1. Learning to Explain: Writing & Peer Review Techniques Laurie Burton Western Oregon University MAA PREP Active Learning Workshop July 9, 2003 Wednesday: Assessment

2. Writing in Teacher Ed: Foundations I, II & III [Problem Solving Focus for “Problems of the Week” (Sandy/Maria) [Text Homework [Journal Readings & Summaries

3. Writing in Teacher Ed: College Algebra [HW written in detail, emphasis on exploring understanding and communicating knowledge. [Symbolic proficiency strong component of homework.

4. Writing in Teacher Ed: Geometry \Emphasis on exploring in Lab component of class. [Symbolic & computational proficiency strong component of homework. [Students write extensive vocabulary & concepts list [Geo-Jeopardy Final Exam

5. Writing in Teacher Ed: Abstract Algebra \HW written in detail, emphasis on exploring understanding and communicating knowledge at a more abstract level. [Symbolic proficiency strong component of homework, especially in settings of number properties. [Students start working with lesson plans and creating materials for children.

6. Writing in Teacher Ed: “Manipulatives” Course [Writing in this class will be the focus of this conversation. [“Everyone” takes this class. [My attitude, with many of them, is that this is last chance I have to really “get some math” out of them.

7. “Manipulatives” Course Assessment Components [Weekly readings and summaries [Multiple Choice exams (with more than 1 correct answer) [Review of completed class work [Story Problems [Portfolios [Create Game: Final Presentation

8. “Manipulatives” Course Story Problems [Many of the students think this is an odd class for story problems, but each week after lab, they students write two story problems to show their understanding of the current mathematical topic(s) we are studying

9. Story Problems Example Whole Number Addition [Write a story problem that results in solving the problem: 17 + 18 = ? Typical Student Work: [Sally has two types of stickers, she has 17 cherry stickers and 18 lemon stickers. How many stickers does Sally have all together?

10. Story Problems Examples Non-Base 10 Addition Write a story problem that results in solving the problem: (321) five + (4423) five = ? Typical Student Work: [Mary’s candies can be packed in 5- piece packs, 5-pack super-packs, 5- super-pack cases and 5-case shipping boxes.

11. [Mary has 3 cases, 2 super-packs and 1 pack of candy and Mary’s friend Jose gives her 4 shipping boxes, 4 cases, 2 super-packs and 3 packs of candy. [If Mary and Jose pack the candy in the least amount of space, what pack, super-pack, case and shipping box of candy configuration do Mary and Jose have?

12. Strengths of Story Problems [I like the story problem writing assignment because it gives the students pause. [The students really have to think about the mathematics they are considering and they really have to think about how they will speak about these topics in their future classrooms.

13. Strengths of Story Problems [If the student does not understand the mathematics, they have a lot of trouble writing a story problem about the mathematics. [They tend to think hard, work with their peers and seek help from me.

14. “Manipulatives” Course Portfolio Problems [This is where I really emphasize “Learning to Explain.” [Using (way too many) explicit directions as a guide, each week following lab the students write two portfolio problems. [What is a portfolio problem?

15. Components of the Portfolio Problem Each student writes their problems using the following format: [Write out the given problem. [Generally describe the manipulative being used. [Model the problem. [Report the solution to the problem.

16. Problem: Model 3/5 of 7/8 with Cuisenaire Rods Portfolio Problem Example

17. Manipulative: Cuisenaire Rods Portfolio Problem Example

18. Modeling the Problem: [To show 3/5 of 7/8 we must first show 7/8. [What is a good model for 1 here? [If the BROWN ROD = 1, then the BLACK ROD = 7/8. Portfolio Problem Example

19. 7/8 1 Portfolio Problem Example

20. [However, since the black rod is 7W rods, we can’t divide it into 5 parts to help us compute 3/5 of 7/8. [We increase our model for 1 to TWO Brown Rods and our model for 7/8 to TWO Black Rods Portfolio:Modeling

21. 7/8=14W 1 [We see that 14 W rods can’t be divided into 5 parts and so we continue to add to our models for 7/8 and 1 until 7/8 can be broken into 5 parts Portfolio:Modeling

22. 7/8=35W 1 = 40W Portfolio:Modeling

23. 7/8=35W [We see that 35 W rods can be divided into 5 parts [We must break our model for 7/8 into 5 equal parts. [35/5 = 7, Wait! Our model already is in 5 parts! Portfolio:Modeling

24. This is 3/5 of 7/8 [Three black rods = 21 W [1 = 40 W [3/5 of 7/8 = 21 W/ 40 W Solution [3/5 of 7/8 = 21/40 Portfolio:Modeling

25. [It is a lot of work for the students to write at this level of, well, “perfection.” [It is a lot of work for me to grade this amount of papers. [On second thought, I’m getting pretty fast at grading these. Portfolios in Action

26. [It is really, really worth it. [The beginning of the term is tough. [The students are not used to high level expectations. [The students are not used to a lot of weekly homework. [The students need help! Portfolios in Action

27. [The Peer Review system is simple and extremely helpful to the students. [The quality of papers soared after I instituted Peer Review in the course. Peer Review & Portfolios

28. Here is how it works: [Prior to the due date, students bring a good draft of their problem to class. [The students pair up and trade papers. [The students use the HW grading rubric as a guide as they read and analyze each other’s papers. Peer Review & Portfolios

29. [The students ask a lot of questions, especially at the beginning of the term. [Most students make incredible progress and at the end of the term have a notebook full of well- explained, nicely illustrated problems to refer to when they are finally in their own classrooms. Peer Review & Portfolios

30. [Collecting intensive written homework, regardless of the class (teacher ed, calculus) is a big commitment. [Students, to say the very least, are quite engaged in courses where quality written work is expected. [I think it is worth it and I always have. Value of Writing Assignments

31. NEXT! FIGURATE NUMBERS