Before we begin …

1. Before we begin … Work the puzzle with your tablemates. • All pieces must be used. • Fit the pieces together so that what is written along the segments of one piece matches what is written along the segments of adjacent pieces. • Once completed, your puzzle will be a “design” or “path.” Coweta Committed to Student Success

2. Tarsia for card sorts • Free download of Tarsia software at http://www.mmlsoft.com/index.php/products/tarsia • Lots of already created puzzles and card sorts available for free download at http://www.mrbartonmaths.com/jigsaw.htm Coweta Committed to Student Success

3. Middle School Math Madras Middle School January 21, 2014

4. Coweta Committed to Student Success

5. Coweta Committed to Student Success

6. Agenda Focus on Mathematics and Language • Literacy in Mathematics – Dr. Paula Baker • “The Problem with Math Is English” • Updates and Sharing • Next Meeting Coweta Committed to Student Success

7. Connecting math and language In one word, state what comes to mind for most people when you say “mathematics.” Solve the following problem. Find the ugloft of a bipkad if the rexnuza is 20. ugloft: area bipkad: circle rexnuza: diameter Coweta Committed to Student Success

8. Connecting math and language Solve: • - • = 1 + 3 + 5 + 7 Coweta Committed to Student Success

9. Mathematics and language • It is not an ELL problem. • It is an ALL problem. • And ALL students are MLLs. Coweta Committed to Student Success

10. Factors contributing to problem • Difficulty of the English language itself • Learning the vocabulary is part of the learning • Some math terms are rarely used outside the math classroom • Others are used, but in different ways • Math terms can have different meanings in different math contexts • Ambiguity • Isolation of mathematics and language arts Coweta Committed to Student Success

11. Use the language and vocabulary of a reading teacher • Identify character(s) and setting (activate schema/plan) • Identify main idea, implied main idea, supporting details • Make an inference • Draw a conclusion • Summarize Coweta Committed to Student Success

12. Use the language and vocabulary of a reading teacher Macy and Mark went to a movie. Tickets were $8.25 each. How much changedid Mark receive if he paid for both tickets with a $20 bill? Who are the characters? What is the setting? Activate the buying/getting change schema. Coweta Committed to Student Success

13. Identify main idea, implied main idea, and supporting details • The main idea of a math problem – what skill do we need to solve the problem. • The information in the details (facts) is needed to make inferences. Example: Lindsey is replacing the tiles in her foyer. She is using 1 sq. foot tiles. The entry is 6 feet by 6 feet. How many tiles does she need for the foyer? (area problem) Coweta Committed to Student Success

14. Make an inference or draw a conclusion Math problems need more that what is explicitly written. Sam and 3 friends went to Pizza Place. They decided on the buffet combo meal for the lunch. Each buffet combo meal is $4.50. How much did they pay for lunch? How many students would answer $13.50? There are 4 people – not 3. Coweta Committed to Student Success

15. Connect and reflect Make Connections • Text to self: What math experience was it like? • Text to text: How did it connect to previous assignments/work? • Text to world: How do people use this? Reflect • What part of the strategy went well? • What can I do differently next time? • What did I learn from other students? Coweta Committed to Student Success

16. Quick Writes Quick writing is short and focused writing in response to a specific prompt. • Warm Up • Skill Intro • Ticket out the Door • Daily Reflection Example: 3 – 2 – 1 • 3 things you have learned • 2 things you can share with a classmate • 1 thing you would change Coweta Committed to Student Success

17. The Last Word Students copy down a concept or problem on the front of a note card. On the back, they explain how the problem is solved and what it means to them. If there is time, the students could share in small groups what the concepts/problems mean. http://www.cpm.org/pdfs/CPM_conference/2008/util_reading_strat_math_classroom.pdf Coweta Committed to Student Success

18. Term Organizer (Brainstorming) This strategy activates prior knowledge while also encouraging students to explore connections and relationships between ideas. Write a mathematical term (that will soon be studied in class) on the board or overhead projector and ask students to share words/phrases they associate with this word. Then have students (in their study teams) sort the resulting list of words into categories and explain why they chose their categories. http://www.cpm.org/pdfs/CPM_conference/2008/util_reading_strat_math_classroom.pdf Coweta Committed to Student Success

19. Think-Aloud Talking through a problem out loud with students. Students need to understand this is a strategy that they should be using at home while completing their homework, or in their study teams. Important points are • Predicting what happens next • Picturing the problem • Making comparisons • Identifying the problem • Fixing the problem • Making comments/reasoning the answer http://www.cpm.org/pdfs/CPM_conference/2008/util_reading_strat_math_classroom.pdf Coweta Committed to Student Success

20. Language-based problems in math • Careless vocabulary • Shortcuts • “Naked” numbers Coweta Committed to Student Success

21. Careless vocabulary “The difference between the right word and the almost-right word is like the difference between lightning and lightning bug.” – Mark Twain Coweta Committed to Student Success

22. Careless vocabulary • Cancel • Implies something is deleted or eliminated • Reality is that expression(s) have been rewritten as equivalent expressions where 1 or 0 appear and their properties can be used • Reduce • Implies that the quantity gets smaller • Reality is that the quantities are equivalent Coweta Committed to Student Success

23. Shortcuts • Imply efficiency, but taught too soon and too often impedes students’ conceptual understanding • Focus is on the “how to” rather than “what” and “why” • The less students’ do with paper and pencil, the less they do with their brains Coweta Committed to Student Success

