The document describes the Guided Math instructional framework developed by Laney Sammons. It is a flexible approach that uses whole class instruction, small group work, and independent work to meet students' unique needs. Key aspects include establishing a numerate classroom environment, ongoing assessment to form flexible groups, and using whole class, small group, and independent work components daily. The goal is to promote deep understanding and address gaps through differentiated instruction.

1. Guided Math A Framework for Math Instruction Laney Sammons

2. Background Information My experience Lessons learned in kindergarten Differentiating to meet diverse needs Links to literacy instruction and the Guided Reading model Development of the Guided Math framework

3. What is Guided Math? Guided Math is a flexible instructional framework that enables teachers to promote the deep mathematical understanding and computational fluency of their students by determining their unique needs and then prescriptively addressing those needs through a combination of whole class instruction, small group instruction, math workshop, and conferences within a classroom environment supportive of numeracy.

4. Samuel E. Hubbard Elementary School Forsyth, Georgia Small town in an area that has been predominately poor and rural, but is gradually becoming suburban. Pre-K through Fifth Grade Title I School of Distinction for 10 years 63% Free/Reduced Lunch 34% Minority Students 924 Students Why Implement the Guided Math Framework?

5. Samuel E. Hubbard Elementary School Forsyth, Georgia Georgia implemented new, more rigorous math performance standards for Kindergarten through Second Grade in 2006-2007. Guided Math implemented in 2007-2008 Why Implement the Guided Math Framework? 2007 (New Standards) 2008 (Guided Math)

6. Samuel E. Hubbard Elementary School Forsyth, Georgia The new math performance standards were implemented in grades three to five in 2007-2008. Guided Math implemented in 2008-2009 Why Implement the Guided Math Framework? 2008 (New Standards) 2009 (Guided Math)

7. Samuel E. Hubbard Elementary School Students Exceeding Standards in Math Why Implement the Guided Math Framework? First and second grades had experienced gains in the percentage of students exceeding in 2008 when they implemented Guided Math. In 2009, the percentage of students exceeding standards continued to increase.

8. The Traditional Approach to Teaching Math Large group instruction All students work on the same level Primarily instruction and practice from text book Emphasis on paper and pencil work One correct answer Individual work

9. Does this approach work? Successful for some students Less successful for those who quickly acquire mastery Even less successful for struggling students Encourages emphasis on computation skills Little opportunity for communication More emphasis on evaluation, rather than assessment for learning

10. Why should we explore different ways to teach math?

11. To more effectively teach math, we must reach students at all levels of achievement provide diverse methods of learning allow more opportunities for observation and communication by students encourage active engagement by students

12. How can we effectively teach math when we have a classroom of students at many different levels of achievement?

13. The Guided Math framework offers a daily menu of instruction from which teachers can choose based on the needs of their students and upon the standards being taught.

14. The Foundational Principles of Guided Math All children can learn mathematics A numeracy-rich environment promotes mathematical learning. Learning at its best is a social process Learning mathematics is a constructive process. An organized classroom environment supports the learning process.

15. The Foundational Principles of Guided Math

16. Daily Components Classroom Environment of Numeracy Math Warm-up/Calendar Board Individual Conferences Ongoing Assessment Guided Math Framework

17. Guided Math Framework Choice Components Whole-Class Instruction Small-Group Instruction Math Workshop

18. Use of Manipulatives Creating a Classroom Environment of Numeracy

19. Read literature that promotes exploration and application of math concepts

20. Focus on Mathematical Vocabulary

21. Display a Mathematics Word Wall

22. Link Math to Real Life

23. Link Math to Real Life Goal Setting Self-monitoring of achievement by students

24. Demonstrate, model, and do “think alouds” of problem solving strategies.

25. Integrate math into all curricular areas.

26. Math-Related Classroom Responsibilities Attendance Lunch counts Fund raising Class elections Field Trip Collections Total cost of the trip Total amount collected Percentage of total amount needed

28. Daily Framework for Solving a Problem of the Week from Action Packed Problem Solving by Michelle Windham and Beth Pollock Available through Action Packed Publications

29. Create and display of class-made charts tell of math processes and activities .

30. Create and display of class-made charts tell of math processes and activities.

31. Use student calendars and/or agendas.

32. Creating Math Rich Classroom Environments Frequently use graphing activities based on classroom activities. Provide instruments of measurement (thermometers, rulers, scales, measuring cups).

