Intelligent Adaptive Learning:A Powerful Element for 21st Century Learning & DifferentiationTim Hudson, PhD

Senior Director of Curriculum Design

DreamBox Learning

timh@dreambox.com@DocHudsonMath

Introduction• Senior Director of Curriculum Design for

DreamBox Learning• Over 10 years in public education:

o HS math teachero K-12 Math Curriculum Coordinatoro Strategic Planning Facilitator

• Consulted for Authentic Education• PhD in Educational Leadership• Co-author of a chapter in NCTM book on

Math Intervention Models: Reweaving the Tapestry (I get no royalties)

How can we leverage technology to improve

student learning?

“Flip”

Classrooms?“Blended” Learning?

Apps & iPads?Online

Videos?

Which schedule is better?BLOCK

• 8 courses/semester• 4 classes/day• Each course meets

every other day• 90-minute periods

TRADITIONAL• 8 courses/semester• 8 classes/day• Every course

meets every day• 45-minute periods

Scheduling is a means to what ends?

What is happening during class?

Which blended model is better?FLIPPED-CLASSROOM ENRICHED-VIRTUAL

Blending is a means to what ends?

What is happening during class?What is happening on the

computers?H. Staker, M. Horn, Classifying K-12 Blended Learning, © 2012

The Quality of Digital Learning Experiences is

just as important as the Quality of

Classroom Learning

Experiences

Plan Schooling Backwards

• “Contemporary school reform efforts… typically focus too much on various means: structures, schedules, programs, PD, curriculum, and instructional practices (like cooperative learning)• [or blended learning]• [or flipped learning]• [or iPads, hardware, etc]

p. 234-235, Wiggins & McTighe, © 2007

Plan Schooling Backwards

• Certainly such reforms serve as the fuel for the school improvement engine, but they must not be mistaken as the destination…[which is] improved learning.”

p. 234-235, Wiggins & McTighe, © 2007

Plan Curriculum Backwards

1. Identify desired results

2. Determine acceptable evidence

3. Plan learning experiences and instruction

Understanding by Design, Wiggins & McTighe, ©2005

Key Questions1. What do you want

students to accomplish?

2. How will you know they’ve achieved it?

3. What technologies can help students meet

goals?

Plan Schooling Backwards

• “The first stage in the design process calls for clarity about priorities expressed as achievements.”

• “…take time to clarify not just goals, but also the needed assessment evidence and initial data before [you] generate a detailed action plan [for blended learning, block scheduling, etc.].”

p. 204, 227, Wiggins & McTighe, © 2007

12

Let’s Take a Poll!

Question #1: Have you ever used Wolfram Alpha?

Math Learning Goals

Wolfram|Alpha

Wolfram|Alpha

Wolfram|Alpha

17

Let’s Take a Poll!

Question #2: If computers can solve math problems so efficiently, why do we drill our

students in answering them?

Better Goals for StudentsDavid Bressoud, Mathematical Association of America (www.maa.org/columns)Regarding Wolfram|Alpha:• “If computers can solve [math] problems so

efficiently, why do we drill our students in answering them?

• “There are important mathematical ideas behind these methods, and showing one knows how to solve these problems is one way of exhibiting working knowledge of these ideas.”

Better Goals for StudentsDavid Bressoud, (cont’d)

• “The existence of Wolfram|Alpha does push instructors to be more honest about their use of standard problems executed by memorizing algorithmic procedures.

• “If a student feels that she or he has learned nothing that cannot be pulled directly from Wolfram|Alpha, then the course really has been a waste of time.”

New Teacher Induction

What do you offer students in your classroom that they can’t

get online for free?

Pop Quiz• 3,998 + 4,247 =• 288 + 77 = • 8 + 7 =• What is a good strategy?• What is fluency?• How is fluency learned?• Can you get this from Wolfram|Alpha?

Compensation

Learning Principles

• “An understanding is a learner realization about the power of an idea.”

• “Understandings cannot be given; they have to be engineered so that learners see for themselves the power of an idea for making sense of things.”

p. 113, Schooling by Design, Wiggins & McTighe, ©2007

What do you remember about math from when you were in middle &

high school?

