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Guided math power_point_by_the_author_of_guided_math


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Guided math power_point_by_the_author_of_guided_math

  1. 1. Guided Math A Framework for Math Instruction Laney Sammons
  2. 2. Background Information <ul><li>My experience </li></ul><ul><li>Lessons learned in kindergarten </li></ul><ul><li>Differentiating to meet diverse needs </li></ul><ul><li>Links to literacy instruction and the Guided Reading model </li></ul><ul><li>Development of the Guided Math framework </li></ul>
  3. 3. What is Guided Math? <ul><li>Guided Math is a flexible instructional </li></ul><ul><li>framework that enables teachers to </li></ul><ul><li>promote the deep mathematical understanding </li></ul><ul><li>and computational fluency of their students by </li></ul><ul><li>determining their unique needs and then </li></ul><ul><li>prescriptively addressing those needs through a </li></ul><ul><li>combination of whole class instruction, small </li></ul><ul><li>group instruction, math workshop, and </li></ul><ul><li>conferences within a classroom environment </li></ul><ul><li>supportive of numeracy. </li></ul>
  4. 4. Samuel E. Hubbard Elementary School Forsyth, Georgia <ul><li>Small town in an area that has been predominately poor and rural, but is gradually becoming suburban. </li></ul><ul><li>Pre-K through Fifth Grade </li></ul><ul><li>Title I School of Distinction for 10 years </li></ul><ul><li>63% Free/Reduced Lunch </li></ul><ul><li>34% Minority Students </li></ul><ul><li>924 Students </li></ul>Why Implement the Guided Math Framework?
  5. 5. Samuel E. Hubbard Elementary School Forsyth, Georgia <ul><li>Georgia implemented new, more rigorous math performance standards for Kindergarten through Second Grade in 2006-2007. </li></ul><ul><li>Guided Math implemented in 2007-2008 </li></ul>Why Implement the Guided Math Framework? 2007 (New Standards) 2008 (Guided Math)
  6. 6. Samuel E. Hubbard Elementary School Forsyth, Georgia <ul><li>The new math performance standards were implemented in grades three to five in 2007-2008. </li></ul><ul><li>Guided Math implemented in 2008-2009 </li></ul>Why Implement the Guided Math Framework? 2008 (New Standards) 2009 (Guided Math)
  7. 7. Samuel E. Hubbard Elementary School <ul><li>Students Exceeding Standards in Math </li></ul>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. 8. The Traditional Approach to Teaching Math <ul><li>Large group instruction </li></ul><ul><li>All students work on the same level </li></ul><ul><li>Primarily instruction and practice from text book </li></ul><ul><li>Emphasis on paper and pencil work </li></ul><ul><li>One correct answer </li></ul><ul><li>Individual work </li></ul>
  9. 9. Does this approach work? <ul><li>Successful for some students </li></ul><ul><li>Less successful for those who quickly acquire mastery </li></ul><ul><li>Even less successful for struggling students </li></ul><ul><li>Encourages emphasis on computation skills </li></ul><ul><li>Little opportunity for communication </li></ul><ul><li>More emphasis on evaluation, rather than assessment for learning </li></ul>
  10. 10. Why should we explore different ways to teach math?
  11. 11. To more effectively teach math, we must <ul><li>reach students at all levels of achievement </li></ul><ul><li>provide diverse methods of learning </li></ul><ul><li>allow more opportunities for observation and communication by students </li></ul><ul><li>encourage active engagement by students </li></ul>
  12. 12. How can we effectively teach math when we have a classroom of students at many different levels of achievement?
