MansfieldMansfield

Leading the Way Leading the Way to to

Accelerating Math Accelerating Math Achievement Achievement

Bill Hanlon

What are you doingWhat are you doingto improve instruction?to improve instruction?

Organizing Student LearningOrganizing Student Learning5 + 1 5 + 1

Instruction, concept development-linkage Note taking Homework Test Preparation Assessment

Bill Hanlon bill@hanlonmath.com800.218.5482

+1+1

Student-teacher relationships

Answering the Question:Answering the Question:

 What are you doing to help my

child learn?

Rules in MathematicsRules in Mathematics

Don’t make sense!

Good News!Good News!

Teachers are already employing many of the best practices needed to increase student achievement.

Best practicesBest practices

Note takingHomeworkTests

Components of an Effective LessonComponents of an Effective Lesson Before presenting a lesson, refer to the assessment blueprint for

the unit.

Introduction

 Daily Reviews

   Daily Objective

  Concept and Skill Development and Application

  Guided / Independent / Group Practice

  Homework Assignments

   Closure

 Long-Term Memory Review

Build on Strengths

What’s needed?What’s needed?

Refinement & Reinforcement of those practices.

Quiet ConversionsQuiet Conversions

Change is difficult for people.

Culture: If I wait long enough, this too will pass

Best PracticesBest Practices

Relentlessly supporting best practices will eventually crowd out poor instructional strategies.

Build Trust & ConfidenceBuild Trust & Confidence

Students will work for teachers for no other reason than loyalty.

Law of Reciprocity

Increasing Student Increasing Student AchievementAchievement

No simple answer-

what works is work

It’s about you!!!It’s about you!!!

You cannot and should not depend on products, programs or services to address the needs of your student population, close the

achievement gap or increase student achievement.

Actions follow beliefsActions follow beliefs

10 simple 2-letter words

If it is to be, it is up to me

2 Standards2 Standards

My Kid

Common Sense

Student-Teacher RelationshipsStudent-Teacher Relationships

1. Treat your students the way you want your own children treated.

2. Build success on success.

3. Talk to your students. Be friendly.

4. Talk positively to your students about their opportunity to be successful.

5. Call home early with information and good news.

6. Make testing as much a reflection of your instruction as their studying.

7. Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time).

8. Tell them you like them.

9. Go over expectations explicitly and give examples.

10. Build trust, make sure they know you are there for them by telling them you are.

11. Tell them you want them to succeed.

12. Continually answer the question; “What am I doing to help my students learn?”

Unsuccessful StudentsUnsuccessful Students

Contributing FactorsContributing Factors

Contributing FactorsContributing Factors

How do you see your students?

Contributing FactorsContributing Factors

How do your students see you?

Contributing FactorsContributing Factors

What are you currently doing to motivate, to address, unsuccessful students?

Anything special for ELL, special education, or students living in poverty?

Contributing FactorsContributing Factors

Belief Systems

– Teachers believing in students– Students believing in themselves– Teachers believing in themselves

Contributing factorsContributing factors

What factors do you control?

Success on SuccessSuccess on Success

Success on Success– Teach students how to learn effectively and

efficiently.auditoryvisualkinesthetic

Concentration times

StudyingStudying

Reading Thinking Reflecting Organizing Writing

Analyzing Visualizing Reviewing Remembering Recalling

ExpectationsExpectations

Grade Distributions

BalanceBalance

 

Vocabulary & Notation

Concept Development & Linkage

Memorization of Important Facts & Procedure

Applications

Appropriate Use of Technology

Balance in mathematics has been defined as:

 Balance should be reflected in assessments and in the delivery of instruction.

Vocabulary & NotationVocabulary & Notation

There is no more single important factor that effects student achievement than vocabulary and notation

VocabularyVocabulary

Find the degree of

4x2y3x5

VocabularyVocabulary

Best Bet?

– Bet AProbability of winning is 3/5

– Bet BOdds of winning 3 to 5

Language AcquisitionLanguage Acquisition

Double meanings

areavolumeoperationpowermeanfeetproduct

MLLMLL

Math Language Acquisition

SpeakingSpeaking

Oral recitation

Speaking

Working in pairs (groups)

Oral RecitationOral Recitation

Language Acquisition

Teaches students how to learn

Embeds in short tem memory

Classroom Oral RecitationClassroom Oral Recitation

Procedure – Adding/Subtracting Fractions

1. Find a common denominator

2. Make equivalent fractions

3. Add/Subtract numerators

4. Bring down denominator

5. Reduce

Classroom Oral RecitationClassroom Oral Recitation

Quadratic Formula

2 4

2

b b acx

a

Time on TaskTime on TaskStake and local school districts usually determine the classroom time available to teachers and students. However, regardless of the quantity of time allocated to classroom instruction, it is the classroom teacher and school administrator who determine the effectiveness of the time allotted. 

According to a survey conducted by the American Association of School Administrators, teachers identify student discipline as the single greatest factor that decreases time on task in the classroom. Generally, teachers with well-managed classrooms, have fewer disciplinary problems. These classrooms typically have teachers who have established rules and procedures are in the classroom when the students arrive, and begin class promptly. They reduce the “wear and tear” on themselves and students by establishing procedures for make-up work, they arrange their room to accommodate their teaching philosophy and style, and they develop routines that increase overall efficiency. The benefits of establishing these classroom procedures and routines become apparent as the total time on task approaches the allocated time. 

When teachers begin class immediately, students view them as better prepared, more organized and systematic in instruction, and better able to explain the material. Students also see these teachers as better classroom managers, friendlier, less punitive, more consistent and predictable, and as one who values student learning. 

Routines like beginning class immediately, reviewing recently taught material, orally reciting new material, having students take notes, and ending the class by reviewing important definitions, formulas, algorithms, and the daily objective keep students engaged and on task. Quality time on task is not a “silver bullet” that can cure all the problems facing education. However, it can play an important role in increasing student

achievement.

1st Essential - Instruction1st Essential - Instruction

Content - InstructionContent - Instruction

What you teach affects student achievement

How you teach it affects student achievement

SubtractionSubtraction

5 – 1 15 – 6 8 – 8 14 – 6

13 – 5 9 – 2 15 – 9 7 – 1

14 – 5 16 – 9 4 – 4 10 – 4

6 –2 12 – 4 10 – 3 6 – 3

When will I ever use this?When will I ever use this?

Pythagorean Theorem

Parabola

Circumference

Knowledge, Interest, & EnthusiasmKnowledge, Interest, & Enthusiasm

Use simple straight forward Use simple straight forward examples that clarify what you examples that clarify what you

are teaching. are teaching.

Do not get bogged down in Do not get bogged down in arithmetic.arithmetic.

MultiplicationMultiplication

by 11

by 25

Different Ways to Measure theDifferent Ways to Measure the

Same Standard

Finding Measures of Central TendencyFinding Measures of Central Tendency 1. Find the mean of the following data: 78, 74, 81, 83,

and 82.

2. In Ted’s class of thirty students, the average on the math exam was 80. Andrew’s class of twenty students had an average 90. What was the mean of the two classes combined?

3. Ted’s bowling scores last week were 85, 89, and 101. What score would he have to make on his next game to have a mean of 105?

Finding Measures of Central TendencyFinding Measures of Central Tendency

0

1

2

3

4

5

70 80 90 100

Scores

Fre

qu

en

cy

4. One of your students was absent on the day of the test. The class average for the 24 students present was 75%. After the other student took the test, the mean increased to 76%. What was the last student’s score on the test?

5. Use the graph to find the mean.

I can’t teach __________ I can’t teach __________ because my kids don’t know because my kids don’t know __________________________

Show them how - LinkageShow them how - Linkage

Introduce new concepts using familiar language

Review and reinforceCompare and contrastTeach in a different context

+ Polynomials

6 7 2 = 6(100) + 7(10) + 2(1)

6 10 + 7 10 + 22

6 n + 7 n + 22

6x + 7x + 22

5 3 2 + 3 4 1 =

8 7 3

(5 +3)(100)

+(2 + 1)(1) =+ (3 + 4)(10)

(8)(100) + (3)(1) =+ (7)(10)

(800) + (3) =+ (70)

213 =

9 8 7

(4 +3+2)(100) + (2+2+3)(1) =+ (1+6+1)(10)

(9)(100)

(900)

+362412 +

(7)(1) =+(8)(10)+

(80)+ (7) =+

123 + 271 =

8 9 6

(1 +5+2)(100) + (3+2+1)(1) =+ (2+0+7)(10)

(8)(100)

(800)

502+

(6)(1) =+(9)(10)+

(90)+ (6) =+

Addition - Left to RightAddition - Left to Right

(5x + 3x + 2) + (3x + 4x + 1)2 2

= 8x + 7x + 32

5 3 2 + 3 4 1 = 8 7 3

(5x + 3x ) + (3x + 4x) + (2 + 1)2 2

Add / Subtract

Rational Expressions

1

+

3

12

26

56

36

+

1+

312

=56

1+

415

=920

1+

314

=712

1+

315

=815

2+

315

=1315

3+

1023

=2930

3+

415

=

20+

4135

=19

2+

X3Y

=

XY

2+

X3Y

=2Y + 3X

XY

A+

BCD

=AD + BC

BD

A C +

B D=

BD

3+

x-12

x+3=

(x-1)(x+3)

3+

x-12

x+3=

(x-1)(x+3)

3(x+3) + 2(x-1)

Relations & Functions

Functions

Special relation in which no

2 ordered pairs have the

same 1st element.

Menu

Hamburger ……….4

Hotdog ……………3

Sandwich …………5

00

00

00

400(H, ) (Hd, ) (S, )300 500

H, Hd, S,400 300 500

400H, Hd,( S), 300 500

.501,

2,

3,

100

150

.50(1, )

(2, )

(3, )

(10, ? )

100

150

Cold Drinks

.501,

2,

3,

100

150

.50(1, )

(2, )

(3, )

(10, ? )

100

150

C = n x .50 = .50n or

y = x12

50(1, )

(4, )200

100(2, ) 150(3, )

175(4, )

Basic Facts & ProceduresBasic Facts & Procedures

Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning.

MemorizationMemorization

Memorizing can help students absorb and retain information on which understanding and critical thought are based.

The more sophisticated mental operations of analysis, synthesis, and evaluation are impossible without rapid and accurate recall of bodies of specific knowledge.

It is my job to teach:It is my job to teach:

Reading

Writing

ReadingReading

Assign readingExplicitly introduce vocabulary & notationPreview readingConnect readingCheck understanding of readingCorrect their understandingUse paper & pencil

Organizing Student ThinkingOrganizing Student Thinking

What’s the easiest way to help students to organize their thinking?

Writing

WritingWriting

Definitions Procedures Linkages Applications Compare & contrast Describe what they understand Describe difficulty experienced Summarize Explain

Problem SolvingProblem Solving

Go back to definition Look for a pattern Make a table or list Draw a picture Guess & Check

Examine a simpler case

Examine a related problem

Identify a sub-goal Write an equation Work backward

2nd Essential - Note taking2nd Essential - Note taking

Researchers - #1 Memory Aid - Writing it Down

Complete homework assignment

Prepare for unit test

Prepare for high-stakes tests

Note TakingNote Taking

Rules and examples

TitleDate ObjectiveVocabulary & NotationPattern DevelopmentRuleExamplesVariation

Algebra Algebra

Address the challenges brought on by an increasing student population enrolling in algebra.

Hpot,Ball, Qback

Helping Students SucceedHelping Students Succeed

Students not rememberingStudents not remembering

Do it right on the first go around

Take the time you need to more fully and appropriately develop concepts and skills

Link concepts/skills to previously learned material & outside experiences

Student deficienciesStudent deficiencies

To address student deficiencies:

– Use the long term memory review

– Use linkage when introducing new concept or skill

Make sure students understand the concept or skill beforepracticing

Use simple straight forward examples to clarify what you are teaching!

Increase difficulty later.

3rd Essential - Homework3rd Essential - Homework

PracticePractice

Guided

Group

Independent

HomeworkHomework

Homework should reflect what you say you value.

– Vocabulary & Notation– Conceptual understanding & Linkage– Basic Facts & Procedures

HomeworkHomework

Page 270, 1–32 odd

HomeworkHomework

Read Sec. 9.4 - Expressions involving logarithms

Define logarithmWrite a procedure for converting logarithms to

exponentialsExplain why when multiplying log with the

same base, you add the logs log (AB) = logA + logB

Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21,23, 31

HomeworkHomework

Read Sec 9.4 - Adding FractionsDefine FractionDraw a model for adding fractionsWrite a procedure for adding fractionsExplain the link between adding fractions

and decimalsPage 270, 1, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31

ReviewsReviews

  Recently taught material

Long term review

Student Assessment

What do your students know?

How do you know they know it?

Assessing Student Work

1+

413

=712

5+

247

18= 18

24=

34

CD = 72

18 x 4

24 x 3

= 72

= 72

Reducing Method

18/24 = 3/4

1824

=34

5=

241572

7=

182872

+

4372

4th Essential- Test Preparation4th Essential- Test Preparation

Test what you say you value:

Instruction – Assessment – Balance

Cumulative Questions

Practice Tests - Parallel construction

Setting a Date

TestingTesting

Testing drives instruction

TestsTests

Test Design

– Design tests that encourage study.

– Test what you say you value

Test PreparationTest Preparation

Do you know what you are going to test your students on BEFORE you begin to teach a unit?

Use the * System in notes for test prep

Practice TestsPractice Tests

TestsTests

Monitor student learning

Memory AidsMemory Aids

Help your students remember

5th Essential - Tests5th Essential - Tests

Form A ~ Form B

Organizing Student LearningOrganizing Student Learning

Making the connection -Instruction to

Note taking toHomework to

Test Preparation toTests

Organizing Student LearningOrganizing Student Learning

Helps students focus and study more effectively and efficiently resulting in increased student achievement

This organization strategy leads toThis organization strategy leads to

Transparency

Credibility

Trust

Next stepsNext steps

What are you willing to do to increase student achievement?

– Address linkage/concept development– Address student notes– Address homework assignments– Address test preparation– Look at yourself

KISSKISS

What are you willing to do?What are you willing to do?

SummarySummaryMy Kid StandardSuccess on Success ModelSimple straight forward examplesOrganize students for learning; “5 + 1”Demonstrate – think aloudIt’s about you!