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

~ 5 Essentials ~ ~ 5 Essentials ~ Organizing Student LearningOrganizing Student Learning

InstructionNote takingHomeworkTest PreparationAssessment

Organizing Student Learning

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.

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

LearningLearning

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

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?”

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

Expectation - GoalsExpectation - Goals

Being the best!

What does it take to be the best?

What are you willing to do?

Math WarsMath Wars

It’s not traditionalist vs. constructivist, students need to get the whole picture.

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

1st Essential - Instruction1st Essential - Instruction

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.

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

Leading the departmentLeading the department

Leaders make sure all department members know what and how material is assessed and what a good answer looks like.

Leaders make sure all members teach and assess the standards on high-stakes tests.

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

Frequency

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

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

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)

+ 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

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

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

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

− ± −=

PracticePractice

Guided

Group

Independent

3rd Essential - Homework3rd Essential - Homework

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 – 33 multiples of 3

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 –33 multiples of 3

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

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

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

Why Teacher Expectancies???Why Teacher Expectancies???Concept Development

• Not a matter of if they are going to forget, it is a matter of when

• Understanding and ability to reconstruct information

• Test preparation; different was of measuring the “mean”

• Triangle Sum Theorem / Pythagorean Theorem 

Linkage

• Provides an opportunity to make students more comfortable, review & reinforce

• Slope, distance formula to Pythagorean Theorem, Equation of a Circle

 

Reviews

• 1st - short term knowledge, recently taught material

• 2nd – long term knowledge, address mastery, student deficiencies, high stakes tests – not necessarily part of that year’s curriculum, but based on student knowledge

Why Teacher Expectancies???Why Teacher Expectancies???

Homework

• Homework should reflect what is valued, vocabulary and notation, important facts, procedures, open-ended questions on concept development

• Guided practice

• Reading – introduce vocabulary words, preview reading, relate to previous knowledge, retell the reading, summarize reading assignment

 

Testing

• Make testing a reflection of your teaching

• Test what you value as in homework

• Ask questions with the same formality they are asked on high-stakes tests – avoid the disconnect

Why Teacher Expectancies???Why Teacher Expectancies???Note Taking

• Number one memory aide – writing it down

• Helps students complete their homework

• Foundation for test preparation

• Teachers should be very prescriptive and directive 

Oral Recitation

• Imbeds information in short term memory 

Improving Student Grades

• Use simple, straight-forward examples that do not bog students down in arithmetic – focus on concepts being taught

• Teach the big idea

• Use practice tests

Improving Students’ AchievementImproving Students’ Achievement

• State the day’s objective, teach it, and then tell them what you taught the and what they should have learned when you close the lesson – closure.

• Develop concepts. Teach to the big ideas.

• Link concepts to previously learned material and and/or real-world experiences.

Have a positive attitude – build success on success.

Treat students the same way you want your own children treated.Try these strategies:

• Use, simple, straightforward examples that clarify what is being taught.

• Use numbers in examples that allow students to focus on the concept and don’t bog students down in arithmetic.

Improving Students’ AchievementImproving Students’ Achievement

• Incorporate guided practice to monitor student learning before assigning homework.

• Use practice tests to prepare students for unit tests. In first yea algebra, use multiple test versions.

• Tell students how you personally remembered (learned) important information.

Try these strategies (continued):

• Use choral recitation to imbed information in short-term memory.

• Require students to take notes and keep notebooks.

• Require student reading as part of the daily assignment

• Require students to write about what they have learned.

• Use the second review period to reinforce long-term knowledge and address student deficiencies.

Questions for the departmentQuestions for the department

What does the data look like?What are the root causes and contributing

factors of the data results?Do all department members know what

and how material is assessed and what a good answer looks like?

Do all members teach and assess the standards on high-stakes tests?

QuestionsQuestions

How does the department monitor individual student progress on standards?

How does staff intervene with students not meeting proficiency?

What are the department’s most commonly used interventions for students not achieving?

How successful are those interventions?

PlanPlan

– Specific

– Measurable

– Achievable

– Relevant

– Timely