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Curriculum & Instruction
Planning and Implementing Scaffolds in Mathematics to Support Struggling Students Including Students with
Disabilities
Introduction
Kathleen R. ScholandMattituck-Cutchogue UFSDTeacher, 7-12 Math Department Coordinator NYSED Common Core Institute Fellow
Donna KartWappingers Central School DistrictTeacher, Instructional CoachNYSED Common Core Institute Fellow
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Session Objectives
• Curriculum: Participants will learn strategies the presenter uses to create scaffolds for struggling learners when planning for instruction.
• Instruction: Participants will receive and share strategies used to assist struggling learners during instruction.
Essential Question
How do I use instructional scaffolding strategies to assist struggling learners?
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What is Scaffolding in Education?
It is the creation of support features that help an individual student or a group of students transition from tasks at which they are successful due to sufficient procedural skill and conceptual development to tasks that are difficult for them to complete independently.
•Scaffolding is part of the lesson development stage.•Scaffolding is also part of instructional practice.
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Curriculum
Creating Scaffolds for Struggling Learners when Planning for Instruction
•“Struggling learners” includes not only students with disabilities, but also any student who struggles including English language learners.
•This is where your R.E.A.L.I.T.Y. as an educator influences the scaffold you create.
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R.E.A.L.I.T.Y.
✓Reframe your thinking
✓Evaluate your students’ needs
✓Analyze the big picture
✓Lesson study
✓Instructional planning
✓Teach for learning
✓Your reflection (Scholand, K. R.,
2015)
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R: Reframe Your Thinking
Creating scaffolds begins with knowing where you are as a learner.
● What is new in the Standards than what I’ve taught before?● What is new about this content than what I’ve taught
before?● What do I need to know from the previous grade-level to
teach this lesson?● What concepts do I need to relearn?
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R: Reframe Your Thinking
Read the Module Table of ContentsAnalyze the teaching sequence
Read the Module OverviewFocus standards
Foundational standardsPractice standards
Read the supporting documentsProgressionsPerformance Level Descriptions (PLDs)
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E: Evaluate Your Students’ Needs
Creating scaffolds also involves knowing the learning needs of your students.
● Who are the students in my class?● What are the learning needs of individual students?● Where do students usually struggle?● What gaps might they have in their learning?● Why might these gaps remain?
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E: Evaluate Your Students’ Needs
Review available reportsLook for trends and individual areas of concern.
Talk with other educatorsUnderstand the collective needs of students.
Understand the particular needs of students.Inquire about concepts or practices where students struggle.
Foster a relationship with studentsProvide opportunities for students to share their interests
and learning experiences.
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A: Analyze the Big Picture
Now that you have framed where you are as a learnerand who your students are as learners,
•know where the curriculum stands in the overall scheme of mathematics,
•know where the topics and lessons fit into this scheme,
•know the expectations for student understanding and performance as they relate to a student’s overall progress in the mathematics continuum.
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A: Analyze the Big Picture
Reread the Progression document to understand the development of the mathematics.
What is the Module Overview saying?What are the Focus Standards?What are the Foundational Standards?What are the Practice Standards?
What is the Topic Overview saying?What are the Mid- and End-of-Module tasks?What is the progression of Exit Tickets in the Topic?
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L: Lesson Study
It doesn’t matter whether you are usingthe EngageNY Module resources or
other publishers’ resources.
Lesson Study begins the work of creating scaffolds.
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L: Lesson Study
Work through the Examples and Exercises.What is the purpose of each exercise or example?Where, in the development of the lesson, might gaps exist for my students?Do the exercises and examples get students to the Exit Ticket independently?Where would additions be helpful for concept development? For practice?What additions are need to bring students to the point of independent success?
Work through the Problem Set tasks.What is the purpose of each problem?Where might gaps exist for students?Where would additions be helpful?Can students do these independently?
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G7 M1 L2: Is there a constant number such that the first quantity multiplied by this constant gives the second quantity?
Example 1: Pay by the Ounce Frozen Yogurt Constant Multiplier: 0.40
Example 2: A Cooking Cheat Sheet Constant Multiplier: 8
Exercise 1: Calories Burned while Jumping Rope Constant Multiplier: 11
Example 3: Summer Job Constant Multiplier: 28
Lesson Summary: Example Constant Multiplier: 10
Exit Ticket: Making Juice Constant Multiplier: ¼
Problem Set #1: Cran-apple Juice Mixture Constant Multiplier: 5/3 or 3/5
Problem Set #2: Filling the Bathtub Constant Multiplier: 1 ½
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I: Instructional Planning
This is where planning for and creating scaffolds occurs.
Whenever possible, plan collegially, but customize based on your reality.
