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2. Vital Results - Reasoning and Problem Solving

Mathematics

Draft July 1997

QUESTIONING/PROBLEM SOLVING 2.1 TYPES OF QUESTIONS:

Grades K-2, (5-8 year-olds)

Grades 3-5, (8-11 year-olds)

Grades 6-8, (11-14 year-olds)
Students ask a variety of questions. This is evident when students:

2.1 Types of Questions Cross Referenced to Field of Knowledge Standards:

5.1-7.19

Ask:

· Why.

· How things work.

· How did they get done.

· Reflective questions (I wonder, I think).

· Compare/contrast.

· Questions that make connections.

· Ask questions about how things get done and how they work.

· Ask questions to determine why events occur.

· Ask questions that compare and contrast, to determine similarities and differences.

· Ask questions that help make connections within and across fields of knowledge and/or between concepts.

· Ask reflective questions that connect new ideas to personal experience.

· Ask questions to determine if the data necessary to solve the problem is presented.

· Formulate and solve a variety of meaningful problems.

· Extract pertinent information from situations and figure out what additional information is needed.

PROBLEM SOLVING 2.2 PROBLEM SOLVING PROCESS:

Grades K-2, (5-8 year-olds)

Grades 3-5, (8-11 year-olds)

Grades 6-8, (11-14 year-olds)
Students use reasoning strategies, knowledge, and common sense to solve complex problems related to all fields of knowledge. This is evident when students:

2.2 Problem Solving Process Cross Referenced to Field of Knowledge Standards:

5.1-7.19

· Distinguish between extraneous and pertinent information.

· Create and use a variety of strategies and approaches to solving problems and uses or learns approaches that other people use, as appropriate.

· Solve problems in ways that make sense and explain why these ways make sense, e.g., defends the reasoning, explains the solution.

· Create and use a variety of approaches and understands and evaluates those of others.

· Make connections among concepts in order to solve problems.

· Invoke problem solving strategies, such as illustrating with sense-making sketches to clarify situations or organizing information in a table.

· Determine, where helpful, how to break a problem into simpler parts.

· Use algebra, graphing, sound reasoning, and other strategies to solve unknown or undecided quantities.

· Integrate concepts and techniques from different areas of mathematics.

· Work effectively in terms when the nature of the task or the allotted time makes this an appropriate strategy.

· Explore logical reasoning using proportional and spatial reasoning and reasoning from graphs.

2.3 TYPES OF PROBLEMS:

Grades K-2, (5-8 year-olds)

Grades 3-5, (8-11 year-olds)

Grades 6-8, (11-14 year-olds)
Students solve problems of increasing complexity. This is evident when students:

2.3 Types of Problems Cross Referenced to Field of Knowledge Standards:

· Solve problems that are brief, clear, and concise.

· Solve problems in which the information needed for a solution can be organized within a simple system with teacher assistance.

· Solve problems in which the information needed for a solution can be organized within a simple system with assistance. · Solve problems that require processing 3 or more pieces of information.

· Solve problems that are related to diverse topics, including the less familiar.

2.4 IMPROVING EFFECTIVENESS:

Grades K-2, (5-8 year-olds)

Grades 3-5, (8-11 year-olds)

Grades 6-8, (11-14 year-olds)
Students devise and test ways of improving the effectiveness of a system. This is evident when students:

2.4 Improving Effectiveness Cross Referenced to Field of Knowledge Standards:

· Not Applicable · Move beyond a particular problem by making connections, extensions, and/or generalizations; for example students:

    · Explain a pattern that can be used in similar situations.

    · Explain how the problem is similar to other problems he/she has solved.

    · Explain how a solution can be applied to school subjects and in real world situations.

· Explain how the mathematics used in a problem is like other concepts in mathematics.

· Verify and interpret results with respect to the original problem situation.

· Make the solution into a general rule that applies to other circumstances.

· Generalize solutions and strategies to new problem situations.

2.5 MATHEMATICS DIMENSIONS:

Grades K-2, (5-8 year-olds)

Grades 3-5, (8-11 year-olds)

Grades 6-8, (11-14 year-olds)
Students produce solutions to mathematical problems requiring decisions about approach and presentation, so that final drafts are appropriate in terms of these dimensions: understanding, approach, reasoning, observations and extensions, mathematical language, mathematical representation, presentation. This is evident when students:

2.5 Mathematics Dimensions Cross Referenced to Field of Knowledge Standards:

· Develop strategies to solve problems with teacher assistance.

· Develop mathematical language in communicating the solution.

· Use mathematical representation to communicate the solution.

· Use approach and reasoning strategies, and reasoning skills to solve the problem.

· Demonstrate observations, connections, application, extensions, and generalizations.

· Demonstrate use of mathematical language in communicating the solution.

· Demonstrate the use of mathematical representation to communicate the solution through graphs, plots, charts, tables, models and diagrams.

· Show work to support solution. · Demonstrate use of criteria in a clear, logical fashion.

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Last updated: Aug. 12, 1997