Too many grades of D or F in math?

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Too many grades ofD or F in math?
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Today

• Todays presentation focuses on what we can do to
  help struggling students, students living in
  poverty, become successful in their study of
  mathematics.

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MLL

• In a right triangle, the altitude from the right
  angle to the hypotenuse divides the hypotenuse
  into two segments in which the altitude is the
  geometric mean of the lengths of the two segments.

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Geometric Mean
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Geometric Mean

• Proportion
• - Proportions
• equal fractions

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Equivalent Fractions
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MLL

• Math Language Learners

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Vocabulary Notation

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

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Vocabulary

• Find the degree of the monomial
• 4x2y3z5

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Vocabulary

• Best Bet?
• Bet A
• Probability of winning is 3/5
• Bet B
• Odds of winning 3 to 5

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Language Acquisition

• Double meanings
• area
• volume
• operation
• power
• mean
• feet
• product

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MLL

• Solve
• Find the roots
• Find the zeroes
• Find the value of the variable that makes the
  open sentence true

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Speaking

• Oral recitation
• Speaking
• Working in pairs (groups)

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Oral Recitation
Language Acquisition Teaches students how to
learn Embeds in short tem memory
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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

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Classroom Oral Recitation

• Quadratic Formula

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Rules in Mathematics

• Dont make sense!

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Math Rules!

• Division by Zero
• Dividing Fractions
• Rules for Exponentials
• Rules for Integers

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Understanding

• What does do you understand really mean?

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Understanding

• Divide Fractions
• Flip Multiply

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Understanding

• ax b c
• 4x 2 30
• 5x 4 3x 16
• 2(3x 4) 2 4x 10
• x/3 x/4 6
• (x 4)/2 (x 3)/5 x 5

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Axiom

• The more math you know,
• the easier math gets!

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Way of Thinking

• Math is more than just a body of knowledge,
• it is a way of thinking that affects the way
  we live.

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Decisions

• Computation 4 x 13 x 25
• Algorithm (rule)
• Properties of Real Numbers

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Decisions

• Finding a common denominator
• Multiply denominators
• Write multiples
• Factor Tree, LCM
• Reducing Method

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Decisions

• Systems of Equations
• Graphing
• Substitution
• Linear Combination
• Cramers Rule

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Decisions

• Quadratic Equations
• Zero Product Property
• Completing the Square
• Quadratic Formula
• Rational Root Theorem

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• The more math you know,
• the easier math gets!

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Answering the Question

• What are you doing to help my child learn?

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Organizing Student Learning

• Preparation really matters!
• Instruction, Concept Development-Linkage
• Note Taking
• Homework
• Test Preparation
• Assessment
• Student-Teacher Relationships
• My Kid Standard

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What are you doingto improve instruction?
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What are you doingto help my child learn?
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Good News!

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

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Best practices

• Note taking
• Homework
• Tests

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Success on Success
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Success on Success

• First Test Important for confidence!
• Grade Distribution
• Success on Success
• Teach students how to learn effectively and
  efficiently.
• Concentration times

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Student-Teacher Relationships

• Treat your students the way you want your own
  children treated.
• Build success on success.
• Talk to your students. Be friendly.
• Talk positively to your students about their
  opportunity to be successful.
• Call home early with information and good news.
• Make testing as much a reflection of your
  instruction as their studying.

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Student-Teacher Relationships

• Teach your students how to study effectively and
  efficiently (visual, audio, kinesthetic,
  concentration time).
• Tell them you like them.
• Go over expectations explicitly and give
  examples.
• Build trust, make sure they know you are there
  for them by telling them you are.
• Tell them you want them to succeed.
• Continually answer the question What am I doing
  to help my students learn?

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Contradictory Rules
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Unsuccessful Students
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Building Succes - STAR System

• 3 Stars on the test unchanged, no computation,
  no manipulation
• 2 Stars on the test, changes in numbers
• 1 Star allows variability, so curriculum is not
  narrowed

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The Phone Conversation

• Introduction
• Pleasure teaching your son/daughter, nice young
  man/lady
• Explanation, how I intend to help your child
  succeed Instruction
• Clear instruction, linkage, memory aids
• Notes, system, very prescriptive
• Homework, comes from notes instruction
• Oral recitation, procedures formulas
• Practice tests, system
• Study/flash cards
• Reviews

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The Phone Conversation

• Permission to use those strategies/consequenes
• Parental help
• Know when tests are scheduled
• Examine student notebooks
• Use flashcards to help study

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1st Essential - Instruction
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Instruction

• Teach for understanding
• Its not a matter of if students will forget
  information, its a matter of when they will
  forget
• Students should be able to reconstruct knowledge
  over time

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Preparation

• Preparation
• Creation of a practice test and choosing
  examples before instruction begins suggests that
  teachers prepared for the unit knowing where
  students traditionally experience difficulty and
  having resources and strategies ready to address
  those difficulties.

