1. Algebra Team Session Mark Ellis October 31, 2006

2. Systems of Linear Equations Forms of representation  Symbolic algebraic  Graphic  Tabular numeric  Verbal How are these forms connected when solving a system of equations? In other words, how do changes in one form affect the other forms of representation?

3. Exploring Systems of Equations Conceptually http://seeingmath.concord.org/sms_interactives.html  Note that the System Solver is a tool intended to illustrate the rationale behind the symbolic operations used to solve systems of linear equations, and not a way to learn what procedures to follow. Review the directions for Part 1 and do A-C. Discuss Steps and Predictions for A, B, and C. Use System Solver to view A, B, and C using tables and graphs. What are some important concepts for this topic?  Solution  Linear relationship  Equality  Transformation Arithmetic Algebraic

4. Systems of Equations Application: Supply and Demand http://illuminations.nctm.org/LessonDetail.aspx?id=L382

5. Language and Mathematics Levels of word knowledge 1. I never saw/heard it before. 2. I’ve heard it but don’t know what it means. 3. I recognize it in context. It has something to do with… 4. I know it and can use it confidently. Students need structured opportunities to develop the understanding to know and to use academic language. Developing mathematics academic language  Marzano, R. J. (2004). Building background knowledge for academic achievement: Research on what works in schools. Alexandria, VA: Association for Supervision and Curriculum Development.

6. Step 1: Teacher Input Provides Examples and Non-Examples  These are intentionally planned to illustrate key aspects of the word/concept. Gives explanation or description with some guided student input Does NOT give formal definition

7. Step 2: Students Restate Students construct their own explanations  Share orally with a peer  Share orally as a class Check against prior examples, non-examples, description Revise, in student language, to correct misunderstandings  Put into writing in a notebook Teacher provides some evaluative comments to correct critical errors but does not impose formal definition

8. Step 3: Nonlinguistic Representation Students collaboratively or individually create: Graphic organizers Drawings Photographs Pictographs Students can also be encouraged to create mental pictures and act out meanings of new words.

9. Step 4: Refining Knowledge Students do activities that refine vocabulary knowledge:  Compare  Classify  Analogize  Add new information  Explain to a friend  Study common roots and suffixes  Make linkages with other terms and phrases Definitions are refined and revised, leading to a mathematically valid wording that includes visual representations and examples (and non-examples).

10. Step 5: Students Discuss the Terms Organize students into small groups asking them to discuss terms in their vocabulary notebook Prompts for discussion could include:  terms interesting to students  questions about specific terms  identify terms with multiple meanings  favorite terms  terms that were difficult to learn and why

11. Step 6: Play Games! Students practice using the words in a meaningful (and fun) context  Charades  Pictionary  Gestures  Taboo  Great web site for classroom games http://www.teachersdesk.org/spell_plans. html http://www.teachersdesk.org/spell_plans. html

12. Reflect on this Method How is it different from traditional vocabulary instruction? What may be challenging for you to implement? What support would you need to fully implement this process?