Math Intervention and the Promise of Adaptive Learning

LEARNING

Intelligent Adaptive Learning™

WHITE PAPER

The necessary gains in math

proficiency can only be achieved if

instruction is streamlined to target

the unique learning profile of each

student: comprehension, skill level,

learning style, and strategies for

processing thought.

Executive Summary

America’s schools are underperforming in math education; many students are

not reaching the level of mathematical proficiency needed to excel in school or in

the workplace. A consensus has emerged that corrective reform and innovation

is necessary to reverse this trend. Pedagogical models that address the needs of

individual students are gaining broader acceptance. The necessary gains in math

proficiency can only be achieved if instruction is streamlined to target the unique

learning profile of each student: comprehension, skill level, learning style, and

strategies for processing thought.

As part of this effort schools use data to identify students who are not making

adequate progress in the core curriculum and are at risk for poor learning

outcomes, and to provide interventions that are appropriate to a student’s level

of need and responsiveness. The widespread use of this ‘Response to Intervention’

(RTI) model is supporting the move toward intervention that is provides an

instructional path that will most effectively improve math proficiency for each

individual student.

“Adaptive learning” is a promising approach that fits within the Response to

Intervention model. It actually goes far beyond the expectation of intermittent

assessment and adjustments to instruction. Formative assessments throughout

the learning process help shape that process. In real-time, every mouse click

is tracked to gain insight into student strategies. Then, based on that insight,

individual learning paths are dynamically created to guide the student through

the curriculum.

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When reaching students

within an engaging

framework, they begin to

proactively drive their own

learning.

Effective adaptive learning has five

capabilities that make it a complete and

effective approach:• Achieving math proficiency is the primary

goal. Getting to that point faster also vital.

• A strong math curriculum aligned with

Common Core State Standards.

• Sound pedagogy is always the

foundation for instruction, because the

goal is to build conceptual understanding

and procedural fluency.

• Instruction integrated with assessment.

Ongoing assessment directs instructional

path step-by-step.

• A highly engaging and interactive

learning environment. Student

engagement has many positive benefits,

including improved student choice and

motivation, persistence, and time on

task. When reaching students within

an engaging framework, they begin to

proactively drive their own learning.

Current Influences on Math InterventionMany students are not reaching the level of

mathematical proficiency needed to excel

in higher education, the workplace, and the

global economy. We have lost our world

leadership position in basic education,

particularly in math education, falling into

the middle ranks of the developed world.

In the United States, a complex framework

of regulation is attempting to standardize,

assess, and improve curricula and teaching

practices for K-12 students. Intervention

must take place in the context of that

framework.

MandatingproficiencywithNoChildLeftBehind.At the federal level, the

Elementary and Secondary Education Act

was reauthorized in 2001 as the No Child

Left Behind (NCLB) Act. This legislation

focuses on improving student performance

in reading and mathematics. Specifically,

it requires that all students in grades 3

and 8 achieve proficiency in mathematics

by 2014.1 The current Administration and

Congress are working on revisions to NCLB.

In the meantime, the 2001 legislation

remains the federal regulatory standard.

Establishingconsistencywithmathstandards.A state-led effort called the

Common Core State Standards Initiative

has been coordinated by the National

Governors Association Center for Best

Practices (NGA Center) and the Council of

Chief State School Officers (CCSSO). Their

K-12 standards for English language arts

and mathematics have been adopted by

most states.2 In those states, it establishes

baseline goals for educational intervention.

Where Common Core has not been

adopted, there typically is alignment

with a strong standards framework such

as the National Council of Teachers of

Mathematics (NCTM) Focal Points.

AddressingdiversitywithIDEA.The

Individuals with Disabilities Education Act

(IDEA), reauthorized in 2004, governs how

states and public agencies provide early

intervention, special education, and related

services to more than 6.5 million eligible

infants, toddlers, children, and youth

with disabilities.3 IDEA changed the way

students are evaluated for special services

by requiring states to allow school districts

to use research-based interventions to

address diverse students’ needs early on.

IdentifyingriskwithRTI.The most

commonly used model developed by

U.S. educational researchers is called

Response to Intervention (RTI). RTI

integrates assessment and intervention

within a multi-level prevention system

to maximize student achievement and

to reduce behavioral problems. With RTI,

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Current research has

documented that early

preparation in mathematics

is the biggest predictor in

later school achievement.

schools use data to identify students at

risk for poor learning outcomes, monitor

student progress, provide evidence-based

interventions, adjust the intensity and

nature of those interventions depending

on a student’s responsiveness, and identify

students with learning disabilities or

other disabilities.4 The RTI framework

is defined by tiers that allow schools to

offer increasingly intensive interventions

to those students who are not making

adequate progress in the core curriculum.

