Mathematic Strategies for Resource/Inclusion

Extravaganza 2013-HHSS Session 4: 2:30pm, Room 307 Julie Acosta 8/19/2013

Objectives:

• Develop a general understanding of Texas Math Standards.

• Increase teachers’ knowledge about updated evidence-based math instructional strategies for teaching students with significant disabilities.

• Define systematic instruction.

Objectives:

• Explain how to apply scaffolded instruction in teaching math.

• Relate the benefits of using scaffolded instruction.

• Provide useful resources to assist teachers in teaching mathematics to students with significant disabilities.

Characteristics of Learning Barriers

• Visual impairment

• Hearing impairment

• Deaf-blindness

• Significant developmental delay

• Orthopedic impairment

• Multiple disabilities

• Autism

Possible Barriers in Learning Math

• Restricted vocabulary

• Communication difficulties

• Memory deficits

• Underdevelopment of learning strategy

• Restricted generalization of skills

• Attention deficits

• Sensory deficits

• Restricted mobility or fine motor skills

Activity 1

1. Current math practices 2. New practice plan

• Each participant will develop his or her own New Practice Plan after completing the training modules

• The New Practice Plan – begins with what you already know

– details the aspects of mathematics teaching that you plan to change as a result of the training

– lists resources required

What to Teach- Standards

• Texas Essential Knowledge and Skills (TEKS)-Mathematics

• ELPS- English Language Proficiency Standards

• CCRS-College and Career Readiness Standards

TEKS-Mathematics

K-8

• Numbers, Operations, and Quantitative Reasoning

• Patterns, Relationships, and Algebraic Reasoning

• Geometry and Spatial Reasoning

• Measurement

• Probability and Statistics

• Underlying Processes and Mathematics Tools

TEKS-Mathematics

• High School

• Algebra I

• Geometry

• Algebra II

• Precalculus

• Mathematical Models with Applications

• Other High School Mathematics Courses

STAAR and STAAR-M Website

STAAR: All students who where first enrolled in grade 9 or below in 2011–2012 and who do not qualify for one of the other STAAR assessments

STAAR-M: Students who were first enrolled in grade 9 or below in 2011–2012 and who are receiving special education services and have a disability that significantly affects academic progress; ARD committee decision based on participation requirements, with LPAC collaboration if student is also an ELL

Resources-STAAR and STAAR-M

• Assessed Curriculum- STAAR and STAAR-M

• Blueprints-STAAR and STAAR-M

• Performance Level Descriptors-STAAR and STAAR-M

• Accommodations-website

TEKS Alignment-Grade Span

• Vertical Alignment Documents

PK Guidelines

K-5th

5th – Algebra I

• Side-by-Side Revised Math TEKS

K-8th

Strategies for TEKS

TEKS What Difficulties will Students Have?

Strategies to Consider

5.4B: represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity

Math Instructional Strategies

• General instructional strategies, such as

• 5E instructional model (Engage, Explore, Explain, Elaborate, and Evaluate)

• Explicit math instruction (guided demonstration and independent practice)

• Evidence-based instructional strategies for students with significant disabilities

What is Evidence-Based Instruction?

Teaching mathematics problems can be structured to support learner differences and abilities. Evidence-based or research-based instructions provide teachers with tried-and-tested strategies to improve student learning.

Evidence-Based Instruction

“An evidence-based practice can be defined as an instructional strategy, intervention, or teaching program that has resulted in consistent positive results when experimentally tested”

(Mesibov & Shea, 2011; Simpson, 2005).

Evidence-Based Instruction

• Systematic instruction is the most substantiated evidence-based instruction (Collins, Kleinert, and Land,

2006)

• Systematic instruction is effective in teaching various math skills to students with moderate and severe disabilities (Browder et al., 2008)

Research Studies

Systematic instruction has been used to teach

• frequency tally and graphing (Ackerman and Shapiro, 1984)

• addition (McEvoy and Brady, 1988)

• one-to-one correspondence (Lagomarcino and Rusch, 1989)

• use of a calculator and graphing (Lovett and Haring, 1989)

• use of a number line and matching numbers (Copeland et al., 2002)

Research Example

Teaching students with moderate disabilities to count money by using the sequential prompting strategy (Colyer and Collins, 1996):

1. Show the flash card ($3.75)

2. State the price as a cashier (“It is three seventy-five”)

3. Tell the student what to do (“Give me three dollars and one more”)

4. Model, and have the student follow

What Is Systematic Instruction?