33. Turn and Talk What are some other ways to create an environment of numeracy ?

34. Morning Math Warm-ups Mathematical Stretches Mathematical Current Events Math-Related Classroom Responsibilities Calendar Board

35. Mathematical Stretches Data Collection and Analysis Tasks

36. Mathematical Stretches Data Collection and Analysis Tasks

37. Mathematical Stretches Data Collection and Analysis Tasks

38. Mathematical Stretches Data Collection and Analysis Tasks

39. Mathematical Stretches Data Collection and Analysis Tasks

40. Mathematical Stretches Data Collection and Analysis Tasks

41. Mathematical Stretches Number of the Day Stretch

42. Mathematical Stretches What’s Next? Stretch

43. Mathematical Stretches How Did My Family Use Math Last Night? Stretch _______________ Makes Me Think of… Stretch

44. Math Current Events Teacher or students bring in articles or web sites with current events that have to do with math: Levels of precipitation Economic statistics Population Vote counts

46. Daily Calendar/Morning Work Problems of the Day Incredible Equations Daily Data Work Calendar Activities Preview new concepts and skills. Maintain previously mastered skills. Regular focus on difficult to master skills

47. Using Coins to Represent the Date

48. Problems of the Day Provide problems with more than one correct answer and multiple methods of solution. Require students to tell how they solved the problem either orally or in writing with multiple representations. Students complete independently; then as a class go over strategies used to solve the problem and possible answers. Include new vocabulary. Present problems in unfamiliar ways. Allow students opportunities to struggle to discover the answers.

49. Daily Calendar Board Provides opportunities for communication through turn and talk, math journals, and cooperative group work. Helps students deepen understanding and develop mathematical reasoning because concepts are filtered through conversation (speaking, listening, reflecting, and refining).

50. Menu of Instruction Whole class instruction Small group guided instruction Math Workshop (independent work or work in cooperative groups)

51. National Mathematics Advisory Panel “ All-encompassing recommendations that instruction should be entirely ‘student centered’ or ‘teacher directed’ are not supported by research.” Teachers must use their professional judgment to determine their methods of instruction.

52. Gradual Release of Responsibility Whole Group Instruction Highest level of teacher support Teacher modeling and think-alouds Mini-lessons, direct instruction Small Group Guided Instruction Moderate level of teacher support Scaffolded instruction tailored to individual needs of students Math Workshop Lowest level of teacher support Independent work by individuals or groups

53. Whole Class Instruction??

54. Whole Class Instruction Advantages Captures everyone’s attention at once. Quick way to present same information to all. Builds mathematical community by creating common experiences. More time can be devoted to the lesson.

55. Whole Class Instruction Challenges Often fails those at top and bottom of class. Fails to target students’ varying levels of competency Difficult to maintain attention of all. Communication opportunities limited. Minimal descriptive feedback from the teacher or peers. Ongoing assessment is more difficult. Students may engage in work based on a misunderstanding and then practice incorrect methods.

56. Effective Uses of Whole Class Instruction When most students are on about the same instructional level for a math concept Introduction of a new series of lessons with an activating strategy to generate interest, enthusiasm, and curiosity Use of literature to teach a math concept Review of previously taught and mastered skills to ensure maintenance Preparing a class for cooperative group work; providing common knowledge about requirements Some assessments (timed math facts tests, for example)

57. Small Group Guided Instruction??

58. Small Group Guided Instruction Is similar to guided reading, but composition of the groups may be even more fluid Homogenous, flexible grouping by level of achievement Requires assessment to determine each student’s level Provides scaffolding to support the learning efforts of students Encourages exploration of math concepts in a risk-free learning environment Maximizes the benefit of co-teaching

59. Small Group Guided Instruction Advantages: Students work at their appropriate levels. Work may be differentiated in procedure, level of difficulty, or by work product. More time can be spent with struggling students. Enhanced communication Students stay focused Incorrect understanding easily detected and corrected Opportunities for ongoing assessment for learning Cooperation among students is encouraged “ the social nature of learning”-Vygotsky

60. Small Group Guided Instruction Challenges More extensive planning required Less direct instruction by teacher of each student Meaningful work must be provided for students who are not in the small group Time must be spent establishing and teaching routines and procedures to ensure uninterrupted small groups.

61. Small Group Guided Instruction Effective Uses: Introduction of new concepts Practice of new skills Instruction with manipulatives Intensive instruction for students having difficulty mastering concepts Introduction of activities that will later become independent work during math workshop Informal assessment Re-teaching based on results of formative assessment

62. Math Workshop Students work independently, in pairs, or in groups. Procedures and routines must be established and practiced. Activities should provide opportunities for exploration or practice of mastered skills . The work need not be related to the work being done in small groups.

