Planning Math Lessons That Reach All Learners

Facilitated by:

Cynthia Santosuosso

1. Situating the Work

NCTM Standards“All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study—and support to learn—mathematics. Equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students.”

NCTM, 2000

Common Core Standards

All students, including those

with disabilities, “must have

the opportunity to learn and

meet the same high

standards if they are to

access the knowledge and

skills necessary in their post

school lives.”

CCSSI, 2010

Key Competencies for Effective Inclusion Practice in Math

• Understanding of mathematics

• Understanding of the strengths and needs of individual learners

• Understanding of alternative instructional strategies and designs

• Skill in applying this knowledge flexibly in the classroom

Mathematics

Learners

Teaching

Classroom Practice

Planning & Decision Making

Today’s Goals

• Deepen your understanding of the math of specific lessons

• Deepen your understanding of individual students’ strengths and needs

• Deepen your understanding of instructional strategies for teaching math

• Enhance your skill in planning accessible math lessons

• Foster collaboration among all the educators who work with a child

4. Introduction to the “Fact Triangles” Lesson

Thank you, Steve Quester, Mead Johnson, and Angela Waite!

The Classroom

• 1st grade• 24 students• Ethnically diverse• 9 students with IEPs

The Teachers

• 1 special education teacher with 11 years of experience

• 1 general education teacher with 21 years of experience

• 1 paraprofessional with 15 years of experience

Math of the Lesson• Everyday Mathematics

curriculum• Studied addition and

subtraction throughout the year

• Worked on renaming numbers and representing number stories before this lesson

• Were briefly introduced to fact triangles and number-naming boxes before this lesson

Math Context

2 5 8 1 1 1 4 1 7 2 0

Do you remember the numbers?

Math Context

2, 5, 8, 11, 14, 17, 20

Composing and Decomposing Numbers

The following ideas are integral to the lesson:• putting a set of objects together and breaking

them apart• recording what they have done using a variety of

symbols• organizing their ideas• using the language of mathematics to discuss

what they are doing

Composing and Decomposing Numbers

• The experiences of manipulating objects, and recording and discussing the process and results are essential in children’s understanding and memorizing of addition and subtraction facts.

• This kind of experience also allows children to grasp basic principles of mathematics, such as the commutative principle (“turnaround facts,” i.e., 3 + 4 = 4 + 3), which is a feature of this lesson.

 

Fact Triangle

Number Naming Boxes

4+3

Links to Common Core Standards

Grade 1

Operations and Algebraic Thinking

• Represent and solve problems involving addition and subtraction.

• Understand and apply properties of operations and the relationship between

addition and subtraction.

• Add and subtract within 20.

• Work with addition and subtraction equations.

Standards of Mathematical Practice• Model with mathematics.• Use appropriate tools strategically.• Attend to precision.• Look for and make use of structure.• Look for and express regularity in repeated reasoning.• Construct viable arguments and critique the reasoning of others.

 

Math Vocabulary Used

• Fact triangles• Turnaround fact• Number-naming boxes

5. Exploring the Demands of the Math Activity

Introducing the Lesson

Explore the Demands of the Activity

•At your tables, discuss the demands of the task: What skills and knowledge do you need to bring to the activity as a learner?

Neurodevelopmental Framework

Neurodevelopmental Framework

Neurodevelopmental Framework

6. Observing a Focal Student

Count off!

• 1-8 of Neurodevelopmental Framework– 1: Higher Order Thinking– 2: Language– 3: Spatial Ordering– 4: Sequential Ordering– 5: Memory– 6: Attention– 7: Psychosocial– 8: Motor coordination

How Does Gabby Handle the Various Demands of the

Activity?• Recall your one neurodevelopmental

construct to focus on • Watch the video and observe Gabby work

on the Fact Triangles activity

• Use the Accessible Lesson Planning chart to record your observations

Fact Triangles: Gabby

Discussion

• How did Gabby meet the demands of the task? What might be her strengths?

• In what ways did she not meet the demands of the task? What might be her weaknesses?

Teachers’ Description of Gabby as a Learner

• Has difficulty connecting separate bodies of information (e.g., understanding how numerals relate to quantities)

• Struggles in reading and math• Has difficulty using materials

independently• Can get frustrated if she is

struggling

Teachers’ Description of Jorge as a Learner

• Is able to count• Can use tools effectively• Struggles with language

Teacher’s Description of Eliza and Peter as Learners

Eliza• Strong literacy skills• Has difficulty working with

a partner• Has weak grapho-motor

skills

Peter• Is unsure of himself in math and other areas• May refuse to undertake tasks that he is not sure of• Tends to compare himself to other children• Has difficulty working with a partner• Has speech and language issues

Teacher’s Description of Sam and Lucas as Learners

Sam• Average student• Tends to be quiet

Lucas• Has speech and language issues

7. Identification of the Mathematical Goals

Why Goals Are Important

Four important steps in planning accessible

Lessons:

• Consider the goals and demands of the lessons

• Think carefully about students’ strengths and weaknesses

• Adapt lessons to build on students’ strengths (“Accommodations”)

• Adapt lessons to improve areas of weaknesses (“Interventions”)

Adaptations vs. Modifications

• Adaptations: Changes in the way the curriculum is presented to facilitate students’ access to the information offered.

• Modifications: Changes in the content and goals of the curriculum. These should only be made if adaptations do not work.

Understanding the Goals of the Lesson

• Work in small groups to review the curriculum materials for the lesson

• Complete the goals worksheet

Goals of the Lesson

• To help students develop automaticity with basic addition facts

• To practice counting

8. Adaptations for Supporting Diverse Learners

Sample Teaching Practices

Adapting the Lesson

• View video of the teachers to identify what teaching strategies they used

• Note your observations in the third column of the Accessible Lesson Planning chart

Adapting the Lesson• How would you change the lesson? What teaching practices

would you use?• View video of the teachers to identify what strategies they

used. View two or three of the following clips:

- Gabby Small-Group Work: The special education teacher working with Gabby and Jorge

- Teacher Working With Lucas and Sam: The paraprofessional working with Lucas and Sam- Teacher Working With Peter and Eliza: The general education teacher

working with Lucas and Sam- Lesson Wrap-Up: The teachers wrapping up the lesson

Teacher Working With Gabby and Jorge

Teacher Working With Lucas and Sam

Teacher Working With Peter and Eliza

Lesson Wrap-Up

Discussion

• How did Steve Quester and Mead Johnson change the lesson, and what instructional strategies do they use to support Gabby’s strengths and needs?

• What additional changes would you make?

9. Reflection on the Workshop

Discussion• What did you learn about planning accessible

math lessons?

• What implications does the work we did today have for your work in your own classroom?

10. Collaborative Lesson Planning

Preparing for Your Assignment

1. Together with the members of your team, select a math lesson that you will teach before the next workshop in

which you will observe your focal child.

2. Explore the mathematics of this lesson hands-on with your teaching team. With your team, analyze the

demands of the lesson or a specific task within that lesson. Take notes in the second column of the Accessible Lesson Planning chart.

3. Discuss the logistics for conducting the observation(s).

11. Wrap-Up

Assignments

• Implement the lesson you analyzed, and observe your focal student. If possible, have the members of your team join you to conduct the observation. Help your team members observe their focal children.

• In preparation for the next workshop:

- read about language functions

- read the curriculum guide for the “Sorting Shapes” lesson

Questions?

Submit Assignments and Session Feedback Form

See you on <Insert date> for Workshop 2!