Common Experience

From a 5th grade teacher in NY:“I had a lot of good people teaching me math when I was a student – earnest and funny and caring. But the math they taught me wasn’t

good math. Every class was the same for eight years:

‘Get out your homework, go over the homework, here’s the new set

of exercises, here’s how to do them. Now get started. I’ll be around.’”

p. 55, Teaching What Matters Most, Strong, Silver, & Perini, ©2001

Typical Teaching Cycle

Whole Class or Small Group Instruction

Guided Practice

Whole Class Assessment

Use Data Formatively to

Plan

Use Data Summativel

y

Teaching as Content Delivery

Whole Class or Small Group Instruction

Guided Practice

Whole Class Assessment

Use Data Formatively to

Plan

Use Data Summativel

y

28

Let’s Take a Poll!

Question #3: How old were you when you decided whether or not you were a "math person?"

Lichtenberg, 1749-99

“We accumulate our opinions at an age when our understanding is

at its weakest.”

At what age did you acquire your mental models of how math is

taught and learned?

30

Transmission View of Learning

High school?

Thinking Mathematically

“They were so concerned with making sure we knew how to do every single procedure we never learned how to

think mathematically.

I did well in math but I never understood what I was doing. I

remember hundreds of procedures but not one single

mathematical idea.”p. 55, Teaching What Matters Most, Strong, Silver, & Perini,

©2001

Let Me Show You How To Do

X

Now You Go DoX

Can You Independently Do

X?

Maybe You Need to Be Shown X

Again

You KnowX

Schooling as Content Delivery

Let Me Show You How To Do

X

Now You Go DoX

Can You Independently Do

X?

Maybe You Need to Be Shown X

Again

You KnowX

Content Delivery cannot ‘give understandings’

Blended Learning Clarified

H. Staker, M. Horn, Classifying K-12 Blended Learning, © 2012

“online delivery of content & instruction”

Time, Place, Path, Pace

H. Staker, M. Horn, Classifying K-12 Blended Learning, © 2012

“Learning is no longer restricted to the pedagogy used by the teacher.”

Learning IS restricted – and impacted by – the pedagogy used by the online teacher, in the online instruction, or in designs of the learning software.

Typical Cycle

At School:Explicit

Instruction & Problem

Solving At

Hom

e:

Pra

ctic

e

Pro

ble

ms

Whole Class Assessment

Maybe You Need to Be

Shown X Again

Use Data Summativel

y

Flipping the classroom?A

t H

om

e:

Explic

it

Inst

ruct

ional

Vid

eos

&

Onlin

e P

ract

ice At School:

Guided Practice & Problem Solving

Whole Class Assessment

Maybe You Need to Watch

the Video Again

Use Data Summativel

y

Pros & Cons

Benefit of Blending &

Flipping

Becoming MORE thoughtful and strategic about the use of precious class time

Danger of Blending &

Flipping

Becoming LESS thoughtful and strategic about how students learn and make sense of things

40

Transmission View of Learning

y = mx + b

Learning Myth

“Presentation of an explanation, no matter how brilliantly worded, will not connect ideas unless students have had ample

opportunities to wrestle with examples.”

From Best Practices, 3rd Ed., by Zemelman, Daniels, and Hyde, ©2005 From Understanding by Design, Wiggins & McTighe,

©2005

“If I cover it clearly, they will ‘get it.’”

Kid Snippets: “Math Class”

Don’t Start by Telling

“Providing students with opportunities to first grapple with specific information relevant to a topic has been shown to create a

‘time for telling’ that enables them to learn much more from an

organizing lecture.”

• How People Learn, p. 58

44

Let’s Take a Poll!

Question #4: Are you currently working on differentiated instruction in your classroom,

school, or district?

Differentiation Defined• Teachers have a responsibility to ensure that all of

their students master important content.• Teachers have to make specific and continually

evolving plans to connect each learner with key content.

• Differences profoundly impact how students learn and the nature of scaffolding they will need at various points in the learning process.

• Teachers should continually ask, “What does this student need at this moment in order to be able to progress with this key content, and what do I need to do to make that happen?”