• TierI–Coreinstruction.Core instruction

tries to prevent failure and optimize

learning by offering the most effective

instruction possible to the greatest

number of students. It usually takes place

in a regular education setting as whole

class instruction that produces good

results for most students.

• TierII–Supplementalinstruction.Supplemental instruction applies to

students who experienced difficulties

with Tier I instruction. It tries to address

instructional challenges that could be

contributing to individual students’

learning difficulties. It may be in the

classroom or in a special education

setting and involves instruction to small

groups of students or individuals. Some

students might need more support than

others, but most students will respond

quickly and make good progress.

• TierIII–Intensiveinterventionsandcomprehensiveevaluation.This

tier addresses students who did not

show progress in Tiers I and II. It tries

to accelerate their learning with more

intensive help and provide the child with

more effective strategies for learning.5

The Importance of Math ProficiencyThe Institute of Education Sciences (IES)

is the primary research arm of the U.S.

Department of Education. One of IES’

primary research centers, the National

Center for Education Statistics (NCES),

conducts the National Assessment of

Educational Progress known as The Nation’s

Report Card. According to The Nation’s

Report Card for 2009, only 26 percent of

twelfth-graders performed at or above the

Proficient level in mathematics.6 Obviously,

we have a long way to go before we meet

our nation’s goals for math education.

These deficiencies in math have

consequences far beyond a student’s

grade in math class. Current research

has documented that early preparation

in mathematics is the biggest predictor

in later school achievement. Six large

longitudinal studies (from school entrance

to grade 5) were recently completed

by researchers in England, the U.S., and

Canada, examining links between early

numeracy, literacy, attention ability, socio-

emotional skills and, later, reading and

math achievement. The report showed that

early math skills had the greatest predictive

power for future success in school, followed

by reading, and then attention skills. In

their words, “Particularly impressive is the

predictive power of early math skills, which

supports the wisdom of experimental

evaluations of promising early math

interventions.”7

The fact that a head start in learning

will help children achieve more academic

success down the road is not news in itself.

What is striking, according to this study,

is that mastery of these basic education

concepts supersedes every other predictor,

including social and emotional adjustment,

in guaranteeing children’s academic

success. As such, a marked shift in how

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Teachers have more

students and more

mandated achievement

goals, but less federal,

state, and local funding

for classroom aides and

technology.

schools address their students’ education is

in order.8

Funding for RTI programsUnder IDEA, federal special education

funds are distributed through three state

grant programs and several discretionary

grant programs. Part B of the law, the main

program, authorizes grants to state and

local education agencies to offset part of

the costs of the K-12 education needs of

children with disabilities. It also authorizes

pre-school state grants. Districts may use

up to 15 percent of IDEA Part B funds for

Coordinated Early Intervention Services

(CEIS); that is, for students who have

not been identified as needing special

education, but who may need additional

academic support to succeed. These funds

can be used to support the implementation

of school wide RTI programs and the

purchase of RTI materials.

Additionally, Title I (Improving Academic

Achievement of the Disadvantaged) and Title

III (Language Instruction for Limited English

Proficient and Immigrant Students) funds

may be used to support RTI programs. It is

important to note that Title I, Title III, and

CEIS funds may only be used to provide

services that supplement, and not supplant,

what schools would otherwise provide as a

part of core instruction.

Challenges to Successful Math InterventionAll educational settings have some

common challenges, and they certainly

apply to teaching mathematics:

Classsize.In traditional classroom

settings, the students always outnumber

the teachers. A large ratio of students to

teachers can lead to disciplinary problems,

student inattention and apathy, and a

one-size-fits-all presentation of learning

material.

Lackofresources.Teachers and

administrators are under increasing

pressure to do more with less.

Governmental mandates for education

have increased dramatically, but they have

not been anywhere close to fully funded.

On the contrary, a recessionary economy,

resistance to taxes, and strapped state

governments have slashed budgets for

many schools.

Lackoftime.The most basic resource

— time — is usually limited to 50 minutes

of daily math instruction in American

schools. Furthermore, American schools

average only 180 days in a school year.

