Geometry CC PD 2013

Reflections of Geometry CC Summer PD

Greenville County Teachers Geometry Common Core PD experiences with Carnegie Learning educator Janet Tomlinson and Valerie Muller.


Standards of Mathematical Practices with Teacher Summary's

Teachers not only summarized the SMP's but also evaluated each other on whether the summaries were complete. There was also a discussion and reflection about each of the standards.


Constructions

Teachers performed constructions with patty paper, a mirra, compass, and Geometers Sketchpad

Teachers were addressing (SMP #5) Use appropriate tools strategically.


Quadrilaterals

The following images show teacher explorations of Quadrilaterals with Geometers Sketchpad


Geometers Sketchpad Investigations

Triangle Center Investigations

Word Wall

Can you create a picture from vocabulary?

Making Conjectures from Quadrilateral Investigations

Teachers made some discoveries with Geometers Sketchpad and shared their conjectures with the class.


Euler Line Investgations

Teachers explored the relationships with the various triangle centers

Teachers noted there are many mathematical concepts that can be tied in such as the ratio of the orthocenter-centroid to centroid-circumcenter. Other concepts were discussed such as slope and writing a function.


Coordinate Geometry

Teachers explored properties of quadrilaterals and demonstrated proof of their reasoning. The sticky notes show how groups were assessing each other using yellow for a positive critique and blue for a negative. "Warm and cool" as it was described. A suggestion was given to have the teacher go back and evaluate student comments to avoid groups that gave an incorrect assessment to avoid mean or too negative critiques.


Teachers created proofs from problems to validate conjectures to theorems. Teachers also were finding coordinate patterns based on transformations of polygons. Some problems required tools such as the mirra, patty paper, and compass.


The great benefit of the technology of Geometers Sketchpad is not only the ability to create the geometry but also to manipulate, change, and investigate your conjectures.

Compositions of Transformations

Using tracing paper, teachers looked for various solutions by performing transformations.


Lessons and Activities

Lessons Learned

Deepen students thinking with higher order questions.


  • What is it?
  • How do I find it?
  • Why do I care?
  • Where is it located?
  • Why is it important?
  • Show me your evidence.
  • How does this connect to what you already know?
  • What new questions do you have?
  • What is the relationship?
  • Is there a ...?
  • Is slope important...?
  • How many different ways...?
  • How did you know?


-Our standards are not a checklist or a to do, but ideas that are to be connected and show relationships.


-Students need to know how to use tools strategically and know there is more than one tool they can use to solve a problem. i.e. patty paper, mirra, compas, technology.


-Technology drives what students can do today. Students are able to explore more now.

-Students are more empowered with tech now more then ever (from beyond the classic setting with just compass and straightedge)

-With tech you can do so much more not just pressing buttons that allows room for discovery.

-You want your students to improve their critical thinking from whenever you get them.

-Teachers complain: "these kids don't think." If you have them a whole year, the following year teacher should see improved thinking and reasoning.


Encourage further thinking with

-I notice...

-I wonder...



-Rigor in Geometry goes way beyond just solving a quadratic equation, instead ask students, "What is the system of equations that defines the quadrilateral?"

-Write the equation of the perpendicular lines for this...


-All students need hands on learning from low math skill level to advanced.