1. Capacity Development and School Reform Accountability Dale Carothers, Mathematics Specialist Altoria Henley, Mathematics Specialist

2. Our Group Expectations: Silence cell phones. Participate and share. Listen with an open mind. Ask questions. Work toward solutions. Use time effectively.

3. Session Goals Teachers will understand how to optimize instructional time by learning how to use the components of an effective classroom. Teachers will be able to plan how to adapt the components of an effective classroom in their school setting.

4. Session Outcomes Components of an Effective Mathematics Classroom Focus on Curriculum Identify the Sunshine State Standards Strands and Content Objective Focus on Instruction Focus on the Learner Focus on Classroom Environment Evidence of different learning styles being met

5. FCIM Plan – Do – Check – Act (PDCA) Cycle 5 5

6. Applying FCIM to School-based processes for Data-Driven Results 6 PLAN: Design or revise the mathematics learning process components to improve results DO: Implement the plan and measure its performance CHECK: Assess the measurements and share the results with stakeholders ACT: Decide on changes needed to improve the mathematics learning process Plan

7. Opening Activity What is your perspective of an effective classroom? 1.Journal it. 2. After your journal writing, write a strategy on a sticky for each chart.

8. Components of a Model Classroom

9. Focus on Curriculum Ask yourself is the following evident, not evident, or unable to determine. What is the learning objective for lesson? Is the learning objective(s) evident to students? Is the learning objective grade level appropriate?

10. Identifying the Sunshine State Standards Strands for Teacher and Students Number Sense, Concepts, Operations Measurements Geometry and Spatial Sense Algebraic Thinking Data Analysis and Probability

11. Focus on Instruction Identify instructional practices Identify grouping format Identify research-based instructional strategies Focus on the learner Focus on Classroom Environment

12. Focus on Instruction Identify the instructional practices used during instruction. Instructional Practices CoachingModelingTeacher Directed Q and A DiscussionPresentationsStudent Directed Q and A Hands on experiences Providing directions/ Instructions Technology Demonstrations Learning Centers LectureProviding opportunity for practice

13. Grouping Format Whole Group Small Group Paired Individual

14. Focus on Learner Student Actions Instructional Materials Level of Student Work Level of Class Engagement

15. Student Actions What are your students doing? Listening Reading Speaking Working with hands-on manipulatives Writing in journal

17. Instructional Materials Easily Accessible Computer Software Lab/activity Sheet Real-world objects Websites Content- specific manipulatives Overhead/ board/ flip chart Student Created materials Videos Hand-held technology/ Calculators Published print materials TextbookResource Books

18. Level of Student Work Bloom’s Taxonomy EVALUATION- Making judgments and justifying positions SYNTHESIS- Putting information together in new ways ANALYSIS-Breaking down information into parts APPLICATION-Using information in a new way COMPREHENSION-Understanding information KNOWLEDGE-Recalling information Ex. Basic Math Facts

19. Depth of Knowledge & Complexity Level “Knowledge Sort Activity”

20. DOK & Complexity Level Key Words / Tasks Level 1 (Low) Recall Level 2 (Moderate) Skill/Concept Level 3 (High) Strategic Thinking Level 4 (High) Extended Thinking “Identify”“Classify”Requires reasoning, planning, using evidence, and a higher level of thinking than the previous levels. Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time “Recall”“Organize” “Recognize”“Estimate” “Use”“Make Observations” “Measure”“Collect and Display Data” Drawing Conclusions Task demands should be high Requires rote response “Compare Data”Citing EvidenceWork should be complex Performing an algorithm “Explain”,”Describe”, “Interpret” (depending on the object of the action Logical argument Following a procedure

21. Level of Engagement Highly Engaged Most students are authentically engaged. Dysfunctional Many students actively reject the assigned task or substitute another. Well Managed Students are willingly compliant, ritually engaged.

22. Focus on Environment Materials are available Models/exemplars of quality student work Routines and procedures are evident. Scoring rubrics are displayed/provided. Students interact with classroom environment. Student Success Walls and Word Walls

24. Word Wall Purpose A word wall is a systematically organized collection of words displayed in large letters on a wall in the classroom (Cunningham,1995). Word walls serve many purposes. Teachers can use them to facilitate word analysis; provide models of commonly misspelled words; or to build vocabulary for a unit of study.

25. “ Education Not Decoration Dr. Darla Shaw, Coordinator of Graduate Reading, Western Connecticut State University It’s no longer enough for classroom walls to be attractive.” “A working word wall, if developed properly, can bring real life to a classroom.” “Children who learn in a classroom with a working word wall, have a distinct advantage over students who don’t have such a resource in their room.”