  13. 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. 14. The Foundational Principles of Guided Math <ul><li>All children can learn mathematics </li></ul><ul><li>A numeracy-rich environment promotes mathematical learning. </li></ul><ul><li>Learning at its best is a social process </li></ul><ul><li>Learning mathematics is a constructive process. </li></ul><ul><li>An organized classroom environment supports the learning process. </li></ul>
  15. 15. The Foundational Principles of Guided Math
  16. 16. <ul><li>Daily Components </li></ul><ul><li>Classroom Environment of Numeracy </li></ul><ul><li>Math Warm-up/Calendar Board </li></ul><ul><li>Individual Conferences </li></ul><ul><li>Ongoing Assessment </li></ul>Guided Math Framework
  17. 17. Guided Math Framework <ul><li>Choice Components </li></ul><ul><li>Whole-Class Instruction </li></ul><ul><li>Small-Group Instruction </li></ul><ul><li>Math Workshop </li></ul>
  18. 18. Use of Manipulatives Creating a Classroom Environment of Numeracy
  19. 19. Read literature that promotes exploration and application of math concepts
  20. 20. Focus on Mathematical Vocabulary
  21. 21. Display a Mathematics Word Wall
  22. 22. Link Math to Real Life
  23. 23. Link Math to Real Life <ul><li>Goal Setting </li></ul><ul><li>Self-monitoring of achievement by students </li></ul>
  24. 24. Demonstrate, model, and do “think alouds” of problem solving strategies.
  25. 25. Integrate math into all curricular areas.
  26. 26. Math-Related Classroom Responsibilities <ul><li>Attendance </li></ul><ul><li>Lunch counts </li></ul><ul><li>Fund raising </li></ul><ul><li>Class elections </li></ul><ul><li>Field Trip Collections </li></ul><ul><ul><li>Total cost of the trip </li></ul></ul><ul><ul><li>Total amount collected </li></ul></ul><ul><ul><li>Percentage of total amount needed </li></ul></ul>
  27. 27.
  28. 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. 29. Create and display of class-made charts tell of math processes and activities .
  30. 30. Create and display of class-made charts tell of math processes and activities.
  31. 31. Use student calendars and/or agendas.
  32. 32. Creating Math Rich Classroom Environments Frequently use graphing activities based on classroom activities. Provide instruments of measurement (thermometers, rulers, scales, measuring cups).
  33. 33. Turn and Talk What are some other ways to create an environment of numeracy ?
  34. 34. Morning Math Warm-ups <ul><li>Mathematical Stretches </li></ul><ul><li>Mathematical Current Events </li></ul><ul><li>Math-Related Classroom </li></ul><ul><li>Responsibilities </li></ul><ul><li>Calendar Board </li></ul>
  35. 35. Mathematical Stretches Data Collection and Analysis Tasks
  36. 36. Mathematical Stretches Data Collection and Analysis Tasks
  37. 37. Mathematical Stretches Data Collection and Analysis Tasks
  38. 38. Mathematical Stretches Data Collection and Analysis Tasks
  39. 39. Mathematical Stretches Data Collection and Analysis Tasks
  40. 40. Mathematical Stretches Data Collection and Analysis Tasks
  41. 41. Mathematical Stretches Number of the Day Stretch
  42. 42. Mathematical Stretches What’s Next? Stretch
  43. 43. Mathematical Stretches <ul><li>How Did My Family Use Math Last Night? Stretch </li></ul><ul><li>_______________ Makes Me Think of… Stretch </li></ul>
  44. 44. Math Current Events <ul><li>Teacher or students bring in articles or web sites with current events that have to do with math: </li></ul><ul><li>Levels of precipitation </li></ul><ul><li>Economic statistics </li></ul><ul><li>Population </li></ul><ul><li>Vote counts </li></ul>
  45. 45.
