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2. Vital Results - Reasoning and Problem Solving

Problem Solving

Draft July 1997

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

 · Identify problem.

· Use information from reliable sources, including prior knowledge, observation, and trying things out.

· Identify patterns.

· Decide on course of action, solution.

· Explain solution.

· Demonstrate results using drawings, manipulative, etc.

 · Determine characteristics of the problems.

· Use information from a variety of reliable sources including text, media, etc.

· Use a variety of appropriate approaches to solve problems.

· Reflect justify and verify answers and solutions.

· Use manipulative, models, drawings, charts, tables and webs and so on to model problems.

· Transfer strategies from one situation to others.

· Gather information from observation and experimentation.

· Distinguish fact and opinion.

· Identify patterns and connections.

 · Respond to information by distinguishing and articulating fact from opinion.

· Select, apply and justify appropriate methods and tools.

·Find meaning in patterns and identify relevant connections.

· Evaluate approaches for effectiveness and make accurate adjustments.

· Consider, test, and justify more than one solution.

· Make valid generalizations.

· Formulate a strategy for solving a problem using a series of steps.

· Use charts, graphs, models etc. to support solution.
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:

5.1-7.19

 · Solve, clear, brief, and concise problems. · Solve problems that require processing several pieces of information.

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

· Identify possible factors and present reasonable solutions to problems.

· Sort out pertinent information.

 · Solve problems by integrating information from several, reliable resources.

· Solve problems that have more than one possible solution.
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 (e.g. transportation, plant life cycle, respiratory system). This is evident when students:

2.4 Improving Effectiveness Cross Referenced to Field of Knowledge Standards:

5.1-7.19

 · Determine the existence of a problem within a system.

· Explore possible solutions.

 · Identify casual relationships within a system.

· Evaluate the effectiveness of a system.

Design, implement and evaluate the effects of possible improvements.

 · Understand and apply a continuous improvement strategy to a system. Within this strategy, students should: Make changes and monitor their effects over time. Identify further possible improvements. Implement and evaluate results.
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, and presentation. This is evident when students:

2.5 Mathematics Dimensions Cross Referenced to Field of Knowledge Standards:

7.2-7.3, 7.6-7.10

 · Demonstrate an understanding of the problem.

· Explore possible solutions.

· Present a possible solution in narrative, visual, musical, kinesthetic, or mathematical form.

 · Use strategies and reasoning skills to problem solve.

· Demonstrate observations, connections and begin to use applications, extensions, and generalizations.

· Demonstrate use of mathematical language in communicating the solution.

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

· Solution support the correct answer.

· Demonstrate use of above criteria in a clear, logical fashion.

 · Use and defend a variety of strategies and approaches.

· Determines how to break a complex problem into simpler parts.

· Integrates concepts and techniques from different areas of mathematics.

· Uses and invents a variety of approaches and understands and evaluates those of others.

· Formulates conjectures and argues (short of formal proof) why it must be or seems true.

· Makes sensible, reasonable estimates.

· Make generalizations and/or connections to real world applications.
PROBLEM SOLVING Grades K-2, (5-8 year-olds) Grades 3-5, (8-11 year-olds) Grades 6-8, (11-14 year-olds)
2.2 PROBLEM SOLVING PROCESS: Students use reasoning strategies, knowledge, and common sense to solve complex problems related to all fields of knowledge.

2.3 TYPES OF PROBLEMS: Students solve problems of increasing complexity.

2.4 IMPROVING EFFECTIVENESS: Students devise and test ways of improving the effectiveness of a system (e.g. transportation, plant life cycle, respiratory system).

2.5 MATHEMATICS DIMENSIONS: Students produce solutions to mathematical problems requiring decision about approach and presentation so that final drafts are appropriate in terms of these dimensions: understanding, approach, reasoning, observations and extensions, mathematical language, mathematical.

Examples of Classroom Activities for Standard

2.2,

2.3,

2.4,

2.5.

This will vary from team to team.

 Mathematic/problem solving

Scientific experimentation

Art projects

Team meetings/class discussions

Projects across content areas

 Math portfolio problem solving

Science experiments/projects

Scientific method

Art projects

Team meetings/class discussions

Projects across content areas

Math program

Problem solving groups

Math/science write-ups

Self assessments

Theme studies

Team meetings

Vt. Math portfolio system

Class discussions Science experiments

Art projects

Projects across content areas

Examples of Assessment Strategies for Standards

2.2,

2.3,

2.4,

2.5

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Last updated: Aug. 12, 1997