Accelerating Mathematical Accelerating Mathematical Achievement byAchievement by

Unlocking the Language of Unlocking the Language of MathematicsMathematics

Bill Smith

Curriculum Coordinator

Educational Consultant

ASCD

NCEA

Title 1

March 2008

bI live and work in the world

OfOfMathematicMathematicss

And who are you?

But I already have so much to do! But I already have so much to do! I don’t know if I can do it!I don’t know if I can do it!

I’m here today as I’m here today as hostage?hostage?

How Are We Doing?How Are We Doing?

Test yourself: answer True or False 1. ______________ American students are more proficient

in Reading than Math. 2. ______________ Nearly 76% of K – 5 teachers prefer

teaching Reading over Math.

3. ______________ Nearly two-thirds of American grade 8 students lack proficiency in Math.

4. ______________ Most states had a graduation rate of 90% or higher last year.

5. ______________ The graduation rate in 2005 was greater than in 1970.

6. ______________ Last year, 57% of 9th grade students who were not promoted to 10th grade dropped out of school.

Continued 7. ______________ Most states require 90 minutes of

direct math instruction per day. 8. ______________ American students consistently

score in the top quarter on international tests. 9. ______________ 30% of all students entering 4 year

colleges last year were required to take a remedial math class.

10. _____________ The number of American students pursuing advanced math degrees has declined for each of the past three decades.

11. _____________ Nearly 60% of American doctors reported that they had difficulty with mathematics.

12. _____________ Research found that eating chocolate could improve your math performance.

You Do The MathYou Do The MathRemediation Does Not WorkRemediation Does Not Work

At grade 3 over 15% At grade 3 over 15% of the students of the students receive remedial math receive remedial math helphelp

At the end of grade 4 At the end of grade 4 this number increases this number increases to almost 20%to almost 20%

By the end of grade 8 By the end of grade 8 almost 2/3 of the almost 2/3 of the students fail to meet students fail to meet grade level standardsgrade level standards

What is Needed?What is Needed?

It is not more remediation! It is not more remediation! We cannot continue to waste students’ We cannot continue to waste students’

time…teachers’ energy…and taxpayers’ time…teachers’ energy…and taxpayers’ money on what doesn’t work!!money on what doesn’t work!!

“Insanity is doing the same thing over and over again and expecting a different result.”

-Albert Einstein

It’s a New Mindset

Acceleration of instruction.

15% are already here

15% are struggling

The other 70%

Now do the Math

Mathematics is a Journey…Mathematics is a Journey…not a Destinationnot a Destination

Direct Instruction in the Direct Instruction in the Language of Mathematics Language of Mathematics

isis

the Key to Making Changethe Key to Making ChangeIn Elementary and Middle In Elementary and Middle

School Math!School Math!

However, mathematics truly However, mathematics truly can be a “can be a “foreign language”foreign language”

to many students and even to to many students and even to many adults. many adults.

For too many students, math is

something learned at school and is not even

spoken at home.

Memories of Math InstructionMemories of Math Instruction

Tales from the MATH Jungle

Building student confidence in using the language of mathematics will raise

achievement

and conquer the and conquer the Fear FactorFear Factor!!

The Math Gene

Attitudes about math can and are passed from generation to generation!

Zachary Ashley

Teachers can compensate for academic gaps and make needed accommodations for learning styles…..but teachers can not often compensate for negative attitudes.

Reflect on ThisReflect on This

We need to help all children open the secret door

to Mathematical Understanding.

And the Key to Unlocking the Math is Understanding the Language of Mathematics.

The Language of Mathematics is a tool for communicating and

demonstrating understanding.

Research

All students need and can benefit from All students need and can benefit from direct vocabulary instructiondirect vocabulary instruction

What is lacking in most math classes is a What is lacking in most math classes is a systematic approach in teaching systematic approach in teaching vocabulary and languagevocabulary and language

Without a solid foundation in the language Without a solid foundation in the language of mathematics, students have increasing of mathematics, students have increasing difficulties as they progress through the difficulties as they progress through the gradesgrades

The Challenges of the Language

Many math terms are spelled differently and have different meanings.

Then again…some words might be spelled the same and have totally different meanings.

And then, there’s a whole new world of technical terms.

