Tiered Intervention in Math
Tier 1: Rich, Differentiated Classroom Instruction:
“I can access grade level curricula with additional time and support from the teacher.”
Tier 1 Intervention incorporates frequent use of small group instruction, frequent daily formative assessment to drive instruction and incorporate evidence based learning strategies into instruction.
Fundamental to differentiation is the understanding that one does not alter the outcome but rather provides alternatives in instruction, assessment, and/or environment to meet the needs of the learner.
Differentiating Is…
Providing choice as much as possible.
Students can choose:
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Manipulatives (choosing which manipulative to use or choosing not to use any)
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How to show or represent their work
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The strategy for solving the problem
Responsive Pedagogy:
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Using open-ended questions, rich tasks or low-floor, high-ceiling1
tasks so that all students have an entry point and the challenge level can be easily adapted. -
Providing choice and parallel tasks that demonstrate understanding in different ways through complex and creative tasks that challenge all students.
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Enriching learning by providing questions, tasks, projects and or research that allows for deeper learning of concepts beyond the curriculum.
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Leveraging technology to provide alternative tasks, target gaps in skills and knowledge, and provide more practice.
Responsive Instruction:
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Allowing more time when students need it.
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Arranging small group instruction to target the needs of specific groups.
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Providing more explicit instruction and worked examples for struggling learners in an effort to help students learn to work more independently.
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Explicitly teaching and reinforcing self-coping strategies to create independence.
Responsive Assessment:
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Prioritizing understanding and process over product.
Differentiating Is Not …
- Requiring all students to use the same materials and follow the same procedures and steps.
- Providing tasks that students are successful at but fail to push their learning forward.
- Accepting incomplete work because students didn’t have time to finish.
- Using only full class instruction.
- Talking students through every task so they don’t have a chance to develop self-coping strategies.
- Allowing struggling learners to over-rely on extra supports and inefficient strategies.
- Giving the same task to all students all the time – teaching to the resource and not the learner.
- Using only closed tasks and questions (those with only one right answer).
- Allowing only high achieving students to participate in open or creative tasks.
- Rewarding quick and efficient completion of practice with more work.
- Teaching next year’s outcomes.
- Using technology to entertain and occupy learners.
Process for Responsive Instruction:
Gersten (2009) suggests that Response to Intervention begins with “High quality instruction and universal screening for all students.”2
In a true RTI (Response to Intervention) model, you would use a universal screen to see where everyone is at and what areas are needed for instruction. Tier 1 intervention refers to ways to dig deeper in the classroom to support areas where understanding is not happening. In Tier 1 intervention, there may be things we do for some students within the context of the classroom (either in whole class, small group, paired or small group instruction.)
The chart below offers some online resources for Tier 1 Intervention support. This is not a prescriptive list, nor is it an exhaustive list; it provides a starting place for utilizing high impact intervention strategies.
Classroom instruction links that can be used for Tier 1 intervention.
Grade Level
Responsive Instruction in Classrooms
Description
All grade levels
Thinking and philosophy considerations in creating small groups across all grade levels.
Ministry resources: Multi grade application.
Targeted/Group Approaches – Module 2 – Targeting Mathematics Instruction: Knowing Our Learners focuses on fostering a positive mathematics environment to support the needs of individual learners.
Module 3 – Instruction in Mathematics: Effective Instructional Practices provides suggestions for Instructional approaches that support the learning needs of students and enhance mathematical thinking.
All grade levels
This website has many supports for intervention in math.
All grade levels
Ontario Ministry of Education Document – very user friendly philosophical research and practical application (with examples) great information.
All grade levels
Examples and strategies for whole class, small group, pairs and individual support. (Alberta Education)
Specific to middle years and high school
This booklet provides an “at a glance” look at effective and differentiated instruction in Mathematics. It includes classroom scenarios that describe how teachers assess, plan and adapt their instruction to determine and address their students’ interests, learning needs and preferences.
Content shows progression of learning to show how you can adapt concepts to students of varying entry levels.
(Ontario Resource)
All grade levels
This article describes how to support students with disabilities who struggle to understand the core concepts that underlie operations and algorithms.“CRA may be implemented at all grade levels individually, in small groups, or for the entire class. It can be used with children at the elementary or secondary level.”
Gr. 7-12
3 minute video showing progression of concrete-pictorial-symbolic instruction: The Concrete-Representational-Abstract (CRA) model, also known as Concrete-Pictorial-Abstract, is a three-stage method of teaching mathematical concepts that provides students with hands-on activities that allow them to understand a concept before using or memorizing the algorithms.
