Csrqi Stw09 Presentation

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This is the presentation of the Mathematics Improvement Toolkit from the partners of the National Forum for Middle Grades Reform. This presentation was given at the 2009 Schools to Watch conference in Washington DC.

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Csrqi Stw09 Presentation

  1. 1. The National Forum Mathematics Improvement Toolkit Presented by: Deborah Kasak Sara Freedman Emily Fagan Anna McTigue Stephen Best
  2. 2. Goals for this Presentation
  3. 3. Goals for this Presentation • Provide background on the purpose of the toolkit, and the teaching and learning needs it was designed to meet • Introduce the toolkit and its components • Try out some of the actual PD activities embedded within these tools • Provide additional information for future use and identify interested sites
  4. 4. What is the Mathematics Improvement Toolkit?
  5. 5. What is the Mathematics Improvement Toolkit?  Joint venture of four groups to address the needs of special populations  Provides support for teachers, professional developers, decision makers, and students around middle grades mathematics instruction  Addresses specific instructional needs that are often ignored.
  6. 6. Goal of the Project
  7. 7. Goal of the Project  Create professional development resources to address instructional needs of: English Language Learners Students with Special Needs Students and Teachers in Rural Settings Communities and Families
  8. 8. Partners
  9. 9. Partners  National Forum for Middle Grades Reform  Turning Points (Center for Collaborative Education)  Talent Development (Johns Hopkins University)  Educational Development Center  Middle Start (Academy for Educational Development)  Funded by the U.S. Department of Education (Comprehensive School Reform program)
  10. 10. Common Ideas and Considerations
  11. 11. Common Ideas and Considerations  Mathematics instruction need to focus on building deeper conceptual understanding
  12. 12. Common Ideas and Considerations  Mathematics instruction need to focus on building deeper conceptual understanding  Resources are designed for use with math teachers and others supporting mathematics learning for ALL students
  13. 13. Common Ideas and Considerations  Mathematics instruction need to focus on building deeper conceptual understanding  Resources are designed for use with math teachers and others supporting mathematics learning for ALL students  Materials need to focus on getting teachers to reflect on practice
  14. 14. Common Ideas and Considerations  Mathematics instruction need to focus on building deeper conceptual understanding  Resources are designed for use with math teachers and others supporting mathematics learning for ALL students  Materials need to focus on getting teachers to reflect on practice  Effective professional development requires extensive time and ongoing implementation
  15. 15. Teaching High-Level Mathematics to English LanguageTool #1 Learners
  16. 16. Teaching High-Level Mathematics to English LanguageTool #1 Learners  Issue: Teachers need support to ensure that English language learners have access to and are successful in learning high-level mathematics.
  17. 17. Teaching High-Level Mathematics to English LanguageTool #1 Learners  Issue: Teachers need support to ensure that English language learners have access to and are successful in learning high-level mathematics.  Primary Resources: Professional development workshops that include videos, a participants’ packet and facilitator materials.
  18. 18. Teaching High-Level Mathematics to English LanguageTool #1 Learners  Issue: Teachers need support to ensure that English language learners have access to and are successful in learning high-level mathematics.  Primary Resources: Professional development workshops that include videos, a participants’ packet and facilitator materials.  Combines a focus on English language learners with general issues regarding deepening understanding of concepts in mathematics
  19. 19. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners
  20. 20. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners Who are the English language learners in our schools today?
  21. 21. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners Who are the English language learners in our schools today?  English language learners are the fastest growing segment of the school population. 1 out of 10 students enrolled in public schools is an English language learner.  Nearly 1 out of 3 students enrolled in urban schools is an English language learner.  The percentage of English language learners enrolled in schools is increasing throughout the United States, in suburban and rural, as well as urban, communities.
  22. 22. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners
  23. 23. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners What do we know about their experience in our schools?
  24. 24. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners What do we know about their experience in our schools?  English language learners have a strong desire to receive an education. They have the highest daily attendance rate of any segment of the school population.  English language learners have the lowest out of school suspension rates of any segment of the school population.