The Top 10 Confusing Math The Top 10 Confusing Math TermsTerms

The Top 10 Confusing Terms The Top 10 Confusing Terms For My Students For My Students

10. Similar…like all others

9. Range…a place with cattle

8. Substitute…a new teacher to terrorize

7. Expression…what’s on your face

6. Pi…a dessert, or do you spell it desert

5. Property…what I own

4. Odd…yes, I sometimes feel this way in math

3. Mean…no, my teacher is really nice

2. Compute…but I do not have a computer

1. Right Angle…you mean there is no left angle

And the signs can also And the signs can also be confusing: be confusing:

< >, ≠, ∑, √, ≈, *,( ),≥ ≤ , ∞, +, -, ÷, ×, %

Look at the Language

As part of the mid-year assessment in a 2nd grade class, the teacher asked the students to “write the first 4 even, whole numbers in order”.

One student wrote 0, 6, 8, 9. When the teacher asked this student to look it over he changed the answer…adding 10 to the list.

What was his reasoning?

Processing the Language Takes Time

Teaching vocabulary using a systematic approach is a powerful tool for student achievement

It takes time and practice Model, clarify, and

reinforce the language Marzano and Pickering 2005

Reflect on this statement:

Many of us have mastered “street math” and retain little

of our “school math.”

Think, Pair, Share

Could it be the way we Could it be the way we learned mathematics?learned mathematics?

Math is Math is Alive & KickingAlive & Kicking

The answer is 24.The answer is 24.

What is the question?What is the question?

What is the Question?

1. What’s the question if the answer is 96 square inches?

________________________________________________________________________

2. What’s the question if the answer is 30 square inches?

________________________________________________________________________

3. What’s the question if the answer is 126 square inches?

________________________________________________________________________

4. What’s the question if the answer is 20 inches?

________________________________________________________________________

5. What’s the question if the answer is 252 square inches?

________________________________________________________________________

12 in.

16 in. 5 in.

A B

C D E

Children are learning their math facts Children are learning their math facts differently.differently.

investigating how facts relate to each otherinvestigating how facts relate to each other developing patternsdeveloping patterns applying number strategiesapplying number strategies

Children will be doing more than arithmetic.Children will be doing more than arithmetic. Children will be striving to achieve high Children will be striving to achieve high

goals.goals. Children will be actively involved in doing Children will be actively involved in doing

mathematics.mathematics.

Children will be speaking and writing Children will be speaking and writing mathematically.mathematically.

Children will be working with one another.Children will be working with one another. Children will be evaluated in a variety of ways.Children will be evaluated in a variety of ways. Children will be using math tools to solve Children will be using math tools to solve

problems.problems. Children will be using technology.Children will be using technology.

What Great Math Teachers Do Differently

Understand the MathUnderstand the Math

Able to break it downAble to break it down

Focus on the Language of the MathFocus on the Language of the Math

Make ConnectionsMake Connections

Utilize Multiple StrategiesUtilize Multiple Strategies

Assessment and ActivitiesAssessment and Activities

Math is More Math is More Than NumbersThan Numbers

Math is:Math is:

• logical thinking

• making connections

• solving problems

• communicating reasoning

And, the vocabulary provides a And, the vocabulary provides a common language that can be common language that can be

understood by all.understood by all.

Student

Learning

Ahead

The Five Mathematical The Five Mathematical Food GroupsFood Groups

Numbers & Operations

PatternsGeometry

Measurement

Data Analysis =

++ + +

Number SenseNumber Sense understand and use numbers to understand and use numbers to

communicate mathematicallycommunicate mathematically represent and classify numbersrepresent and classify numbers use operations and demonstrate how use operations and demonstrate how

they relate to one anotherthey relate to one another compute fluentlycompute fluently solve problemssolve problems make reasonable estimatesmake reasonable estimates

Activity Fun With NumbersActivity Fun With Numbers

Having Fun With Money

Below are ten occupations and a list of Below are ten occupations and a list of money. Match the amount of money to money. Match the amount of money to the appropriate occupations.the appropriate occupations.

Hint:Hint: The clue is finding an amount that The clue is finding an amount that has something to do with the occupation.has something to do with the occupation.

Example: Optometrist =$20.20Example: Optometrist =$20.20

What about $0.07?What about $0.07?

Having Fun With MoneyHaving Fun With Money

1.1. News Reporter News Reporter a. a. $2.41$2.412.2. History ProfessorHistory Professor b. b. $36+$52$36+$523.3. BallerinaBallerina c. c. $20.20$20.204.4. Sales ClerkSales Clerk d. d. $9.11$9.115.5. Piano TunerPiano Tuner e.e. $7.47$7.47

6.6. Telephone OperatorTelephone Operator f.f. $3.14$3.147.7. Financial PlannerFinancial Planner g.g. $14. 92$14. 928.8. ParamedicParamedic h.h. $22$229.9. Jet PilotJet Pilot i.i. $4.11$4.1110.10. Baker Baker j. j. $401,000$401,000

Adapted from the work of Dr. Donna KnoellAdapted from the work of Dr. Donna Knoell

The Beauty of Math A:1 B:2 C:3 D:4 E:5 F:6 G:7 H:8 I:9 J:10

K:11 L:12 M:13 N:14 O:15 P:16 Q:17 R:18 S:19 T:20 U:21 V:22 W:23 X:24 Y:25 Z:26

Use this mathematical formula to find the following percents associated with the following terms by adding the values of each letter.