Gr. K-6
13 minute video showing the relationship of concrete-pictorial-symbolic instruction: This video explains how to use CRA to differentiate during whole class instruction.
All grade levels
The Think Aloud strategy is especially helpful in a class of diverse learners, EAL in particular. The teacher can think aloud while teaching a concept to the whole group, allowing the students to see and hear the teacher’s thought process and how that correlates to the actions of the teacher. Another way to use this strategy is by having students lead the think aloud.
Elementary
4 minute elementary video: “Guided Math” in this context is a structure for teaching whereby a teacher supports each child’s development of mathematical proficiency at increasing levels of difficulty, within the context of a small group.
Gr. K-9
Low floor, high ceiling tasks. The Open Questions resources are designed to provide scaffolding that allows students the opportunity to develop a deeper understanding of math concepts.
All grade levels
Daily Routines – Number Talks as well as other ideas for students to think and talk about math.
All grade levels
Interleaved practice gives ideas of how to allow children to choose strategies to solve problems rather than provide a single strategy to be practiced. Students learn how to choose and use a strategy that works for them.
All grade levels
Parallel and Open-ended Questions
Grades 2-6 but could be adapted to all grade levels.
Reciprocal teaching happens after teacher modeling. Students are in small groups monitoring comprehension applying four strategies: predicting, clarifying, questioning, and summarizing (Miller & Veatch, 2011)
Tier 2: Small Group Targeted Instruction:
“I can access grade level curricula once learning gaps are intentionally addressed and supported (by the classroom teacher or interventionist.)”
Tier 2 Intervention involves explicit, direct, systematic instruction for struggling or at-risk learners that is based on assessment data to address gaps, using evidence based strategies.
The following table contains links that support small targeted group instruction:
Small Targeted Group Instruction Strategies
Description
Evidence-based ways to teach math that can be used with your current curriculum.
The eight recommendations in this guide are designed to help teachers, principals, and administrators use Response to Intervention for the early detection, prevention, and support of students struggling with mathematics.
More math related content may be added by the Ministry at a later date.
General principles and suggestions for modifying mathematical and executive functioning demands in activities for young children.
This RTI guide will help you prepare by exploring the:
Tier two support is in addition to regular math instruction. It is expected that students interact with grade-level math as much as possible during class time (with continuing support provided), but support time will target specific foundational gaps identified by screeners. (Recommendations from the SaskMATH Working Group.)
Thinking aloud helps students, especially those who struggle with mathematics, to clarify their ideas, identify what they do and do not understand, and learn from others when they hear how their peers think about and approach the problem.
Yale Dyslexia – Helping Students with Poor Working Memory
Tier 3: Intensive Interventions
“I am not able to access grade level curricula but need an individual plan and goals to address my learning needs from where I am at.”
Tier 3 Intervention is supported by responsive instruction and support at the individual level, through targeted and/or group approaches and when needed, intensive individual support. It should involve a collaborative approach with professionals who can support the goal setting and intervention plans for the student. See: National Center on Intensive Intervention.
The following table contains links that support intensive interventions:
Intensive Intervention Strategies
Description
During this one-hour webinar, Dr. Scheller will discuss Dyscalculia and pose a best practice method for assessment that targets the key strengths and weaknesses exhibited by students with this learning disorder.
Intervention Central provides teachers, schools and districts with free resources to help struggling learners and implement Response to Intervention.
Institute of Education Sciences (IES), the nation’s leading source for rigorous, independent education research, evaluation and statistics.
The NCII supports implementation of intensive intervention in literacy, mathematics, and behavior for students with severe and persistent learning and/or behavioral needs, often in the context of their multi-tiered system of support (MTSS) or special education services.
1Low floor, high ceiling tasks have entry points for learners at all stages of their understanding. As such they have room for extension and enrichment as well as differentiation for struggling learners. See Samples of Low Floor, High Ceiling tasks : Millennium Mathematics Project., N., 2017. Creating a Low Threshold High Ceiling Classroom. [online] https://maths.org/home. Links to low floor/high ceiling tasks can be found in the article, “Creating a Low Threshold High Ceiling Classroom available at: <https://nrich.maths.org/7701> [Accessed 20 July 2021]. Can be downloaded directly from: https://saskmath.ca/wp-content/uploads/2021/11/Creating-a-Low-Threshold-High-Ceiling-Classroom.pdf
2Gersten, R.M.,(2009) Assisting students struggling with mathematics: Response to intervention (RTI) for elementary and middle schools. Washington, DC: U.S. Dept. of Education, National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, p.4.
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