  25. 25. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners
  26. 26. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners However...  English language learners have the lowest standardized test scores of any segment of the school population.  English language learners have the highest dropout rate of any segment of the school population.
  27. 27. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners However...  English language learners have the lowest standardized test scores of any segment of the school population.  English language learners have the highest dropout rate of any segment of the school population. Why do you think this is so? THINK WRITE PAIR SHARE
  28. 28. Letʼs look at a typical word problem
  29. 29. Letʼs look at a typical word problem A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job?
  30. 30. Letʼs look at a typical word problem A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job? What specific challenges do you think an English language learner in the middle grades might have in trying to answer the question posed by this problem? (Notice that you are NOT solving the problem; instead, you are analyzing the difficulties raised for a diverse group of English language learners as they approach the problem.)
  31. 31. WRITE: Use the handout to record your responses
  32. 32. WRITE: Use the handout to record your responses A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job?
  33. 33. WRITE: Use the handout to record your responses A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job?
  34. 34. WRITE: Use the handout to record your responses A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job? BEST PRACTICE: PROVIDING an ORGANIZING TEMPLATE • saves time • focuses English language learners’ attention on the mathematical concepts rather than copying in a new language • creates expectations about # and quality of responses
  35. 35. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners
  36. 36. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners What are the LANGUAGE challenges in this problem for English language learners? A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job?
  37. 37. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners What are the LANGUAGE challenges in this problem for English language learners? A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only Small Group three workers. How long should it take them to do the job? discussion GROUP #1 #2 #1 #2 Get into groups of four. Assign one person to chart the responses to the first question, one at a time. Take turns listening to each others’ ➟ ➟ responses. ➟ ➟ As each person speaks, ask any questions or make comments that help expand their comments further. ➟ #4 ➟ #3 #4 #3
  38. 38. Teaching High-Level Mathematics Tool #1 to English LanguageTool #1 Learners
  39. 39. Focus 2: Students with Special Universal Design Curriculum Modules Learning Needs
  40. 40. Focus 2: Students with Special Universal Design Curriculum Modules Learning Needs  Issue: Curriculum materials do not support students with special learning needs.
  41. 41. Focus 2: Students with Special Universal Design Curriculum Modules Learning Needs  Issue: Curriculum materials do not support students with special learning needs.  Primary Resources: Modified curriculum resources, student materials, and instructional practices based on Universal Design for Learning principles
  42. 42. Focus 2: Students with Special Universal Design Curriculum Modules Learning Needs  Issue: Curriculum materials do not support students with special learning needs.  Primary Resources: Modified curriculum resources, student materials, and instructional practices based on Universal Design for Learning principles  Resources need to be comprehensive in nature to have full impact on learning.
  43. 43. Focus: Students with Special Learning Needs
  44. 44. Focus: Students with Special Learning Needs  Students come into a class with varying levels of understanding
  45. 45. Focus: Students with Special Learning Needs  Students come into a class with varying levels of understanding  Some students need explicit instruction to get to a functional level
  46. 46. Focus: Students with Special Learning Needs  Students need support for visual, auditory, attention, and memory functions.
  47. 47. Focus: Students with Special Learning Needs  Students need support for visual, auditory, attention, and memory functions.
  48. 48. Focus 2: Students with Special Tool #3Collaboration and Co-Teaching Learning Needs
  49. 49. Focus 2: Students with Special Tool #3Collaboration and Co-Teaching Learning Needs  Issue: Mathematics and Special Educators are sometimes paired to co-teach without specific professional development and preparation
  50. 50. Focus 2: Students with Special Tool #3Collaboration and Co-Teaching Learning Needs  Issue: Mathematics and Special Educators are sometimes paired to co-teach without specific professional development and preparation  Primary Resources: Video, a PowerPoint presentation, and a facilitator guide for a workshop to implement or strengthen co-teaching.
  51. 51. Focus 2: Students with Special Tool #3Collaboration and Co-Teaching Learning Needs  Issue: Mathematics and Special Educators are sometimes paired to co-teach without specific professional development and preparation  Primary Resources: Video, a PowerPoint presentation, and a facilitator guide for a workshop to implement or strengthen co-teaching.  Teachers benefit from seeing and discussing a video example of co-teaching
  52. 52. Letʼs try a task...
