curriculum & instruction planning and implementing scaffolds in mathematics to support...

Curriculum & Instruction

Planning and Implementing Scaffolds in Mathematics to Support Struggling Students Including Students with

Disabilities

I am concerned that there have not been enough clear examples or criteria thus far for participants to be able to do this. Much has been done about "pre" scaffolds (e.g., editing lessons) but there doesn't seem to be much about "in the moment." Sufficient examples will be necessary to help participants understand what this means/how to generate these.-Peter Coe

are they doing this in the session? lets add facilitator's notes here - both on slide and notes to help those who choose to turnkey: time, groupings, prompt, any protocols - do they share with whole group?

Please include slide(s) with examples from CCI project-Peter Coe

add this acronym on previous slide so when they get here they are prepared

add context to notes section - what the levels are for, etc.

anything we can do about this visual to make it easier to see?can we add notes why it's here?

wcsd

I think it will be important to establish criteria for these. How does a participant know what is a good strategy? How will the facilitator make sure that what is shared is worthy of sharing?-Peter Coe

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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Where We Live and Work

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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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Essential Understanding

Every teacher has a differentR.E.A.L.I.T.Y.

(Scholand, K. R., 2015)

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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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Peter Coe

So again, a slide may not be necessary, but we need to describe an example that illustrates what this means. "For example, when I examine seventh grade module 1, I read the Progression on Ratio and Proportion and learn about the way that students are exposed to ratio tables in Grade 6. This will inform the way I think about G7 M1."

Please also be specific, using slides, of how this is done, using an example from the CCI project (for example, consulting the Progressions and how specifically, this affects the process)-Peter Coe

Kris Cole

please add slides to address Peter's comment.

please include examples in the notes section

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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Kris Cole

include a description of what is to be done with this information - lay this out for folks

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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Peter Coe

I think it would be really great somewhere (if not here, perhaps after the next slide) where we can show an example from a module where you can model this thinking. "In looking at this sequence of exercises from Module 1, Lesson 3, I noticed that some students might struggle to answer the third exercise, which involves non-whole numbers, since examples 1 and 2 involve only whole numbers."

"Lesson Study" has a particular meaning (traditional Japanese form of professional development). I'm not sure that's what is meant here. Please be clearer showing slides with examples from the CCI project.-Peter Coe

Kris Cole

please address Peter's request

please include an explanation in the notes section.

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




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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 #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 #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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Scaffolding Strategies

Build a LadderBuild a Bridge

Harness learning Styles

Build Links

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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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https://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

Example of a Rung on a Ladder

Grade 7 Module 1 Lesson 4

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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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http://upload.wikimedia.org/wikipedia/commons/e/e7/Arch_bridge_icon.svg

add example in notes

Example of a Bridge

Grade 7Module 1Lesson 4

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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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Example of a Harness

Grade 7Module 1Lesson 7

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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 #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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Peter Coe

Are both of these examples of Links? Or is it just the second?

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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where are these differences/ this list coming from? modifications will need to be spelled out - we have been using "adapting" instead of modifying for fear of losing shifts in rigor when people think "modifying". Peter - thoughts?Yes, I'm not sure this distinction is important. (It may be, but it isn't coming across in the slides.) Adapting is a good, consistent word.-Peter Coe

Donna Kart

From articles and classes and my own learning curve, these get mixed up. See notes below on my comments to each. I will focus on scaffolds and briefly discuss differentiating

Kris Cole

let's add references where applicable for people who want to dive in deeper

Donna Kart

Done. I added an additional slide and will add to it later

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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http://www.niu.edu/taconnections/2008/fall/scaffolding.shtml

http://www.edutopia.org/blog/scaffolding-lessons-six-strategies-rebecca-alber

http://www.mathwire.com/strategies/is.html

http://www.edutopia.org/blog/9-strategies-motivating-students-mathematics-alfred-posamentier

http://www.edutopia.org/blog/9-strategies-motivating-students-mathematics-alfred-posamentier

Peter Coe

Can we title these or name them, rather than just putting the links?

Donna Kart

Absolutely, Done! I didn't get to finish because I had to go out to a meeting!

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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Peter Coe

I can see where the left side comes from clearly, with examples, in the slides. I can't see where the right side comes from clear, with examples in the slides.

Donna Kart

My belief is these will all come out of the shared strategies but we summarized what we felt were the most important. I will discuss all of these on slide 36. You can see my notes and please let me know if I should add more to it.

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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