Keep the design principles intact: focus, coherence, rigor.
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I: Instructional Planning
● What are the key concepts to be taught in this lesson?● What are the non-negotiable understandings that students
must take home?● What suggestions might an instructional support person
give?● From what additional resources might understanding and
inspiration be drawn?
What scaffolds might I want to create?
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G7 M1 L2: Is there a constant number such that the first quantity multiplied by this constant gives the second quantity?
Example 1: Pay by the Ounce Frozen Yogurt Constant Multiplier: 0.40
Example 2: A Cooking Cheat Sheet Constant Multiplier: 8
Exercise 1: Calories Burned while Jumping Rope Constant Multiplier: 11
Example 3: Summer Job Constant Multiplier: 28
Lesson Summary: Example Constant Multiplier: 10
Exit Ticket: Making Juice Constant Multiplier: ¼
Problem Set #1: Cran-apple Juice Mixture Constant Multiplier: 5/3 or 3/5
Problem Set #2: Filling the Bathtub Constant Multiplier: 1 ½
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Additional Problems
Example 1: Pay by the Ounce Frozen Yogurt Constant Multiplier: 0.40 Example 2: A Cooking Cheat Sheet Constant Multiplier: 8 or 1/8Exercise 1: Calories Burned while Jumping Rope Constant Multiplier: 11Example 3: Summer Job Constant Multiplier: 28Lesson Summary: Example Constant Multiplier: 10
Exit Ticket: Making Juice Constant Multiplier: ¼
Exit Ticket #2: Making Juice Constant Multiplier: 4Model Problem #1: Buying Hot Dogs Constant Multiplier: 2.50Model Problem #2: Flowers Sold by the Music Club Constant Multiplier: 0.8 or 5/4
Problem Set #1: Cran-apple Juice Mixture Constant Multiplier: 5/3 or 3/5
Problem Set #2: Filling the Bathtub Constant Multiplier: 1 ½
Problem Set #3: Fabric Store Constant Multiplier: 12
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Scaffolding
The creation of additional problems and their location in a lesson should be strategic.
The last slide shows examples of problems that are Bridges and Links.
They Bridge guided examples to independent tasks.
They Link foundational conceptual understanding to more complex understanding.
These are two of four scaffolding strategies to be shared.
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Build a LadderThis is a vertical scaffolding strategy.•Look at the end-of-lesson expectations for student learning.
•Decide if the examples and exercises are sufficient for your struggling learners to progress (climb up the ladder).
•If not, create an additional task (rung on the ladder) to help the student climb to the end-of-lesson expectation(s).
ie: simplify the context of the task, break the task into parts,add a preliminary step, change the vocabulary
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Build a LadderOctober 2014 NTIThe Number System: Crafting Teaching Sequences for Extended Interventionshttps://www.engageny.org/resource/october-2014-nti-grades-6-12-mathematics-turnkey-kit-teachers
https://www.engageny.org/resource/december-2014-nti-grades-6-12-mathematics-turnkey-kit-teachers-session-2
December 2014 NTIExpressions and Equations: Crafting TeachingSequences for Instant, Short-Term and Extended Interventions
HARD
EASY
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Build a BridgeThis is a horizontal scaffolding strategy.•Look at the progression of examples and exercises.
•Decide if your struggling learners will need a bridge between your instructional example and their independent work on an exercise or problem set.•If so, create an additional task or plan for discussion that will connect their understanding gained from the guided example to the understanding needed to independently succeed on the exercise.
http://upload.wikimedia.org/wikipedia/commons/e/e7/Arch_bridge_icon.svg
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Harness Learning Styles
This is a strategy where you access students’ learning styles by creating an auditory, visual and/or kinesthetic component to the task.
This is when you honor the concrete-pictoral-abstract transitions that are needed to facilitate learning.
Attention Getters: songs, manipulatives, diagrams, pictures, graphic organizers
Instructional Technology: personal white boards, Smart Boards, computer programs, response systems
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Build LinksThis is a scaffolding strategy that offers students something different while maintaining the conceptual development in the lesson.
Things to consider:
•Differentiation Strategies: Think-Pair-Share, Jigsaw, Gallery Walk, Matchings•Use the Practice Standards to create a different dimension to a problem: critique the reasoning of another student, model the result with a diagram, create a similar problem that demonstrates an understanding of the concept.•Manipulate the Formatting.