  46. 46. Daily Calendar/Morning Work <ul><li>Problems of the Day </li></ul><ul><li>Incredible Equations </li></ul><ul><li>Daily Data Work </li></ul><ul><li>Calendar Activities </li></ul><ul><li>Preview new concepts and skills. </li></ul><ul><li>Maintain previously mastered skills. </li></ul><ul><li>Regular focus on difficult to master skills </li></ul>
  47. 47. Using Coins to Represent the Date
  48. 48. Problems of the Day <ul><li>Provide problems with more than one correct answer and multiple methods of solution. </li></ul><ul><li>Require students to tell how they solved the problem either orally or in writing with multiple representations. </li></ul><ul><li>Students complete independently; then as a class go over strategies used to solve the problem and possible answers. </li></ul><ul><li>Include new vocabulary. </li></ul><ul><li>Present problems in unfamiliar ways. </li></ul><ul><li>Allow students opportunities to struggle to discover the answers. </li></ul>
  49. 49. Daily Calendar Board <ul><li>Provides opportunities for communication through turn and talk, math journals, and cooperative group work. </li></ul><ul><li>Helps students deepen understanding and develop mathematical reasoning because concepts are filtered through conversation (speaking, listening, reflecting, and refining). </li></ul>
  50. 50. Menu of Instruction <ul><li>Whole class instruction </li></ul><ul><li>Small group guided instruction </li></ul><ul><li>Math Workshop (independent work or work in cooperative groups) </li></ul>
  51. 51. National Mathematics Advisory Panel <ul><li>“ All-encompassing recommendations that instruction should be entirely ‘student centered’ or ‘teacher directed’ are not supported by research.” </li></ul><ul><li>Teachers must use their professional judgment to determine their methods of instruction. </li></ul>
  52. 52. Gradual Release of Responsibility <ul><li>Whole Group Instruction </li></ul><ul><ul><li>Highest level of teacher support </li></ul></ul><ul><ul><li>Teacher modeling and think-alouds </li></ul></ul><ul><ul><li>Mini-lessons, direct instruction </li></ul></ul><ul><ul><li>Small Group Guided Instruction </li></ul></ul><ul><ul><ul><li>Moderate level of teacher support </li></ul></ul></ul><ul><ul><ul><li>Scaffolded instruction tailored to individual needs of students </li></ul></ul></ul><ul><ul><ul><li>Math Workshop </li></ul></ul></ul><ul><ul><ul><ul><li>Lowest level of teacher support </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Independent work by individuals or groups </li></ul></ul></ul></ul>
  53. 53. Whole Class Instruction??
  54. 54. Whole Class Instruction <ul><li>Advantages </li></ul><ul><ul><li>Captures everyone’s attention at once. </li></ul></ul><ul><ul><li>Quick way to present same information to all. </li></ul></ul><ul><ul><li>Builds mathematical community by creating common experiences. </li></ul></ul><ul><ul><li>More time can be devoted to the lesson. </li></ul></ul>
  55. 55. Whole Class Instruction <ul><li>Challenges </li></ul><ul><ul><li>Often fails those at top and bottom of class. </li></ul></ul><ul><ul><li>Fails to target students’ varying levels of competency </li></ul></ul><ul><ul><li>Difficult to maintain attention of all. </li></ul></ul><ul><ul><li>Communication opportunities limited. </li></ul></ul><ul><ul><li>Minimal descriptive feedback from the teacher or peers. </li></ul></ul><ul><ul><li>Ongoing assessment is more difficult. </li></ul></ul><ul><ul><li>Students may engage in work based on a misunderstanding and then practice incorrect methods. </li></ul></ul>
  56. 56. Effective Uses of Whole Class Instruction <ul><li>When most students are on about the same instructional level for a math concept </li></ul><ul><li>Introduction of a new series of lessons with an activating strategy to generate interest, enthusiasm, and curiosity </li></ul><ul><li>Use of literature to teach a math concept </li></ul><ul><li>Review of previously taught and mastered skills to ensure maintenance </li></ul><ul><li>Preparing a class for cooperative group work; providing common knowledge about requirements </li></ul><ul><li>Some assessments (timed math facts tests, for example) </li></ul>
  57. 57. Small Group Guided Instruction??
