1. Using Technology to Connect Real-World Data with Science and Math in Middle School Lori Andersen, MSEd, NBCT The College of William & Mary

2. Why? Mathematics curriculum for students gifted in mathematics should emphasize: ◦ depth over breadth ◦ concepts over facts ◦ real-world problems ◦ higher order reasoning ◦ Interdisciplinary connections ◦ metacognition ◦ inquiry-based learning ◦ technology tools

3. The problem Accelerated math instruction is offered BUT often does not incorporate elements of best practice in curriculum design for gifted learners. Appropriate instruction for gifted learners must offer increased depth and complexity.

4. Middle School Math Many gifted students take Algebra I in middle school. These courses should be enriched with activities that ◦ Increase depth of knowledge ◦ Use inquiry learning ◦ Make connections to other subjects and the real-world

5. Algebra I Connections to Physics Linear Functions ◦ Motion at constant speed Quadratic Functions ◦ Uniformly Accelerated Motion ◦ Freefall Multiple representations of data & functions

6. Theme Mathematical models are used to make predictions about the state of a system. To select an appropriate model, we must understand function types. Develop understanding of function types through hands-on, kinesthetic activities.

7. Developing a “feel” for functions Allowing students to be the objects of study ◦ Kinesthetic connections between representations ◦ Make abstract graphical representations more concrete ◦ Attach physical meaning to numerical coefficients and equation forms

8. “Playing” with mathematics Real-world data collected by students Use of technology allows students to easily try out different types of functions Critical evaluation of “goodness of fit” of function models

9. Sample Activity -1 Exploring Functions http://andersen-ncnc2011.wmwikis.net/ ◦ Students use motion detector to explore the meanings and multiple representations of slope and y-intercept. ◦ Investigation of data to discover differences between function shapes and form of equations. ◦ Connections to physical science – velocity and acceleration

10. Vocabulary Building DefinitionCharacteristics Examples Non-Examples Center for Gifted Education, The College of William and Mary, 2009 Linear Model

11. Sample Activity - 2 Playing with Parabolas ◦ Students use an Excel spreadsheet to explore the relationships between the equation and graph representations of quadratics. ◦ What do the coefficients mean? How do they affect the graph?

12. Sample Activity - 3 Video Analysis of Ball Toss ◦ Students examine data from motion in a video clip. Which model is the best for this data? ◦ Where will the shuttle be at t = 1 second? At t = 2 seconds? ◦ What are the limitations of this model?

13. Sample Activity - 4 Video Analysis of Shuttle Launch ◦ Students examine data from motion in a video clip. Which model is the best for this data? ◦ Where will the shuttle be at t = 4 seconds? At t = 10 seconds? ◦ What are the limitations of this model?

14. Vocabulary Building DefinitionCharacteristics Examples Non-Examples Center for Gifted Education, The College of William and Mary, 2009 Quadratic Model

15. Taking it farther Other function types – the possibilities are endless Analysis of motion in the movies Other types of data – different meanings of slope

16. Technologies Data Logging Software ◦ Logger Pro 3.5 Software  http://www.vernier.com/soft/lp.html http://www.vernier.com/soft/lp.html ◦ Tracker (open source)  http://www.cabrillo.edu/~dbrown/tracker/ http://www.cabrillo.edu/~dbrown/tracker/ Ultrasonic motion sensor ◦ http://www.vernier.com/go/gomotion.html http://www.vernier.com/go/gomotion.html Spreadsheet software Graphing Calculator