K__N__O__W__L__E__D__G__E__= % H__A__R__D__W__O__R__K__= % A__T__T__I__T__U__D__E__= %

Find out how far the love of god will take you: L__O__V__E__O__F__G__O__D__= %

Think In Smart GroupsThink In Smart Groups

Patterns, Relations & AlgebraPatterns, Relations & Algebra

understand and utilize patternsunderstand and utilize patterns use algebraic relationshipsuse algebraic relationships use mathematical models to solve use mathematical models to solve

problemsproblems determine changesdetermine changes

What’s My Pattern?What’s My Pattern?

22 24 26 28 30

22 33 55 99 1717

1 3 9 27 81

The Triangle Theater

You are in seat number 399.

Which seat number is directly in front of you?

v 1

2 3 4

5 6 7 8 9

10 11 12 13 14 15 16

? ? ? ? ? ? ? ? ?

GeometryGeometry

analyze and describe properties analyze and describe properties of two and three dimensional of two and three dimensional geometric shapesgeometric shapes

develop spatial relationshipsdevelop spatial relationships apply geometric principles to apply geometric principles to

solve problemssolve problems

MeasurementMeasurement

utilize appropriate units of measure for utilize appropriate units of measure for time, length, weight, area, and volumetime, length, weight, area, and volume

apply appropriate techniques, tools, apply appropriate techniques, tools, and formulas to determine and formulas to determine measurementsmeasurements

Hole In OneHole In One

How can you cut a hole in How can you cut a hole in the index card big enough the index card big enough to fit over your head?to fit over your head?

Remember the hole must Remember the hole must be intact…no gluing of be intact…no gluing of the ends is allowed.the ends is allowed.

Data Analysis and StatisticsData Analysis and Statistics collect, organize and display datacollect, organize and display data select and use appropriate statistical select and use appropriate statistical

methods to analyze datamethods to analyze data make predictions based on datamake predictions based on data understand and apply basic concepts understand and apply basic concepts

of probabilityof probability

Munchkin Math!!Munchkin Math!!

problem solvingproblem solving

predictionprediction

data collectiondata collection

measures of central tendencymeasures of central tendency

graphinggraphing

real life experiencesreal life experiences

Strong Mathability =Strong Mathability =A Balanced Program of StudiesA Balanced Program of Studies

that focuses on problem solving.that focuses on problem solving.

It Is Not Alien It Is Not Alien Math!Math!

guess and checkguess and check

work backwardswork backwards

look for a problem within the problemlook for a problem within the problem

look for a pattern/sequencelook for a pattern/sequence

make a tablemake a table

organize a listorganize a list

use manipulatives to act it outuse manipulatives to act it out

No Problem – I Have a Strategy

Real Life ProblemsReal Life Problems

You have $10 to spend on your friends and yourself.

How many Big Macs can you buy?

You look at the Value Menu and see that small fries are $.99 and medium drinks are $.99.

Use an algebraic expression to show what you buy with your $10.00.

Today’s SpecialBig Macs $1.49 each

Now the adult version.Now the adult version.

You are driving in rural Maine when you notice your gas gauge. It reads between ¼ full and empty.

You know that your new SUV holds 18 gallons of gas and you can go about 270 miles on a full tank.

The next gas station is at Exit 108, approximately 30 miles away!

Do you think you have enough fuel to make it to the gas station?

And Sometimes There Are No And Sometimes There Are No Easy Answers !Easy Answers !

Let’s Do The Math!Let’s Do The Math!

90% of a 90% of a student’s time student’s time

is spent is spent outside the outside the classroom.classroom.

Parent InvolvementParent Involvementis Essential.is Essential.

It’s too big a job for It’s too big a job for schools alone!schools alone!

The ingredients: The ingredients: showing parents what Math showing parents what Math

really is!really is!

