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[Music] Welcome to the overview
on The Instructional Process

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in Interventions.

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Response to Intervention, or RtI,
is a system of timely detection

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and prevention to support students
who are potentially at risk.

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In RtI, services are 
organized as tiers,

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with Tier 1 representing high-quality
core instruction for all students.

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Tier 2 supplements the Tier 1 core
with small-group instruction

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for students who need more help
with foundational skills.

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Tier 3 usually entails one-on-one
tutoring on a few targeted skills

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for students who have not progressed
after a reasonable amount of time

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in Tier 2 interventions and 
require more intensive assistance.

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Students who are placed in Tier 2
and Tier 3 mathematics interventions

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need explicit and systematic 
instruction to build proficiency

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in foundational mathematics skills.

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Such instruction includes:
providing models and demonstrations

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of problem solving, verbalizing 
thought processes through thinkalouds,

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guided and scaffolded practice,
corrective and specific feedback,

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and frequent cumulative review.

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There is strong research 
evidence that this kind

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of instruction improves students'
proficiency at working with operations

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and word problems.

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This is true for students of 
all skill and grade levels.

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Let's explore the characteristics 
of explicit and systematic instruction

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in more depth.

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"Systematic instruction" means 
that teachers introduce mathematics

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concepts gradually
and in a logical order.

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Students are given many opportunities
to apply new math concepts

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in a wide variety of contexts.

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"Explicitness" means giving clear
explanations of concepts

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and using step-by-step modeling
to show how to solve problems

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and perform operations.

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Teachers should discuss the reasoning
behind each step as it is demonstrated.

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Sharing the reasoning behind 
using particular strategies

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when solving problems is 
referred to as a thinkaloud.

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Schools should look for 
intervention curriculum materials

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that include sample scenarios 
or dialogues that teachers can use

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as thinkalouds when explaining 
math concepts.

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It is important to select 
instructional materials

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that include many examples of 
both easy and difficult problems

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so that students will 
have adequate practice.

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Students in Tiers 2 and 3 
usually need more extensive

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practice in solving problems,
beginning with guided

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and scaffolded practice.

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Teachers and students begin
by solving problems together.

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As students begin to master skills,
they carry out more and more

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of the problem solving 
on their own.

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Students are moved to 
independent problem solving only

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when they demonstrate little need
for support and are likely

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to experience success 
on their own.

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During practice, students 
should be encouraged to talk

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out loud to both their peers
and the teacher about their choices

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of strategies,

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reasoning behind problem solving 
steps, and solutions.

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When students talk about their 
reasoning, teachers are able

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to provide helpful 
corrective feedback.

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This feedback often involves reteaching
and additional guided practice

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and should provide specific information
about what students did accurately

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and what errors they may 
need to correct.

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Finally, explicit instruction includes
frequent and cumulative review sessions

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to ensure that students retain 
knowledge and skills.

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Cumulative review helps students make
connections across the mathematics

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topics they are studying.

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Students in Tiers 2 and 3 often 
struggle with the meaning

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of abstract mathematics symbols
and the relationships between symbols

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and concepts.

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These students can benefit by learning
to create their own visual

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representations as part
of problem solving,

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while teachers can use concrete
materials and visual representations

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such as number lines, arrays,
strip diagrams, graphs,

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and simple drawings
to make mathematics concepts

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and relationships explicit.

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Number lines are especially powerful
visual representations and can be used

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with younger students to demonstrate 
counting strategies,

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teach principles of addition
and subtraction, and show

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and compare magnitude.

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Older students can use both open
and double number lines

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to perform operations 
with rational numbers.

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For students to get the most benefit 
from visual and concrete

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representations, they need systematic
and consistent exposure to examples.

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Many intervention materials lack
adequate examples of this type,

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so teachers may need
to create their own.

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While concrete objects
and manipulatives are especially useful

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at the initial stages
of concept development,

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they should not be overemphasized
as the goal is

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to eventually help students move 
beyond such tools.

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Teachers should scaffold students 
toward the abstract level,

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using manipulatives only as long 
as necessary.

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As students move away 
from concrete objects

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and visual representations
and toward using abstract symbols,

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it is important that the language
and sequence of problem-solving steps

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remains consistent.

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Students in Tier 2 and 3 
mathematics interventions need

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extra support to stay motivated.

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Teachers need to praise students' 
effort and engagement in lessons,

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their completion of mathematics tasks, 
and the accuracy of their work.

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Praise is most effective
when it is connected

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to specific accomplishments and 
recognizes students' efforts as well

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as concrete progress.

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Students can be motivated
by charting their progress

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and then setting short-term goals
or challenges for themselves.

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Others will require more tangible
rewards to remain motivated, however,

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so it is important to adjust 
strategies accordingly.

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In summary, teaching students receiving 
Tier 2 and Tier 3 interventions

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in an intentional way demands a high
level of skill, careful preparation,

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and adequate professional development
in mathematics and pedagogy.

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Teachers need to understand the 
underlying concepts

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of the skills they are teaching
if they are going

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to communicate them effectively 
to struggling students.

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[Music] To learn more
about The Instructional Process

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in Interventions in math, please 
explore the additional resources

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on the Doing What Works website.