Mansfield

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Mansfield
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Leading the Way to Accelerating Math
Achievement

• Bill Hanlon

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What are you doingto improve instruction?
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Organizing Student Learning5 1

• Instruction, concept development-linkage
• Note taking
• Homework
• Test Preparation
• Assessment
• Bill Hanlon bill_at_hanlonmath.com
• 800.218.5482

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• Student-teacher relationships

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Answering the Question
 What are you doing to help my child learn?
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Rules in Mathematics

• Dont make sense!

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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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Components of an Effective Lesson
Before presenting a lesson, refer to the
assessment blueprint for the unit. Introduction
 Daily Reviews    Daily Objective   Con
cept and Skill Development and Application  
Guided / Independent / Group
Practice   Homework Assignments
   Closure  Long-Term Memory Review
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• Build on Strengths

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Whats needed?

• Refinement Reinforcement
• of those practices.

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Quiet Conversions

• Change is difficult for people.
• Culture If I wait long enough, this too will pass

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Best Practices

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

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Leadership

• Lead by demonstrating success in classrooms where
  teachers will modify their instruction to
  increase student achievement.

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Build Trust Confidence

• Students will work for teachers for no other
  reason than loyalty.
• Law of Reciprocity

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Increasing Student Achievement

• No simple answer-
• what works is work

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Its 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.

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Actions follow beliefs

• 10 simple 2-letter words

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• If it is to be, it is up to me

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2 Standards

• My Kid
• Common Sense

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My Kid Standard

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

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Common Sense Standard

• Appeal to teachers common sense and experience,
  do not get into a citation battle.

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Learning

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

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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.
• 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.

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Unsuccessful Students
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Contributing Factors
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Contributing Factors

• How do you see your students?

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Contributing Factors

• How do your students see you?

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Contributing Factors

• What are you currently doing to motivate, to
  address, unsuccessful students?
• Anything special for ELL, special education, or
  students living in poverty?

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Contributing Factors

• Belief Systems
• Teachers believing in students
• Students believing in themselves
• Teachers believing in themselves

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Contributing factors

• What factors do you control?

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Success on Success

• Success on Success
• Teach students how to learn effectively and
  efficiently.
• auditory
• visual
• kinesthetic
• Concentration times

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Studying

• Reading
• Thinking
• Reflecting
• Organizing
• Writing

• Analyzing
• Visualizing
• Reviewing
• Remembering
• Recalling

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Study skills

• Good students space learning sessions over time
  and do not cram
• Good students identify the main idea in new
  information, connect new material to what they
  already know, and draw inferences about its
  significance
• Good students make sure their study methods are
  working properly by frequently appraising their
  own progress

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Study skills

• Good students adjust studying according to
  several factors
• the demand of the material
• the time available for studying
• what they already know about the topic
• the purpose importance of assignment
• the standards they must meet

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Expectation - Goals

• Being the best!
• What does it take to be the best?
• What are you willing to do?

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Expectations

• Grade Distributions

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Math Wars

• Its not traditionalist vs. constructivist,
  students need to get the whole picture.

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Balance
Balance in mathematics has been defined as

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• Vocabulary Notation
• Concept Development Linkage
• Memorization of Important Facts Procedure
• Applications
• Appropriate Use of Technology

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

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

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Vocabulary

• Find the degree of
• 4x2y3x5

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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

• Math Language Acquisition

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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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Time on Task
Stake 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.
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1st Essential - Instruction
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Content - Instruction

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

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Subtraction
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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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Use simple straight forward examples that clarify
what you are teaching. Do not get bogged down
in arithmetic.
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Multiplication

• by 11
• by 25

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Leading 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.

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Different Ways to Measure the

• Same Standard

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Finding Measures of Central Tendency

• Find the mean of the following data 78, 74, 81,
  83, and 82.

2. In Teds class of thirty students, the average
on the math exam was 80. Andrews class of
twenty students had an average 90. What was the
mean of the two classes combined?
3. Teds 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?
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Finding Measures of Central Tendency
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 students score on the test?
5. Use the graph to find the mean.
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I cant teach __________ because my kids dont
know _____________
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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
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(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
74
1
19
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5
4
75
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C

A
C
AD BC
A


D
BD
B
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Relations Functions
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Functions
Special relation in which no 2 ordered pairs
have the same 1st element.
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Cold Drinks
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C n x .50 .50n or y x
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Basic Facts Procedures

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

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Memorization

• 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.

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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
• Summarize
• Explain

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Problem 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

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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 Var
iation
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Algebra

• Address the challenges brought on by an
  increasing student population enrolling in
  algebra.
• Hpot,Ball, Qback

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Helping Students Succeed
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Students 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

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Student deficiencies

• To address student deficiencies
• Use the long term memory review
• Use linkage when introducing new concept or skill

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• Make sure students understand the concept or
  skill
• before
• practicing

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• Use simple straight forward examples to clarify
  what you are teaching!
• Increase difficulty later.