Leading and Managing a Differentiated Classroomby C.A. Tomlinson & M.B. Imbeau, ASCD, © 2010, pp. 13-14

Rethink Differentiation

Our mental models of learning often cause us to differentiate in two wrong ways:

1. around knowledge, skills, and procedures rather than ideas, understanding, and complex performance

2. in response to student knowledge AFTER being shown a skill instead of in response to student thinking when solving an unfamiliar problem or at the point of conception formation.

Formative Assessment

• What incorrect answers would we expect on a problem like 29 + 62?• 81 Student does not regroup to the tens place• 81 Student adds columns from left to right• 811 Student adds each column independently• 92 Arithmetic error in ones place• 33 Student believes this is a subtraction

problem• How would you score each error?• How would you respond to each error?• What lesson(s) need to come before & after?• Which of these errors are “naturally occurring?”

Pop Quiz

For a bicycle race, Donald’s time was:

3 hours, 4 minutes, and 11 seconds.

Keina’s time was:

2 hours, 58 minutes, and 39 seconds.

How long was Keina finished before Donald crossed the finish line?

Hours Minutes Seconds

3 4 112 58 39

\ 3 X71\61

3

\2 \

6 3\5 1

50 2

304 – 298 = ?

one strategy

Oxford University, 1992

“To the person without number sense, arithmetic is a bewildering territory in

which any deviation from the known path may rapidly lead to

being totally lost. The person with number sense…has, metaphorically, an effective ‘cognitive map’ of that

same territory.”Ann Dowker, Computational Estimation Strategies of Professional

Mathematicians,Journal for Research in Mathematics Education, Vol. 23(1), January 1992

Constant Difference

52

Let’s Take a Poll!

Question #5: Did you learn the Constant Difference strategy for subtracting in elementary

school?

How can we leverage technology to improve

student learning?

Improve Learning

Goals

Guaranteed Curriculum

Require Student Thinking

Require

Student

‘Doing’

DreamBox Pedagogical Design

Student Engages within a Context

Student Transfers &

Predicts

Student Receives Feedback

EngineAdapts & Differentiates

Student Independently Transfers

Engineered for Realizations

Student Engages within a Context

Student Transfers &

Predicts

Student Receives Feedback

Engine Adapts &

Differentiates

Student Independently Transfers

Division with Remainders

57

Let’s Take a Poll!

Question #6: How many gumballs would you pack first?

Division with Remainders

Ma & Pa Kettle

3rd Grade

3rd Grade

4th Grade

4th Grade

A

CB

Continuous Embedded Assessment

Multiplying Fractions

Engaging LearningExperience with Context

Individuals are Presented with Accessible Problems

or Questions

Individuals Make a Prediction, Answer the Problem, Take a Guess

Individuals Receive Instant, Specific Feedback Based on their Prediction

Data from that Prediction Informs the next Problem

Presented or Question Posed

Original, Independent, Strategic Thinking

Engaging LearningExperience with Context

Self-Directed, Coherent, Connected Paths

Individuals are Presented with Accessible Problems

or Questions

Individuals Make a Prediction, Answer the Problem, Take a Guess

Individuals Receive Instant, Specific Feedback Based on their Prediction

Data from that Prediction Informs the next Problem

Presented or Question Posed

Seamless • DreamBox

Lessons, Practice, & Assessments look identical to students

• These are not banks of practice items.

• Students need no prior instruction to engage in the lessons.

Original, Independent Thinking

Feedback, Realization

s

Practice or Assessmen

t

Feedback, Realization

s

New Problem or New Lesson

Assessments throughout the curriculum assess the skills taught in a unit

UnitPretest

Lesson1

Lesson3

Lesson4

Lesson2

Lesson5

Students who demonstrate understanding of this concept skip the unit and move to a new skill assessment

Lesson 3

Lesson 4Lesson 1

Lesson 2 Lesson 5

Students who don’t have these skills work through a unique sequence of lessons in the unit to learn those concepts

Why is DreamBox so Effective?Integrated Assessment and Instruction

Primary Engagement Environment

Persevere: Build Optimally

Look for Structure: Quick Images

Intermediate Engagement Environment

Sequenced Challenges

Timely, Specific Feedback

Kindergarten Data Report

Student Reporting by Proficiency

DreamBox Combines Three Essential Elements to Accelerate Student Learning

Q & A

timh@dreambox.com@DocHudsonMath

www.dreambox.com