|
Thinking and Reasoning Standards and Benchmarks
Thinking and Reasoning Standard and Benchmarks Standard 1:
Understands and applies the basic principles of presenting an argument
Level III (Grade 6-8)
- Evaluates arguments that are based on quantitative data and mathematical concepts
- Questions claims that use vague references such as "leading experts say..." or are based on the statements of people speaking outside of their expertise (e.g., celebrities)
- Questions conclusions based on very small samples of data, biased samples, or samples for which there is no central sample
- Makes basic distinctions between information that is based on fact and information that is based on opinion
- Identifies and questions false analogies
- Identifies and questions arguments in which all members of a group are implied to possess nearly identical characteristics that are considered to be different from those of another group
- Compares and contrasts the credibility of differing accounts of the same event
Level IV (Grade 9-12)
- Understands that when people try to prove a point, they may at times select only the information that supports it and ignore the information that contradicts it
- Identifies techniques used to slant information in subtle ways
- Identifies the logic of arguments that are based on quantitative data
- Identifies or seeks out the critical assumptions behind a line of reasoning and uses that to judge the validity of an argument
- Understands that to be convincing, an argument must have both true statements and valid connections among them
- Uses tables, charts, and graphs in constructing arguments
- Evaluates the overall effectiveness of complex arguments
Thinking and Reasoning Standard and Benchmarks Standard 2:
Understands and applies basic principles of logic and reasoning
Level III (Grade 6-8)
- Uses formal deductive connectors ("if...then," "not," "and," "or") in the construction of deductive arguments
- Understands that some aspects of reasoning have very rigid rules but other aspects do not
- Understands that when people have rules that always hold for a given situation and good information about the situation, then logic can help them figure out what is true about the situation
- Understands that reasoning by similarities can suggest ideas but cannot be used to prove things
- Understands that people are using incorrect logic when they make a statement such as "if x is true, then y is true; but x isn't true, therefore y isn't true"
- Understands that a single example can never prove that something is true, but a single example can prove that something is not true
- Understands that some people invent a general rule to explain how something works by summarizing observations
- Understands that people overgeneralize by making up rules on the basis of only a few observations
- Understands that personal values influence the types of conclusions people make
- Recognizes situations in which a variety of conclusions can be drawn from the same information
Level IV (Grade 9-12)
- Understands the differences between the formal and informal uses (e.g., in everyday situations) of the logical connectors: "if...then," "not," "and," "or"
- Analyzes the deductive validity of arguments based on implicit or explicit assumptions
- Understands that formal logic is mostly about connections between statements and that these connections can be considered without attention to whether the statements themselves are true or not
- Understands that people sometimes reach false conclusions either by applying faulty logic to true statements or by applying valid logic to false statements
- Understands that logic can be used to test how well any general rule works
- Understands that proving a general rule to be false can be done by finding just one exception; this is much easier than proving a general rule to be true for all possible cases
- Understands that logic may be of limited help in finding solutions to problems if the general rules upon which conclusions are based do not always hold true; most often, we have to deal with probabilities rather than certainties
- Understands that very complex logical arguments can be formulated from a number of simpler logical arguments
- Identifies counter examples to conclusions that have been developed
Thinking and Reasoning Standard and Benchmarks Standard 3:
Effectively uses mental processes that are based on identifying similarities and differences
Level III (Grade 6-8)
- Compares consumer products on the basis of features, performance, durability, and cost, and considers personal tradeoffs
- Selects criteria or rules for category membership that are relevant and important
- Articulates abstract relationships between existing categories of information
- Compares different sources of information for the same topic in terms of basic similarities and differences
Level IV (Grade 9-12)
- Identifies abstract patterns of similarities and differences between information on the same topic but from different sources
- Identifies abstract relationships between seemingly unrelated items
- Identifies the qualitative and quantitative traits (other than frequency and obvious importance) that can be used to order and classify items
Thinking and Reasoning Standard and Benchmarks Standard 4:
Understands and applies basic principles of hypothesis testing and scientific inquiry
Level III (Grade 6-8)
- Understands that there are a variety of ways people can form hypotheses, including basing them on many observations, basing them on very few observations, and constructing them on only one or two observations
- Understands that there may be more than one valid way to interpret a set of findings
- Questions findings in which no mention is made of whether the control group is very similar to the experimental group
- Reformulates a new hypothesis for study after an old hypothesis has been eliminated
Level IV (Grade 9-12)
- Identifies and critiques studies in which data, explanations, or conclusions are presented as the only ones worth considering
- Tests hypotheses statistically
- Presents alternative explanations and conclusions to one's own experiments and those of others
- Critiques procedures, explanations, and conclusions in one's own experiments and those of others
Thinking and Reasoning Standard and Benchmarks Standard 5:
Applies basic trouble-shooting and problem-solving techniques
Level III (Grade 6-8)
- Identifies alternative courses of action and predicts likely consequences of each
- Selects the most appropriate strategy or alternative for solving a problem
- Examines different alternatives for resolving local problems and compares the possible consequences of each alternative
Level IV (Grade 9-12)
- Applies trouble-shooting strategies to complex real-world situations
- Understands that trouble-shooting almost anything may require many-step branching logic
- Engages in problem finding and framing for personal situations and situations in the community
- Represents a problem accurately in terms of resources, constraints, and objectives
- Provides summation of the effectiveness of problem-solving techniques
- Reframes problems when alternative solutions are exhausted
- Examines different options for solving problems of historical importance and determines why specific courses of action were taken
- Evaluates the feasibility of various solutions to problems; recommends and defends a solution
Thinking and Reasoning Standard and Benchmarks Standard 6:
Applies decision-making techniques
Level III (Grade 6-8)
- Identifies situations in the community and in one's personal life in which a decision is required
- Secures factual information needed to evaluate alternatives
- Identifies the values underlying the alternatives that are considered and the criteria that will be used to make a selection among the alternatives
- Predicts the consequences of selecting each alternative
- Makes decisions based on the data obtained and the criteria identified
- When appropriate, takes action to implement the decision
- Analyzes personal decisions in terms of the options that were considered
- Uses a decision-making grid or matrix to make or study decisions involving a relatively limited number of alternatives and criteria
Level IV (Grade 9-12)
- Analyzes current or pending decisions that can affect national or international policy and identifies the consequences of each alternative
- Uses a decision-making grid or matrix to make or study decisions involving a relatively large number of alternatives and criteria advocate
- Evaluates major factors that influence personal decisions
|
Selected Standards and Benchmarks
used by permission:
Copyright
2003 McRel
Mid-continent Research for
Education and Learning
2550 S. Parker Road, Suite 500
Aurora, CO 80014
Telephone: (303) 337-0990
www.mcrel.org/standards-benchmarks
|
