accelerating mathematical achievement by unlocking the language of mathematics bill smith curriculum...
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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
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