26. Word walls need to… Type of Word Walls be specific to the math content being studied. be connected to words with their visual cues. be arranged by strands, topics or categories. be student interactive. High frequency mathematics words Common patterns, phrases related to signs and symbols Content Specific Math Genres Reinforcement of current skills and concepts

27. Floor Plan All classroom areas should be visible to the teacher. Designate whole, small and independent student work areas. Determine the technology area and the number of students per computer. Make sure that portfolios, assessments and math centers are accessible to students.

28. Mathematics Classroom Floor plan will depend on the grade level you are teaching. (It should maximize classroom space and focus on student instruction.) Instructional and purposeful visual aids are key components of an effective classroom. (Curriculum focused word walls, math content charts and math center activities)

29. Mathematics Word Wall

30. Working Word Wall

31. The Language IN Mathematics Strategies for Developing Mathematics Vocabulary

32. Helping students become independent learners is an important goal Connecting Mathematics strategies to high student achievement. Activity #2

33. Evidence of Different Learning Styles Needs Being Met Rotational Model Small Group Instructions Step by Step Handouts Visual Representations of Content Language Translations Computer Instruction

35. Research states the following interventions are found to be effective…

36. Research –Based Instructional Strategies for Interventions Scaffolding Instruction Concrete-Representation- Abstract Instruction Direct/Explicit Instruction Verbalization while problem solving 5 Step Process to Solving Problems DRAW Strategy STAR Strategy Teaching Skills to Mastery Metacognitive Strategies

37. Exploration Activity Each group will have an intervention strategy with a description. Create a lesson using the strategy on your description card.

38. Technology com. Destination Math FCAT Explorer Florida Achieves Gizmos Learning Village Nettrekker (Learning Village) Brain Pop

39. Print Rich Environment “ The moment one steps foot inside a classroom one can usually tell what is important to the teacher in terms of the type of working literacy (Mathematical) environment he or she sets up for the students.” P-Child 39

40. Elements of a Print Rich Environment  Word Walls  Bulletin Board Displays  Graphic Organizers  Mathematics Vocabulary  Student Generated Work  Classroom Libraries  Mathematics Work Stations

41. A Print-Rich Environment Doesn’t Contain: Coloring Worksheets Unrelated Math Worksheets Puzzles and games that doesn’t relate to the curriculum. Stale word walls Words on every object in the room

42. Suggestions from Marzano 1. Present explanation or description of words 2. 5-7 Vocabulary Words per Unit of Study 3. Present pictorial examples 4. Students generate explanations or descriptions 5. Students create pictorial examples 6. Frequently, ask students to review words in their own explanations, definitions, and/or examples

43. What should students know & be able to do? Define Pronounce Give examples Use in Writing (Short & Extended Responses) Use verbally Recognize as sight words Identify in real-life Compare/contrast Visualize Integrate

44. Instructional Strategies for Vocabulary Development Techniques from Supplemental Education Instruction (SEI) Frayer Model Graphic Organizers Math Journals Math Word Banks Bingo/Wordo

45. Techniques from SEI Sing or Chant words Use physical gesture and/or act out Make up gestures Act it out & Verbalize Verbalize & Act it out Illustrate words Create posters using student representations Systematic Review Activities

46. Charts That Support Learning Functional Charts Anchor Charts Teacher-created Procedural information Schedules Rubrics Rotational Co-authored Reinforce concept learning Visual reminders of incidental learning Teaching tool

47. Some samples of anchor charts… What types of math anchor charts could be used in your content area? Create your own.

48. Frayer Model Video Frayer Model Instructional Video Activity #1 Graphic Organizer Video Activity #2

49. Word Sort Activity There are two types of word sorts: closed and open. 1. In closed word sorts the teacher defines the process for categorizing the words. This requires students to engage in critical thinking as they examine sight vocabulary, corresponding concepts, or word structure. 2. In open word sorts the students determine how to categorize the words, thereby becoming involved in an active manipulation of words.

50. Mathematics is a Language Math vocabulary development is an essential piece of language instruction when teaching mathematics in the classroom.

51. Marilyn Burns, 2005 “ The standard for mathematics should be the same as the standard for reading-bringing meaning to the printed symbols. In both situations, skills and understanding must go hand in hand. The challenge is, how do we help students develop meaning and make sense of what they do?”

