leadership summit k-12 mathematics november 3, 2015 dr. lynda luckie

Leadership Summit

K-12 Mathematics

November 3, 2015Dr. Lynda Luckie

The Learning System

Questions to consider…• Where are we in terms of student

achievement and the systems that affect it?

• Where are we along the rubric of the School Keys?

NOT EVIDENT

EXEMPLARY

The Silent Epidemic:

Perspectives of High School

Dropouts

A Research Report for the Bill and Melinda Gates FoundationMarch 2006

The Silent Epidemic

• Bill and Melinda Gates Foundation’s research on high school dropouts shows that…

• 45 % of students who drop out did not feel their previous schooling had prepared them for high school.

The Silent Epidemic• Many felt behind when they

left elementary school.

• 47% said classes  weren’t interesting.

• 81% called for more “real-world” learning opportunities.

• Two-thirds said they would have stayed if their schools had demanded more of them.

The Silent Epidemic

What does this have to do with us as teachers ?

As administrators?

As support personnel?

As district – level leaders?

So Why Are Kids Having So Much Difficulty with Math?

The Poverty of “E”s

The Poverty of “E”s

• The Poverty of Exposure– Poverty because of low-level

questions and classroom work– Rote learning v creativity, grit,

and strenuous mental gymnastics

– A set of destinations and a set of rules to get there v a map and how to read it

– Discrete algorithms for a correct answer v how to attack a new or different kind of equation

The Poverty of “E”s

• The Poverty of Exposure

• The Poverty of Experience– Traditional problems v rigorous

tasks– Ritual engagement v authentic

engagement– Textbook generated v related to

their world

The Poverty of “E”s

• The Poverty of Exposure

• The Poverty of Experience

• The Poverty of Expectations– What do you expect them to

learn/produce/achieve?

Frustrated Math Teachers

The Research Says…

• The impact of decisions regarding instruction made by individual teachers is far greater than the impact of decisions made at the school level.

» Robert Marzano» What Works in Schools: Translating

Research into Action, 2003

The Research Says…

• Differences in the effectiveness of individual classroom teachers are the single largest contextual factor affecting the academic growth of students.

» W. Sanders» The School Administrtor

According to Teacher Keys - GADOE

• It is estimated that only about 3% of the contribution teachers make to student learning is associated with teacher experience, educational level, certification status, and other readily observable characteristics.

According to Teacher Keys - GADOE

• The remaining 97% of teachers’ effects on student achievement is associated with intangible aspects of teacher quality that defy easy measurement, such as classroom practices.

Teacher Efficacy

Teacher Efficacy

Imm

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Conte

nt

Teacher EfficacyB

est

Practice

/Pedagog

y

Imm

ers

ion in

Conte

nt

Teacher Efficacy

Com

pelli

ng

Nat

ure

Best

Practice

/Pedagog

y

Imm

ers

ion in

Conte

nt

It’s Time to Move Our Cheese!

Best PracticeFocus on Four

1. Good Questioning2. Critical Thinking & Number

Sense3. The Workshop Model for

Differentiated Instruction4. Collaboration

1. Good Questioning

Best PracticeFocus on Four

Best Practice…

…it’s all about the questions we ask.

Too often we give our children answers to remember rather than problems to solve, effectively keeping them IN the box.

What Are Genuine Questions?

–They are questions the teacher asks for which s/he has no way of knowing what the answer will be.

• NOT, “How many angles does a parallelogram have?”

• INSTEAD, “Tell me what you know about a parallelogram.”

Traditional Question

• What is the name of this shape?

Application Question

• Tell me everything you know about this shape.

OR

• If this is a hexagon, draw other kinds of hexagons you know about. Record some shapes that are NOT hexagons.

OR

• Compare and contrast these two shapes.

Traditional Question

• What is the name of this shape?

Application Question

• Tell me everything you know about this shape.

Or…• If this is a pentagon inscribed in a

circle, draw other pentagons inscribed in circles you know about. Explain how they are different.

Or…

• Compare and contrast these two figures.

So…

…what kinds of questions are we

asking?

Find the Answer

 12 ÷ 3

 4 x 2

How Many Ways Can You Represent Each of These?

 12 ÷ 3

 4 x 2

Find the Answer

 - 16 + (- 8)

 (2x + 4) x (3x – 6)

How Many Ways Can You Represent Each of These?

 - 16 + (- 8)

 (2x + 4) x (3x – 6)

Mr. Billingsley’s Trip

A taxi charges: for the first 1.5 miles $2.40

for every additional ¼ mile .10

Mr. Billingsley paid $12.00 for his taxi ride from work to home. How far is Mr. Billingsley’s work place from home?

Mr. Billingsley’s TripA taxi charges: for the first 1.5 miles $2.40

for every additional ¼ mile .10

Mr. Billingsley paid $12.00 for his taxi ride from work to home. How far is Mr. Billingsley’s work place from home?Renee’s solution:

$12.00 - $2.40 = $9.60$9.60 ÷ $0.10 = 9.69.6 x 1.5 = 14.4Mr. Billingsley’s work place is 14.4 miles from

his home.