  53. 53. Letʼs try a task... • Watch a video clip from a lesson taught by co-teachers
  54. 54. Letʼs try a task... • Watch a video clip from a lesson taught by co-teachers • As you watch, jot down your ideas about the questions:
  55. 55. Letʼs try a task... • Watch a video clip from a lesson taught by co-teachers • As you watch, jot down your ideas about the questions: • What roles did the co-teachers take?
  56. 56. Letʼs try a task... • Watch a video clip from a lesson taught by co-teachers • As you watch, jot down your ideas about the questions: • What roles did the co-teachers take? • What actions did they take to support student learning?
  57. 57. Letʼs try a task...
  58. 58. Co-teaching Roles
  59. 59. Co-teaching Roles • Work with a partner and brainstorm roles that co-teachers could take to benefit students.
  60. 60. Co-teaching Roles • Work with a partner and brainstorm roles that co-teachers could take to benefit students. • Record your ideas on the handout.
  61. 61. Focus 2:Language in the MathSpecial Students with Classroom Learning Needs Tool #4
  62. 62. Focus 2:Language in the MathSpecial Students with Classroom Learning Needs Tool #4  Issue: Sometimes difficulty with language presents an obstacle to learning mathematics
  63. 63. Focus 2:Language in the MathSpecial Students with Classroom Learning Needs Tool #4  Issue: Sometimes difficulty with language presents an obstacle to learning mathematics  Primary Resources: Video, a PowerPoint presentation, and a facilitator guide for a workshop exploring the language demands and challenges in mathematics and offering vocabulary and writing strategies to address these challenges.
  64. 64. Focus 2:Language in the MathSpecial Students with Classroom Learning Needs Tool #4  Issue: Sometimes difficulty with language presents an obstacle to learning mathematics  Primary Resources: Video, a PowerPoint presentation, and a facilitator guide for a workshop exploring the language demands and challenges in mathematics and offering vocabulary and writing strategies to address these challenges.  With instruction and support in communication skills, students can more deeply develop and express their mathematical ideas.
  65. 65. Focus 2:Language in the MathSpecial Students with Classroom Learning Needs Tool #4
  66. 66. Focus 2:Language in the MathSpecial Students with Classroom Learning Needs Tool #4 Language Module topics: ✦ Demands and challenges of language ✦ Instructional strategies ✦ Planning for vocabulary instruction ✦ Writing strategies for mathematics
  67. 67. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development
  68. 68. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Issue: Access to quality mathematics PD
  69. 69. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Issue: Access to quality mathematics PD  Primary Resources: Online professional development program, PD materials focusing on depth of understanding and appropriate instruction
  70. 70. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Issue: Access to quality mathematics PD  Primary Resources: Online professional development program, PD materials focusing on depth of understanding and appropriate instruction  High quality PD in mathematics education requires reflection on practice and sample tasks and cases.
  71. 71. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development
  72. 72. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community
  73. 73. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community
  74. 74. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community Modifying a Task: Task 1  Focus on mathematics The Old Farmer’s Almanac tasks as a lens to suggests that you can tell the temperature outside by examine teaching counting the chirps a cricket practice and student makes in 14 seconds and adding 40 (to get the understanding temperature in degrees Fahrenheit). Use this to find how many chirps the cricket makes when it is 72 degrees. middlestart
  75. 75. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community Modifying a Task: Task 2  Focus on mathematics tasks as a lens to The cost of a taxi in the city of Boston is $2.50 for using examine teaching the cab, plus $0.30 for every fifth of a mile. What is the practice and student cost of a two mile ride? understanding What is the cost of an N-mile ride? middlestart
  76. 76. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community Modifying a Task: Task 3  Focus on mathematics tasks as a lens to examine teaching Write an expression to x represent the area of the practice and student figure at right. x understanding 5 x middlestart
  77. 77. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community Modifying a Task: Task 4  Focus on mathematics Which of the following is true about the tasks as a lens to equation at the right? examine teaching a) If you cancel the x’s, the equation says 1/2 = 1, which is impossible, so there is no x+1 = 1 practice and student solution. x+2 b) It might have solutions, because n could understanding be a fraction or negative number. c) It can’t have any solutions, because x + 1 can’t be equal to x + 2, so that ration can’t be equal to 1. middlestart
  78. 78. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community Modifying a Task: Task 5  Focus on mathematics What type of sequence is shown in the figures tasks as a lens to at the right? Explain. examine teaching a) Linear b) Quadratic 1 3 6 practice and student c) Exponential understanding d) None of the above 10 15 middlestart
  79. 79. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding
  80. 80. Letʼs try a task...
