10/22/15 } Deep conceptual understanding } Computational fluency } - PDF document

10/22/15 } Deep conceptual understanding } Computational fluency } The ability to apply their Turn and Talk mathematical knowledge to solve problems Laney Sammons Share with th a partn tner. } The ability to communicate mathematical ideas with precision 2 3 What t is differenti tiati tion? Too often we begin our instruction } Gaps in foundational knowledge and skills. A teacher attending to the learning aiming toward the middle and needs of a particular student or small } Misconceptions praying for ricochet. 
 } Need for additional challenges group of students, rather than teaching Jennifer Taylor-Cox 
 a class as though all individuals in it } Different learning styles were basically alike. Tomlinson and Allan Principles of Di Differenti tiate ted Instr tructi tion Flexible grou Flexible g roupin ping is a h is a hallm allmark ark of differenti tiate ted instr tructi tion. 
 § Focus on essential ideas and skills Guided Math is a Tom d Allan § Responsiveness to individual differences Tomlin linson on an and Allan flexible instructional § Integration of assessment and instruction The Guided Math framework supports framework. § Ongoing adjustment of content, process, flexible grouping and aligns with the and products to meet students’ levels of principles of differentiated instruction. prior knowledge, critical thinking, and expression styles. Tomlinson and Allan 1

10/22/15 Using a combination of It promotes… Prescriptively addresses } environment of numeracy unique needs of students } deep conceptual } math warm-ups understanding } whole class instruction } computational fluency } small group instruction } strategic competence } math workshop } conferences } adaptive reasoning } balanced assessments } productive disposition From Adding It Up by the National Research Council which influenced the development of the CCSS Small-Group Instr tructi tion Small-Group Instr tructi tion Small-Group Instr tructi tion Advanta tages Challenges Challenges Ø Composition of the groups may • Easy to differentiate • Targeted, be even more fluid than for • Mathematical timely Guided Reading. communication assessment Ø Groups are usually homogenous, • Social nature of learning • Planning to yet flexible-- grouped by the • Monitoring of student work meet student needs of students. • Feedback needs Ø Students are continuously • Maintain attention • Math work assessed either formally or • Use of manipulatives stations • Precision and timeliness of • Management of informally to determine their instruction (response) Math Workshop instructional needs. The he heart of the Guided Math Framework • Relationship building 15 Small-Group Instr tructi tion Small-Group Instr tructi tion Teaching new Practicing new skills concepts Ø Teachers provides scaffolding to Informal assessment support the learning efforts of Using manipulatives students When Wh en is is s small- all-grou roup p Ø The risk-free, supportive instr tructi tion most t effecti tive? environment encourages students to explore math concepts. Introducing independent work Ø The format maximizes the benefit of co-teaching Providing intense remedial When do you th think small-group instruction or extra challenge instr tructi tion should be used? 17 2

10/22/15 Use large-group mini lesson only when there is a compelling reason to do so. All students Students are engaged in More questioning hands-on learning communicate than telling mathematically Allows teachers to Students receive timely Allows teachers to and specific differentiate assess informally feedback (both planned and spontaneous) 3

10/22/15 Effecti Ef tive Small-Group Small-Group Instr tructi tion Reflect 
 Instr tructi tion Requires What t are five words th that t describe • Instr tructi tional Framework small-group instr tructi tion? to to Support t It t • Targete ted Lessons Turn and Talk • Accurate te Grouping of Share th these with th a partn tner. Stu tudents ts Organizati tion, Planning, and Teach an d Teachin ing 29 30 Small-Group Instr tructi tion Small-Group Instr tructi tion Small-Group Instr tructi tion Where? Supplies? Procedure? • Small table, group of desks, • Instructional: Dry erase board, • Plan and teach transitions or floor manipulatives, lesson • Break them down into materials, recording forms • Sit in the middle teachable components • Student: pencils, paper, • Revisit when needed calculators, markers, manipulatives 31 32 33 Scheduling Guided Math th 
 Small-Gr Sma -Group up Lesso ssons ns Varying Time with th Ea Each Group Based q Math Warm-up (15-20 minutes max). on th their Needs It may include any of these: Meeti ting with th q Calendar Board Gr Group ups s on n Different Di t Da Days q Math Stretches during th the Week q Daily Review q Problem of the Week q Mini Lesson (10 minutes— only if needed) q Math Workshop with Small-Group Instruction (50-60 minutes) 4

10/22/15 Sma Small-Gr -Group up Lesso ssons ns Planning • Big Ideas (already mapped out in Stage 1 of each unit) • Criteria for success and prerequisite knowledge/skills needed • Teaching Point • Differentiation • Materials 39 Let’s Look at a Lesson } What foundational knowledge The Str tructu ture of a Lesson and skills do students need to be successful with the lesson? 1. Connection (link to prior knowledge) } How will you know if students 2. Teaching Point have gaps in these areas? } How can you address these gaps 3. Active Engagement most effectively and move 4. Link (reflection and encouragement students to the current to continue to use this knowledge) instructional focus? 42 Small-Group Instr tructi tion Read one of the sample Guided&Math&Small.Group&Lesson& & Problem 1: Use an area model Overview :& lessons in the handout. & & to show that ¾ = 6/8 . & Informal&Assessment:& What do you notice? 
 & & Problem 2: Draw an area model to & Small.Group&Lesson& Need&for&Additional&Challenge& What questions do you have? Connection:& & represent the equivalence of two & & & & fractions, and express the & & Teaching&Point:& Need&for&Rebuilding&Foundational&Knowledge& & (List&Common&Gaps&and&Ways&to&Address&Them)& equivalence as the sum and product & & of unit fractions & Turn and Talk Active&Engagement:& & Problem 3: Decompose to create & & Share with th a partn tner. & equivalent fractions by drawing an & & area model and then dividing the area & & Link:& model into smaller parts. & & & From EngageNY—Grade 4 Laney&Sammons& 5


 
 
 10/22/15 What t kinds of assessments ts could be used to to dete termine wheth ther How does this approach Problem 1: Use an area model to stu tudents ts possess th this knowledge show that ¾ = 6/8 . impact lesson planning? an and skill? d skill? 
 Problem 2: Draw an area model to represent the equivalence of two fractions, and express the How could you effecti tively fill equivalence as the sum and product Turn and Talk gaps in th these areas? 
 of unit fractions Problem 3: Decompose to create equivalent Share with th a partn tner. fractions by drawing an area model and then Turn and Talk dividing the area model into smaller parts. Share with th a partn tner. From EngageNY—Grade 4 Reflecti tions 
 1. What t are one or tw two “ah ahas as!” you got t from th the session? 
 2. What t are one or tw two “huhs huhs?” th that t sti till rem remain ain? ? 
 Laneyas@aol.com On Facebook: Teachers Using Guided Math 6