• Systematic instruction refers to a well-planned sequence for instruction.

• It is designed before the activities and lessons are developed, and it is based on student characteristics.

• It involves a variety of instructional methods, including scaffolded instruction, system of prompts, and reinforcement.

Scaffolding Instruction

Scaffolding instruction is “the systematic sequencing of prompted content, materials, tasks, and teacher and peer support to optimize learning.”

(Dickson, Chard, and Simmons, 1993, p. 12)

Zone of Proximal Development • Zone of proximal development (ZPD) is “…the area

between what the child can accomplish unaided and the level the same child can accomplish with assistance.”

(Beed, Hawkins, and Roller, 1991)

• Scaffolding provides the support as needed and leads to independent task performance.

(Graves and Braaten, 1996)

Scaffolding Instruction

“The goal of scaffolding is to support

students until they can apply the new skills

and strategies independently.”

(Larkin, 2001)

Scaffolding Instruction for Mathematics

“The purpose of scaffolding instruction is to provide students who have learning problems a teacher supported transition from primarily seeing and hearing the teacher demonstrate and model a particular math concept/skill to performing the skill independently.”

(http://fcit.usf.edu/mathvids/strategies/si.html)

Procedures

• Teacher initially describes/models the concepts/skills several times.

• Teacher models the skill with the students’ input (for example, with questions and answers).

• Teacher gradually fades directions as students demonstrate increased levels of competency in performing the skill.

• Teacher monitors students to perform the skill with few or no prompts.

Scaffolding Instruction Procedures

(Beed et al., 1991)

Teacher modeling

Modeling with student input

Cueing specific elements

Cueing specific strategies

Providing general cues

Foldable

Teacher Modeling-TASK 1 Problem 5: Thomas is inviting 6 friends to his pizza party.

Each friend will eat 2/3 of a pizza. How many pizzas does

he order for his party?

Model/Diagram

Number Sentence

Solution

Teacher Modeling

0 1 2 3 4 3

1

3

2

3

4

3

5

3

7

3

8

3

10

3

11

3

3

3

6

3

9

3

12

1 friend

2 friend

3 friend

4 friend

5 friend

6 friend

pizzas

Thomas needs to order 4 pizzas for his 6 friends to get of a pizza. 3

2

Modeling with Student Input-TASK 2

Problem 1: Katy drinks ¾ of a bottle of apple juice each

day. How much juice will be drunk in 5 days?

Model/Diagram

Number Sentence

Solution

Modeling with Student Input-Step 1

4

3

day 1 day 2 day 3 day 4

day 5

Modeling with Student Input-Step 2

4

3

day 1

day 2 day 3

day 5

day 4

Modeling with Student Input-Step 3

= 4

13

1 whole

day 1 day 2 day 3 day 4

day 5

Modeling with Student Input-Step 4

= 4

13

In 5 days, she will drink

bottles of juice. 4

13

Cueing Specific Elements-TASK 3

Problem 5: Thomas is inviting 6 friends to his pizza party.

Each friend will eat 2/3 of a pizza. How many pizzas does

he order for his party?

Model/Diagram

Number Sentence

Solution

Cueing Specific Elements

= 4 pizzas

1 whole

3

2

Math Interventions Found Effective for Students with Disabilities

1.) Reinforcement and corrective feedback for fluency

2.) Concrete-Representational-Abstract Instruction (Teacher Directed/Explicit Instruction)

3.) Direct/Explicit Instruction/Modeling (Teacher Directed/Explicit Instruction)

4.) Demonstration Plus Permanent Model

5.) Verbalization while problem solving

Math Interventions Found Effective for Students with Disabilities

6.) Big Ideas (Strategy Learning)

