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New Jersey Core Curriculum Content Standards

May 1996

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All Students Will Develop Reasoning Ability And Will Become Self-Reliant, Independent Mathematical Thinkers

**Descriptive Statement:** Mathematical reasoning is the critical
skill that enables a student to make use of all other mathematical skills.
With the development of mathematical reasoning, students recognize that
mathematics makes sense and can be understood. They learn how to evaluate
situations, select problem-solving strategies, draw logical conclusions,
develop and describe solutions, and recognize how those solutions can
be applied. Mathematical reasoners are able to reflect on solutions to
problems and determine whether or not they make sense. They appreciate
the pervasive use and power of reasoning as a part of mathematics.

**Cumulative Progress Indicators**

By the end of Grade 4, students:

1. |
Make educated guesses and test them for correctness. |

2. |
Draw logical conclusions and make generalizations. |

3. |
Use models, known facts, properties, and relationships to explain their thinking. |

4. |
Justify answers and solution processes in a variety of problems. |

5. |
Analyze mathematical situations by recognizing and using patterns and relationships. |

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicators 2, 3, and 5 above, by the end of Grade 8, students:

6. |
Make conjectures based on observation and information, and test mathematical conjectures and arguments. |

7. |
Justify, in clear and organized form, answers and solution processes in a variety of problems. |

8. |
Follow and construct logical arguments, and judge their validity. |

9. |
Recognize and use deductive and inductive reasoning in all areas of mathematics. |

10. |
Utilize mathematical reasoning skills in other disciplines and in their lives. |

11. |
Use reasoning rather than relying on an answer-key to check the correctness of solutions to problems. |

Building upon knowledge and skills gained in the preceding grades, and especially demonstrating continued progress in Indicators 2, 5, 8, 9, 10, and 11 above, by the end of Grade 12, students:

12. |
Make conjectures based on observation and information, and test mathematical conjectures, arguments, and proofs. |

13. |
Formulate counter-examples to disprove an argument. |

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