Ensuring Access to the General Education

Curriculum in Mathematics

Goals of the Session• Use NCSC mathematics resources to add

supports and accommodations to a gen ed lesson for students with significant cognitive disabilities.

• Reflect on current practices that might be unintentional barriers for student access to the general ed curriculum.

6 Step Process1.Identify the grade level content standard(s) in

the gen ed lesson.2.Identify student outcomes or learning

objectives in the gen ed lesson.3.Determine Strand, Instructional Families, and

grade level CCCs related to the standard(s) and learning objectives.

4.List the instructional activities for All students.4a. Determine individual student barriers to accessing the instruction, participating in instructional activities, and demonstrating learning.

5. Determine supports for SCD.6. Use NCSC curriculum and instructional resources.

6 Step Process: Steps 1 and 2

Step1: Identify the grade level content standard(s) in the gen ed lesson.

• If the standard is not listed, go to step 2.

Step 2: Identify the student outcomes and learning objectives in the gen ed lesson.

• Guiding questions:• What are the desired outcomes for ALL

students?• How will students demonstrate their knowledge

and skills?• What are the observable student

performances?• Use Content Modules to clarify content.

6 Step Process: Step 3Step 3: Determine Strand, Instructional Families, and grade level CCCs related to the standard(s) and learning objectives.

• Identify the Strand: 1) Geometry 2) Numbers and Operations 3) Measurement 4) Patterns, Relationships and Functions 5) Data, Probability, and Statistics.

• Identify the Instructional Family(s).• Identify the CCCs before student’s grade level

for support and after student’s grade level for stretch.

• Embed those CCCs in the lesson, if appropriate.• Use Content Modules to define terms and to clarify content.

6 Step Process: Step 4Step 4: Identify the instructional activities for All students.

• Identify the instructional activities that move students toward achievement of the objectives.

• Typical classroom activities. i.e., lecture, taking notes, small and large group work, etc.

• Use Curriculum Resource Guide for additional ideas on how the content is taught in a general education classroom.

• Pay particular attention to UDL (representation, action and expression, and engagement) in the lesson. Add UDL activities that expand possibilities:

– for student interaction with materials and activities – for student response options– for gaining and maintaining student interest

Use UDL Principles Multiple Means of Engagement give learners

various ways of acquiring information and knowledge and provide options for comprehension by the highlighting of critical features.

Multiple Means of Representation give learners various ways of acquiring information and knowledge and provide options for expressive skills and fluency.

• Multiple Means of Expression provide learners alternatives for demonstrating what they know and provide options for recruiting interest, sustaining effort, and self regulation.

6 Step Process: Step 4a

Step 4a: Determine individual student barriers to accessing instruction, participating in activities, and demonstrating learning.

• Examine all activities.• List individual student barriers.• Consider all students.• Use UDL principles.• Add activities as necessary.

Guiding Questions• Is the student actively participating in each part of the

instructional activity? • Are the activities moving the student toward outcomes

linked to the grade level content standard(s)?– Can the student access instruction? – Is targeted information provided in student’s mode of

communication? – Can the student interact with instruction and materials?– Does the student have the means to demonstrate

knowledge, skills, and concepts? – What will engage the student in the activity? – How will the student remain motivated long enough to

learn?

Use UDL Principles

Examples of Additional Considerations for Emerging Readers and Communicators

Multiple means of Engagement: Show the end first; present the concrete example of the graph; with the end in mind, have students at multiple levels solve in multiple ways; count or solve using a calculator, graph paper, 2 and 3 dimensional manipulative materials

Multiple Representation: 2 dimensional paper; 3 dimensional objects; etc.

Multiple means of Expression: Picture problem choices: present 2 choices of possible correct responses and include words or pictures, tactile representations

6 Step Process: Step 5

Step 5: Determine student supports.• Communication

• How does the student communicate with the teacher, in small groups, and with partners, etc.

• Is the salient vocabulary for the lesson included in the students’ communication systems?

• UDL: Multiple means of representation, expression, and engagement

• Other

6 Step Process: Step 6Step 6: Use NCSC Curriculum and Instructional Resources.1. Content Modules – Explanation of difficult or complex

mathematical /ELA concepts2. Curriculum Resource Guides (CR) - Examples of how

academic content is taught in general education 3. Element Cards - Description of how to teach specific

concepts and skills for remediation of skills4. MASSIs and LASSIs – Intensive, scripted instructional

lessons in math and ELA that include evidence-based practices

5. Instructional Resource Guides - Evidence-based prompting and instructional strategies

6. UDL Units - Models of universally designed instruction that illustrate how to target the CCCs within general education lessons

Let’s Practice!Begin with a Gen Ed Lesson

Step 1: The Standard(s)Step 1: Identify the grade level content Standard(s).

