The document discusses the importance of mathematical reasoning and statistics in education, highlighting their roles in problem-solving and understanding real-life scenarios. It emphasizes the need for students to develop skills in conjecturing and questioning data to avoid biased conclusions and prepare for advanced degrees. The content includes practical applications and pedagogical strategies for teachers to enhance student learning.

1. Sarel van Greunen
Mathematics and AP Mathematics Teacher
Statistics and
Mathematical Reasoning

2. What is Mathematical reasoning?
• Solving problems
• Deciphering real-life scenarios in a Mathematical way
• Making sense of Mathematics

3. How does Statistics fit in here?
• Lay-man’s definition of Statistics:
Making sense of numbers
• Statistics teaches the basic principle of conjecturing

4. Mathematical Reasoning
Foundation
Walls
Windows
Doors
Roof
Definitions
Methods
Axioms
Conjectures
Properties
Statements/Theorems
Reason
Problem solving

5. Conjecture
• What do you think of when you see the following pictures?
https://img.wonderhowto.com/img/31/86/63550363988846/0/do-
makeup-bruised-halloween-black-eye-bloody-nose.1280x600.jpg
http://lafdatv.com/wp-content/uploads/2016/07/wife-final.jpg

6. Conjecture
• Conjecturing is a crucial skill
• Help learners to look at historic data AND make predictions about
future events
• Teach students to not make conclusions based on biased data
• Teach students the process of questioning data
• Train them the basic skills needed for Masters and Doctorates
degrees.