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Algebra

• Note taking

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• Solving Linear Equations
• Obj. To solve linear equations that are not in
  the ax b c format.
• Strategy Take a problem you do not recognize
  and change into one you do recognize (ax b
  c) by using the Properties of Real s

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• Ex. Solve 2(3x 4) 5 15
• How does this problem look different from
  equations in the ax b c format?
• Answer-
• How can you get rid of the parentheses?
• Answer-

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• 2(3x 4) 5 15
• 6x 8 5 15
• Now what do you do to put the the equation in ax
  b c format?
• 6x 3 15

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• 6x 3 15
• Equation is now in ax b c format, how do you
  solve it?
• Answer
• 6x 18
• x 3

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Guided Practice

• Give students an opportunity to solve one or two
  equations to ensure understanding

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• Ex. Solve for y. 6y 2 2y 34
• How is this problem different?
• Answer-
• What do you have to do to write in ax b c
  format?
• Answer-

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• 6y 2 2y 34
• 6y 2 2y 2y 34 2y
• 4y 2 34
• Now the equation is in ax b c format, what do
  you do next?
• Answer-

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• 4y 2 34
• 4y 32
• y 8
• What Properties allowed you to subtract and
  divide both sides of the equation by the same
  numbers?
• Answer-

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Guided Practice

• Provide students an opportunity to solve
  equations with variables on both sides of the
  equation.

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Math

• Explain to students that you cant make math
  harder, you can only make problems longer.

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• Solve for x. 7(2x 1) 3 4x 10
• How is this equation different from the equations
  we have solved before?
• Answer-
• Whats the general strategy for solving these
  equations?
• Answer-

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• Solve for x. x/2 x/3 10
• How is this equation different from equations
  that we have solved before?
• Answer-
• How do we get rid of the fractions?
• Answer-

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General Strategy

• Write the general strategy for solving linear
  equations that are not in ax b c format.

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3rd Essential - Homework

• Page 117, 1- 33 odd
• OR

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Homework

• Read Section 3.4, Solving Linear Equations
• Define Distributive Property
• Addition Property of Equality
• Write an equation in ax b c format
• Write the Order of Operations
• How does D-Prop help you solve equations?
• Write a strategy for solving linear equations
  that are not in ax b c format
• Page 117, 1, 3, 7, 11, 12 ,13, 19, 21, 24, 29

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Regular Reviews

• Short and long term

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Time on Task
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Questioning

• Student achievement rises when teachers ask
  questions that require students to apply,
  analyze, synthesize, and evaluate information in
  addition to simply recalling facts.

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Kinds of Questions

• Directed
• Echo
• Cue
• Conceptual

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3rd Essential - Homework
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Practice

• Guided
• Group
• Independent

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Homework

• Homework should reflect what you say you value.
• Vocabulary Notation
• Conceptual understanding Linkage
• Basic Facts Procedures

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Homework

• Page 270, 132 odd

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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 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

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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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Reviews
  Recently taught material Long term review
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Student Assessment
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Assessing Student Work
What do your students know? How do you know they
know it?
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18
3

24
4
Reducing Method 18/24 3/4
18 x 4
72
24 x 3
72
CD 72
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5
15

24
72
7
28


18
72
43
72
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4th Essential- Test Preparation
Test what you say you value Instruction
Assessment Balance Cumulative
Questions Practice Tests - Parallel
construction Setting a Date
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Testing

• Testing drives instruction

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Tests

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

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Test 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

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Practice Tests
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Tests

• Monitor student learning

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Memory Aids

• Help your students remember

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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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Next 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

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KISS
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What are you willing to do?
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Summary

• My Kid Standard
• Success on Success Model
• Simple straight forward examples
• Organize students for learning 5 1
• Demonstrate think aloud
• Its about you!

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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
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• Linkage
• Provides an opportunity to make students more
  comfortable, review reinforce
• Slope, distance formula to Pythagorean Theorem,
  Equation of a Circle
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• Reviews
• 1st - short term knowledge, recently taught
  material
• 2nd long term knowledge, address mastery,
  student deficiencies, high stakes tests not
  necessarily part of that years curriculum, but
  based on student knowledge

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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
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• 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

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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

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Improving Students Achievement
Have a positive attitude build success on
success. Treat students the same way you want
your own children treated.
Try these strategies

• State the days 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.

• Use, simple, straightforward examples that
  clarify what is being taught.
• Use numbers in examples that allow students to
  focus on the concept and dont bog students down
  in arithmetic.

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Improving Students Achievement
Try these strategies (continued)

• 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.

• 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.

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Questions 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?

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Questions

• How does the department monitor individual
  student progress on standards?
• How does staff intervene with students not
  meeting proficiency?
• What are the departments most commonly used
  interventions for students not achieving?
• How successful are those interventions?

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Plan

• Specific
• Measurable
• Achievable
• Relevant
• Timely