  58. 58. Small Group Guided Instruction <ul><li>Is similar to guided reading, but composition of the groups may be even more fluid </li></ul><ul><li>Homogenous, flexible grouping by level of achievement </li></ul><ul><li>Requires assessment to determine each student’s level </li></ul><ul><li>Provides scaffolding to support the learning efforts of students </li></ul><ul><li>Encourages exploration of math concepts in a risk-free learning environment </li></ul><ul><li>Maximizes the benefit of co-teaching </li></ul>
  59. 59. Small Group Guided Instruction <ul><li>Advantages: </li></ul><ul><ul><li>Students work at their appropriate levels. </li></ul></ul><ul><ul><li>Work may be differentiated in procedure, level of difficulty, or by work product. </li></ul></ul><ul><ul><li>More time can be spent with struggling students. </li></ul></ul><ul><ul><li>Enhanced communication </li></ul></ul><ul><ul><li>Students stay focused </li></ul></ul><ul><ul><li>Incorrect understanding easily detected and corrected </li></ul></ul><ul><ul><li>Opportunities for ongoing assessment for learning </li></ul></ul><ul><ul><li>Cooperation among students is encouraged </li></ul></ul><ul><ul><li>“ the social nature of learning”-Vygotsky </li></ul></ul>
  60. 60. Small Group Guided Instruction <ul><li>Challenges </li></ul><ul><ul><li>More extensive planning required </li></ul></ul><ul><ul><li>Less direct instruction by teacher of each student </li></ul></ul><ul><ul><li>Meaningful work must be provided for students who are not in the small group </li></ul></ul><ul><ul><li>Time must be spent establishing and teaching routines and procedures to ensure uninterrupted small groups. </li></ul></ul>
  61. 61. Small Group Guided Instruction <ul><li>Effective Uses: </li></ul><ul><ul><li>Introduction of new concepts </li></ul></ul><ul><ul><li>Practice of new skills </li></ul></ul><ul><ul><li>Instruction with manipulatives </li></ul></ul><ul><ul><li>Intensive instruction for students having difficulty mastering concepts </li></ul></ul><ul><ul><li>Introduction of activities that will later become independent work during math workshop </li></ul></ul><ul><ul><li>Informal assessment </li></ul></ul><ul><ul><li>Re-teaching based on results of formative assessment </li></ul></ul>
  62. 62. Math Workshop <ul><li>Students work independently, in pairs, or in groups. </li></ul><ul><li>Procedures and routines must be established and practiced. </li></ul><ul><li>Activities should provide opportunities for exploration or practice of mastered skills . </li></ul><ul><li>The work need not be related to the work being done in small groups. </li></ul>
  63. 63. Math Workshop Activities <ul><li>Follow-up work from small group lesson </li></ul><ul><li>Paper and pencil practice of previously mastered skill for maintenance </li></ul><ul><li>Mathematical Investigations/ Problems of the Week </li></ul><ul><li>Math games (for example Math 24) </li></ul><ul><li>Work with manipulatives </li></ul><ul><li>Math journals </li></ul><ul><li>Multidisciplinary Connections (where Language Arts, Science or Social Studies relate to Math) </li></ul>
  64. 64. Versatiles
  65. 65. Activboard
  66. 66.
  67. 67. Mathematical Investigations <ul><li>Questions posed by either the teacher or by students </li></ul><ul><li>See “Teaching Children Mathematics” for examples </li></ul><ul><li>Work individually, in pairs, or groups to research and solve </li></ul><ul><li>Experimentation may be required </li></ul><ul><li>Students can present their finding to the class using a multi-media display, oral report, or other creative presentation. </li></ul><ul><li>Vary in length from lasting a single day to lasting several weeks. </li></ul>
  68. 68. Mathematical Investigations <ul><li>Helps students gain deeper understanding of math concepts. </li></ul><ul><li>Promotes connection of math concepts to real life. </li></ul><ul><li>Develops research skills. </li></ul><ul><li>Supports the development of oral and written communication skills. </li></ul><ul><li>Allows students whose strengths lie in other areas to integrate those strengths into their study of mathematics. </li></ul><ul><li>Provides an opportunity for assessment (both formal and informal) </li></ul>
  69. 69.
  70. 70. Math Games: Can you solve it? Math 24 card
  71. 71.