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Preparation

• Practice test
• Cover curriculum appropriately (rigor)
• Grades - Fair Portable
• Benchmarked
• Unit questions reflect questions on
• Curriculum
• Unit
• HSPE
• Semester exams
• College Entrance exams (ACT SAT)

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Content - Instruction

• What you teach affects student achievement
• How you teach it affects student achievement

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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

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When will I ever use this?

• Pythagorean Theorem
• Parabola
• Circumference

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Knowledge, Interest, Enthusiasm
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Systems
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Functions

• C 10 .05m
• y 10 .05x
• y .05x 10
• y (1/20)x 10

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Use simple straight forward examples that clarify
what you are teaching. Do not get bogged down
in arithmetic.
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Show them how - Linkage

• Introduce new concepts using familiar language
• Review and reinforce
• Compare and contrast
• Teach in a different context

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6(100) 7(10) 2(1)
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5 3 2

3 4 1
(5 3)(100)
(2 1)(1)
(3 4)(10)
(8)(100)
(3)(1)
(7)(10)
(800)
(3)
(70)
8 7 3
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Addition - Left to Right
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(4 32)(100)
(223)(1)
(161)(10)
(9)(100)
(900)
9 8 7
123
(1 52)(100)
(321)(1)
(207)(10)
(8)(100)
(800)
8 9 6
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Add / Subtract Rational Expressions
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15
30
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1
19
3


5
4
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C

A
C
AD BC
A


D
BD
B
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LINKING

• Introduce using familiar language
• Review Reinforce
• Compare Contrast
• Teach in different context

Increased Student Achievement
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Why Linking?

• Its not a matter of if students are going to
  forget information, its a matter of when.
• Linking concepts will allow students to
  reconstruct concepts and skills

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It is my job to teach

• Reading
• Writing

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Reading

• Assign reading
• Explicitly introduce vocabulary notation
• Preview reading
• Connect reading
• Check understanding of reading
• Correct their understanding
• Use paper pencil

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Organizing Student Thinking

• Whats the easiest way to help students to
  organize their thinking?
• Writing

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Writing

• Definitions
• Procedures
• Linkages
• Applications
• Compare contrast
• Describe what they understand
• Describe difficulty experienced
• Describe how to solve a problem
• Summarize
• Explain

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2nd Essential - Note taking
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Note Taking
Researchers - 1 Memory Aid - Writing it
Down Complete homework assignment Prepare
for unit test Prepare for high-stakes tests
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Rules and examples
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• Title
• Date
• Objective
• Vocabulary Notation
• Pattern Development
• Rule
• Examples
• Variation

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• Use simple straight forward examples to clarify
  initial teaching!
• Increase difficulty later.

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Note check

• Student notes reflect instruction
• Contain title, date, objective, definitions, how
  to say it, pattern development, linkage, rules
  and exercises with developed rules
• White space
• Star System
• Explanations Cautions

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3rd Essential - Homework
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• Make sure students understand the concept or
  skill
• before sending home to
• practice

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Homework

• Page 270, 132 odd

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Homework-Studying

• Reading
• Thinking
• Reflecting
• Organizing
• Writing

• Analyzing
• Visualizing
• Reviewing
• Remembering
• Recalling

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Homework

• Read Sec. 9.4 - Expressions involving
  logarithms
• Define logarithm
• Write a procedure for converting logarithms to
  exponentials
• Explain why when multiplying logs 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

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Homework

• Read Sec 9.4 - Adding Fractions
• Define Fraction
• Draw a model for adding fractions
• Write a procedure for adding fractions
• Explain the link between adding fractions and
  decimals
• Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31

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4th Essential Test Preparation
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4th Essential- Test Preparation
Test what you say you value Instruction
Assessment Balance Questions reflecting other
high-stakes tests Cumulative questions Practice
tests - Parallel construction Setting a date
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Differentiation

• 1355 41
• 1355 47

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Differentiation

• x2 7x 12 0
• x2 7x 2 0
• Leads to decisions!

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Tests

• Test Design
• Design tests that encourage study.
• Test what you say you value

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5th Essential - Tests

• Form A Form B

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Organizing Student Learning

• Making the connection -
• Instruction to
• Note taking to
• Homework to
• Test preparation to
• Tests

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Organizing Student Learning

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

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This organization strategy leads to

• Transparency
• Credibility
• Trust

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Summary

• Student-teacher relationships
• parent communication
• 1) Preparation
• 2) Understanding instruction
• 3) Notes that reflect reinforce instruction
• 4) Homework that supports and reflects
  instruction
• 5) Test preparation
• 6) Parallel constructed tests

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Contact Information

• Schedule Conference or Work with Schools
• Bill Hanlon
• bill_at_hanlonmath.com
• 800.218.5482
• www.hanlonmath.com
• www.rpdp.net