Process Standard: Reasoning and Proofs

1
Process StandardReasoning and Proofs

• Instructional programs from prekindergarten
  through grade 12 should enable all students to
• recognize reasoning and proof as fundamental
  aspects of mathematics
• make and investigate mathematical conjectures
• develop and evaluate mathematical arguments and
  proofs
• select and use various types of reasoning and
  methods of proof.

2
Standards

• Instructional programs from pre-kindergarten
  through grade 12 should enable all students to
• Recognize reasoning and proof as fundamental
  aspects of mathematics
• Make and investigate mathematical conjectures
• Develop and evaluate mathematical conjectures
• Select and use various types of reasoning and
  methods of proof

3
The habit of asking why is essential for students
to develop sound mathematical reasoning (p. 344).
4
Reasoning Proof Activities

• Carpet Square Maze
• The Border Problem

5
What makes something a proof?

• Convince yourself
• Convince a friend
• Convince your enemy

6
Difference between mathematical proof and
statistical arguments

• It is important that students recognize the
  difference between a statement that is verified
  by mathematical proof (i. e., a theorem) and one
  that is verified empirically using statistical
  arguments.
• Most mathematical theorems have a (sometimes
  hidden) quantifier, for every.
• The angle sum of every triangle in Euclidean
  geometry is 180 degrees.
• Men are taller than women.

7
Assignment

• Read the content of pgs. 19-22 of TLHSM
• Work How Many Oranges?
• Answer Question 6, pg. 24 of TLHSM
• Your Mathematics Story
• Will be due next class meeting

8
Levels Of Demand

• Memorization (low level)
• Procedures without connections (low level)
• Procedures with connections (high level)
• Procedures with connections (high level)

9
Assignment

• Answer questions 2, 10, 15 on pgs. 23-27 of
  TLHSM
• For 10, provide web address and print-out of
  what you find in addition to the written
  responses