Some reformers are pushing toward a 200-

day school year, which would align with

Thailand, Scotland and the Netherlands,

but still leave us trailing Israel, Luxembourg,

South Korea, and Japan, which leads with a

243-day school year.9

Needforindividualizedstudentinstruction.Large class sizes and shrinking

resources make the need for tailored

student learning much more difficult.

Teachers have more students and more

mandated achievement goals, but less

federal, state, and local funding for

classroom aides and technology. This is

unfortunate, because research and actual

practice are showing that adapting the

pace, mode, and style of instruction based

on the wide spectrum of student needs can

be effective in closing the gaps in student

achievement.

Lackofsubject-specificexpertiseamongteachers.An additional challenge

is more specific to math education — a lack

of math expertise among many teachers.

In the Fall 2005 issue of American Educator,

a journal published by the American

Federation of Teachers, authors Deborah

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Strong curriculum and

pedagogy assure that the

math proficiency outcomes

desired are achieved.

Loewenberg Ball, Heather C. Hill, and

Hyman Bass described the dimensions of

this problem:

“That the quality of mathematics

teaching depends on teachers’ knowledge

of the content should not be a surprise.

Equally unsurprising is that many U.S.

teachers lack sound mathematical

understanding and skill. This is to be

expected because most teachers — like

most other adults in this country — are

graduates of the very system that we seek

to improve. Their own opportunities to

learn mathematics have been uneven

and often inadequate, just like those of

their non-teaching peers. Studies over the

past 15 years consistently reveal that the

mathematical knowledge of many teachers

is dismayingly thin.”10

Assumptions for Effective Math PedagogyIn the face of all these challenges, the

good news is that all children can learn

mathematics. But to develop effective

math pedagogy for all students, additional

basic assumptions need to be present

throughout the process:

•Not all students learn at the same rate

or in the same way.

• Intervention is proactive, not reactive.

• Even talented students may need

intervention opportunities to be

accelerated beyond the curriculum that

other students follow.

• Intervention is about teaching and the

opportunity to learn. It is not a deficit

model for math education.

• The term intervention usually indicates

that the students’ difficulties or particular

strengths are in the early stages, when

they can be identified and addressed

before they become a concern.

• Response to Intervention is based on

discovering what works best for an

individual student, not what might be

the “best” intervention for everyone.

Additional methods are tried until

students respond to the intervention and

improve their skills.11

Solution: Adaptive Learning for Math“Adaptive learning” is an approach that

overcomes many of the current challenges

to implementing the RTI model and

providing very effective math intervention.

Strong curriculum and pedagogy assure

that the math proficiency outcomes desired

are achieved. The adaptive technology

adjusts instruction to address the individual

student needs overcoming time and staff

resource constraints.

To address the challenges of improving

student performance in math, the first

and foremost goal is a strong math

curriculum. Math instruction should focus

on the foundational domains of counting

and cardinality; comparing; numbers

and operations in a base ten system; and

algebraic thinking.

But a strong curriculum isn’t enough.

The pedagogy itself is of equal importance

and can be significantly improved by

moving towards an adaptive learning

model. However, this can be confusing, with

many solutions promising differentiation

and individualized learning experiences. A

truly adaptive online environment means

ensuring a child is always working at the

right place in the right curriculum.

To be effective, an adaptive learning

strategy should include the following:

• Build a foundation of understanding and

skills for struggling learners, immersing

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Instruction should connect

new learning to what the

student already knows and

provide opportunities to

apply new concepts and

skills to relevant problems.

them in lessons that build conceptual

understanding and procedural

knowledge.

• Lesson design needs to build accuracy,

efficiency, and understanding.

• Provide regular practice, which leads to

automaticity.

• Empower learners to make self-directed

choices as their confidence grows.

• Aligning to math standards is key, but

an effective curriculum also needs to

complement core requirements with

research-based analyses of progression

and comprehension.

• Students who struggle typically need

more time to grapple with new ideas

in order to be successful. But simply

allowing students to go at their own

the pace is not sufficient. Flexible,

dynamic lesson paths must be adapted

to fit individual student needs.

•Make connections explicit. Too often,

students who need intervention fail

to look for relationships or make

connections among mathematical

ideas on their own. With this in mind,

lessons need to provide clear visual

models to guide the student toward

under-standing and articulating

mathematical relationships. With strong

virtual manipulations, models can, over

time, be removed and students will

work with numbers and other abstract

representations.

• Provide a wide variety of learning paths

through the curriculum adapted to a

child’s specific needs.