Recipe for Forging Family Recipe for Forging Family PartnershipsPartnerships

Supermarket Family Supermarket Family Math Math

A Fun Filled Family Learning Event

ObjectivesObjectives

to educate parents about the unique language of to educate parents about the unique language of mathematics and the changing nature of math mathematics and the changing nature of math instructioninstruction

to promote the importance of parents as educators to promote the importance of parents as educators by strengthening the family and school partnershipby strengthening the family and school partnership

to support parents in expanding their own to support parents in expanding their own mathematical learningmathematical learning

to help parents make connections between what to help parents make connections between what students are doing in the classroom anstudents are doing in the classroom and at homed at home

Objectives - continuedObjectives - continued

to provide practical suggestions about to provide practical suggestions about specific activities that work best at home specific activities that work best at home and how to use these activitiesand how to use these activities

to encourage parents to model positive to encourage parents to model positive attitudes towards mathematical learningattitudes towards mathematical learning

to alleviate anxiety parents may associate to alleviate anxiety parents may associate with math as a result of their with math as a result of their own own experiencesexperiences

A Look At the Line Up

Loaded with Learning Activities!

Math Story HourMath Story Hour““You may have tangible wealth untold:You may have tangible wealth untold:

Caskets of jewels and coffers of gold.Caskets of jewels and coffers of gold.

Richer than I you can never be-Richer than I you can never be-

I had a mother who read to me.”I had a mother who read to me.”

Strickland GillilanStrickland Gillilan

““The Reading Mother”,The Reading Mother”,

Best Loved Poems of the American PeopleBest Loved Poems of the American People

ObjectivesObjectives

engage parents, children, and staff members in engage parents, children, and staff members in a memorable math literacy experiencea memorable math literacy experience

model using literature books to reinforce math model using literature books to reinforce math skills skills

suggest techniques for integrating mathematics suggest techniques for integrating mathematics through literature through literature

provide parents with resources and ideas that provide parents with resources and ideas that foster literacy experiences and promote foster literacy experiences and promote mathematical learning in the homemathematical learning in the home

Milk & Cookies, Then Home to BedMilk & Cookies, Then Home to Bed

Math BingoMath Bingo

ObjectivesObjectives strengthen the home-school strengthen the home-school

connectionconnection engage students, parents, and staff in engage students, parents, and staff in

an academic-based activity that is funan academic-based activity that is fun familiarize parents with grade level familiarize parents with grade level

mathematics vocabulary mathematics vocabulary put books into the hands of put books into the hands of

students students

It’s Fun to Watch Families Learn TogetherIt’s Fun to Watch Families Learn Together

BenefitsBenefits parents and students learn that math can parents and students learn that math can

be funbe fun event helps strengthens the home/school event helps strengthens the home/school

connectionconnection families enjoy a fun filled activity togetherfamilies enjoy a fun filled activity together many families will recreate the activities at many families will recreate the activities at

home and continue the learning processhome and continue the learning process community partnerships that benefit community partnerships that benefit

everyone are formedeveryone are formed

Some students learn by Some students learn by doing…some learn by doing…some learn by

listening…some learn by listening…some learn by watching. But none of them watching. But none of them

truly own something new truly own something new unless they can internalize unless they can internalize

this learning.this learning.

The language is a powerful The language is a powerful tool for unleashing the tool for unleashing the mathematician in each mathematician in each

student.student.

How You Can Help All How You Can Help All StudentsStudents

Make language part of every math lesson.Make language part of every math lesson. Directly teach all new mathematical terms.Directly teach all new mathematical terms. Scaffold language whenever needed.Scaffold language whenever needed. Help all students to communicate their Help all students to communicate their

mathematical reasoning. mathematical reasoning. Help each child see that math is a Help each child see that math is a

important part of everyday life.important part of everyday life.

Stimulate each child’s natural mathematical Stimulate each child’s natural mathematical interest.interest.

Keep parents informed about their child’s learning.Keep parents informed about their child’s learning. Promote the belief that math is fun – use Promote the belief that math is fun – use

investigations and games.investigations and games. Provide guidance – resist the temptation to give Provide guidance – resist the temptation to give

answers.answers. Encourage each child to try a number of strategies Encourage each child to try a number of strategies

to work through the mathematics.to work through the mathematics.

Above all else – create an environment that values mathematics and model positive attitudes about math.

Success in tomorrow’s job Success in tomorrow’s job market will require more than market will require more than computational competence. It computational competence. It will require the ability to apply will require the ability to apply knowledge to solve problems knowledge to solve problems

and communicate and communicate mathematically.mathematically.

-National Research Council-National Research Council

Thank you!Thank you!

QuestionsQuestions

Bill SmithBill SmithEDucational XtensionsEDucational Xtensions™™

20 Chapel Street20 Chapel StreetPembroke, MA 02359Pembroke, MA 02359

E-Mail AddressE-Mail Addressdragginfl@aol.com

617-688-9933617-688-9933www.stbridgetschool.uswww.stbridgetschool.us