2. Why do I, as a middle grades mathematics teacher, need to know about calculus and analytic geometry? Kara Fisher

3.  Scenario: Based on the CBR graphing activity from June 26 At the end of a two day class activity with the CBR, students ask :  Why do we need to know this? Will this be on the EOG?  Why students what a good question. We are learning about what the graphs represent. We have talked about how each dip and curve mean a change in rate or speed.  Right, Ms. Fisher. We walked at different speeds to represent the changes in the graph.

4.  Now if you want to know how fast you were walking at a specific point on the curve of the graph, you would find the derivative. That is what you will learn about in Calculus.  The derivative? Can you give us an example? http://www.ima.umn.edu/~arnold/graphics. html http://www.ima.umn.edu/~arnold/graphics. html  Can you see how understanding graphs now will help you in finding derivatives in Calculus?  That looks cool! I can’t wait for Calculus!

5. Good future calculus student Build a solid foundation Provide meaningful experiences Use imagery and concept building activities Make connections to higher level mathematics

6. Use of meaningful activities with class discussions Build foundation for derivatives Make connections to higher level mathematics Slope/ graph understandings “These experiences may go a long way in helping our students become more successful in graphing and interpreting functions in the classroom and in real-world context.” Pilipczuk, Graphing functions Article support “I think I would not have been as afraid or confused in calculus if my middle grades teacher would have at least mentioned or done a brief overview of calculus for me.” By, Julie Rao Colleague support

7. Non-routine problem solving “Thickening” student understanding by “folding back” Extensive group work with community discussions Building skills needed for more complex math situations Article support “…folding back again and again to enable them (students) to build broader, but also more sophisticated or deeper understanding.” (Pirie and Kieren) “teacher… becomes a part of the mathematical learning community.” (Listening to Students) Colleague support I think this is powerful to acknowledge because many of our students need the same support to be successful in math. That being said, I think I am realizing part of the reason for needing to know about calculus and analytic geometry as a middle grades math teachers is to be able to provide a great support system for our students as they progress in their math classes. By, Kelly Nelson

8. Imagery/concept building activities Encourage visualization and drawing of work Use of manipulatives Demonstrations Use of visuals Building blocks for geometry and calculus Article support “Imaging is an important component in the development of what the Standards calls mathematical power”. “Students who reason from dynamic images tend to be powerful mathematics students.” Math Connections: Spatial Sense and Mathematical Power, Reynolds. Colleague support “I think that using manipulatives and imagery is key in helping to build a stronger foundation in math for our middle grades students.” By, Kelly Nelson