24. Adding fractions Coweta Committed to Student Success

25. Simplifying fractions Coweta Committed to Student Success

26. “Naked” numbers • Numerals in isolation without units, descriptors, or context • Too much focus on drill and practice results in students losing sight of the meaning of numbers and numerals • Numerals represent something • Procedural fluency is important, but it should be a complement and by-product of conceptual understanding Coweta Committed to Student Success

27. Effect of using “naked” numbers How would your students work the following problem? Sasha was given two expressions: 25 x 28 and 24 x 28 How much more is the value of the first expression? The “naked” numbers cause most students fail to see the comparison of units: 25 sets of twenty-eights to 24 sets twenty-eights Coweta Committed to Student Success

28. Instructional strategies • Use ambiguity to your advantage. • Be aware of drifting, and pull students back on course. • Incorporate multiple perspectives. • Use manipulatives using a “hands on, brains on” approach. Coweta Committed to Student Success

29. Ambiguity Make ambiguous questions an asset. • Are a square and a rectangle similar? Ask an ambiguous question at the beginning of an instructional unit and then again at the end to generate interesting dialogue, deepen student knowledge of the concept, and develop awareness of language issues in math. Coweta Committed to Student Success

30. Ambiguity 2. Danielle claims that Figure B has more shaded area than Figure A. Alex claims the opposite. Who is correct? Explain your reasoning. Some ambiguous questions allow students to explain their interpretations of terms and provide an opportunity for a significant teachable moment. Figure A Figure B Coweta Committed to Student Success

31. Ambiguity 3. Given a 1-by-1 square, what would the square look like if you made it twice as big? Draw and label the original and the larger square. Justify your reasoning. Ambiguous questions containing phrases that have a vague meaning – in this case, “twice as big”– provide an opportunity to address the problem of drifting. Drifting refers to moving from an appropriate definition or perspective to one that is narrow or incorrect. Coweta Committed to Student Success

32. Drifting Task: Give a real-life example of slope. Drifting is the result of a tendency to move to plain- English definitions of terms that can have a different meaning in mathematics. Repeated patterns also promote drifting. For example, a student may believe that a quotient is always less than the dividend because he has worked repeatedly with whole number division problems. Coweta Committed to Student Success

33. Multiple perspectives You have taught multiplying mixed numbers using the standard algorithm, but Jessica just isn’t getting it. You are working with her using the problem 3½ x 2½. How could you explain it so that Jessica can build some conceptual understanding of what is going on? Coweta Committed to Student Success

34. Finding Work done with manipulatives or with diagrams should be accompanied by written symbolic work. 2 + ½ 6 1½ 3 + ½ 1 ¼ Coweta Committed to Student Success

35. Finding Work done with manipulatives or with diagrams should be accompanied by written symbolic work. 6 1½ 1 ¼ Coweta Committed to Student Success

36. Updates and sharing • STEM activities from DefinedSTEM are on the shared drive. • GaDOE and Georgia Tech’s CEISMC are partnering to offer free self-paced STEM courses for teachers. • A middle school algebra course focuses on STEM best practices in unit plan development and classroom instructional delivery. • For more information and to register, visit www.ceismc.gatech.edu/freeplucourses. Coweta Committed to Student Success

37. Updates and sharing • Unit-by-unit learning target documents continue to be created and posted to intranet and shared drive. • Continue to make note of items/ instructional sequences that need to be improved so that these can be addressed at the 2014-2015 planning workshop. Coweta Committed to Student Success

38. Updates and sharing • CRCT will have the same format as usual, but expect items to be more rigorous. • Formula sheet for CRCT remains the same as last year’s. • CRCT resources are posted on intranet and shared drive. • OAS has some state-created tests: • Formative assessment items for 6th – 8th • 6th grade: Multiple choice for Units 1-3 • 7th and 8th: Multiple choice for Units 1-2 Coweta Committed to Student Success

39. Updates and sharing • The state has released CRCT “instructional readiness indicators” and have analyzed 2013 CRCT results to provide school and district reports regarding student performance levels. • Needs additional support • On track • Commendable Coweta Committed to Student Success

40. Updates and sharing Readiness Level Threshold Scores Students are categorized as Needs Additional Support in a content area if their scale score on the 2013 CRCT is less than the On Track threshold. Coweta Committed to Student Success

41. Data at a glance Coweta Committed to Student Success

42. Data at a glance Coweta Committed to Student Success

43. Data at a glance Coweta Committed to Student Success

44. Updates and sharing • Additional items to share? • Suggestions/concerns/questions? Coweta Committed to Student Success

45. Next meeting • Smokey Road Middle School • Media Center • March 4, 2014 • 4 – 5 p.m. • Focus: Reviewing for exams Coweta Committed to Student Success

46. Resources Burns, P., Roe, B., & Smith, S. (2002). Teaching reading in today’s elementary schools. Boston, MA: Houghton Mifflin. Manzo, A. V., Manzo, U. C., & Estes, T. H. (2001).  Content area literacy: Interactive teaching for active learning. New York: Wiley. Molina, C. (2012). The problem with math is English: A language-focused approach to helping all students develop a deeper understanding of mathematics. San Francisco, CA: Jossey-Bass. Stephens, E., & Brown, J. (2000). A handbook of content literacy strategies: 75 practical reading and writing ideas. Norwood, MA: Christopher-Gordon. Coweta Committed to Student Success