52. Benefits of Math and Literature Integration The story provides structure for children to explore math concepts. Math and literature are interrelated and not separate entities. Literature provides the connection between the “real world” experience and the highly structured discipline of mathematics.

53. How We Teach in Mathematics Mathematics Standards Numbers and Operations Algebra Geometry Measurement Data Analysis/Probability Mathematics Processing Standards Problem Solving Reasoning and Proof Communication Connections Representation

54. Math Classroom Libraries Provide a variety of math literature books Library is well organized and displayed. Change literature as the year progresses based on math content introduced/reinforced. Have a space where students can review books. Have an area where students can review books, read or listen to books on tape. Provide vocabulary words and activities aligned to the skills identified in the literature.

55. Connections to Mathematics The Curriculum Connection Making “Real-World” Connections The literature selection creates the environment for students to use: Mathematics skills Reading skills Writing skills Critical thinking skills Math vocabulary development-”Word Walls” Daily graphing activities Estimation (guessing) jar activities Math learning centers/games Integrating math and literature Using math journals

56. Mathematics Library Your Thoughts and Reflections

57. Vocabulary Journals Spiral notebooks/steno pads Composition books/3-ring binders Personal favorites -organize by strand Simple form -4 boxes Graphic organizer –Frayer model Commercial -grid paper & lines

58. Math Journal Structure Date every entry so that student growth or lack of it is evident. Entries include vocabulary words, sentences of explanation, equations, diagrams, charts, graphs, etc. Journal entries stay in the journal and are not torn out.

59. Math Journal Possibilities Vocabulary-words, pictures and numbers Formulas, algorithms, procedures Anchor problems Problems of the Day/Week On-going formative assessment of skills, concepts and connections Small group feedback

60. Student Portfolios “Portfolios themselves do not have a profound effect on student progress; rather it is the use of constructive, precise and frequent feedback that has the strong effect on student learning.” Bob Marzano (1998) Mid-Continent Regional Educational Library 60

61. Student Portfolios Defined A student portfolio can be defined as: “A cumulative and ongoing collection of entries that are selected and commented on by the student, the teacher and/or peers, to assess the student’s progress in the development of a competency. (Simon, & Forgette-Giroux, 2000). 61

62. Portfolio Components Required Artifacts: Student Data Checks (Current FCAT, Fall Diag., Winter Diag.- Student Goal Worksheet) Embedded Assessment Data Evidence of Remediation Mastery/Enrichment based on Embedded Assessment Data Portfolio Feedback Sheet Short and Extended Response for specified benchmarks in appropriate grade levels End of Year Reflection Suggested Artifacts: Solutions to difficult problems that detail problem solving abilities. Use of mathematics in another discipline Problems created by the student Responses to challenging questions and problems Project based learning samples 62

63. Another definition… “A purposeful collection of student work that tells the story of student achievement or growth.” J. Arter, 1995 63

64. Important factors to consider… Purpose to be served by the portfolio. Specific skills to be assessed or developed by the portfolio. How you will manage the portfolio (include time for student self- assessment and conferencing)? What sections will be included in the portfolio? 64

65. Reflections Looking back at today’s presentation, what mathematics background knowledge must children know in order to complete the activities? How will you utilize instructional strategies to support conceptual depth and understanding in mathematics? What other math skills are related to today’s presentation? In what ways will you revise your current instructional strategies to incorporate more in- depth understanding and critical thinking? How will you assess student’s understanding of the math skills and concepts?

66. Michael Fullan and Andy Hargreaves “It is what teachers think, do, and are, at the level of the classroom, that ultimately shapes the kind of learning that young people get.”

67. Spring 2008 67 Questions and Concerns 67

68. Mathematics Capacity Development Team Michelle White, Mathematics Manager Michelle.white@palmbeach.k12.fl.us Shabana Ahmad-Farook farook@palmbeach.k12.fl.us Bobbie Brooks brooksb@palmbeach.k12.fl.us brooksb@palmbeach.k12.fl.us Dale Carothers carothers@palmbeach.k12.fl.us Cara Hayden haydenc@palmbeach.k12.fl.us haydenc@palmbeach.k12.fl.us Altoria Henley altoria.henley@palmbeach.k12.fl.us altoria.henley@palmbeach.k12.fl.us Sharon Martinez martinezs@palmbeach.k12.fl.us Kim Pirtle pirtlk@palmbeach.k12.fl.us Carol Sheffield sheffic@palmbeach.k12.fl.us Thank you for all that you do for our students!