  72. 72. Work with Manipulatives <ul><li>Give students time to explore prior to focused work </li></ul><ul><li>Provide clear guidelines for use of manipulatives </li></ul><ul><li>Establish procedures for ready access and storage </li></ul><ul><li>Provide a variety of manipulatives for use in problem solving </li></ul>
  73. 73. Math Journals <ul><li>Support a more complete understanding. </li></ul><ul><li>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. </li></ul><ul><li>Encourage use of illustrations and sketches for visual learners and to promote the use of multiple representations. </li></ul><ul><li>Can be used for documentation of research and experimentation during investigations and to record processes, strategies, and solutions for the problem of the week. </li></ul>
  74. 74. Multidisciplinary Connections <ul><li>Activities that incorporate math with other subject areas </li></ul><ul><ul><li>Graphing </li></ul></ul><ul><ul><li>Measurement </li></ul></ul><ul><ul><li>Data tables </li></ul></ul><ul><ul><li>Probability </li></ul></ul><ul><ul><li>Economics </li></ul></ul><ul><ul><li>Comparative studies </li></ul></ul>
  75. 75. Math Conferencing
  76. 76. Math Conferencing <ul><li>Occurs throughout the day with individual students in any of the components </li></ul><ul><li>Sometimes used to “trouble shoot” </li></ul><ul><li>Prompts self-assessment by students </li></ul><ul><li>Assists teacher in monitoring comprehension and identifying teaching points </li></ul><ul><li>Increases communication </li></ul><ul><li>Provides descriptive feedback for students </li></ul>
  77. 77. Structure of Conferences (based on Lucy Calkins’ writing conferences) <ul><li>Conferences should be brief and conducted in a conversational tone. </li></ul><ul><li>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. </li></ul><ul><li>Compliment: The teacher gives an authentic compliment based on some aspect of the child’s work. </li></ul><ul><li>Teaching Point : The teacher presents a teaching point emphasizing that this is something “really good mathematicians” do. </li></ul><ul><li>Link : Finally, the conference ends with the teacher encouraging the students to always think about this idea and use it in similar situations. </li></ul>
  78. 78. Making a Choice
  79. 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. 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. 81. Sample Guided Math Schedule Day Activity Component Friday Math Huddle Create class chart to post in classroom for reference Whole Class
  82. 82. Assessment
  83. 83. “… assessment is not an end goal, but a means to achieving instructional outcomes.” National Council of Teachers of Mathematics
  84. 84. Rationales for Assessment <ul><li>Informing teaching decisions </li></ul><ul><li>Systematically assessing the child’s strengths and knowledge </li></ul><ul><li>Finding out what a child can do, both independently and with teacher support </li></ul><ul><li>Documenting progress for parents and students </li></ul><ul><li>Summarizing achievement and learning over a given period </li></ul><ul><li>Reporting to administrators, school board, and various stakeholders </li></ul><ul><ul><ul><ul><ul><li>Fountas and Pinnell </li></ul></ul></ul></ul></ul>
  85. 85. Balanced Assessment Observation Communication Product Balanced assessment provides a “photo album” of student achievement rather than just a “snapshot.”
  86. 86. Assessment to Inform Teaching <ul><li>Probably the most important for teachers </li></ul><ul><li>Especially important for guided math because students who excel in one area of math may have difficulties in another area </li></ul><ul><li>Accurate grouping demands ongoing, timely, and accurate assessment </li></ul>
  87. 87. Turn and Talk <ul><li>What kinds of assessment can </li></ul><ul><li>you use to determine guided </li></ul><ul><li>math groups? </li></ul>
  88. 88. How can you assess students to determine grouping prior to and during instruction? <ul><li>Observation of an assigned task </li></ul><ul><li>Small group discussion of problem solving related to the concept to be studied </li></ul><ul><li>Written explanation of understanding by students in their math journals </li></ul><ul><li>Paper and pencil pretest </li></ul><ul><li>Formative test results </li></ul><ul><li>Performance in earlier work on sequential math concepts </li></ul><ul><li>Checklist </li></ul><ul><li>Conferencing </li></ul>
  89. 89. Ticket Out the Door <ul><li>How can you use these methods in your classroom? </li></ul><ul><li>How can using Guided Math help you with your math instruction? </li></ul>
  90. 90. <ul><li>Resources </li></ul><ul><li>Guided Math: A Framework for Mathematics Instruction by Laney Sammons </li></ul><ul><li>Available online at </li></ul><ul><li> </li></ul><ul><li>Or at other online book sites. </li></ul><ul><li>To be published in Spring 2010: </li></ul><ul><li>Mathematical Stretches for Grades K-2 </li></ul><ul><li>By Laney Sammons </li></ul>
  91. 91. <ul><li>Join a Guided Math Group : </li></ul><ul><li> </li></ul>
  92. 92. Questions? <ul><li>Laney Sammons </li></ul><ul><li>[email_address] </li></ul>