63. Math Workshop Activities Follow-up work from small group lesson Paper and pencil practice of previously mastered skill for maintenance Mathematical Investigations/ Problems of the Week Math games (for example Math 24) Work with manipulatives Math journals Multidisciplinary Connections (where Language Arts, Science or Social Studies relate to Math)

64. Versatiles

65. Activboard

67. Mathematical Investigations Questions posed by either the teacher or by students See “Teaching Children Mathematics” for examples Work individually, in pairs, or groups to research and solve Experimentation may be required Students can present their finding to the class using a multi-media display, oral report, or other creative presentation. Vary in length from lasting a single day to lasting several weeks.

68. Mathematical Investigations Helps students gain deeper understanding of math concepts. Promotes connection of math concepts to real life. Develops research skills. Supports the development of oral and written communication skills. Allows students whose strengths lie in other areas to integrate those strengths into their study of mathematics. Provides an opportunity for assessment (both formal and informal)

70. Math Games: Can you solve it? Math 24 card

72. Work with Manipulatives Give students time to explore prior to focused work Provide clear guidelines for use of manipulatives Establish procedures for ready access and storage Provide a variety of manipulatives for use in problem solving

73. Math Journals Support a more complete understanding. Reinforce comprehension by having students explain concepts or procedures in their own words as a follow-up to a whole class or small group lesson. Encourage use of illustrations and sketches for visual learners and to promote the use of multiple representations. Can be used for documentation of research and experimentation during investigations and to record processes, strategies, and solutions for the problem of the week.

74. Multidisciplinary Connections Activities that incorporate math with other subject areas Graphing Measurement Data tables Probability Economics Comparative studies

75. Math Conferencing

76. Math Conferencing Occurs throughout the day with individual students in any of the components Sometimes used to “trouble shoot” Prompts self-assessment by students Assists teacher in monitoring comprehension and identifying teaching points Increases communication Provides descriptive feedback for students

77. Structure of Conferences (based on Lucy Calkins’ writing conferences) Conferences should be brief and conducted in a conversational tone. Research: The teacher asks about a student’s work and listens for evidence that the child understands the concepts being taught. From this, she determines additional teaching points both for the individual student and the class as a whole. Compliment: The teacher gives an authentic compliment based on some aspect of the child’s work. Teaching Point : The teacher presents a teaching point emphasizing that this is something “really good mathematicians” do. Link : Finally, the conference ends with the teacher encouraging the students to always think about this idea and use it in similar situations.

78. Making a Choice

79. Sample Guided Math Schedule Day Activity Component Monday Activating Strategy Problem Solving Think-Aloud Prep for independent work Whole Class Tuesday Read-aloud Independent work/conferencing Guided Math Group 1 Whole Class Workshop Conferencing Small Group

80. Sample Guided Math Schedule Day Activity Component Wednesday Problem challenge minilesson Independent work/conferencing Guided Math Group 2 Whole Class Workshop Conferencing Small Group Thursday Independent work/conferencing Guided Math Group 3 Guided Math Group 1 Workshop Conferencing Small Group

81. Sample Guided Math Schedule Day Activity Component Friday Math Huddle Create class chart to post in classroom for reference Whole Class

82. Assessment

83. “… assessment is not an end goal, but a means to achieving instructional outcomes.” National Council of Teachers of Mathematics

84. Rationales for Assessment Informing teaching decisions Systematically assessing the child’s strengths and knowledge Finding out what a child can do, both independently and with teacher support Documenting progress for parents and students Summarizing achievement and learning over a given period Reporting to administrators, school board, and various stakeholders Fountas and Pinnell

85. Balanced Assessment Observation Communication Product Balanced assessment provides a “photo album” of student achievement rather than just a “snapshot.”

86. Assessment to Inform Teaching Probably the most important for teachers Especially important for guided math because students who excel in one area of math may have difficulties in another area Accurate grouping demands ongoing, timely, and accurate assessment

87. Turn and Talk What kinds of assessment can you use to determine guided math groups?

88. How can you assess students to determine grouping prior to and during instruction? Observation of an assigned task Small group discussion of problem solving related to the concept to be studied Written explanation of understanding by students in their math journals Paper and pencil pretest Formative test results Performance in earlier work on sequential math concepts Checklist Conferencing

89. Ticket Out the Door How can you use these methods in your classroom? How can using Guided Math help you with your math instruction?

90. Resources Guided Math: A Framework for Mathematics Instruction by Laney Sammons Available online at http://www.teachercreatedmaterials.com/estore/product/50534 Or at other online book sites. To be published in Spring 2010: Mathematical Stretches for Grades K-2 By Laney Sammons

91. Join a Guided Math Group : http://tech.groups.yahoo.com/group/guidedmath/

92. Questions? Laney Sammons [email_address]