7.) Strategy Instruction (Student Directed/Implicit Instruction)

a.) Metacognitive strategies: Self-monitoring, Self-Instruction

b.) Structured Worksheets; Diagramming

c.) Mnemonics (PEMDAS)

d.) Graphic organizers

Math Interventions Found Effective for Students with Disabilities

8.) Computer-Assisted Instruction

9.) Monitoring student progress

10.) Teaching skills to mastery

*Source 1: Shanon D. Hardy, Ph.D Powerpoint Slides, February 25, 2005 Access Center, Accessed from: http://www.k8accesscenter.org/index.php/category/math/

*Source 2: Seifert, Kathy. (2010). University of Minnesota Powerpoint Lecture, EPSY 5615 accessed 3/10/2010

Providing general cues

Cueing specific strategies

Cueing specific elements

Modeling with student input

Teacher modeling

(Beed et al., 1991)

Using Questioning to Stimulate Mathematical Thinking:

LEVELS OF THINKING GUIDE QUESTIONS

Memory: recalls or memorizes information • What have we been working on that might help with this

problem?

Translation: changes information into another form

• How could you write/draw what you are doing?

• Is there a way to record what you've found that might

help us see more patterns?

Interpretation: discovers relationships

• What's the same? What's different?

• Can you group these in some way?

• Can you see a pattern?

Application: solves a problem - use of appropriate

generalizations and skills

• How can this pattern help you find an answer?

• What do think comes next? Why?

Analysis: solves a problem - conscious knowledge of the

thinking

• What have you discovered?

• How did you find that out?

• Why do you think that?

• What made you decide to do it that way?

Synthesis: solves a problem that requires original,

creative thinking

• Who has a different solution?

• Are everybody's results the same? Why/why not?

• What would happen if....?

Evaluation: makes a value judgment

• Have we found all the possibilities? How do we know?

• Have you thought of another way this could be done?

• Do you think we have found the best solution?

Revised Bloom’s Taxonomy Foldable

Bloom's Taxonomy “Revised” Key Words, Model Questions, & Instructional Strategies

Bloom's Taxonomy “Revised” Key Words, Model Questions, & Instructional Strategies

“A good teacher makes you think when you don’t want to.”

(Fisher, 1998, Teaching Thinking)

4 Essential Questions for Student Learning

1. What do we want our students to learn?

2. How will we know they are learning?

3. How will we respond when they don’t learn?

4. How will we respond when they do learn?

(Dufour)

Lessons on Bundling the TEKS: Dual Coding:

Content + Process

Chinese Proverb

“He who learns but does not think is lost”

Two Approaches to Promote Access to General Curriculum

1. Universal design of learning (UDL) Handout

• Multiple means of representation give learners various ways of acquiring information and knowledge.

• Multiple means of action and expression provide learners with alternatives for demonstrating what they know.

• Multiple means of engagement tap into learners' interests, offer appropriate challenges, and increase motivation.

(from http://www.cast.org/research/udl/index.html)

Two Approaches to Promote Access to General Curriculum

2. Assistive technology (AT)

• Promoting access to general curriculum

• Definition:

“an item or piece of equipment or product system acquired commercially, off the shelf, modified, or customized, and used to increase, maintain, or improve functional capability for an individual with disabilities”

(Beard, Carpenter, and Johnson, 2007, p. 4)

Application of Assistive Technology in Learning Mathematics

Area Examples of Application

Cognitive Process A calculator, computer-assisted programs, concrete

models (such as abacus)

Fine-Motor A computer switch, touch screens

Visual-Spatial Process Prints in Braille, prints in large fonts, screen reader

Hearing Process Amplifiers, communication board, printed materials

Communication

Augmentative and alternative communication (AAC)

systems (for example, eye gazing device,

communication boards, and AAC devices)

Memory and

Organization Prompting sheets, video camera

UDL and AT for Mathematics

• Accessibility Strategies Toolkit for mathematics (Brodesky et al., 2004) Toolkit

• Curriculum Access for Students with Low-Incidence Disabilities: The Promise of UDL (Jackson, 2005) Article

• Assessing Students’ Needs for Assistive Technology (ASNAT), Chapter 8, AT for Mathematics (WATI, 2009) Chapter

Closure

Take out your Change of Practice Plan. Think about what you learned in this module and relate it to your classroom. Write down some ideas of what you want to start to use in your classroom.

Where do we go from here?

Questions/Discussion: