# Inclusive Mathematics Practices

## Definition

California Common Core State Standards (CaCCSS) are organized by mathematical practice standards (all grade levels) and content standards at each grade level. They are organized in Domains – Clusters – Standards.

“The standards call for learning mathematical content in the context of real-world situations, using mathematics to solve problems, and developing “habits of mind” that foster mastery of mathematics content as well as mathematical understanding. The standards for kindergarten through grade 8 prepare students for higher mathematics. The standards for higher mathematics reflect the knowledge and skills that are necessary to prepare students for college and careers and productive citizenship” (M. Kirst, 2013).

California Common Core State Standards: Mathematics. (2013). p. 3

In order to develop these “habits of the mind” for all students, inclusive practices must be incorporated into mathematics’ instruction. This section of this website will showcase practices that teacher educators can use to help their candidates support all students in mathematical understanding.

- Make sense of the problem

- Four Square graphic organizer (form on a dry erase)
- Use concrete objects
- Draw the objects to solve the problem

- Four Square graphic organizer (form on a dry erase)
- Reason abstractly (Abstract ideas are often invisible, complex and subjective, as compared with concrete ideas that are usually visible and objective)

- Move from concrete to abstract
- Use visuals
- Emphasize student life experiences

- Move from concrete to abstract
- Construct viable arguments and critique other's reasoning

- Allow them in a variety of forms (oral, drawing,…)
- Use sentence frames
- Strategically assign pairs or groups for critiquing

- Allow them in a variety of forms (oral, drawing,…)
- Model with mathematics

- 'Relatable' real-world application
- Review critical vocabulary

- 'Relatable' real-world application
- Use appropriate tools strategically

- Allow for a large variety of tools (do not designate just one tool)
- Allow for a move from concrete tools to abstract
- Color-coding

- Allow for a large variety of tools (do not designate just one tool)
- Attend to precision

- Teach vocabulary
- Create active word wall
- Use error analysis to target your teaching
- Color code symbols and then fade use

- Teach vocabulary
- Look for and make use of structure

- KWL chart
- Visuals for patterns
- Graphic organizer for value structure
- Graph paper for representation

- KWL chart
- Look for and express regularity of repeated reasoning

- Play games with patterns
- Explore repetition through movement; jump, clap, stomp

- Play games with patterns

Other important inclusive practices include;

- Allow for student voice to demonstrate thinking
- Value perspectives
- Let students create connections; reinforce them
- Help students create their own math identity
- Use problem-based learning/project-based learning

### MTSS Math

Using the MTSS Framework in mathematics: Some schools have been using multi-tiered systems of support in mathematics.

MTSS/RTI Glossary of Terms

Response to Intervention in Math

California Dept of Education Mathematics Framework has a Universal Access chapter

Overview of Tiered Supports: Continuum of Support

Tier 1/Universal Supports: Tier 1 or Universal Supports for mathematics instruction is considered to be the core curriculum, instruction aligned to the CCSS. Tier 1 includes lessons designed using the UDL framework and instruction differentiated for all students in the class. For EL/EB this also includes ELD and any language supports needed to access the curriculum, Specially Designed Academic Instruction in English (SDAIE), Sheltered Instruction Observation Protocol (SIOP), Culturally Responsive Teaching (CRT)... For students with disabilities this includes any modifications or accommodations needed to access the curriculum. Tier 1 also involves universal screening of students to determine which students need additional, Tier 2 or Tier 3, supports.

- Tier 1 - Core Instructional Interventions
- MTSS for Mathematics: Learning Resources Part 2
- MTSS/RTI: Mathematics
- High-Quality Mathematics Instruction: What Teachers Should Know
- Applying Learning Strategies to Beginning Algebra Part 1 (PDF)
- Applying Learning Strategies to Beginning Algebra Part 2 (PDF)
- Mathematics:Identifying and Addressing Student Errors (PDF)

Tier 2/Supplemental or Strategic Supports: Tier 2 also called strategic or supplemental supports are considered to be additional supports in mathematics. Tier 2 typically involves small group intervention for students for whom Tier 1 is not enough. This intervention is targeted and focuses on key mathematics skills and typically could be separate interventions for computation and reasoning. Students are assessed at least monthly on skills being taught to determine progress and adjustments are made to intervention based on these assessments.

- Distinguishing Between Tier 2 and Tier 3 Instruction in Order to Support Implementation of RTI
- MTSS for Mathematics: Learning Resources Part 3
- Self-Regulated Strategy Development: Students with a Specific Learning Disability

Tier 3/Intensive Supports: Tier 3 also called intensive supports is intensive intervention that is constantly informed by data. We use the model from the National Center on Intensive Intervention, data-based individualization. This process is guided by ongoing data that is collected weekly to inform and adapt the intervention. Interventions are validated by research and typically focused on only a one or two skills in order to intensify the intervention effectively.

- MTSS for Mathematics: Learning Resources Part 4
- Intensive Intervention (Part 1): Using Data-Based Individualization To Intensify Instruction
- Intensive Intervention (Part 2) : Collecting and Analyzing Data for Data-Based Individualization
- System of Least Prompts: Children and Students with Intellectual Disability

### Instructional Cycle

The practices in this section are guided by the Inclusive Practices Teaching Cycle.

#### High Leverage Practices (HLP)

- HLPs in Instruction (CEEDAR)
- HLP11 Identify and prioritize long- and short-term goals
- HLP12 Systematically design instruction toward a specific learning goal
- HLP13 Adapt curriculum tasks and materials for specific learning goals
- HLP14 Teach cognitive and metacognitive strategies to support learning and independence
- HLP15 Provide scaffolded supports
- HLP16 Use explicit instruction
- HLP17 Use flexible grouping
- HLP18 Use strategies to promote active student engagement
- HLP19 Use assistive and instructional strategies
- HLP20 Provide intensive Instruction
- HLP21 Teach students to maintain and generalize new learning across time and settings
- HLP22 Provide positive and constructive feedback to guide students’ learning and behavior

Mathematics includes a conceptual understanding of key math concepts, procedural skills and fluency (calculation), and application or use of math in a situation that requires math knowledge.

## Assessment

- Accommodations in Assessment
- Assessment Accommodations
- Teacher Tools connected with the KU Assessment
- Accommodations, Modifications, and Alternative Assessments
- Examples of Accommodations from State Assessment Policies

## Assignment/Activities

### Lesson Plan Supports

A powerpoint of the **UDL model lesson** demonstration of an elementary mathematics lesson with UDL principles is linked below. This was utilized in a university course team taught (district/university) at a residency site.

Lesson plan with UDL supports during planning used during teacher preparation.

Model of a Lesson Plan for Math

- Lesson Plan with UDL Assignment for Teacher Preparation Course. Candidates can design a lesson or upload and augment a required curriculum such as GO!Math!.

Ask students to be responsible for one step – prep ahead.

### Choice Boards

**Make a TIC-TAC-TOE Activity Sheet**

- Review the website links to see samples of Tic-Tac-Toe activity sheets teachers have made for their students.
- Differentiated Instruction with Think-tac-toe
- Choice Boards, Menus and Tic-tac-toe
- Tic-tac-toe Menu Boards

- Using the TIC-TAC-TOE template, choose a topic, specify the grade level, and fill in with activities that students could choose from and complete to demonstrate their knowledge. Activities should allow for a variety of learning styles and preferences

### Tic-tac-toe template

Choose 2 number cards and make a 6-digit number with them. Using number words, word process the number you created using the word bank provided.

Choose 2 number cards and make a 6-digit number with them Explain the value of each number.

Choose 3 number cards and make a number less than 400,000,000. If you can’t do it with the three cards you drew, choose another.

Choose 2 number cards and make a 6-digit number with them. Using number words, write out the number you created.

Choose 3 number cards. Make a 9-digit number. Tell the value of each 3 in the number you created.

Choose 2 number cards and use the egg carton to place the numbers in that match their place value. Tell your partner the value of each.

Choose 3 cards and make a 9-digit number with them. Using number words, write out the number you created.

Choose 2 number cards and make the largest 6-digit number you can with those cards.

Choose 2 number cards. Make a 6-digit number and write the number in expanded form.

**Math Handout with UDL**

Reaching and teaching All math students 12 page handout Scott Marfilius (2010)

To support inclusive education teachers must determine strategies to:

- Help with the recall of mathematical facts/fluency, to support learning for difficulties with long- or short-term memory
- Multi-sensory practice
- Fact sheets
- Calculators

- Help with the interpretation of data represented in graphs, tables or charts, to compensate for difficulties with visual discrimination
- Color coding graphs
- Use of colored pencils or ink
- Use visual patterns for problem solving

- Allow access to tactile and other equipment for work on shape, space and measures, to overcome difficulties with sight or in managing visual information
- Developing 3-D models of math data/equation amounts
- Auditory sharing of each step of the problem

- Help with interpreting or responding to oral directions, to compensate for difficulties with hearing or in auditory processing
- Sentence frames
- All questions posted visually and said auditorily
- Wait time for processing
- Use of white boards + so students do not blurt answers

- Allow assignments/problems designed to have smaller steps, which hold students into the content and pace of the lesson
- Teach to question mid-problem
- Grade each step in problem solving (not just the final answer)
- Ask students to be responsible for one step – prep ahead

NCSC Math High School Mathematics – Measurement Lesson

## Additional Resources

### Articles

Carnell, L., & Tillery, M. (2005). *Preparing preservice teachers for inclusive coteaching: A new approach for mathematics methods instruction. Teaching Children Mathematics.* 11(7)

Hott, B., Isbell, L., & MOntani, T.O. (2014). Strategies and interventions to support students with mathematics disability. *Council for Learning Disabilities*, 1-9.

Powell, S., & Fuchs, L. (2018). *Effective word-problem instruction: Using schemas to facilitate mathematics reasoning.* Exceptional Children. 51(1), 31-42.

Small, M., & Lin, A. (2010). *More good questions: Great ways to differentiate secondary math instruction.* NCTM Store, Reston, Virginia.

Tan, P., & Thorius, K.K. (2018). *En/countering inclusive mathematics education: A case of professional learning.* Mathematics Teacher Education. 6(2)

Tan, P. (2017). *Advancing inclusive mathematics education: Strategies and resources for effective IEP practices.* International Journal of Whole Schooling, 13(3), 28-38.

White, D., DuCloux, K., Carreras-Jusino, A., Gonzlalez, D., & Keels, K. (2016). *Preparing preservice teachers for diverse mathematics classrooms through a cultural awareness unit. *Mathematics Teacher Educator. 4(2)

Weisenburgh-Snyder, A., Malmquist, S., Robbins, J., & Lipshin A. (2015). A model of MTSS: Integrating precision teaching of Mathematics and a multi-level assessment system in a generative classroom. Learning Disabilities: A Contemporary Journal, 13(1), 21-41.

Witzel, B., & Allsopp, D. (2007). *Dynamic concrete instruction in an inclusive classroom.* Mathematics Teaching in the Middle School. 13(4)

### Videos/Modules

- Inclusive Strategies in teaching Math to Students who are Blind
- Accessibility Learning Webinar Series: Learning Tools for the Inclusive Classroom
- Differentiation in the secondary classroom - 8th grade math (ESL)
- Sheltered Instruction for Math ELL and Special Needs Students Webinar, Sponsored by HELP Math
- Inside Mathematics: Public Lessons