1. Back to the Future Writing in the Mathematics Classroom

2. Introductions  Carl Blankenhorn  Math Teacher  Schurr High School, Montebello USD  Lauren Swanson  Whittier College, Department of Education  Former HS Science Teacher, LAUSD

3.  Culminating tasks  Cross-curricular lessons  Writing across the curriculum  Projects

4.  Understand the reasons  Understand some methods  See some activities

5. Engaging in Argumentation is now a Cross-Curricular Expectation

6. Reflective  A way to quickly check for understanding  Makes the students accountable for material

7. Reflective – example  What was the most difficult class you took in college and why?  Write for 3 minutes and then pass it to the person on your right.  Do you agree? Has this information changed the way you thought about the question?

8. Debrief: Reflective How did writing about your college experience and then reading what another person wrote help you think through the question?

9. Methods  Entrance slips (informative for yesterday’s work)  Exit slips (today’s work)  Quick-writes with peer review (informs students of their own understanding)

10. Explanatory  More formal  More in depth  Supported by evidence  Using their own work  Research-based

11. Portfolios  Three ring binder  Table of Contents  Homework  Corrected Quizzes  Five Questions  Reflection Essay

12. Methods  Explanatory writing can be used to check for conceptual and procedural understanding  Explanatory writing can be used as an introduction to proof  Explanatory writing can be used as a research opportunity

13. Explanatory - example On November 19, 1863, Abraham Lincoln spoke at a cemetery dedication in Gettysburg, Pennsylvania. He said, “Four score and seven years ago…” Lincoln was referring to the year 1776. Using mathematics, determine the number of years there are in a score. Explain your reasoning and answer the question: how many years are there in a score?

14. Debrief: Explanatory Writing  Communication of the idea with clarity is crucial.  Like with portfolios, learning how to explain their solutions will help students transfer their understanding to other kinds of problems.  SBAC Training  Free-Response Questions

15. Argumentative Writing  Construct viable arguments and critique the reasoning of others  Formal peer review  Open-ended questions

16. Argumentative - example The Acme Widget Corporation has decided to give 5 percent of its employees a 5 percent raise. If the company’s total payroll is $3,000,000.00 and the average employee earns $25,000.00, how much is the total cost of salaries for the corporation after the raise? Do you want to work for the Acme Widget Corporation?

17. Answer  $3,007,500.00  The answer matters less than the process  How did you get it?  How did your neighbor get the answer?  Justify why you have the “better way”

18. Debrief: Argumentation  A time for a carousel  Groups can critique each other

19. Research Opportunities  Fibonacci – Patterns in Algebra I  M.C. Escher – Rigid Transformations in Geometry  Leonard Euler – Euler line Geometry  Carl Friedrich Gauss – Fundamental Theorem of Algebra Algebra II or PreCal  Archimedes – Did he discover Calculus?

20. Plagiarism: I am against it

23. Questions and/or Comments? Lauren Swanson  Department of Education, Whittier College  lswanson@whittier.edu lswanson@whittier.edu Carl Blankenhorn  Math Department, Schurr High School, Montebello USD  blankenhorn@carl@montebello.k12. ca.us blankenhorn@carl@montebello.k12. ca.us