There is something wrong with Renee’s solution. Show how you would solve the problem.Explain the error in Renee’s solution.

What Number Makes Sense?

The following is a textbook question on the topic of numbers and number operations.

Tickets to a concert cost $15 per adult and $8 per child. Mr. Adams bought tickets for 4 adults and 5 children. How much did he spend altogether?

What Number Makes Sense?

Read the problem. Look at the numbers in the box. Put the numbers in the blanks where you think they fit best. Read the problem again. Do the numbers make sense?

CONCERT TICKETSTickets to a concert cost ______ per adult and ______ per child. Mr. Adams paid _____ for tickets. He bought tickets for _____ adults and ______ children. 4 5 9 $8 $15

$100

Typical Task

Typical Task

Dollar Line Task Function and Pattern

• Think of a situation which could be represented in the graph below.

• Write a full description of the situation (be sure to tell what each axis represents in your situation.)

• What questions could be answered by your completed graph?

From Balanced Assessment

Typical Textbook Problem

Make It More Engaging

Even Better

Real World?

ALWAYS ask yourself…

• What mathematics do I want my students to learn by doing this activity/task?

1. Good Questioning 2. Critical Thinking and Number

Sense

Best PracticeFocus on Four

Frayer Models

Conceptual Understanding

• These are…• These are not…

These are____________________.

These are not________________________.

Which of these are______________?

Explain how you know.

These are__SQUARES__.

These are not__SQUARES_.

Which of these are_SQUARES__?

Explain how you know.

These are_numbers that round to 600__.

These are not__numbers that round to 600___.

Which of these are_numbers that round to 600___?

Explain how you know.

597642

563633 576

541 678515

525651

692588

555539

640679

Three’s a Crowd!

three-fourths six-eighths two-thirds

centimeter inch millimeter

square rectanglecircle

What I Know about…

What’s My Rule?

WHAT’S MY RULE?Theme: Sports

Yes NoStrike Stick

Split Puck

Pin Hoop

Gutter Goal

Rule: Bowling Terms

WHAT’S MY RULE?Theme: Geometry

Yes NoTriangle Cube

Rectangle Pyramid

Square Pentagon

Quadrilateral Octagon

Rule: Plane figures with less than 5 sides.

WHAT’S MY RULE?Theme: _______________

Yes No

Rule: _________________________

Logic Puzzles

Number Sense• an understanding that allows

students to approach concepts, ideas, and problems with an intuitive feel for numbers and their relationships

• an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations

Wikipedia

Another Definition of Number Sense

“Number sense can be described as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. No substitute exists for a skillful teacher and an environment that fosters curiosity and exploration at all grade levels.”

From Hilde Howden, “Teaching Number Sense,” Arithmetic Teacher, 36(6). (Feb. 1989), p. 11.

7 + 6 = ?

How did yousolve this equation?

38 + 38 = ?How did yousolve this equation?

395 + 56= ?How did yousolve this equation?

What Do Kids Say?

6 + 5 = + 4

What Do Kids Say?

6 + 5 = + 4

Are we teaching them to THINK?

6 + 5 = +

Even higher level…

Teaching Kids to Think Algebraically

6 + 5 = + + +

Even higher…

Teaching Kids to Think Algebraically

6 x 5 = x 3

…with multiplication

Teaching Kids to Think Algebraically

6 x 5 = x

…with multiplication

Teaching Kids to Think Algebraically

What Do Kids Say?

.06 + .15 = + 4

.06 + .15 = +

Higher level

Teaching Kids to Think

Algebraically

.06 + .15 = + +

Even higher…

Teaching Kids to Think

Algebraically

.06 + .15 = x 3

…with multiplication

Teaching Kids to Think

Algebraically

.06 + .15 = x

…with multiplication

Teaching Kids to Think

Algebraically

.06 + .15 = ? ?

Even higher…

Teaching Kids to Think

Algebraically

My Personal Favorite

s for Number Sense

Spotlight on Number Examples

Critical Thinking/Number Sense

Implications for Teaching

We need to replace the question, “Does the student know it?”

with the question, “How does the student understand it?”

John Van de Walle

Copyright © Allyn and Bacon 2010

1. Good Questioning 2. Critical Thinking and Number

Sense3. The Workshop Model for

Differentiated Instruction

Best PracticeFocus on Four

Workshop Model for Math

A Strategic Model for Differentiated

Instruction

Turn and Talk

• What happens in each setting? Small Groups Whole Group

• What do the groups look like?

– Heterogeneous or homogeneous?

Nuts and Bolts

• What do the groups look like?

– Heterogeneous or homogeneous?

Nuts and Bolts

HOMOGENEOUS GROUPS!

WHY??????

Nuts and Bolts

• How do you determine your small groups?

Nuts and Bolts

• WITH DATA!

• Tickets out the Door–Weekly assessments

• Formative and Summative Assessments

How Can You Determine Small Groups?

