Algebra Team Session

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 • I never saw/heard it before. • I’ve heard it but don’t know what it means. • I recognize it in context. It has something to do with… • 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

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?