Standard 1: Mathematics as Problem Solving
In grades 5-8, the mathematics curriculum should include numerous experiences
with problem solving as a method of inquiry and application so that students
can:
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Use problem solving approaches to investigate and understand mathematical
content
Benchmarks 12A (Habits of Mind: Values and Attitudes)
Grades 3-5, page 286
Keep records of their investigations and observations and not change
the records later.
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Formulate problems from situations within and outside mathematics
Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Grades 3-5, page 11
Scientists’ explanations about what happens in the world come partly
from what they observe, partly from what they think. Sometimes scientists
have different explanations for the same set of observations. That usually
leads to their making more observations to resolve the differences.
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Develop and apply a variety of strategies to solve problems, with emphasis
on multi-step and non-routine problems
Benchmarks 2A (The Nature of Mathematics: Patterns and Relationships)
Grades 6-8, page 28
Usually there is no right way to solve a mathematical problem; different
methods have different advantages and disadvantages.
Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Grades 3-5, page 11
Scientific investigations may take many different forms, including
observing what things are like or what is happening somewhere, collecting
specimens for analysis, and doing experiments. Investigations can focus
on physical, biological, and social questions.
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Verify and interpret results with respect to the original problem situation
Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Grades 6-8, page 12
If more than one variable changes at the same time in an experiment,
the outcome of the experiment may not be clearly attributable to any one
of the variables. It may not always be possible to prevent outside variables
from influencing the outcome of an investigation (or even to identify all
of the variables), but collaboration among investigators can often lead
to research design that are able to deal with such situations.
Benchmarks 1B (The Nature of Science: Scientific Inquiry)
Grades 6-8, page 12
What people expect to observe often affects what they actually do observe.
Strong beliefs about what should happen in particular circumstances can
prevent them from detecting other results. Scientists know about this danger
and take steps to try and avoid it when designing investigations and examining
data. One safeguard is to have different investigators conduct independent
studies of the same question.
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Generalize solutions and strategies to new problem situations
Benchmarks 3B (The Nature of Technology: Design and Systems)
Grades 3-5, page 50
The solution to one problem may create other problems.
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Acquire confidence in using mathematics meaningfully
Benchmarks 1C (The Nature of Science: The Science Enterprise)
Grades 3-5, page 1
Science is an adventure that people everywhere can take part in, as
they have for many centuries.
Benchmarks 1C (The Nature of Science: The Science Enterprise)
Grades 6-8, page 17
Important contributions to the advancement of science, mathematics,
and technology have been made by different kinds of people, in different
cultures, at different times.