• Observation of an assigned task• Small group discussion of problem solving

related to the concept to be studied• Written explanation of understanding by

students in their math journals• Paper and pencil pretest• Formative test results (TICKET OUT THE

DOOR)• Performance in earlier work on sequential

math concepts • Checklists and Conferencing

Sample TOD

Sample TOD

Why Tickets out the Door?

• Quick formative assessment

• It’s the DRIVER !• Helps determine your

groups• Does not give students

permission to forget• Wake up call

Math Workshop Model

Teacher Facilitated

Group

Interactive Practice

At Your Seat

Math Workshop Logistics

Teacher Facilitated

Interactive Practice

At Your Seat

1st Rotation Group A Group B Group C

2nd Rotation Group C Group A Group B

3rd Rotation Group B Group C Group A

Group A: ________________________________

Group B: ________________________________

Group C: ________________________________

What Does This Look Like in a 90 Minute

Block?

• Mini Lesson – How long?• Group Rotations – How

long?• Formats for small groups?

Where in the room?

ALWAYS Ask Yourself…

• What mathematics do I want my students to learn by doing this activity?

• Are there students who may already be proficient in this area?

• Are there students who will need more time?

Students Need to Know…

• Which group are we in today?

• Where are our meeting areas?

• Do we know what materials we need?

• Do we know our schedule?• Can we work

independently?

Make It Your Own

Make It Your Own

So…how do you keep everyone engaged?

With QUALITY work!Meaningful math gamesPractice that reinforcesMath JournalsPair/group activities

NOT something they’ve never seen before!!

Interactive Practice Examples

ALL about PRACTICE

• iPad practice apps• Laptop interactive

activities/programs• Scavenger Hunts• Meaningful math partner

games

Scavenger Hunts

The Power of Meaningful Math

Games

The Power of Meaningful Math

Games

…Meaningful Practice

Games for Primary

My Rolls:

1. ________

2. ________

3. ________

4. ________

5. ________

6. ________

Total: ____________

Closest to 100

1. Roll the dice exactly SIX times.2. Decide if your roll will be a “one” or a

“ten.”3. Fill in the grid AND record it in the box.4. Add all six rolls. Closets to 100 wins.

Closest to 100

• Use a 10 x 10 grid.• Students take turn rolling the dice

exactly SIX times. • When they roll, they decide

whether they want that number of ones or tens. Eg: Student rolls 4…they can get four “ones” or four “tens.” Record on the 10 x 10 grid.

• After six rolls, student closest to 100 without going over wins.

Domino Drawings

• Students use large Double Six or Double Nine dominoes and can work with a partner.

• Work together to:– Draw domino– Write a number sentence to

show sums of dots.

Make Ten Concentration

Use two sets of cards

Fraction Building

1/3one-third

2/4two-

fourths

1/8one-

eighth

1/5one-fifth

Use colored cubes to build and record collections.

Race to 50

What I Rolled Solution Total

Race to 50

• Materials– 10 sided dice– +/- die or spinner– Recording Sheet

• Directions– Players take turns rolling two dice

and the +/- die and solve, recording what they rolled and the solution on the recording sheet.

– First player to 50 wins.

Games for Intermediate Grades

Pattern Block Fraction Pizza

Pattern Block Money

Rectangular Array Game

Knock Out Three

Is It True?

More Is It True?

Games for MS/HS

Spin for Expressions

Spin for Expressions• Materials:

– Plus/minus spinner– A number cube– Expression playing cards

• Pass out all the expression cards FACE DOWN.• The dealer then rolls the number cube to determine

the value of the variable, and then spins the spinner to determine if the value is positive or negative.

• Each player will turn over one card and evaluate his/her expression. The player with the greatest value for that round takes all the cards.

• The player with the most cards at the end of the game is the winner.

Domino Cards

Spinning for Polynomials

• Materials– Polynomial Spinner– Dice

• Student one spins spinner 3 times and combines the monomials. Student two does the same.

• Roll dice for value of x, and highest final number wins.

Spinning for Polynomials

24 GAME

Workshop Model Tips…

• Ensure that students understand directions before dismissing them.

• Practice transitions to and from whole group areas.

• Practice moving from station to station.• Set routines for what to do when assignments

are complete (e.g., Anchor Packets).• Establish positive reinforcements for meeting

expectations.

Workshop Model Tips…

• Set expectations for behavior when working independently or with partners.

• Have back-up seat-work assignments for students who are not on task.

• Establish a signal for redirection and transitions.

• And most of all…

Biggest Tip…

• Don’t make it harder than it is!!

At the end of the day…

So…how do you keep everyone engaged?

With QUALITY work!Meaningful math gamesPractice that reinforcesMath JournalsPair/group activitiesNOT something they’ve never

seen before!!

The Workshop Model in Action

This Teacher Said…

“I know more about what my students know and how they think in 8 days than in the entire first semester!”

Best PracticeFocus on Four

1. Good Questioning2. Critical Thinking & Number

Sense3. The Workshop Model for

Differentiated Instruction4. Collaboration

• What are you excited about?

• Where does collaboration fit in this model?

• What are your reservations?– How can we deal

positively with them?

Turn and Talk

Remember…it will likely NOT be perfect the first time, or even the second.

You WILL see positive results!