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Alaska Department of Education & Early Development
Mathematics and Science Education

Chapter 4: Content

Shifting the Content of Mathematics and Science to Reach All Students
How Mathematics and Science Content Standards Relate to Alaska 2000 Goals
Alaska Content Standards in Mathematics
Alaska Content Standards in Science
Other Choices for Developing Criteria or Benchmarks

The Alaska 2000 Education Initiative restructures Alaskan schools to prepare students for the changing world in this technological age. The Alaska Content Standards were created to describe acceptable student performance. They are intended to raise the achievement of all students while ensuring that all students have equal educational opportunity. They are not intended to standardize the educational process in Alaska. Rather, they are designed as guideposts to help school districts define what they want their students to know, be able to do, and be committed to in the 21st Century.

Local curriculum committees are expected to apply these content standards as they determine the curriculum guidelines for their schools and school districts. The curriculum decisions made locally will go far beyond the content standards. They will involve not only questions of content, or what is taught, but also extremely important decisions about how to structure, pace, present, and assess the teaching of that content.

This chapter reviews content considerations in light of the Alaska 2000 Goals and the Alaska Content Standards for Mathematics and Science. It provides a response to questions of how science and mathematics education can contribute to accomplishment of the Alaska 2000 Goals and provides examples of how these outcomes might be achieved through continuums of experiences and expectations.

Shifting the Content of Mathematics and Science to Reach All Students

The new images of math and science content focus on developing mathematical and scientific reasoning at all levels of schooling. The key elements of the Alaska Content Standards help define what this reasoning will look like for students. The Benchmarks provide specific examples of developmentally appropriate experiences for students at specific levels.

Math

The major content changes in math include an emphasis at each grade level on problem solving, mathematical reasoning, and communication skills to express our mathematical reasoning. At each grade level students will develop their concepts of numbers, operations on numbers, measurement, estimation and computation, patterns/functions/relations, geometry, and statistics/probability through problems and projects that require complex, integrated, and applied mathematical reasoning. This implies that students will experience each strand of the key elements at each grade level. Students at all grade levels will develop robust and concrete understandings of the ways that number systems work, how the basic operations are applied in both simple and complex mathematical reasoning, how they represent real patterns in the physical world, how we represent those patterns as functions and algebraic terms, how you can use these algorithms to solve more complex problems than the simple problems and patterns, and how you can determine whether or not data that is collected is a result of chance or is a result of a cause/effect relationship. These stimulating discoveries happen in developmentally appropriate ways at each grade level for all students. Students who need more time to develop basic computational skills will not be prevented from engaging in these complex and rewarding tasks. Instead they will use manipulatives, calculators, and computers to do speedy calculations as they use their reasoning skills to determine what types of operations are appropriate for the problem at hand. Computational skills will still be an expected outcome of instruction, but students will realize that they can create their own patterns of computations that represent their own lines of reasoning. This approach acknowledges that some students construct computational knowledge more slowly than other students. Often students require a meaningful application before they are motivated to succeed at computational skills.

The following lists summarize the major shifts in the content of math curriculum:

Math Content Standard A: Content

• All children are capable of learning at high levels.
• All mathematical reasoning requires a basic understanding of numeracy, measurement tools, exact or estimated computations, how the symbols relate to physical patterns, geometric relationships, and the relative certainty of predictions that we can make. These skills should be taught side by side every year of school.
• Algebraic, geometric, and statistical thinking require application of the basic numeracy concepts. If students understand how number systems work and what they represent they will apply these basic understandings at every level of mathematics. The content of all math courses should reflect and build upon these connections.

Math Content Standard B Problem Solving

• The underlying purpose of math is to use pattern recognition skills to solve problems.
• Students should learn to flexibly try several problem solving strategies in search of a solution.

Math Content Standard C: Communication

• Mathematical reasoning can be communicated with concrete objects, pictures of concrete objects, oral and written language, and mathematical symbols. Students should learn to use all of these modalities to explain their mathematical thoughts.
• Children learn mathematical reasoning better in a community of learners that requires them to explain their thoughts and listen to other's explanations.

Math Content Standard D: Reasoning

• Students should be asked to perform complex mathematical reasoning by extending the logic from simple patterns and models to more complex situations.
• By strategically applying different types of logic students will learn to recognize which type of logic is being used in different situations and respond accordingly.

Math Content Standard E: Connections

• Mathematical reasoning can be used to solve problems in all areas of life.

Science

The major content changes in science imply that all students are capable of learning complex concepts if provided with developmentally appropriate experiences. All students will study all of the disciplines of science in an integrated approach. Science content will place greater emphasis on the inquiry skills (science process skills and reasoning) at the expense of time spent memorizing science facts. Students will learn to use their skills of inquiry to construct deeper explanations for physical phenomena and to find and verify facts. Therefore they will encounter fewer concepts and facts in school, but they will develop skills for lifelong synthesis, analysis, and application of scientific information. They will spend more time determining how to interpret information that is provided to them and determining what perspectives are represented by different data collection methods and interpretations. They will develop an understanding of the historical, social, cultural, and environmental contexts which influence our interpretation and application of scientific data, and they will have many opportunities to apply scientific and technological knowledge to solve current and real problems. They will see many different types of people using scientific thinking in a variety of ways to satisfy a wide variety of needs.

The following lists summarize the major shifts in the content of science curriculum:

Science Content Standard A: Content

• All children are capable of learning at high levels.
• Schools will provide greater emphasis on concepts and process skills, less emphasis on specific facts.
• Less is better; in-depth study enhances learning.

Science Content Standard B: Inquiry

• If students first learn to think critically and analytically, they can develop strategies to learn the basic facts. Most scientific work uses the process skills of science to deepen our understanding of systems and phenomena.

Science Content Standard C: Nature and History of Science

• People learn most rapidly in a community of learners.
• People perceive experiences differently; this variety strengthens our understanding of physical phenomena; we can learn to appreciate those differences.

Science Content Standard D: Applications and Technology

• Learning is more meaningful when it is integrated into the world outside of school.
• Mastering technology will help students function in today's world.

• Math Performance Standards. indicates PDF Files which require Adobe Acrobat Reader.
  This free software is available here.

• Math Performance Standards with Glossary: These are the same Math Standards as above but in Word 97 format with a glossary attached. Defined words are in bold and are followed by a number in parentheses. Click on the number and you will be taken to the glossary definition.

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Last modified on: Nov. 28, 2000