  81. 81. Letʼs try a task... Shade 6 of the small squares in the rectangle shown below. Using the diagram, explain how to determine each of the following: 1. the percent area that is shaded 2. the decimal part of the area that is shaded 3. the fractional part of the area that is shaded.
  82. 82. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work
  83. 83. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work
  84. 84. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work
  85. 85. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work
  86. 86. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development Tasks as Tasks as enacted they Tasks as by appear in set up by teachers curriculum teachers Student and materials learning students
  87. 87. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development Mathematical Task Framework (Stein & Smith) Tasks as Tasks as enacted they Tasks as by appear in set up by teachers curriculum teachers Student and materials learning students
  88. 88. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online middlestart community Module 1 - Case 1: David Orcutt Focus on mathematics This mini-case provides an introduction to the use of cases as a reflective professional development tool, and is not intended  for sustained use. This also uses student work examples to explore understandings and misconceptions around fractions, percents, and decimals. tasks as a lens to INTRODUCTION AND CONTEXT David Orcutt is one of two 7th grade mathematics teachers in the lone junior high school for this district. The district serves students from a largely rural agricultural and recreational area which includes two villages. The school is a 7-8 school in a small school building next to the district’s examine teaching high school. In fact, a number of teachers are on the faculty of both schools to provide appropriate coverage for topic areas. David has four classes among his other duties as the 7th grade advisor and a track coach. In his three years of teaching, he has learned that students coming in from the two K-6 schools in practice and student the district (as well as a small but growing migrant labor population that is becoming a more permanent fixture in the area) often have varying skills and understanding in mathematics. To understand each of the student’s abilities and conceptions about basic topics, he has devised a two week introduction to his course which addresses a different topic from the grade 4-6 understanding standards each day or two, and uses this to establish norms for classroom participation, work expectations, etc. The following sample of classroom interaction starts by asking students to take out the homework task from the previous day, which was really a pre-assessment of sorts to understand student knowledge of decimals, percents, and fractions. CLASSROOM ACTIVITIES  Review student work David starts class by greeting all students at the door as they come in, and has a problem on the board, which he reminds students to get a paper out and copy the problem down after they have taken their homework out from the previous day. Meanwhile, he checks attendance and missing assignments from the previous day, and then begins wandering through the aisles to see what students are doing with the problems on the board, and whether they have their homework out. Review brief case studies He quickly scans the homework for each student, noting whether they have all twenty problems  done, and whether they have them numbered, the problem written down, and the answer underlined for each. Most do, which results in him writing a “10” on the top of the page, but a couple did not finish, receiving 5 and 7 points respectively, and three others had 3 points deducted from these for not organizing their work properly. For these, David underlined a few of the answers to encourage reflection they had in their work that were not already underlined, and had jotted down the words “show your steps” on some of these papers. While doing this, he marked on a copy of a grade sheet the points for the homework assignment for each student. Following this fairly quick review (which took four minutes from the time he started moving around the room), he told the students they would review the answers of the homework. He circled the room as he called out problem numbers, and would look around the room to see who was looking at him (or not) and would call out the names of students to state what their answer was. Once one student gave the answer, he would call on two other students and ask if they came up with the
  89. 89. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community same answer as the original student, or if they had something different. At every problem in which all students agreed on the answer, he would quickly ask if any other answers were out there, and unless a quick response came, he would say “correct” and repeat the problem number and answer and move on. When students disagreed, he would quickly survey students in the room to see which of the stated answers other students got, or, what other answers people came up with,  Focus on mathematics and unless it seemed that one was an outlier, would note that problem number of the whiteboard, so that the class could go through it after checking homework. Six of the problems were noted on the board, and he they asked, problem by problem, if there were any volunteers to go to the board and do the problem. Two of the problems had no volunteers, so he asked one student what tasks as a lens to answer they got for the problem, then asked if anyone had a different answer, and had both (or more if several different answers arose) go up to the board to write their explanation or procedures for the problem. One of the two problems that had contested answers was the following: examine teaching ! Emma was asked to order the following numbers from smallest to largest: .43, 8%, and .7 ! Emma’s order was: .7, 8%, .43 ! Is she correct? Why or why not? Two students wrote their answers on the board initially as shown below. practice and student Student D: No because .43 is just about half and .7 is almost full and 8% is like 8 1s. .43 .7 8% Student F: She is correct because 7 is the smallest and 43 is the biggest understanding The following dialog is taken from this activity: DO: “So, what do we think everyone. We have two answers here. What do we think?” Student H: “[D] is right. Emma didn’t get the right answer.”  Review student work DO: “And why is that?” H: “Well, sort of right. Emma didn’t get the right answer, but [D] didn’t get it right either.” DO: “[F], what you you think? You said Emma got the right answer. Explain what you said.”  Review brief case studies F: “Well, the numbers get larger, um, in Emma’s order, and, um, the dots and percents are the same cause you can change from dots to percents and so I, um put them in order, and so, um, 7 is smallest, then 8, then 43.” to encourage reflection H: “But they aren’t the same. Dots are two places different.” DO: “[D], what do you think? You said Emma wasn’t right, just like [H], but she said you weren’t either. What do you think?” D: “I was just trying to see what they are close to, and .43 is close to .5, which is a half. .7 is bigger. It is nearly a whole thing, and definitely more than half. The percents don’t have the decimals, so I thought 8% is like 8 whole things. But I think [H] is kinda right, um, ‘cause you have to do move the dot two places.”
  90. 90. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community DO: “Let’s see what someone else says. [G], how about you? What did you say?” G: “I said Emma was wrong. It should be 8%, .43, .7 in that order because I put them all in percents.”  Focus on mathematics DO: “Aha. There we go. You put them all in percents. All in the same units. That is exactly what we want to do when we have decimals and percents together is put them in the same units. [H], is that what you meant? Is that what you did?” tasks as a lens to H: “Yeah, I made them all the same, but I didn’t do percents. I changed percents to fractions, so they were all some part of 100.” DO: “Excellent. There we go. We want to change them all to the same, and the best way is to change them to fractions. Since we have percents, we should change them to parts of 100. That examine teaching is what percents really are. They are parts of 100. So, when you have all of your test right, for instance, you have 100%. You get everything out of 100. So, how do we want to change these to fractions of 100?” practice and student C: (called on after raising hand) “If it is one place. like .7 was, that is 7 out of 10, because the first place is tenths. Then hundredths. so we could add a zero to the end of that, because .7 is the same as .70, and that is seventy out of a hundred.” understanding DO: “Great. That’s exactly it. Are we okay? Can we move on?” No responses, so they go on to the next question. Shortly thereafter, David moves through the other answers, and to the boardwork task. This task is written on the board already. It was modified by David from a task he had seen in a workshop focusing on differentiation, which was addressing visual learners. The original task from the workshop is below.  Review student work Shade 10 of the small squares in the rectangle shown below. Using the diagram, explain how to determine each of the following: a) the percent area that is shaded, b) the decimal part of the area that is shaded, and c) the fractional part of the area that is shaded.  Review brief case studies to encourage reflection David’s modified version that is on the board is the following: Shade 10 of the boxes in the rectangle shown below (same rectangle). Find the percent area that is shaded. David says that, in the interest of time, he is going to go through it, and asks students to watch. He shades in 10 of the rectangles, picking them at random, and shading individual rectangles.
  91. 91. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community DO: “So, it really doesn’t matter which ones I pick, it will be the same. What I really care about is how many total ones we have. [A], how many total boxes are there?” A: “40”  Focus on mathematics DO: “And how did you get that?” A: “I counted ten across, and there are four rows, so it was four times ten.” tasks as a lens to DO: “Exactly... or you could count everyone of them if you didn’t figure that out. So, what next (looking at A)?” A: “Well, it is a quarter. There are 10 out of 40, and if we write that as a fraction (DO pauses A with examine teaching a hand gesture and writes this on the board as the fraction 10/40, and then motions for him to proceed)... so yeah, that’s it. And then you can cross out the zeros, cause 10 out of 40 is like 1 out of 4, and that’s a quarter. And a quarter is always 25%.” practice and student DO: “Exactly. Does everyone see that? Once [A] got it to a fraction, he could easily change it to a percent. If it was a fraction you didn’t know already, like... suppose we had 12 shaded boxes instead? You could make it 12 out of 40, and then cross multiply to figure out the number out of 100 (as he draws on the board ‘12/40 = n/100’ and then proceeds to write, ’12 x 100 = n x 40’), understanding and so in this case you could multiple 12 and 100...[A], what is that?” A: “Twelve and a hundred? That’s one thousand two hundred.” DO: “and divide that by 40 and we would get 30. Thirty percent... if it was twelve out of 100.” Do you all see that?  Review student work The class seems to agree quietly, and David moves on to the next part of class...  Review brief case studies to encourage reflection
  92. 92. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work  Review brief case studies to encourage reflection  Teachers share examples, observations, and reflections on their own and others practice.
  93. 93. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work  Review brief case studies to encourage reflection  Teachers share examples, observations, and reflections on their own and others practice.
  94. 94. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work  Review brief case studies to encourage reflection  Teachers share examples, observations, and reflections on their own and others practice.
  95. 95. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Online community  Focus on mathematics tasks as a lens to examine teaching practice and student understanding  Review student work  Review brief case studies to encourage reflection  Teachers share examples, observations, and reflections on their own and others practice.
  96. 96. Collaborative Online Tool #5 Focus 3: Rural Education Professional Development  Initial module: Developing Student Understanding of Mathematics  Content modules: Issues in the instruction of...  Ratio and Proportion  Patterns, Functions, and Algebraic Reasoning  Measurement and Geometry  Skill and strategy module: Issues in the instruction of Problem Solving and Use of Inquiry
  97. 97. Tool #6 Engaging Families and Communities
  98. 98. Tool #6 Engaging Families and Communities  Issue: Schools struggle with this in general and many mathematics issues for students arise from parent/community misunderstandings, stereotypes, and attitudes toward math.
  99. 99. Tool #6 Engaging Families and Communities  Issue: Schools struggle with this in general and many mathematics issues for students arise from parent/community misunderstandings, stereotypes, and attitudes toward math.  Primary Resources: Online PD tools for schools and teachers that guide them through family engagement Resources to guide communication with parents
  100. 100. Tool #6 Engaging Families and Communities  Issue: Schools struggle with this in general and many mathematics issues for students arise from parent/community misunderstandings, stereotypes, and attitudes toward math.  Primary Resources: Online PD tools for schools and teachers that guide them through family engagement Resources to guide communication with parents  Audience for these resources needs to be broader than mathematics teachers alone.
  101. 101. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities
  102. 102. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities
  103. 103. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities  Sample discussion materials (big picture) and communications
  104. 104. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities  Sample discussion materials (big picture) and communications
  105. 105. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities  Sample discussion materials (big picture) and communications  Strategies to provide an awareness of approaches to learn mathematics
  106. 106. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities  Sample discussion materials (big picture) and communications  Strategies to provide an awareness of approaches to learn mathematics  Discussion of deeper issues and research
  107. 107. Focus #6Family Engagement Tool 4: Engaging Families and Communities  Needs assessment and introductory activities  Sample discussion materials (big picture) and communications  Strategies to provide an awareness of approaches to learn mathematics  Discussion of deeper issues and research
  108. 108. For more information…
  109. 109. For more information…  Visit: http://www.middlegrademath.org to find out more about the tools...  And come back to the site again in August, when all of the resources will be available.

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