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Additional Problems
Example 1: Pay by the Ounce Frozen Yogurt Constant Multiplier: 0.40 Example 2: A Cooking Cheat Sheet Constant Multiplier: 8 or 1/8Exercise 1: Calories Burned while Jumping Rope Constant Multiplier: 11Example 3: Summer Job Constant Multiplier: 28Lesson Summary: Example Constant Multiplier: 10
Exit Ticket: Making Juice Constant Multiplier: ¼
Exit Ticket #2: Making Juice Constant Multiplier: 4Model Problem #1: Buying Hot Dogs Constant Multiplier: 2.50Model Problem #2: Flowers Sold by the Music Club Constant Multiplier: 0.8 or 5/4
Problem Set #1: Cran-apple Juice Mixture Constant Multiplier: 5/3 or
3/5Problem Set #2: Filling the Bathtub Constant Multiplier: 1 ½
Problem Set #3: Fabric Store Constant Multiplier: 12
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Example of a Link
Exit Ticket Susan and John are buying cold drinks for a neighborhood picnic. Each person is expected to drink one can of soda. Susan says that if you multiply the unit price for a can of soda by the number of people attending the picnic, you will be able to determine the total cost of the soda. John says that if you divide the cost of a -pack of soda by the number of sodas, you will determine the total cost of the sodas. Who is right and why?
Exit Ticket #2 Susan and John are buying cold drinks for a neighborhood picnic. Each person is expected to drink one can of soda.
● Susan says that if you multiply the unit price for a can of soda by the number of people attending the picnic, you will be able to determine the total cost of the soda.
● John says that if you divide the cost of a -pack of soda by the number of sodas, you will determine the total cost of the sodas.
Who is right and why?
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T: Teach for Learning
So, let’s get back to your R.E.A.L.I….
•This is where implementing scaffolds and in-the-moment adjustments occur; when on-the-spot scaffolding is needed.
•This is when planning to teach will give you the advantage!
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Our role as Math Common Core Fellows
Some of our responsibilities to assist teachers:● Create additional scaffolds for struggling
learners.● Add vocabulary for English Language
Learners.● Model Problems that teachers can refer
parents to so they can assist their child in doing the homework.
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Instruction
Instruction is the of the lesson!
This is where we engage, communicate, discuss, question, give immediate and precise feedback and assess while still being flexible and responsive to the needs of all students.
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What strategies or scaffolds have been successful in your classroom?
● This room is filled with experienced practitioners!
● What works for me might or might not work for you!
● A strategy is successful if it has worked for you and your student has progressed in his learning!
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Time to TALK!For the next several minutes, please share in your table group a
successful strategy or scaffold that you have used during a lesson that has helped you to implement the math modules.
We will share out!
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Dale’s Cone of Experience
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Source: Adapted from E. Dale, Audiovisual Methods in Teaching, 1969, NY: Dryden Press.
Scaffolding vs. Differentiating
Scaffolding versus DifferentiatingBreaking it down PROActive Response Show and Tell Adapting examples
Tapping into prior knowledge Adapting an assignment Time to talk Alternative projects Pre-teach vocab More accessible text
Visual aides And lots more of each too!
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Some Interesting Articles and Links
Instructional Scaffolding to Improve Learninghttp://www.niu.edu/taconnections/2008/fall/scaffolding.shtml
6 Scaffolding Strategies to Use With Your Studentshttp://www.edutopia.org/blog/scaffolding-lessons-six-strategies-rebecca-alber
Instructional Strategies in Math including Differentiationhttp://www.mathwire.com/strategies/is.html
9 Strategies for Motivating Students in Mathematicshttp://www.edutopia.org/blog/9-strategies-motivating-students-mathematics-alfred-posamentier
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Y: Your reflection
Your reflection informs the decisions you will make tomorrow and in the future.
● Your reflection gives you the opportunity to build onto your strengths.
● It positions you to support others as they are building scaffolds for their struggling learners.
● Respectful, collegial sharing is vital for building our capacity as learners.
Consider Peer Review of your experience.
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R.E.A.L.I.T.Y.
✓Reframe your thinking
✓Evaluate your students’ needs
✓Analyze the big picture
✓Lesson study
✓Instructional planning
✓Teach for learning
✓Your reflection (Scholand, K. R.,
2015)
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Wrap-Up
We have discussed how we make curricular and instructional decisions that relate to
when, where, and what scaffolds are needed.
•We have shared strategies we use when planning scaffolds for instruction.
•We have shared strategies for strategies and scaffolds that occur during instruction.
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Summary
• Ladder• Bridge• Harness• Link
• Model• Question• Prior Knowledge• Differentiate
Instructional Strategies:Curricular Strategies:
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Closing
It is your R.E.A.L.I.T.Y.that will best inform
the decisions you make regarding the creation of scaffolds
for struggling learners.
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Thank You
Kathleen R. ScholandMattituck-Cutchogue [email protected]
Donna KartWappingers Central School [email protected]
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