1. Warm Up A line passes through the points (0,-4) & (2, -6). What is the equation of the line in slope intercept form? Write at least one sentence to explain your answer.

2. Warm Up A line passes through the points (0,-4) & (2, -6). What is the equation of the line in slope intercept form? Write at least one sentence to explain your answer.

3. LITERACY-BASED DISTRICT-WIDE PROFESSIONAL DEVELOPMENT Aiken County Public School District January 15, 2016 LEADERS IN LITERACY CONFERENCE

4. Writing in the Mathematic Classroom Jennifer Wilson Aiken High School jwilson3@acpsd.net LEADERS IN LITERACY CONFERENCE

5. Essential Question & Outcomes EQ: How can incorporating writing into a mathematics class increase student understanding? O1: Attendees will become aware of some of the research that supports including writing in the math classroom. O2: Attendees will acquire examples of mathematical writing that they can use in a mathematics classroom. O3: Attendees will acquire tools that can support writing in their classroom.

6. Background School Improvement Plan to meet Adequate Yearly Progress (Kansas) Problem Solving, Reading & Writing every quarter. Monthly staff development on strategies AVID Professional Learning Community Art, AVID, Science and Math teacher Common objective – Improve constructed response scores

7. Why do we care? South Carolina Career and Readiness Standards 3. Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. a. Construct and justify a solution to a problem. 6. Communicate mathematically and approach mathematical situations with precision. c. Use appropriate and precise mathematical language.

8. Research National Research Council (2002) “One of the best ways for students to show their reasoning is to explain or justify their solutions to others. Once a procedure for adding fractions has been developed, for example, students should sometimes be asked to explain and justify that procedure rather than just doing practice problems. In the process of communicating their thinking they hone their reasoning skills.”

9. Research Fostering algebraic thinking: A guide for teachers “Fostering convincing-argument skills among students takes time and practice. It can, and should, be a part of regular instruction, with teachers asking students why their answers work, and getting students in the habit of writing down their arguments in a coherent way.”

10. Research Classroom instruction that works Students who were exposed to summarizing and note taking scored on average 1 standard deviation above students who were not exposed to these strategies.

11. Why should students care? AVID “It is up to the mathematics teacher to help such students realize that writing exposes their areas of limited understanding or confused thinking, that writing helps them remember what they are learning as they find connections with prior knowledge, and that writing about mathematics will be necessary to communicate with others whether inside or outside the mathematics community.”

12. Daily Writing Warm Ups Work is not enough – justify Increase expectations for vocab Differentiate

13. Daily Writing Warm Ups How did you do?

14. Examples

15. Examples – ESOL student

16. Examples – Student 3

17. Example – Student 3 (1 week later)

18. Developing their summarizing skills. Summary Frames (Marzano) Give students a framework to help them structure their response. Sentence Stems UPIC 3-2-1

19. Summary Frames UPIC (based on Polya’s 4 steps of problem solving) U: Understand – What was the question? What did you know? P: Plan – What are the strategy did you use to solve the problem? I: Implement – Explain the process. C: Conclude – What is the answer?

20. Summary Frames 3-2-1 3 - Mathematical vocabulary words that I can use 2 – Steps/formulas used 1 – Answer to the original problem

21. Vocabulary is Key! Teaching mathematics today. “In mathematics, vocabulary is highly specialized… all students need an explicit introduction to and explanation of these vocabulary words in order to apply them to their understanding of mathematical concepts.”

22. Direct Instruction of Vocab Frayer Model

23. Direct Instruction of Vocab Build your own glossary.

24. Gauge Vocabulary Readiness Knowledge Rating Chart

25. Gauge Vocabulary Readiness List – Group – Label Give students a list of vocabulary terms to group. After they have organize them into groups. They must label the group based on a mathematical relationship.

26. I’m not ready to do this every day! TOD – Ticket Out the Door Use your graphic organizer and notes to explain how you find the solution to a system of equations by using the graphing method. Use correct mathematical vocabulary, complete sentences and good paragraph structure.

27. I’m not ready to do this every day! A picture is worth 100 words As clearly as you can, write a detailed explanation of what is represented by this graph. Be sure to include the meaning of: The independent variable The dependent variable The units The y-intercept The relationship that exists between the x and y axes (rate of change)

28. I’d like to do something longer Essays or Project Explanations

29. I’d like to do something longer Snark Soda Snark soda is the number one selling soft drink in Geostan. The pictures show the top and side views of the bottle. They are accurate and drawn full size. Your task is to approximate the volume of the liquid in the bottle as accurately as possible and write a detailed explanation of how you obtained your estimate. Make sure you account for all aspects of the bottle. Explain if your approximation is an over or under estimate. Why?

30. What they wrote is not adequate. We may not be English teachers, but we can guide them to do some editing. Peer Edit – Read the paragraph backwards and circle misspelled words. -Highlight relevant mathematical vocabulary (give word list) -Underline the sentence that gives the answer. -Make corrections -Fix spelling errors -There should be at least ____ vocabulary words (you determine minimum) -If the entire paragraph is underlined, it is a run-on sentence.

31. What they wrote is not adequate. Essays or Project Explanations Pair up with the English teacher to have it count in both classes. You can grade based on the math content/vocabulary They can grade organization/structure.

32. References Barton, M., & Heidema, C. (2000). Teaching Reading in Mathematics (2nd ed.). Aurora, CO: McRel. Dooley, K., & Swanson, M. (2002). The Write Path: Teacher Guide for Mathematics. AVID Press. Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Portsmouth, N.H.: Heinemann. Kilpatrick, J. (2002). Helping children learn mathematics. Washington, DC: National Academy Press. Lehmann, E. (2015). Teaching mathematics today (2nd ed.). Huntington Beach, CA: Shell Education. Marzano, R., & Pickering, D. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, Va.: Association for Supervision and Curriculum Development. South Carolina Career and College Readiness Standards. (2015). South Carolina Department of Education Columbia.

33. Questions?

34. Contact Information Jennifer Wilson jwilson3@acpsd.net

35. Editing Determine if it is possible to have an obtuse equiangular or a scalene equiangular triangle. Justify your response. An Equiangular Obtuse triagnle isn't possible because an obtuse triangle can only have one obtuse angle and for it to be equiangular all the angles would have to be the same. A Scalene Equiangular triangle isn't possible because to have an equangular triangle all the angles and sides have to be the same.

36. Editing Determine if it is possible to have an obtuse equiangular or a scalene equiangular triangle. Justify your response. An Equiangular Obtuse triagnle isn't possible because an obtuse triangle can only have one obtuse angle and for it to be equiangular all the angles would have to be the same. A Scalene Equiangular triangle isn't possible because to have an equangular triangle all the angles and sides have to be the same.