CCSS Mathematics Standards: Grade 6, Expressions and Equations, EE6 and EE9

EE6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

EE7: Solve real world and mathematical problems by writing and solving equations of the form x + p = q for cases in which p, q, and x are nonnegative rational numbers.

EE9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as a dependent variable, in terms of the other quantity, thought of as the independent variable. (Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation.

Step 2: Student Outcomes/Learning Objectives

Step 2: Identify student outcomes or learning objectives in the gen ed lesson.

Students will be able to: – Identify a pattern involving the number of tiles required to

form a border around a pool with length l and width w. – Write a symbolic expression that describes the number

of tiles needed to form a border around a pool. • Key words in learning objectives:

– Pattern– Length– Width– Symbolic expression

Step 3:Determine the Strand,

Instructional Families, and CCCs related to the Standard(s) and

Learning Objectives.

Five Mathematics Strands

Patterns, Relations and

Functions

Geometry

Measurement

Data, Probability

and Statistics

Number Operations

Step 3: Strand, Instructional Families, and CCCs

Strand: Patterns, Relations, and FunctionsInstructional Family: Problem Solving and Using VariablesGrade level CCCs: 6.PRF.1d1 and 6.PRF.2a2 and 6.PRF.2a3

CCCs: • 6.PRF.1d1

– Solve real-world single step linear equations• 6.EE.7

• 6.PRF.2a2 – Use variable to represent numbers and write

expressions when solving real-world problems• 6.EE.6

– Use Content Module to define variable and expressions.

• 6.PRF.2a3– Use variables to represent two quantities in a real-world

problem that change in relationship to one another• 6.EE.9

Core Content Connectors

After student grade level for stretch

Core Content Connectors• CCCs before student’s grade level for

support• 2.PRF.1c5: Write of select an equation

representing the problem and its solution. – 2.OA.1

• 4.PRF.1e3: Solve multiplicative comparisons with an unknown using up to 2-digit numbers with information presented in a graph or word problem. – 4.OA.2

• CCCs after student grade level for stretch • 7.PEF.1g1: Solve real-world multi-step problems

using whole numbers– 7.EE.3

Content Module DefinitionsFrom Learning Objectives:

– Pattern is a discernible regularity in the world or in a manmade design. As such, the elements of a pattern repeat in a predictable manner.

– Length is the longest dimension of an object. – Width is the distance from side to side.– Symbolic (symbol) is something that represents an idea,

process, or a physical entity. The purpose of a symbol is to communicate meaning.

– Expression is a phrase made up of variables and/or numbers and symbols. Example: 3x + 4

From CCCs:– Variable is a letter that represents a value.– Linear Equation is an equation whose solution falls on a line

when graphed. (Priority standard)

Step 4: Instructional ActivitiesStep 4: List the instructional activities for ALL students.• In large group, teacher demonstrates and students predict

the possible dimensions of a pool with the area of 36ft X 36ft.

• In large group, teacher guides students through predicting the number of tiles it would take to surround the 36ft X 36ft pool.

• Work in small group. • Predict the number of tiles that would be needed to put a

border of tiles around the entire pool.• Participate in small group to build a pool 36 sq. feet on poster

board– Math question: what are the possible dimensions for the pool using

only whole numbers. 1ft X 36ft? 2ft X 18ft? 3ft X 12ft? 4ft X 9ft? 6ft X 6ft?

Step 4: Instructional Activities, cont.

• Participate in small group to build a pool 36 sq. feet on poster board– Math question: what are the possible dimensions

of the pool using only whole numbers. 1ft X 36ft? 2ft X 18ft? 3ft X 12ft? 4ft X 9ft? 6ft X 6ft?

• Participate in small group in using algebra tiles to make border around the pool with each tile representing 1 ft. X 1 ft.

• Students predict the number of tiles that would be needed for tiles around the entire pool.

Step 4a: Barriers

Step 4a: Determine individual student barriers to accessing instruction, participating in activities, and demonstrating learning.• Make a list for individual students

according to the gen ed instructional activities.

Universal Design for Learning (UDL)

http://bookbuilder.cast.org/29

Provide multiple means of representation

Provide multiple means of expression

Provide multiple means of engagement

Can the student access instruction? Is targeted information provided in student’s mode of communication?

