problems. S/T/S
Case Studies
Simulations (Role Play)
Debate
Formulating Models
5. Participate in reasoned discussion of public policy about scientific innovations. S/T/S
Case Studies
Debate
Simulations (Role Play)
6. Act on their reasoned decisions and evaluate the effectiveness of their actions. S/T/S

Science/Technology/Society Instructional Strategies

What is STS?
Science/Technology/Society (STS) education teaches students to understand science and technology and how it affects their lives and world events. It also prepares students to make critical and responsible decisions for themselves and for society on technological issues. The STS approach is used throughout the United States. The core components of STS instruction are: