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RtI Math Student Achievement for ALL Aligning work Systemically and Systematically

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RtI Math Student Achievement for ALL Aligning work Systemically and Systematically

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    1. RtI + Math = Student Achievement for ALL Aligning work Systemically and Systematically Wendy Strickler, Ph.D and Holly Sampson , M.Ed Hamilton County Educational Service Center

    2. Logistics

    3. Mathematics = ALL Students Why do we care? Do you know… According to recent survey data, What percent of the US population are unable to calculate a 10% tip on a lunch?

    4. What percent of eighth-graders can not correctly shade 1/3 of a rectangle?

    5. What percent can not solve a word problem that required dividing fractions?

    6. Here’s a little help… 27% 58% 45%

    7. Answers *58%- Tip *27%- Rectangle *45%- Fractions in Problem Solving

    8. Student Exhibiting Mastery in Algebra Readiness Components Student success in algebra is an indicator that they will be successful in college. Student success in algebra is an indicator that they will be successful in college.

    9. Overall Objectives Learn and discuss components of curriculum, instruction and assessments necessary for tiered intervention support. Review and further understand the systems within the schools/district we work to further enhance the support to our students. Engage participants in an examination of effective mathematic instructional strategies and begin sharing possible resources for interventions and best practices in mathematics instruction.

    10. Quick Math Try this: 101 - 102 = 1 Make one move to create a true statement.

    11. 101 =102 - 1 101- 10˛ = 1

    12. There’s more than one way to skin a cat… Important to acknowledge how individual students work and to continue to build on what we know so we can help students make gains. Working systemically and systematically can help us achieve this.

    13. Systemic / Systematic ??? We’ve always provided support for our students when they need help. It’s not about tweaking something we are already doing. Good intentions- but are we getting the right results. Biggest bang for our Work? Re thinking our energies and knowledge around the research to further support students in a systemic and systematic from the district down to the classroom to individuals students that need the most help at a particular time. We’ve always provided support for our students when they need help. It’s not about tweaking something we are already doing. Good intentions- but are we getting the right results. Biggest bang for our Work? Re thinking our energies and knowledge around the research to further support students in a systemic and systematic from the district down to the classroom to individuals students that need the most help at a particular time.

    14. Systemic / Systematic A few examples of systemic work. Possible Talking Pts. : Teachers: working together to support the needs of students. Thinking of ways to support students at all levels that is cohesive and uniform. Students: Relationship between the computation fluency and how that connects the bigger concepts. How to work systematically to tackle problems in math. A few examples of systemic work. Possible Talking Pts. : Teachers: working together to support the needs of students. Thinking of ways to support students at all levels that is cohesive and uniform. Students: Relationship between the computation fluency and how that connects the bigger concepts. How to work systematically to tackle problems in math.

    15. Turn and Talk What systems are in place within your district/school/team to support mathematics?

    16. Which picture best describes the system/s in which you work? Which picture best describes the system/s in which you work?

    17. Cone represents a healthy school/building systems of instruction and support for students… Premise of RtI for Math is same as RtI for reading --to prevent student underachievement and school failure; provide responsive support to all students Overall process is the same: strong core curriculum and instruction, universal screening, tiered instruction and intervention, continuous progress monitoring and data-based decision making Cone represents a healthy school/building systems of instruction and support for students… Premise of RtI for Math is same as RtI for reading --to prevent student underachievement and school failure; provide responsive support to all students Overall process is the same: strong core curriculum and instruction, universal screening, tiered instruction and intervention, continuous progress monitoring and data-based decision making

    18. This is a conceptualization from the research of a “healthy” school. It shows the idea that 80-90% of students are effectively supported when an effective research validated plan is implemented and sustained throughout all school settings. This graphic also depicts the interrelatedness of academic and behavior support systems. PBS in the classroom includes both behavior and academic support systems because the primary business of classrooms - that is, teaching and learning - requires both the establishment of a social environment conducive to learning as well as effective instruction within sound curriculum. It’s more than effective reading or social skills instruction. It’s the routines, processes, and goals that are in place. A formative assessment feedback loop is critical to determine if the core instruction or curriculum is getting at least 80-90% of students to where they need to be. Continuous study of schools as systems provides convincing evidence that effective behavior supports must include -- in addition to preventive school wide, setting-specific and class-wide processes -- mechanisms for providing strategic intervention to students who are at risk for academic and social failure. These systems for strategic intervention include systematic social skills instruction and other behavioral supports IN ADDITION to the universal supports provided to all students. An effective system will take into account the need to connect some students to this level of support and to provide preventative pre-teaching and re-teaching of specific required behaviors or academic skills. We educators are aware that about 1-5% of students in most schools will need intensive academic interventions. Likewise, about the same percentage of students will need intensive behavioral interventions. Repeatedly, the educational literature tells us that systems of support are both academic and behavioral. If we do not plan behavioral systems of support, we cannot really expect that all students will reach the academic bar. This is a conceptualization from the research of a “healthy” school. It shows the idea that 80-90% of students are effectively supported when an effective research validated plan is implemented and sustained throughout all school settings. This graphic also depicts the interrelatedness of academic and behavior support systems. PBS in the classroom includes both behavior and academic support systems because the primary business of classrooms - that is, teaching and learning - requires both the establishment of a social environment conducive to learning as well as effective instruction within sound curriculum. It’s more than effective reading or social skills instruction. It’s the routines, processes, and goals that are in place. A formative assessment feedback loop is critical to determine if the core instruction or curriculum is getting at least 80-90% of students to where they need to be. Continuous study of schools as systems provides convincing evidence that effective behavior supports must include -- in addition to preventive school wide, setting-specific and class-wide processes -- mechanisms for providing strategic intervention to students who are at risk for academic and social failure. These systems for strategic intervention include systematic social skills instruction and other behavioral supports IN ADDITION to the universal supports provided to all students. An effective system will take into account the need to connect some students to this level of support and to provide preventative pre-teaching and re-teaching of specific required behaviors or academic skills. We educators are aware that about 1-5% of students in most schools will need intensive academic interventions. Likewise, about the same percentage of students will need intensive behavioral interventions. Repeatedly, the educational literature tells us that systems of support are both academic and behavioral. If we do not plan behavioral systems of support, we cannot really expect that all students will reach the academic bar.

    19. Adapted from: Vaughan Gross Center for Reading and Language Arts (2006) and cited resources on slide Adapted from: Vaughan Gross Center for Reading and Language Arts (2006) and cited resources on slide

    20. Tier 1- The Core Curriculum Instruction Assessment

    21. Tier 1-The Core Key Characteristics All students receive this instruction Research-validated core curriculum Instructional gaps filled with supplemental research-based materials Differentiated support Differentiated practices – The average person needs exposure to concepts, vocabulary, etc. avg. 5-7 times/trials to learn it. Know instructional gaps and how to differentiate because of universal screeners and data collectionDifferentiated practices – The average person needs exposure to concepts, vocabulary, etc. avg. 5-7 times/trials to learn it. Know instructional gaps and how to differentiate because of universal screeners and data collection

    22. The Core: Math Curriculum A Balanced Approach Number sense Computation fluency Algebraic thinking Math language Number sense as critical component: lack of number sense seems to be consistent issue for students who fail algebra at 2ndary level Number sense: what number represents, how numbers relate, how numbers can be manipulated Computational fluency seems to be predictor of later math success (only an indicator) Provides supported sequence of learning in same way as grade-level text in reading Algebraic thinking: Fluency with whole numbers Fluency with fractions Geometry and measurement concepts Number sense as critical component: lack of number sense seems to be consistent issue for students who fail algebra at 2ndary level Number sense: what number represents, how numbers relate, how numbers can be manipulated Computational fluency seems to be predictor of later math success (only an indicator) Provides supported sequence of learning in same way as grade-level text in reading Algebraic thinking: Fluency with whole numbers Fluency with fractions Geometry and measurement concepts

    23. Reading digits quickly and accurately Writing digits quickly and accurately Quantity recognition Number sequence Greater/lesser (magnitude) Place value Addition, Subtraction, Multiplication, Division Whole numbers Reading digits quickly and accurately Writing digits quickly and accurately Quantity recognition Number sequence Greater/lesser (magnitude) Place value Addition, Subtraction, Multiplication, Division Whole numbers

    26. Fractions Percents Fractions Percents

    28. Problem Solving (TAPS: Talk Aloud Problem Solving Arthur Whimbey, Jack Lockhead) Math Language How to talk about math problems Problem Solving (TAPS: Talk Aloud Problem Solving Arthur Whimbey, Jack Lockhead) Math Language How to talk about math problems

    29. Tier 1: Math Core Curriculum Checking the Research Base Try: What Works Clearinghouse: http://ies.ed.gov/ncee/WWC/ Johns Hopkins Best Evidence Encyclopedia: www.bestevidence.org Note: What’s Sophisticated about Elementary Mathematics—need to supplement any core program with discussion of coherence, precision, and reasoning in math. E.g.) We often miss showing students the coherence and instead focus on math topics as if they are individualized and separate (e.g. failing to show the relationship between fractions and whole numbers…)Note: What’s Sophisticated about Elementary Mathematics—need to supplement any core program with discussion of coherence, precision, and reasoning in math. E.g.) We often miss showing students the coherence and instead focus on math topics as if they are individualized and separate (e.g. failing to show the relationship between fractions and whole numbers…)

    30. Quick Math The answer is 42. What is the question? NNS - BIG IDEA: There are many ways to represent numbers. It is important to differentiate for students – Uses the communication process standard. Safe- especially if the teacher explicitly models this first. Lead into teaching a lesson. Also point in “sophistication” article about moving students toward comfort with the “abstract” nature of math… Think of a problem you’ve recently used with students, how might this be incorporated with that problem ? NNS - BIG IDEA: There are many ways to represent numbers. It is important to differentiate for students – Uses the communication process standard. Safe- especially if the teacher explicitly models this first. Lead into teaching a lesson. Also point in “sophistication” article about moving students toward comfort with the “abstract” nature of math… Think of a problem you’ve recently used with students, how might this be incorporated with that problem ?

    31. Tier 1 – The Core: Math Instruction Explicit instruction Pre-skills are taught to mastery Strategies, including problem-solving and graphic organizers Determine what those preskills are and teach them with diligence. Determine what those preskills are and teach them with diligence.

    32. Tier 1 – The Core: Math Instruction Concrete-representational-abstract sequence Authentic contexts Multiple opportunities to practice with guidance and feedback Concrete: materials Representations: drawings Abstract: numbers, symbols, formulas Research shows that students can vary in number of opportunities that need to master something. Phonemes- 5 trials- 20 for most of students. How do you provide this many opportunities with such a wide variance? In math, Kindergarten all the way to high schooler will need different types of opportunities. How do we provide this AT THE CORE without becoming redundant? And getting behind in our curriculum? Concrete: materials Representations: drawings Abstract: numbers, symbols, formulas Research shows that students can vary in number of opportunities that need to master something. Phonemes- 5 trials- 20 for most of students. How do you provide this many opportunities with such a wide variance? In math, Kindergarten all the way to high schooler will need different types of opportunities. How do we provide this AT THE CORE without becoming redundant? And getting behind in our curriculum?

    33. The Core: Instruction Communication Continuous progress monitoring Cooperative learning such as peer tutoring Communication (using math language)Communication (using math language)

    34. Recap of the Big “9” Instruction at the “Core” Explicit instruction Pre-skills are taught to mastery Strategies, including problem-solving and graphic organizers Concrete-representational-abstract sequence Authentic contexts Multiple opportunities to practice with guidance and feedback Communication Continuous progress monitoring Cooperative learning such as peer tutoring

    35. Video 1 Good Morning Miss Toliver Template- Curriculum, Instruction, Assessment - Even though this is looking for INSTRUCTION- Pke 4:30-6:10 Quick examples ( 1 ˝ minutes) 13:30- 18:00 (4 ˝ minutes )Communication; Concrete, representational, abstract ; progress monitoring, cooperative learning, strategies. Problem solving situations- 23:00- 25: 54 ( almost 3 minutes ) authentic contexts to learn about communication in math and math concepts 9 minutes total Template- Curriculum, Instruction, Assessment - Even though this is looking for INSTRUCTION- Pke 4:30-6:10 Quick examples ( 1 ˝ minutes) 13:30- 18:00 (4 ˝ minutes )Communication; Concrete, representational, abstract ; progress monitoring, cooperative learning, strategies. Problem solving situations- 23:00- 25: 54 ( almost 3 minutes ) authentic contexts to learn about communication in math and math concepts 9 minutes total

    36. Table Talk “Round and Round” What did you see in the video that relates to the big nine? What did you see in the video that relates to the big nine?

    37. Take a Break.. 10 minutes

    38. How do we acquire the information necessary to make instructional decisions for our students? Assessment

    39. Data useful when have purpose and understanding question asking and answering Data is not an end in itself; it is a means to an endData useful when have purpose and understanding question asking and answering Data is not an end in itself; it is a means to an end

    40. Purposes of Assessment One assessment won’t answer all of our questions about student achievement or lack Common to confuse the purposes of measures One assessment won’t answer all of our questions about student achievement or lack Common to confuse the purposes of measures

    41. Purpose of Assessment

    42. What Question are we trying to answer within an RtI Framework? To make decisions need measure of key critical skill that spans the entire curriculum or keystone behaviors for the entire year and beyond. Not mastery tests because measure different skills at different times-not comparable across time. e.g. mastery test for 5-8th grade language arts might include Testing on story description and plot, later how to identify information from a story (table of contents, etc), later summarize across sources of information, later ID fiction versus non-fiction *On-going assessments (e.g. formative, mastery, short-cycle, and informal assessments) are part of all 3 tiers and used in meaningful ways To make decisions need measure of key critical skill that spans the entire curriculum or keystone behaviors for the entire year and beyond. Not mastery tests because measure different skills at different times-not comparable across time. e.g. mastery test for 5-8th grade language arts might include Testing on story description and plot, later how to identify information from a story (table of contents, etc), later summarize across sources of information, later ID fiction versus non-fiction *On-going assessments (e.g. formative, mastery, short-cycle, and informal assessments) are part of all 3 tiers and used in meaningful ways

    43. Tier 1 Assessment Universal Screening Connected to key academic content or behavior Conducted at least 3 times per year on a regular basis, using comparable test forms Administered school wide to all students Used to determine if additional examination is warranted Features: short, few items, focus on critical indicators Universal screeners assess key academic indicators such as the “Big 5” areas of literacy (phonemic awareness, phonics, fluency, vocabulary and comprehension) and the “Big 8” (?) concepts in math Or, indicators of system-wide behavior such as office discipline referrals They are critical indicators or a thermometer of growth, may be different at secondary level (will address later) They Provide “vital signs” of growth and development in areas highly associated with academic success (reading and math) These measures are conducted periodically, usually 3-4 times per year using parallel versions of the test. They are administered to ALL students. As such, they are usually brief and sensitive to small changes over time. Simple, quick, cost effective measures that are easily repeatable for continuous progress monitoring Provides data on all students Reliability is critical. Need a process for integrity checks of data collection (inter-rater reliability) Universal screening measures provide 2 critical pieces of information: 1) Is the Tier 1 core effective? How healthy is our academic system? Are at least 80% of our students demonstrating successful mastery of information? 2) Who are the students whose universal screening data indicate a need for validation of assessment results and possible Tier 2 intervention? Universal screeners assess key academic indicators such as the “Big 5” areas of literacy (phonemic awareness, phonics, fluency, vocabulary and comprehension) and the “Big 8” (?) concepts in math Or, indicators of system-wide behavior such as office discipline referrals They are critical indicators or a thermometer of growth, may be different at secondary level (will address later) They Provide “vital signs” of growth and development in areas highly associated with academic success (reading and math) These measures are conducted periodically, usually 3-4 times per year using parallel versions of the test. They are administered to ALL students. As such, they are usually brief and sensitive to small changes over time. Simple, quick, cost effective measures that are easily repeatable for continuous progress monitoring Provides data on all students Reliability is critical. Need a process for integrity checks of data collection (inter-rater reliability) Universal screening measures provide 2 critical pieces of information: 1) Is the Tier 1 core effective? How healthy is our academic system? Are at least 80% of our students demonstrating successful mastery of information? 2) Who are the students whose universal screening data indicate a need for validation of assessment results and possible Tier 2 intervention?

    44. Tier 1 Assessment 2 Critical Pieces of Information Is the Tier 1 core effective? For all students (aggregated)? For each subgroup of students (disaggregated)? Who are the ~20% of students needing additional support?

    45. Tier 1-The Core: Math Assessment Math Universal Screeners 4 considerations (Fuchs, 2006) Feasible to implement Strong predictor of high stakes tests Developmentally appropriate Accurate cut-score for determining need for additional support (note: because assessment impacts instruction, make sure there is balance) Note IES Recommendation #1: Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at riskNote IES Recommendation #1: Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk

    46. Tier 1-The Core: Math Assessment Universal Screening Possible areas of focus: Number Sense and Computation Fluency Measurement Geometry Patterns, Functions, algebra Data Analysis and Probability Problem Solving CBM gurus have collaborated and have not yet come up with critical skill to assess that would predict future math success. So, we don’t have the same basic skill assessments as predictors. So, we need to assess across areas to make better predictions of future success and areas of need. K-4: Whole numbers K-2, especially magnitude comparison and sequence 4-8+: work with fractionsCBM gurus have collaborated and have not yet come up with critical skill to assess that would predict future math success. So, we don’t have the same basic skill assessments as predictors. So, we need to assess across areas to make better predictions of future success and areas of need. K-4: Whole numbers K-2, especially magnitude comparison and sequence 4-8+: work with fractions

    47. Tier 1: Math Assessment Universal Screening Possible resources: Aimsweb Yearly ProgressPro Intervention Central (Numberfly, Math Worksheet Generator) Using Curriculum Based Measurement for Progress Monitoring in Math, 2007 (Fuchs, Fuchs, and colleagues)

    48. Tier 1: Math Assessment Decision Rules Deno & Mirkin Instructional Mastery criteria Grades 1-3: 20+ digits correct per minute Grades 4-6: 40+ digits correct per minute AIMSweb norms Support lowest 25% of class/grade Ongoing Research In This Area Important to collect data; if all students struggling with skill should have mastered based on ODE, need Tier 1 instruction Research is still ongoing to establish predictive validity of any of these suggested benchmarks. Deno and Mirkin (1977): Mastery—grades 1-3 (20+ digits correct per minute with 2 or less digits incorrect); grades 4+ (40+ digits correct per minute with 2 or less digits incorrect) Fuchs and Fuchs (2009): on “computation” timed tests, grade 1 <5 digits; grades 2-4 <10 digits; grades 5-6 <15 digits On “concepts and applications” timed tests: grade 1 <5 points; grades 2-3 <10 points; grades 4-6 <5 points ALSO use of Tukey method for trend line estimation; Fuchs and Fuchs provides recommendations for inadequate trend line slopes that would cause us concern about student’s progress over time in Tier 1 curriculumResearch is still ongoing to establish predictive validity of any of these suggested benchmarks. Deno and Mirkin (1977): Mastery—grades 1-3 (20+ digits correct per minute with 2 or less digits incorrect); grades 4+ (40+ digits correct per minute with 2 or less digits incorrect) Fuchs and Fuchs (2009): on “computation” timed tests, grade 1 <5 digits; grades 2-4 <10 digits; grades 5-6 <15 digits On “concepts and applications” timed tests: grade 1 <5 points; grades 2-3 <10 points; grades 4-6 <5 points ALSO use of Tukey method for trend line estimation; Fuchs and Fuchs provides recommendations for inadequate trend line slopes that would cause us concern about student’s progress over time in Tier 1 curriculum

    49. Tier 1: Math Assessment Curriculum-Based Assessment (CBA) Creating your own tools Sample grade-level screening tools

    50. CBA Example Kindergarten Number and Operations 3 Questions For Each Indicator = Draw 5 dots Which is bigger: 7 2 Fill in the blank: 2 3 __ 5 Count backward 10 ? 1

    51. CBA Example for High School 3 questions for each indicator Number sense: Identify subsets of the real number system 1) Which number is an irrational number? A) -2 B) C) 3 22/8

    52. Turn and Talk Based on your grade level, discuss a keystone skill that all students need to master. How might a CBM look?

    53. Video 2 Secondary Example Connecting Knowledge www.PD360.com 4:10- 7:06 Concrete, strategies, problem solving, multiple opportunities for practice 7:18- 9:45 Cooperative learning, progress monitoring , multiple opportunities, authentic contexts, representational Student A/ Student B abstract. 4:10- 7:06 Concrete, strategies, problem solving, multiple opportunities for practice 7:18- 9:45 Cooperative learning, progress monitoring , multiple opportunities, authentic contexts, representational Student A/ Student B abstract.

    55. Levels of Support Chart Describe “The Core” within your classroom/ school/district. What system is in place to support the work at this level? What initial or additional supports need to be in place to support the Core-Tier 1? How does this look in other schools within your district (or other districts)? Core-Curriculum, Instruction and AssessmentCore-Curriculum, Instruction and Assessment

    56. Tier 1-The Core Key Characteristics All Students receive this instruction Research-Validated Core Curriculum Instructional Gaps filled with Supplemental Research-based Materials Differentiated Support Differentiated practices – The average person needs exposure to concepts, vocabulary, etc. avg. 5-7 times/trials to learn it. We know this because we have data on our students Differentiated practices – The average person needs exposure to concepts, vocabulary, etc. avg. 5-7 times/trials to learn it. We know this because we have data on our students

    58. Tier 2 Targeted Supports Key Characteristics: Small group or individual instruction in addition to the core Research-based strategies/interventions Regular progress monitoring for efficient changes as needed

    59. Tier 2 : Math Support Focused Targets: Number Sense Fluency in Computation Algebraic Skills Research of from the Nat’l math panel and IES- Institute of education sciences Note: IES Recommendation: interventions at all grade levels should devote about 10 minutes each session to building fluent retrieval of basic arithmetic facts IES Rec: Instructional materials for students receiving interventions should focus intensely on in-depth treatment of K-5: Whole numbers 4-8: Rational numbers Research of from the Nat’l math panel and IES- Institute of education sciences Note: IES Recommendation: interventions at all grade levels should devote about 10 minutes each session to building fluent retrieval of basic arithmetic facts IES Rec: Instructional materials for students receiving interventions should focus intensely on in-depth treatment of K-5: Whole numbers 4-8: Rational numbers

    60. Tier 2 : Math Support Tiered Interventions in Development PALS for Math (Peer-Assisted Learning Strategies) (Fuchs, Fuchs & Karns, 2001) 3-Tier Math Intervention for Grades K-2 (Bryant & Bryant, 2007; focus on number sense and basic skill knowledge and application) Developing Algebraic Literacy (K-3) (D. Allsopp and colleagues) PALS math –Materials, Case Studies, Info Briefs, Podcasts PALS math –Materials, Case Studies, Info Briefs, Podcasts

    61. Tier 2 Math Support Problematic Skills Language of Math Word Problems Multi-step Problems Skills most problematic for students with learning disabilities and math weakness (Bryant): Give participants chance to answer—WHY would these be the areas of difficulty? Marzano’s Building Academic Vocabulary Math Flash (computer program) to build math fact fluencySkills most problematic for students with learning disabilities and math weakness (Bryant): Give participants chance to answer—WHY would these be the areas of difficulty? Marzano’s Building Academic Vocabulary Math Flash (computer program) to build math fact fluency

    62. Tier 2 Math Support: Instruction Increased support and explicitness Increased modeling Increased opportunities for guided instruction Corrective feedback (More opportunities) Note IES Rec: #3Note IES Rec: #3

    63. 63 Explicit and Systematic Instruction Model: Provide explicit examples of new material. Practice: Provide ample opportunities for students to practice new material. Ample is defined by the individual needs of each student. Assess (ongoing): Check students’ understanding of the new material throughout the lesson. Feedback: Immediately correct any incorrect student responses by repeating the teacher model.

    64. Futures Task Force on Academic Outcomes 64 2008 Explicit Instruction Break down the skills into manageable and deliberately sequenced steps. Provide overt instruction in the skills and opportunities to practice (Roshenshine & Stevens, 1986). Step by step manner Clear and detailed explanations Mastery of each step is assured before moving on to the next

    65. Explicit Instruction Modeled, Guided, and Independent Practice “I do” (presentation of materials), “we do” (guided practice), “you do” (independent practice). Feedback and Ongoing Assessment Uses a high number of teacher questions and student responses with frequent checks for understanding.

    66. Sample Intervention Increased Explicit Instruction Steps: 1: Teacher selects problems from student work that warrant explicit instruction, 2: Teacher demonstrates how to perform the algorithm “thinking aloud” the steps, 3: Students imitate the process on similar problems, 4: A completed model remains as a referent on the student’s paper as a permanent. (Rivera & Smith, 1987; 1988; Bryant, Hartman, & Kim, 2003)

    67. 3rd grade OAT Math Released (Spring 2008)

    68. Quick Math BUDDY UP!!! Take one of the Descriptors for Explicit Instruction and Apply it to the math OAT question .Take one of the Descriptors for Explicit Instruction and Apply it to the math OAT question .

    69. 4th grade OAT Math Released (Spring 2008)

    70. 4th grade OAT Math Released (Spring 2008)

    71. OGT Example Spring 2006 Question 4 Standard: NNS Benchmark: G.   Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. Adam was going to buy a new lawn mower from Lawn Care Depot for $169, less a 10% discount. He saw the same mower on sale at Tractors-R-Us. Their mower originally cost $210 and was on sale 1 for 3 off. Determine the sale price of the mower at each store. Show your work or provide an explanation to support your answer. Identify which store would be the most economical place to purchase the mower. (2 points) Students need to set up and solve problems involving percentage and fraction discounts.  To find a percentage discount, you convert the percentage to a decimal. Then you multiply the original cost by the decimal. Finally, you subtract that amount from the original cost to find the discounted price.  For example, what is the discounted price of a pair of $5.50 socks that are marked 20% off.  The discounted pair of socks will cost $4.40.  To find a fraction discount, you simply multiply the original cost by the fraction. Then, you subtract that amount from the original cost to find the discounted price.  For example, what is the discounted price of a $350 video game system that is marked off. The discounted video game system will cost $280 Students need to set up and solve problems involving percentage and fraction discounts.  To find a percentage discount, you convert the percentage to a decimal. Then you multiply the original cost by the decimal. Finally, you subtract that amount from the original cost to find the discounted price.  For example, what is the discounted price of a pair of $5.50 socks that are marked 20% off.  The discounted pair of socks will cost $4.40.  To find a fraction discount, you simply multiply the original cost by the fraction. Then, you subtract that amount from the original cost to find the discounted price.  For example, what is the discounted price of a $350 video game system that is marked off. The discounted video game system will cost $280

    73. Lunch List of suggested places on back table…

    74. Tier 2 Math Support: NCTM recommends 5 processes for strugglers: Communication Problem solving Reasoning/proof Connections (graphic organizer) Representations (draw, diagram)

    75. Process Articles and Jigsaw Discussion Small group Each person chooses one of the articles to read and capture important points of interest. Fill in “Process Standards in A NUTSHELL” Sheet Each person take turns sharing out important aspects of their article. Fill in the sheet provided.

    76. After Jigsaw- whole group – Any Big AH HA’s sharing… After Jigsaw- whole group – Any Big AH HA’s sharing…

    77. RtI Assessments Tier 1: Universal Screening Tier 2: Progress Monitoring (Keystone Skill) and additional information Tier 3: -More frequent progress monitoring -More assessments based upon individualized needs (e.g. pre- requisite skills, diagnostics) *On-going assessments (e.g. formative, mastery, short-cycle, and informal assessments) are part of all 3 tiers and used in meaningful ways To make decisions need measure of key critical skill that spans the entire curriculum or keystone behaviors for the entire year and beyond. Not mastery tests because measure different skills at different times-not comparable across time. e.g. mastery test for 5-8th grade language arts might include Testing on story description and plot, later how to identify information from a story (table of contents, etc), later summarize across sources of information, later ID fiction versus non-fiction To make decisions need measure of key critical skill that spans the entire curriculum or keystone behaviors for the entire year and beyond. Not mastery tests because measure different skills at different times-not comparable across time. e.g. mastery test for 5-8th grade language arts might include Testing on story description and plot, later how to identify information from a story (table of contents, etc), later summarize across sources of information, later ID fiction versus non-fiction

    78. Tier 2: Math Assessment Progress Monitoring-current focus mostly fluency Aimsweb Yearly ProgressPro Intervention Central (Numberfly, Math Worksheet Generator) Using Curriculum Based Measurement for Progress Monitoring in Math, 2007 (Fuchs, Fuchs, and colleagues) Because need repeated frequent measures and indications of predictiveness: computation fluency…Because need repeated frequent measures and indications of predictiveness: computation fluency…

    79. Tier 2: Math Assessment Decision Rules Fuchs and Fuchs (2009) recommendations CBM end levels (after 10-20 weeks of Tier 2 tutoring) Slope of student’s progress “typical” end-of-year benchmarks F&F (2009): using “computation” and “concepts and applications” timed tests to progress monitor students receiving Tier 2 (and conceivably Tier 3) interventions, F&F have recommendations about CBM end levels (final scores after a ‘round’ of Tier 2 tutoring) and slopes derived using the Tukey method; as with the Tier 1 cut-off scores, these can change with further research on RtIF&F (2009): using “computation” and “concepts and applications” timed tests to progress monitor students receiving Tier 2 (and conceivably Tier 3) interventions, F&F have recommendations about CBM end levels (final scores after a ‘round’ of Tier 2 tutoring) and slopes derived using the Tukey method; as with the Tier 1 cut-off scores, these can change with further research on RtI

    80. Tier 2: Math Assessment Curriculum-Based Assessment If progress monitoring probes are not available, can you create a measure of progress monitoring?

    81. CBA Example: 6th grade Algebra 3 questions for each indicator Write math equation Six people are bringing 12 cupcakes each to a party. How many cupcakes will be at the party? Solve these equations 150/3= Write a word problem for these equations 12 / 4 Write an equivalent formula 2(L + W) = 2L + 2W Write the formula Input 1 2 3 Output 3 6 9

    82. Chart Describe the Tier 2 interventions within your classroom/ school. What system is in place to support the work at Tier 2? What initial or additional supports need to be in place to support Tier 2? How does this look in other schools within your district (or other districts)?

    84. Tier 3: Individualized Instruction Key Characteristics: Small group or individualized instruction in addition to the core Research-based strategies/interventions Individualized to students needs based on collaborative problem solving Frequent progress monitoring We have covered everything in tier 1 and 2- at tier 3 you must return to key instruction, curriculum, assessment and figure out WHAT THIS STUDENT NEEDS… Very similar to Tier 2- This is a STUDENT BASED intervention – planning- Side note- What if this were a gifted student? This ALSO counts for them!!! EXTENSIONS We have covered everything in tier 1 and 2- at tier 3 you must return to key instruction, curriculum, assessment and figure out WHAT THIS STUDENT NEEDS… Very similar to Tier 2- This is a STUDENT BASED intervention – planning- Side note- What if this were a gifted student? This ALSO counts for them!!! EXTENSIONS

    85. Tier 3: Individualized Instruction Curriculum Content should align with core curriculum to which student still has access Content should fill in gaps in knowledge/skills as determined through further diagnostics

    86. Tier 3: Individualized Instruction Focused targets: **Fractions and other concepts relating to rational numbers Fluency with standard algorithms Commutative, Associative, Distributive laws Translation of word problems into symbols Basic measurement concepts IES Recs: Whole numbers Rational numbers FluencyIES Recs: Whole numbers Rational numbers Fluency

    87. Tier 3: Individualized Instruction Instructional strategies: Increased opportunities for direct instruction, practice, and feedback Re-teaching skills not yet mastered Using visuals and verbalization Teaching metacognitive strategies GIVE EXAMPLES OF TEACHING TYPE OF PROBLEM, AND HOW TO LOOK FOR SUBSTANTIVE INFORMATION AND DISTRACTOR INFORMATION IES ARTICLEGIVE EXAMPLES OF TEACHING TYPE OF PROBLEM, AND HOW TO LOOK FOR SUBSTANTIVE INFORMATION AND DISTRACTOR INFORMATION IES ARTICLE

    88. Multiple heuristics= Broad concept- I can use this with any problem I am looking at as a strategy for figuring out… Ex: state the problem- key words in the problem- operation for problem, work the problem, check the problem Multiple heuristics= Broad concept- I can use this with any problem I am looking at as a strategy for figuring out… Ex: state the problem- key words in the problem- operation for problem, work the problem, check the problem

    89. Tier 3: Individualized Instruction Assessment Curriculum Based Assessment to specify skills and needs Additional diagnostics Frequent monitoring of progress

    90. Tier 3 Each student participating in Tier 3 should have a collaboratively-developed written plan outlining: Intervention plan and logistics Assessment plan and logistics Goals Each student participating in Tier 3 should have a collaboratively-developed written plan outlining: Each student participating in Tier 3 should have a collaboratively-developed written plan outlining:

    92. Ideas for Supporting Learning

    93. I Forget….. Forgetting happens very quickly… 47% of forgetting occurs in the first 20 min. 62% of forgetting occurs in the first day. 82% of forgetting occurs in the first 3 weeks. Forgetting slows down after 2 weeks….. But then, there is not much left to forget. Therefore, the prime time to process, discuss and reflect is immediately after new information is presented ---- before the forgetting begins. Source: Instruction for All by Paula Rutherford SO--- let’s make some connections while the learning is FRESH! SO--- let’s make some connections while the learning is FRESH!

    95. Students With Math Difficulties… Struggle with Math Language Problem Solving Computational Fluency Math language= communication, connections, journaling, vocabulary Problem Solving- multi- step word problems, representation of information , Computational Fluency- Number Sense, algebraMath language= communication, connections, journaling, vocabulary Problem Solving- multi- step word problems, representation of information , Computational Fluency- Number Sense, algebra

    96. Students with math difficulties… Struggle with Math Language

    97. Strategies Vocabulary - Frayer Model - Marzano’s 6 Steps Journaling Talk Moves

    98. (Prime - Even - Percent ) Choose one of the mathematical words above. (Don’t tell anyone your choice. Don’t write it on your paper) Fill in the outer boxes to help explain your word. Be ready to share your information to your group.

    99. Vocabulary development, uses graphic organizer to organize thinking, Allows choice (when appropriate) -what else? If students share their work before students guess the word, communication is used. Vocabulary development, uses graphic organizer to organize thinking, Allows choice (when appropriate) -what else? If students share their work before students guess the word, communication is used.

    100. Share Why is teaching vocabulary important?

    101. Why We Should Teach Vocabulary Learning is fundamentally and profoundly dependent on vocabulary knowledge. Vocabulary knowledge is highly correlated with overall reading/math achievement. Vocabulary deficiencies are a primary cause of academic failure in Grades 3–12. Vocabulary knowledge affects a student’s ability to participate fully in both social and academic activities. Significant disparities exist in word knowledge among students.

    102. Knowledge of important terms is critical to understanding any subject. The more terms we know about a subject the more skilled we are in that subject.

    103. A Six-Step Process for Teaching New Terms Step 1: Provide a description, explanation, or example of the new term Step 2: Ask students to restate the description, explanation, or example in their own words Step 3: Ask students to construct a picture, symbol, or graphic representing the term or phrase Step 4: Engage students periodically in activities that will help them add to their knowledge of the terms in their notebooks Step 5: Periodically ask students to discuss the terms with one another Step 6: Involve students periodically in games that allow them to play with terms Building Academic Vocabulary, Marzano and Pickering Marzano and Pickering suggest… Marzano and Pickering suggest…

    104. Step 1: Provide a description, explanation, or example of the new term Example: Function

    105. Term: ______________________ Describe: ___________________________ ___________________________________ ___________________________________ ___________________________________ Draw: Level of Understanding 1 2 3 4

    106. Step 2: Ask students to restate the description, explanation, or example in their own words Term: Function Describe: _ Students may not fully understand the term yet. This example shows that the student may think that in a function, if one thing goes up, the other thing must go up, too. Misunderstandings will be clarified in Steps 3 and 4. Students may not fully understand the term yet. This example shows that the student may think that in a function, if one thing goes up, the other thing must go up, too. Misunderstandings will be clarified in Steps 3 and 4.

    107. Step 2: Ask students to restate the description, explanation, or example in their own words Term: Function Describe: It’s when one thing makes another happen or one thing goes up the way that another goes up. Explain step 2. Note that the student may not fully understand the term yet. His example shows that he may think that in a function, if one thing goes up, the other thing must go up, too. Misunderstandings will be clarified in Steps 3 and 4. Option: Click on the video to show how step 2 looks in the classroom. When the video ends, hit the ESC key and click back to the PowerPoint show. Explain step 2. Note that the student may not fully understand the term yet. His example shows that he may think that in a function, if one thing goes up, the other thing must go up, too. Misunderstandings will be clarified in Steps 3 and 4. Option: Click on the video to show how step 2 looks in the classroom. When the video ends, hit the ESC key and click back to the PowerPoint show.

    108. Step 3: Ask students to construct a picture, symbol, or graphic representing the term or phrase. Ask participants to identify what the student drew and how it relates to function. Ask participants to identify what the student drew and how it relates to function.

    109. Types of pictures: Draw the actual thing ? Use a symbol? = Draw an example Represent the idea with graphics Dramatize the drawing with cartoon bubbles Picture drawing needs to be explicitly taught. Read the types and then explain each as the next slides come up which provide examples.Read the types and then explain each as the next slides come up which provide examples.

    110. Symbols Peace Space Examples Conservation Algebra

    111. Graphics

    112. Dramatize /Cartoon Bubbles

    113. Self-Evaluate After Step 3 is completed, ask students to self-evaluate by circling 1 2 3 4 at the bottom of their vocabulary page for each word they’ve learned. 4 - I understand even more about the term than I was taught 3 - I understand the term and I’m not confused about any part of what it means 2 - I’m a little uncertain about what the term means, but I have a general idea. 1 - I’m very uncertain about the term. I really don’t understand what it means.

    114. Term: ______________________ Describe: ___________________________ ___________________________________ ___________________________________ ___________________________________ Draw: Level of Understanding 1 2 3 4

    115. Step 4: Engage students periodically in activities that will help them add to their knowledge of the terms in their notebooks Step 5: Periodically ask students to discuss the terms with one another Step 6: Involve students periodically in games that allow them to play with terms Note that Steps 4-6 Clarify and reinforce students’ learning of terms introduced through steps 1-3.Note that Steps 4-6 Clarify and reinforce students’ learning of terms introduced through steps 1-3.

    116. Step 4: Engage students periodically in activities that will help them add to their knowledge of the terms in their notebooks Solving Analogy Problems Free Association Classifying Terms Comparing Terms It is essential to give students opportunities to reexamine their understanding of the academic terms that were presented to them. Step 4 is that time for review. As they engage in these activities, students should add to or revise their entry for the term in their academic notebooks. They can add to the description, drawing, and/or add other information such as an analogy, etc.It is essential to give students opportunities to reexamine their understanding of the academic terms that were presented to them. Step 4 is that time for review. As they engage in these activities, students should add to or revise their entry for the term in their academic notebooks. They can add to the description, drawing, and/or add other information such as an analogy, etc.

    117. Solving Analogy Problems Examples: Right angle is to 90ş as obtuse angle is to ___________. Subtraction is to division as ______ is to _____.

    118. Solving Analogy Problems This graphic can help students figure out or write analogy problems Click once to add the words oxygen/people Model your thinking about the relationship as you click again to bring in the word AS Click again to reveal the relationship Click the 4th time to reveal the rest of the analogy. Read the entire analogyThis graphic can help students figure out or write analogy problems Click once to add the words oxygen/people Model your thinking about the relationship as you click again to bring in the word AS Click again to reveal the relationship Click the 4th time to reveal the rest of the analogy. Read the entire analogy

    119. Free Association Oral: Call out a term and ask students (as a class, in small groups, or in pairs) to say any word they think of that is related to the term After a few seconds say “stop”. The last person to say a word must explain how it is related to the target Written: Students write terms in notebook. When you say “stop” students exchange with partner and explain how the words are related. This is the quickest and most unstructured method of reviewing terms. There are two types: Oral and Written. If done orally, the teacher should record words on the board, or a recorder should be appointed for each group Do an example orally with the group (use one of the examples below or a word of your choice). Say the word, give one or two examples, and have them continue. Write down the words on the board. You can do it in a list form or use clustering A lot like brainstorming This is the quickest and most unstructured method of reviewing terms. There are two types: Oral and Written. If done orally, the teacher should record words on the board, or a recorder should be appointed for each group Do an example orally with the group (use one of the examples below or a word of your choice). Say the word, give one or two examples, and have them continue. Write down the words on the board. You can do it in a list form or use clustering A lot like brainstorming

    120. Classifying Terms Description: Classifying is the process of grouping items on the basis of similar attributes. Two Types of Classification Tasks: Structured – students are given the categories and place the terms into the correct categories Open-Ended – students are given terms and they come up with categories OR they are given categories and come up with terms Sorting activities are great for classifying and developing students’ higher level thinking skill. Students can sort terms in their notebooks based on categories provided by the teacher or they can write terms on small pieces of paper or index cards cut in half, then arrange them in category columns, using post-its to write the names of the categories. They can also code words on a list based on categories that they or the teacher determines It is much more challenging to develop categories than to sort words into teacher-determined categories, so be sure to provide students with opportunities to do both.   Sorting activities are great for classifying and developing students’ higher level thinking skill. Students can sort terms in their notebooks based on categories provided by the teacher or they can write terms on small pieces of paper or index cards cut in half, then arrange them in category columns, using post-its to write the names of the categories. They can also code words on a list based on categories that they or the teacher determines It is much more challenging to develop categories than to sort words into teacher-determined categories, so be sure to provide students with opportunities to do both.  

    121. Step 5: Periodically ask students to discuss the terms with one another Think Pair Share Interacting with other people about what we are learning deepens the understanding of all involved. As you listen to the sharing, this is another time to correct any more misunderstandings of the words that may remain.Interacting with other people about what we are learning deepens the understanding of all involved. As you listen to the sharing, this is another time to correct any more misunderstandings of the words that may remain.

    122. A Six-Step Process for Teaching New Terms Step 6: Involve students periodically in games that allow them to play with terms What is the Question? Vocabulary Charades Name that Category Draw Me Talk a Mile a Minute Explain that games are one of the most underused instructional tools in education. They provide opportunities to review terms as well as interject an energizing break in the routine of the day. Set aside blocks of time to play these games or use them spontaneously. You need to have taught a number of words before you can play these games. Explain that games are one of the most underused instructional tools in education. They provide opportunities to review terms as well as interject an energizing break in the routine of the day. Set aside blocks of time to play these games or use them spontaneously. You need to have taught a number of words before you can play these games.

    123. Journaling Using Journals in Mathematics Vocabulary Building Allows students to show rationale for work. Captures thinking over time.

    124. “Talk Move” Strategies Talk Move: Revoice -Teacher restates student’s idea then verifies its accuracy  Used to: Highlight particular idea for discussion  Talk Move: Repeat/Rephrase -Student restates what another said -Then move into having them rephrase and check for accuracy Used to: Encourage listening and understanding what others are saying   Talk Move: Adding On -Teacher asks students to expand upon ideas already stated Used to: Validate original ideas Talk Move: Agree/Disagree and Why? -Students analyze ideas and defend their position Used to: further understand and address misconceptions Could talk about ideas for this for days… Here’s one that helps with discussion/ engaging all students.. Communication / reasoning… From: Strategies to Help ELL Students Talk and Write About Math, Javits Grant Could talk about ideas for this for days… Here’s one that helps with discussion/ engaging all students.. Communication / reasoning… From: Strategies to Help ELL Students Talk and Write About Math, Javits Grant

    126. Students with math difficulties… Struggle with problem solving Cannot remember procedural steps Fail to verify answers and settle on first answer Making “borrowing” errors; fail to carry Reach “unreasonable” answers Misplace digit in multi-digit numbers

    127. Strategies Heuristics Analyzing the Type of Problem

    128. Heuristics “General in Nature” Serves different purposes such as helping the child to: understand the problem; simplify the task; identify possible causes; identify possible solutions; think or reason. They are often used in combinations to solve the problem Need to explicitly teach the procedure / heuristics so it becomes a useful tool. Pronounced : (Heer is tics ) Emphasize that these should be Explicitly taught. Posted and Practiced Need to explicitly teach the procedure / heuristics so it becomes a useful tool. Pronounced : (Heer is tics ) Emphasize that these should be Explicitly taught. Posted and Practiced

    129. Breaking apart problem into manageable pieces Work Backwards (What’s the question?) Act it out (Video) Simplify it (Make harder numbers easier at first) State it a different way Make suppositions Use guess and check Use before after concept Heuristics Heuristics

    130. What Can I Use? Make a Table Look for a Pattern Draw a Diagram Compare and Contrast Data Simplify the Problem Write a Mathematical Sentence Make a Graph or Table Work Backward Common Strategies- Start with explicitly teaching a few. Build on the list as needed. Poster created in the room- Visual reps of each type would be beneficial! Common Strategies- Start with explicitly teaching a few. Build on the list as needed. Poster created in the room- Visual reps of each type would be beneficial!

    131. Memory Cues Five Steps for Solving Word Problems Determine what I need to find Decide what information I need in order to find it. Do the math. Check my work to see if it agrees with the first step. Have this on the wall for students to refer to. What other memory cues are used in your classroom? Heuristics! Versus specific strategy Determining type of problem…Have this on the wall for students to refer to. What other memory cues are used in your classroom? Heuristics! Versus specific strategy Determining type of problem…

    132. Determining the Type of Problem 2 Common Underlying Structure of Word Problems Specific Type of Problem Change (over time) - increase/decrease Quantity (compare)- Teach children this! Recommendation from the Nat’l Center on RtITeach children this! Recommendation from the Nat’l Center on RtI

    133. (Change Problem) Sets the stage for Algebra- physical science Sets the stage for Algebra- physical science

    134. Problem 1 Brad has a bottlecap collection. After Madhavi gave Brad 28 more bottlecaps, Brad had 111 bottlecaps. How many bottlecaps did Brad have before Madhavi gave him more? Use your Communication/ problem solving skills to figure out this one. What type of problem is this? How would you represent it? (both bottle cap problems are change… )Use your Communication/ problem solving skills to figure out this one. What type of problem is this? How would you represent it? (both bottle cap problems are change… )

    135. Problem 2 Brad has a bottlecap collection. After Brad gave 28 of his bottlecaps to Madhavi, he had 83 bottlecaps left. How many bottlecaps did Brad have before he gave Madhavi some? This seems intuitive and simple to adults but to children who are mathematically struggling, the ways to solve is not obvious. Teach solution rules, or guiding questions to that lead to the solution equation, through modeling… through fully and partially worked problems. Then allow time to for students to work in pairs. This goes back to the explicit instruction slides – overt teaching, model, practice assess, feedback and I do , we do, you do… This seems intuitive and simple to adults but to children who are mathematically struggling, the ways to solve is not obvious. Teach solution rules, or guiding questions to that lead to the solution equation, through modeling… through fully and partially worked problems. Then allow time to for students to work in pairs. This goes back to the explicit instruction slides – overt teaching, model, practice assess, feedback and I do , we do, you do…

    136. 2 Problem Solving Structures cont… Teach students to recognize the common structures when there are: 1. Problems that have superficial changes but are really the same… (˝ , half, one-half) 2. Irrelevant story information or additional information. Teach them to be detectives… what is the same when it looks different? Give them tools to be gardeners… weed out the extra/ unneeded information that makes them seem new and unfamiliar. Suggestions: Post examples of each type as visual cues for students… Teach them to be detectives… what is the same when it looks different? Give them tools to be gardeners… weed out the extra/ unneeded information that makes them seem new and unfamiliar. Suggestions: Post examples of each type as visual cues for students…

    137. Mike wants to buy 1 pencil for each of his friends. Each packet of pencils contains 12 pencils. How many packets does Mike have to buy to give 1 pencil to each of his 13 friends? Mike wants to buy 1 pencil for each of his friends. Sally wants to buy 10 pencils. Each box of pencils contains 12 pencils. How many boxes does Mike have to buy to give 1 pencil to each of his 13 friends? Compare these two story problems. Notice the subtle difference between the two. What might this do for a struggling student? Compare these two story problems. Notice the subtle difference between the two. What might this do for a struggling student?

    139. Students with math difficulties… Struggle With Memory Problems Poor long-term memory retrieval skills Poor working memory Cannot recall number facts automatically Cannot remember procedural steps

    140. Students with math difficulties… Struggle with Computational Fluency

    141. Strategies Quick Math Facts Individualized Checklists

    142. Students Tracking their Own Work Computational Fluency ( Automaticity of facts) Quick Math Facts Set a goal The student is given a kitchen timer and instructed to set the timer for a predetermined span of time (e.g., 2 minutes) for each practice set. The student completes as many problems as possible before the timer rings. The student then graphs the number of problems correctly computed each day on a time-series graph, attempting to better his or her previous score.

    143. ‘Individualized Self-Instruction Checklist’ Explicitly identify pattern errors within an individual’s work. (Teacher does this WITH the student.) Develop checklists. Students use their checklists to analyze own work. To create such a checklist, the teacher meets with the student. Together they analyze common error patterns that the student tends to commit on a particular problem type (e.g., ‘On addition problems that require carrying, I don’t always remember to carry the number from the previously added column.’). For each type of error identified, the student and teacher together describe the appropriate step to take to prevent the error from occurring (e.g., ‘When adding each column, make sure to carry numbers when needed.’). These self-check items are compiled into a single checklist. Students are then encouraged to use their individualized self-instruction checklist whenever they work independently on their number or word problems. As older students become proficient in creating and using these individualized error checklists, they can begin to analyze their own math errors and to make their checklists independently whenever they encounter new problem types. To create such a checklist, the teacher meets with the student. Together they analyze common error patterns that the student tends to commit on a particular problem type (e.g., ‘On addition problems that require carrying, I don’t always remember to carry the number from the previously added column.’). For each type of error identified, the student and teacher together describe the appropriate step to take to prevent the error from occurring (e.g., ‘When adding each column, make sure to carry numbers when needed.’). These self-check items are compiled into a single checklist. Students are then encouraged to use their individualized self-instruction checklist whenever they work independently on their number or word problems. As older students become proficient in creating and using these individualized error checklists, they can begin to analyze their own math errors and to make their checklists independently whenever they encounter new problem types.

    145. Time to Share Ideas Choose a strategy you use in your classroom. Share it with your partner or small group. Way to connect to their own strategies and skills …. Way to connect to their own strategies and skills ….

    146. Ways to achieve success include: Explicit and Systematic Instruction Showing the work in different ways. (Metacognitive) Embedding process standards within the instruction. Progress monitoring- includes pre/post assessment, student tracking of own work. Wrap UP… Wrap UP…

    147. Resources Building Academic Vocabulary- Teacher’s Manual Marzano and Pickering, 2005 Reading and Writing to Learn Mathematics- A Guide and Resource Book Martinez and Martinez , 2001 Strategies to Help ELL Students Talk and Write About Math Javits Grant,

    148. Resources www.sst13.org www.interventioncentral.org www.bestevidence.org http://ies.ed.gov/ncee/wwc/ www.centeroninstruction.org sc-math.com/math/heuristics.php

    149. Resources National Mathematics Advisory Panel FINAL REPORT Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools (article) NCEE, What Works Clearinghouse, US Dept of Education These (and additional resources) are listed on a page at the back of your resource packet.

    151. Thank you! Please make sure you share your reflection sheets with us! Questions/Comments: Wendy.strickler@hcesc.org Holly.sampson@hcesc.org . .

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