National Standards

MATH STANDARDS

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each;
Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments;
Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable;
Understand histograms, parallel box plots, and scatterplots and use them to display data;
Compute basic statistics and understand the distinction between a statistic and a parameter.

Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions;
Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference;
Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions;
Understand how basic statistical techniques are used to monitor process characteristics in the workplace.

Organize and consolidate their mathematical thinking through communication;
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
Analyze and evaluate the mathematical thinking and strategies of others;
Use the language of mathematics to express mathematical ideas precisely.

CONTENT STANDARD A: As a result of activities in grades 9-12, all students should develop

Abilities necessary to do scientific inquiry

Understandings about scientific inquiry

Students should formulate a testable hypothesis and demonstrate the logical connections between the scientific concepts guiding a hypothesis and the design of an experiment. They should demonstrate appropriate procedures, a knowledge base, and conceptual understanding of scientific investigations.

Designing and conducting a scientific investigation requires introduction to the major concepts in the area being investigated, proper equipment, safety precautions, assistance with methodological problems, recommendations for use of technologies, clarification of ideas that guide the inquiry, and scientific knowledge obtained from sources other than the actual investigation. The investigation may also require student clarification of the question, method, controls, and variables; student organization and display of data; student revision of methods and explanations; and a public presentation of the results with a critical response from peers. Regardless of the scientific investigation performed, students must use evidence, apply logic, and construct an argument for their proposed explanations.

A variety of technologies, such as hand tools, measuring instruments, and calculators, should be an integral component of scientific investigations. The use of computers for the collection, analysis, and display of data is also a part of this standard. Mathematics plays an essential role in all aspects of an inquiry. For example, measurement is used for posing questions, formulas are used for developing explanations, and charts and graphs are used for communicating results.

FORMULATE AND REVISE SCIENTIFIC EXPLANATIONS AND MODELS USING LOGIC AND EVIDENCE.

Student inquiries should culminate in formulating an explanation or model. Models should be physical, conceptual, and mathematical. In the process of answering the questions, the students should engage in discussions and arguments that result in the revision of their explanations. These discussions should be based on scientific knowledge, the use of logic, and evidence from their investigation.

This aspect of the standard emphasizes the critical abilities of analyzing an argument by reviewing current scientific understanding, weighing the evidence, and examining the logic so as to decide which explanations and models are best. In other words, although there may be several plausible explanations, they do not all have equal weight. Students should be able to use scientific criteria to find the preferred explanations.

Students in school science programs should develop the abilities associated with accurate and effective communication. These include writing and following procedures, expressing concepts, reviewing information, summarizing data, using language appropriately, developing diagrams and charts, explaining statistical analysis, speaking clearly and logically, constructing a reasoned argument, and responding appropriately to critical comments.

CONTENT STANDARD C: As a result of their activities in grades 9-12, all students should develop understanding of

Interdependence of organisms

Organisms both cooperate and compete in ecosystems. The interrelationships and interdependencies of these organisms may generate ecosystems that are stable for hundreds or thousands of years.

Living organisms have the capacity to produce populations of infinite size, but environments and resources are finite. This fundamental tension has profound effects on the interactions between organisms.
Human beings live within the world's ecosystems. Increasingly, humans modify ecosystems as a result of population growth, technology, and consumption. Human destruction of habitats through direct harvesting, pollution, atmospheric changes, and other factors is threatening current global stability, and if not addressed, ecosystems will be irreversibly affected.

This project is supported, in part,
by the

Opinions expressed are those of the authors
and not necessarily those of the National Science Foundation.