Can the student interact with instruction and materials? Does the student have the means to demonstrate knowledge, skills, and concepts acquired?

What will engage the student in the activity? How will the student remain motivated long enough to learn?

Step 5: Instructional Supports

Step 5: Determine access supports needed for SCD. • What supports are needed for students to

participate in and learn from the instructional activities?

Menu of Supports and AccommodationsListen How do we know the student is listening? The student can

be given a selection of objects or graphics representing key points in the lecture and can select each object or graphic at the correct point in the lecture. Lecture could be provided digitally, etc.

Take Notes How can the student participate in note-taking/writing? Graphics or objects to collect notes, picture symbols, notes pre-printed and the student could “mark” as they follow, preprogrammed communication devices, adapted keyboards, digital text and a text reader, or take photos

Respond and Participate

How will the student respond to questions? Use graphics to select the correct answer, pre-programmed communication device , such as Classroom Suite, with menu interfaces for each content area

Co-operate and work in groups

How will the student work in a group? Student could work with a peer to fulfill a group role.

Step 6: Instructional ResourcesStep 6: Use Instructional Resources.1. Content Modules – Explanation of difficult or

complex mathematical /ELA concepts2. Curriculum Resource Guide (CR) - Examples of

how academic content is taught in general education 3. Element Cards - Description of how to teach specific

concepts and skills for remediation of skills4. MASSIs – Intensive scripted instructional lessons

that include evidence-based practices for remediation of skills

5. Instructional Resource Guide - Evidence-based prompting and instructional strategies

6. UDL Units - Models of universally designed instruction that illustrate how to target the CCCs within general education lessons

Element Card: 6.PRF.1d1

MASSI: 6.PRF.1d1

6 Step Process1.Identify the grade level content standard(s) in

the gen ed lesson.2.Identify student outcomes or learning

objectives in the gen ed lesson.3.Determine Strand, Instructional Families, and

grade level CCCs related to the standard(s) and learning objectives.

4.List the instructional activities for All students.4a. Determine individual student barriers to accessing the instruction, participating in instructional activities, and demonstrating learning.

5. Determine supports for SCD.6. Use NCSC curriculum and instructional resources.

Presume Competence!

Viewing students through the lens of a disability label may increase the likelihood of misjudging capabilities and bar some students from opportunities to learn what other students their age are learning• (Jorgensen, McSheehan & Sonnenmeier, 2007)

Assume Competence1. What do I assume about the student’s capability?  2. How do I interpret lack of engagement and/or

disruptive behaviors? 3. Do I assume the student doesn’t know something? 4. Do I connect skills and facts to big ideas? 5. Do I start with the standard and work toward skills

and concepts?6. Do I provide supports so students not only

complete an activity but also learn the content?7. Do I provide students ways to interact

with materials and activities?

Goals of the SessionUse NCSC resources to build-in supports

and accommodations to a gen ed lesson for students with significant cognitive disabilities.

Continue to reflect on current practices that might be unintentional barriers for access to the general ed curriculum.

References• Denham, A. & Lewis, P. (2006). The Application of Universal Design for Learning in the

Classroom for students with the most significant disabilities. SPLASH Training. Human Development Institute, University of Kentucky. Lexington, KY.

• Denham, A. (2004). Pathways to Learning for Students with Cognitive Challenges: Reading, Writing and Presenting. Interdisciplinary Human Development Institute, University of Kentucky. [Online] Available: http://www.ihdi.uky.edu/IEI/

• Clayton, J, Michael Burdge, Anne Denham, Harold L. Kleinert, Jacqui Kearns “A Four Step Process for Accessing the General Curriculum for Students With Significant Cognitive Disabilities” Teaching Exceptional Children v. 38, n. 5, pp. 20-27.

• Jorgenson, C (2005). “The Least Dangerous Assumption: A Challenge to Create a New Paradigm” A Resource for Families & Others Interested in Down Syndrome & Developmental Disabilities v.6, n.3.

• Kearns et al. (2010). Alternate Assessment for Students with Significant Cognitive Disabilities:

An Educator's Guide.

• Wiggins, G. and McTighe, J. (2005). “Understanding by Design”. Alexandria, VA.: Association for Supervision and Curriculum Development.

• http://www.learner.org/workshops/algebra/workshop1/lessonplan1.html

• http://illuminations.nctm.org/Lessons.aspx

• http://www.teachersdomain.org/

Ensuring Access to the General Education

Curriculum