Accelerating Math Achievement

Standards & Assessment Conference

Las Vegas, NV

April 2007

The 5 Essentials

Increasing student achievement

in

mathematics

Rules in Mathematics

Don’t make sense!

Rules

• Can’t divide by zero

• Any # to the zero power, except zero, is one

• Rules for exponents

• Rules for integers

• Dividing fractions

Today’s Agenda

• Philosophy & Beliefs

• Student-teacher Relationships

• 5 Essentials

Philosophy & Beliefs

Improving student achievement

No simple answer ~

What works is work!

Philosophy & Beliefs

• Success on Success– Teach students how to learn effectively and

efficiently.• auditory

• visual

• kinesthetic

Concentration times

Philosophy & Beliefs

First test

Over teach – over learn strategy

Teach students content

Teach students their learning style

Teach students how to study

Studying

Reading

Thinking

Reflecting

Organizing

Writing

Analyzing

Visualizing

Reviewing

Remembering

Recalling

Philosophy & Beliefs

Learning

Students learn best when they are given feedback on their performance and praised for doing things well.

Student-Teacher Relationships

My Kid Standard

Student-Teacher Relationships

My Kid Standard

Treat the kids in your school or classroom the same way you want your own kids treated.

Student-Teacher Relationships

Loyalty

Many students will work for a teacher for no other reason than loyalty

Student-Teacher Relationships

Law of Reciprocity

People you like, generally like you. People you don’t like, generally don’t like you.

Good News!

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

Build on Strengths

Professional Practices

• Teachers already employ best practices

– Homework– Note taking– Testing

What’s needed?

• Refinement & Reinforcement

of those practices.

Balance

 

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 & Notation

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

Vocabulary

• Find the degree of

4x2y3z5

Vocabulary

• Best Bet?

– Bet A

• Probability of winning is 3/5

– Bet B

• Odds of winning 3 to 5

Language Acquisition

• Double meanings

areavolumeoperationpowermeanfeetproduct

Reading

• Assign reading

• Explicitly introduce vocabulary & notation

• Preview reading

• Connect reading

• Check understanding of reading

• Correct their understanding

• Use paper & pencil

Writing

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

Classroom 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

5 Essentials

• Organizing Student Learning by connecting:– Instruction– Note taking– Homework– Quizzes/practice tests– Tests

1. Instruction

• What you teach affects student achievement

• How you teach it affects student achievement

Subtraction

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

Patterns & Strategies

12 – 3 =

13 – 4 =

15 – 6 =

17 – 8 =

12 – 4 =

13 – 5 =

14 – 6 =

15 – 7 =

Use simple straight forward examples that clarify what you

are teaching.

Do not get bogged down in arithmetic.

Multiplication

32 43 62 54

x 11 x11 x11 x11

352 473 682

Simple Straight Forward Examples

7 5

x1 1

7 5

Multiplication

7 5

x1 1

8 2 5

Relevance

Creating Interest, & Enthusiasm in finding the circumference

Conceptual Development/Linkage

• Not a matter of “if” students are going to forget, it’s a matter of “when” they will forget.

• Student understanding & comfort level

• Ability to reconstruct knowledge

I can’t teach __________because my kids don’t know__________

Linking

• Introduce new concepts & skills using familiar language

• Review and reinforce

• Compare and contrast

• Teach in a different context

Add / Subtract

Rational Expressions

Linking

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

A+

BCD

=AD + BC

BD

A C +

B D=

BD

2+

X3Y

=

XY

2+

X3Y

=2Y + 3X

XY

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

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

H, Hd, S,400 300 500

400H, Hd,( S), 300 500

Functions

Special relation in which no

2 ordered pairs have the

same 1st element.

Menu

Hamburger ……….4

Hotdog ……………3

Sandwich …………5

00

00

00

.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, )

#1 Memory Aid - Writing it Down

Helps students

Complete homework assignments

Prepare for unit tests

Prepare for high-stakes tests

2. Note taking

Note taking

• Be accommodating

• Be prescriptive & directive

Tell them what to write and where to write it.

Rules and examples

TitleDate ObjectiveVocabulary & NotationPattern DevelopmentRuleExamplesVariation

3. Homework

• Homework should reflect what you say you value.

– Vocabulary & Notation– Reading & Writing– Conceptual understanding & Linkage– Basic Facts & Procedures– Applications

Homework

Typical homework assignment

P 270 1 – 32 odd

Homework

Read Sec 9.2 – Expressions involving Logarithms

Define logarithm

Write a procedure for converting logarithms to exponentials

Explain why when you multiply logs with the same base, you add the logs

log (AB) = log A + log B

P 270 1 – 33, multiples of 3

4. Quizzes/Practice tests

Assess what you say you value

Build confidence

Monitor student learning

Preparation

Instruction – Assessment

Balance

Cumulative Questions

Setting a Date

5. Tests

• Balance

• Format

• Confidence & trust

Connecting

Instruction to

Note taking to

Homework to

Practice Tests/Quizzes to

Tests

Organizing Student Learning

Tying instruction, note taking, homework, practice tests/quizzes, and tests together

helps students study more effectively and efficiently resulting in increased student

achievement