Self-Differentiation via Math Projects

1. Self-Differentiation via Math Projects by Mimi Yang MYP and IB Math Teacher BBIS Math Department Chair presented at AGIS 2013 mimi.yang@bbis.de http://untilnextstop.blogspot.com

2. Imagine “Kevin”… Busy parents Weak math skills Very social / chatty / active Low effort “Has potential” “I don’t like math” Reaching the bottom performers, especially in mathematics, is a challenge at all schools.

3. Obstacles in teaching math to that “bottom” group • Student Motivation • Relevance of topics • Accessibility of abstract topics • Retention of Knowledge • Negative history with math topics

4. Projects as part of the solution Why do projects? • Leverage positive peer pressure • Teach valuable meta-skills/habits of mind/approaches to learning • “Re-package” old, abstract concepts • Incorporate skills practice in a non- repetitive, non-threatening manner • Connect math to student interests • or a tangible product • Allow the more advanced students to incorporate more advanced math

5. Self-differentiation via Projects Inspiration: Renaissance project from an art class • 1. Students watch an introductory video about the Renaissance period • 2. Each student defines their own project – goals, final product, and necessary resources – each student chooses something • appropriate to their own skills level and interest! • 3. Students look through teacher’s provided resources; use the web • 4. Students start first iteration of project based on resources • 5. Students receive on-going feedback, keep written log of progress • 6. Refine, repeat, until final product is complete and polished

6. The Question: Is math really that different from art? How can we structure math projects in such a way that there is a common skills baseline, but still allow students to self-differentiate based on their interests and their own motivation?

7. Project Framework Role of the Teacher Example Projects Bits of Advice

8. Role of the Teacher • Design projects with a creative or choice component built in. • Have a grand vision: Get the kids excited about it. • Provide written instructions with clearly broken down mini-deadlines. • Clearly communicate baseline expectations for overall project, provide ideas for extra enrichment / challenge. • Pace the project to support skills development in class, with parts to be completed outside of class. • Provide on-going, phased feedback with looking over calculations and rough drafts. • Demand excellence in final product. • Create opportunities for kids to present their project. Go back to project framework

9. Example Projects 3-D Geometric Construction Math Pop-Up Book Math Magazine Business Plan Student-Made Review Material Building a Picture with Functions Trigonometry in the Real World Stocks Analysis Hole-in-One Minigolf Tessellations and Construction GeoGebra Animation with Trigonometry Creating a Visually Pattern Go back to project framework

10. 3-D Geometric Construction Students design, measure, and build their own composite solid, and calculate both volume and surface area for this solid. http://bit.ly/3DProjSpecs Go back to example projects

11. Math Pop-Up Book Students create a pop-up book to explain and illustrate all of the topics learned during a year (including interactive practice portions). http://bit.ly/PopUpProj Go back to example projects

12. Math Magazine Students research math topics of interest, then re-explain the findings in their own words, and produce a math magazine compiling all of their digest articles, puzzles, and cartoons. Example magazine:http://bit.ly/GoFigure1http://bit.ly/GoFigure2 Go back to example projects

13. Business Plan Students design a button (or badge) and write a business plan discussing: how much they will bulk order (based on real costs from web vendor), how many they need to sell to break even, how much profit they expect, along with equations, tables, graphs for all considered options. Principal judges whom to award the funding to. Go back to example projects

14. Student-Made Review Material Students create board games, practice tests, scavenger hunt review, or instructional videos for the topics they have studied. They are reviewed by their peers for the quality of their product. Go back to example projects

15. Building a Picture with Functions http://bit.ly/DrawingWithFunctions has a really good integral Calculus version of this. For younger students, you can modify it to only model the outline. Go back to example projects

16. Trigonometry in the Real World Students take pictures of themselves measuring angles of elevation / depression with a simple inclinometer, and then create an illustrated math guide for applying right-triangle trigonometry in order to find heights. Go back to example projects

17. Stocks Analysis Students choose a company, research their stock prices, and then create modeling functions in order to predict future behavior. See http://bit.ly/StocksProj for a very old project handout (needs to be updated to be made more rigorous) Go back to example projects

18. Hole-in-One Minigolf Students design their own hole-in-one golf course puzzle, and then trade it with a friend to solve using compass construction and applied concept of geometric reflection. http://bit.ly/MiniGolfProj Go back to example projects

19. Tessellations and Construction Students create gradually more complex tessellation shapes, in order to explore congruence properties of triangles and quadrilaterals. Go back to example projects

20. GeoGebra Animation with Trigonometry It is possible to create rotating circles in GeoGebra using some simple parametric formulas related to sine and cosine. From there, the students can work on interesting modeling problems of their own design.http://bit.ly/RotatingCircleshttp://bit.ly/RotCircAnalysis Go back to example projects

21. Creating a Visual Pattern Students can create their own visual patterns and then exchange with a friend to carry out the algebraic analysis: finding / testing / applying / connecting the formulas. Go back to example projects

22. Bits of Advice • If the kids are working in groups, always incorporate a detailed individualwriteupto ensure individual understanding. • Don’t worry too much about time. The class time spent on a worthwhile project makes the subsequent learning go faster and the retention longer. • Assign parts to be completed outside of class throughout the project. • Have a formal written assessment immediately following the project, to ensure baseline understanding from all students. • Don’t penalize kids who do only the minimum requirement. Grade everyone based on correctness and overall understanding. Let the extra reward be intrinsic and social. Go back to project framework

23. Questions? • If you think of them later, you can always email me at mimi.yang@bbis.de or reach me at my math blog at http://untilnextstop.blogspot.com • Thank you for helping to spread the joy of mathematics!