• Build on prior knowledge. Instruction

should connect new learning to what

the student already knows and provide

opportunities to apply new concepts

and skills to relevant problems.

• Build a mathematical vocabulary

so the student has a context for

understanding the language of

mathematics.

• Integrate instruction and assessment

to quickly identify learning gaps and

determine the appropriate lesson path.

• Continually assessing comprehension

allows students to skip what they know

and focus on what they’re ready to

learn.

•Monitor and assess not only right and

wrong answers, but what strategies

students use to solve problems.

• Provide scaffolding within lesson

content that identifies and sequences

the concepts and skills that are

essential to the content being taught.

Once the content is scaffolded,

instruction is organized in a way that

supports the student’s learning.

• Feedback on incorrect responses

should do more than repeat the

problem. Effective feedback scaffolds

hints, providing gradual supports that

allow a student to build understanding

of a problem. After all, mistakes

represent prime learning opportunities.

• Provide math instruction within an

engaging learning environment that

helps motivate students and increase

persistence and time on task.

• Provide teachers and administrators with

detailed views of each child’s progress

with insight, in real time, into student

comprehension and academic progress.

Emerging online technology for adaptive

learning provides other benefits that

may not be as obvious. Online learning

benefits teachers by sharing some of

the burden of individualizing classroom

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Effective adaptive learning

has five capabilities: strong

curriculum, state-of-

the-art math pedagogy,

integration of instruction

and assessment, a highly

engaging experience,

and the goal of meeting

proficiency expectations.

instruction, helping make their time more

productive. It’s a highly effective way to

deliver instruction across a diverse student

population.

ConclusionAgainst a backdrop of a complex and ever-

changing regulatory setting, a consensus

view has emerged that education must

support all students in meeting grade

level proficiency standards, even in an

environment of diminishing resources to

address those needs.

All of these factors point to a need for

an increased level of effective instruction.

Response to Intervention (RTI) models

are making headway but are hampered

by resource constraints. Truly adaptive

learning overcomes many of these

constraints combining strong alignment

to math proficiency goals and advances in

technology to deliver truly individualized

instruction. Effective adaptive learning has

five capabilities: strong curriculum, state-

of-the-art math pedagogy, integration

of instruction and assessment, a highly

engaging experience, and the goal of

meeting proficiency expectations.

Endnotes

1. No Child Left Behind – ED.gov. (n.d.). Retrieved from www.ed.gov/esea.

2. Common Core State Standards Initiative. (n.d.). Retrieved from www.corestandards.org.

3. IDEA – Building the Legacy of IDEA 2004. (n.d.). Retrieved from idea.ed.gov.

4. Essential Components of RTI. (2010). Retrieved from www.rti4success.org.

5. Response to Intervention – Tiers without Tears. (n.d.). Retrieved from www.ncld.org.

6. The Nation’s Report Card: Grade 12 Reading and Mathematics – 2009 National Pilot and State Results. (2009). Retrieved from nces.ed.gov.

7. Duncan, G., et al. (2007). School Readiness and Later Achievement. Developmental Psychology, 43, 1428–1446. Retrieved from ccf.tc.columbia.edu.

8. See notes 7 and 9.

9. Obama Proposes Longer School Days, Extended School Year. EDU in Review News Blog. (2010). Retrieved from www.eduinreview.com.

10. Ball, D. L., Hill, H.C, and Bass, H. (2005). “Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide?” American Educator.

11. Berkas, N., and Pattison, C. (2008). Creating or Selecting Intervention Programs. Retrieved from www.nctm.org.

About DreamBox LearningDreamBox Learning Math is changing the way

students engage with and understand math.

Through our innovative technology we deliver

a phenomenal level of individualized math

instruction. Dynamic adaptations, based not just

on answers but on strategies, keep all learners,

from struggling to advanced, in their optimal

learning zone.

DreamBox Learning’s rigorous math curriculum

is aligned with Common Core State Standards

and builds conceptual understanding and

fluency. Our integrated instruction and

assessment, together with detailed reporting,

give teachers and administrators actionable data

on comprehension, proficiency, and academic

progress. Just as important, we offer a highly

engaging experience that teaches in a way that

motivates today’s kids.

Founded in 2006 in Bellevue, Washington,

DreamBox Learning’s award-winning products

target students in kindergarten through fifth

grade and deliver more than 600 core lessons

with unlimited variations. More information can

be found at www.dreambox.com.

For more information, contact Client Care at 877.451.7845, email schools@dreambox.com or visit dreambox.com.

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