Using Gizmos to Stimulate Proof in Mathematics : Using Gizmos to Stimulate Proof in Mathematics Dr. Evan Glazer
eglazer@rvgs.k12.va.us
Director Roanoke Valley Governor’s School for Science and Technology Roanoke, Virginia
Conceptions of Proof : Conceptions of Proof
Conceptions of Proof : Conceptions of Proof
Conceptions of Proof : Conceptions of Proof
Why Proof? : Why Proof? The deception of visualization Gwyneth Paltrow and Jake Gyllenhaal star in Proof, in theaters September 16
Why Proof? : Why Proof? The deception of visualization What is the equation represented in the graph?
Why Proof? : Why Proof? The deception of visualization
NCTM added ‘proof’ in its 2nd edition of the Standards Gwyneth Paltrow and Jake Gyllenhaal star in Proof, in theaters September 16
Why Proof? : Why Proof? NCTM added ‘proof’ in its 2nd edition of the Standards
Think inductively: Make and investigate mathematical conjectures
Show deductively: Why is this happening?
Why Proof? : Why Proof? The deception of visualization
NCTM added ‘proof’ in its 2nd edition of the Standards
Abstract thinking and formal logic
Show incorrect mathematics
Gwyneth Paltrow and Jake Gyllenhaal star in Proof, in theaters September 16
Slide10 : "Proof" that One Equals Two
Maximize Area : Maximize Area What is the relationship between the dimensions of a rectangle with the greatest possible area given a restricted perimeter? http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=72
Minimize Perimeter : Minimize Perimeter What is the relationship between the dimensions of a rectangle with the smallest possible perimeter given a restricted area? http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=73
Concurrent Lines, Medians, and Altitudes : Concurrent Lines, Medians, and Altitudes How do you know the angle bisectors intersect at the center of an inscribed circle?
How do you know the perpendicular bisectors intersect at the center of a circumscribed circle? http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=177
Inscribing Angles : Inscribing Angles What can you conclude about inscribed angles?
How do you know it’s true for all cases? http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=184
Quadratics in Polynomial Form : Quadratics in Polynomial Form Show the vertex trail.
Vary ‘a’ and look for a pattern.
Find the equation of the locus in terms of b and c
Repeat by varying ‘b’ and then varying ‘c’ http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=81
Using Gizmos to Stimulate Proof in Mathematics : Using Gizmos to Stimulate Proof in Mathematics Dr. Evan Glazer
eglazer@rvgs.k12.va.us
Director Roanoke Valley Governor’s School for Science and Technology Roanoke, Virginia