Standards Database Logo
Home | Browse | Search | Purpose | History | Process | Acknowledgment| Reference

 


 


Topic: Logical Reasoning 

Thinking and Reasoning

 Standard 1.  Understands and applies the basic principles of presenting an argument
  Level IV (Grade 9-12)
   Benchmark 2.Develops logical arguments that are based on quantitative data
    Knowledge/skill statements
     1.Develops logical arguments
     2.Develops arguments based on quantitative data
 Standard 2.  Understands and applies basic principles of logic and reasoning
  Level III (Grade 6-8)
   Benchmark 2.Understands that some aspects of reasoning have very rigid rules but other aspects do not
    Knowledge/skill statements
     1.Understands that some aspects of reasoning have very rigid rules
     2.Understands that some aspects of reasoning do not have rigid rules
   Benchmark 3.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
    Knowledge/skill statements
     1.Understands that when people have rules that always hold true for a situation, logic can help them figure out what is true about the situation
     2.Understands that when people have good information about a situation, logic can help them figure out what is true about the situation
   Benchmark 4.Understands that reasoning by similarities can suggest ideas but cannot be used to prove things
    Knowledge/skill statements
     1.Understands that reasoning by similarities can suggest ideas
     2.Understands that reasoning by similarities cannot be used to prove things
   Benchmark 5.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"
    Knowledge/skill statements
     1.Understands incorrect logic
     2.Knows that the statement "if x is true, then y is true; but x isn’t true, therefore y isn’t true" is an example of incorrect logic
   Benchmark 6.Understands that a single example can never prove that something is true, but a single example can prove that something is not true
    Knowledge/skill statements
     1.Understands that a single example can never prove that something is true
     2.Understands that a single example can prove that something is not true
  Level IV (Grade 9-12)
   Benchmark 1.Understands the differences between the formal and informal uses (e.g., in everyday situations) of the logical connectors: "if...then," "not," "and," "or"
    Knowledge/skill statements
     1.Understands formal uses of logical connectors
     2.Understands informal uses of logical connectors
   Benchmark 3.Understands the difference between formal and informal uses (e.g., in everyday situations) of the terms "sufficient" and "necessary"
    Knowledge/skill statements
     1.Understands the formal uses of the term "sufficient"
     2.Understands the informal uses of the term "sufficient"
     3.Understands the formal uses of the term "necessary"
     4.Understands the informal uses of the term "necessary"
   Benchmark 4.Understands the formal meaning of the logical quantifiers: "some," "none," and "all"
    Knowledge/skill statements
     1.Understands the formal meaning of the logical quantifier "some"
     2.Understands the formal meaning of the logical quantifier "none"
     3.Understands the formal meaning of the logical quantifier "all"
   Benchmark 5.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
    Knowledge/skill statements
     1.Understands that formal logic is mostly about connections between statements
     2.Understands that in formal logic connections between statements can be considered without attention to whether the statements themselves are true or not
   Benchmark 6.Understands that people sometimes reach false conclusions either by applying faulty logic to true statements or by applying valid logic to false statements
    Knowledge/skill statements
     1.Understands that when using logical reasoning people sometimes reach false conclusions
     2.Understands that false conclusions may be reached by applying faulty logic to true statements
     3.Understands that false conclusions may be reached by applying valid logic to false statements
   Benchmark 7.Understands that a reason may be sufficient to get a result but may not be the only way to get the result (i.e., may not be necessary), or a reason may be necessary to obtain a result but not sufficient (i.e., other things are also required; some reasons may be both necessary and sufficient)
    Knowledge/skill statements
     1.Understands that a reason may be sufficient to get a result but may not be the only way to get the result
     2.Understands that a reason may be necessary to obtain a result but not sufficient
     3.Understands that some reasons may be both necessary and sufficient to get a result
   Benchmark 8.Understands that logic can be used to test how well any general rule works
    Knowledge/skill statements
     1.Knows that it is important to be able to test how well a general rule works
   Benchmark 9.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
    Knowledge/skill statements
     1.Understands that proving a general rule to be false can be done by finding just one exception
     2.Understands that proving a general rule to be false is easier than proving a general rule to be true
     3.Understands that proving a general rule to be true must be done for all possible cases
   Benchmark 10.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
    Knowledge/skill statements
     1.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
     2.Knows that most often in problem-solving one has to deal with probabilities rather than certainties
   Benchmark 12.Understands that very complex logical arguments can be formulated from a number of simpler logical arguments
    Knowledge/skill statements
     1.Understands complex logical arguments
     2.Understands simple logical arguments
   Benchmark 13.Identifies counter examples to conclusions that have been developed
    Knowledge/skill statements
     1.Understands the concept of a counter example