1. Leading the Way to Accelerating Math Achievement
Bill Hanlon

2. Answering the Question:
 What are you doing to help my child learn?

3. Rules in Mathematics
Don’t make sense!

4. Good News!
Teachers are already employing many of the best practices needed to increase student achievement.

5. Best practices
Note taking
Homework
Tests

6. Components 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

7. Build on Strengths

8. Refinement & Reinforcement
What’s needed?
Refinement & Reinforcement
of those practices.

9. Quiet Conversions Change is difficult for people.
Culture: If I wait long enough, this too will pass

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

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

12. Build Trust & Confidence
Students will work for teachers for no other reason than loyalty.
Law of Reciprocity

13. Increasing Student Achievement
No simple answer-
what works is work

14. 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.

15. Actions follow beliefs
10 simple 2-letter words

16. If it is to be, it is up to me

17. 2 Standards
My Kid
Common Sense

18. My Kid Standard
Treat the kids in your school or classroom the same way you want your own kids treated.

19. Common Sense Standard
Appeal to teachers common sense and experience, do not get into a citation battle.

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

21. 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.
Tell them you want them to succeed.
Continually answer the question; “What am I doing to help my students learn?”

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

23. Studying Reading Thinking Reflecting Organizing Writing Analyzing
Visualizing
Reviewing
Remembering
Recalling

24. 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

25. 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

26. Expectation - Goals Being the best! What does it take to be the best?
What are you willing to do?

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

28. Balance in mathematics has been defined as:
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.

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

30. Vocabulary
Find the degree of
4x2y3x5

31. Vocabulary Best Bet? Bet A Probability of winning is 3/5 Bet B
Odds of winning 3 to 5

32. Language Acquisition Double meanings area volume operation power mean
feet
product

33. 1st Essential - Instruction

34. Content - Instruction What you teach affects student achievement
How you teach it affects student achievement

35. 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

36. When will I ever use this?
Pythagorean Theorem
Parabola
Circumference

37. Knowledge, Interest, & Enthusiasm

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

39. Multiplication
by 11
by 25

40. 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.

41. Different Ways to Measure the
Same Standard

42. Finding Measures of Central Tendency
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 What score would he have to make on his next game to have a mean of 105?

43. 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 student’s score on the test?
5. Use the graph to find the mean.

44. I can’t teach __________ because my kids don’t know _____________

45. Show them how - Linkage Introduce new concepts using familiar language
Review and reinforce
Compare and contrast
Teach in a different context

46. Add / Subtract
Rational Expressions

47. 1 + 3 2 2 6 3 6 + 5 6

48. 1 + 3 2 = 5 6 1 + 4 5 = 9 20 1 + 3 4 = 7 12

49. 1 + 3 5 = 8 15

50. 2 + 3 1 5 = 13 15 3 + 10 2 = 29 30

51. 3 + 4 1 5 = 3 1 19 + = 4 5 20

52. A C + B D = BD A C
AD + BC + = B D BD

53. 2 + X 3 Y = XY 2 + X 3 Y =
2Y + 3X XY

54. 3 +
x-1 2
x+3 =
(x-1)(x+3) 3 +
x-1 2
x+3 =
(x-1)(x+3)
3(x+3) + 2(x-1)

55. Polynomials

56. =
6(100) + 7(10) + 2(1) 2
6 n n 2
6x x 2

57. 8 7 3 5 3 2 + 3 4 1 = (5 +3)(100) + (3 + 4)(10) +(2 + 1)(1) = (8)(100) + =
(5 +3)(100)
+ (3 + 4)(10)
+(2 + 1)(1) =
(8)(100)
+ (7)(10)
+ (3)(1) =
(800)
+ (70)
+ (3) =

58. Addition - Left to Right
412 + +
362
213 =
(4 +3+2)(100)
+ (1+6+1)(10)
+ (2+2+3)(1) =
(9)(100)
(8)(10) +
(7)(1) = +
(900)
(80) +
(7) = +
9 8 7
123
502 + +
271 =
(1 +5+2)(100)
+ (2+0+7)(10)
+ (3+2+1)(1) =
(8)(100)
(9)(10) +
(6)(1) = +
(800)
(90) +
(6) = +

59. (5x + 3x + 2) + (3x + 4x + 1) (5x + 3x ) + (3x + 4x) + (2 + 1) + =
(5x + 3x + 2) + (3x + 4x + 1) 2
(5x + 3x ) + (3x + 4x) + (2 + 1) 2
= 8x + 7x + 3 2

60. Relations & Functions

61. Functions
Special relation in which no 2 ordered pairs have the same 1st element.

62. Menu
Hamburger ……….4
Hotdog ……………3
Sandwich …………5 00

63. H, Hd, S, 4 00 3 5 4 00
H, Hd,( S), 3 5 4 00
(H, ) (Hd, ) (S, ) 3 5

64. Cold Drinks
.50 1, 2, 3, 1 00 50
.50
(1, )
(2, )
(3, )
(10, ? ) 1 00 50

65. .50 1, 2, 3, 1 00 50
.50
(1, )
(2, )
(3, )
(10, ? ) 1 00 50
C = n x .50
= .50n or
y = x 1 2

66. 50
(1, ) 1 00
(2, ) 1 50
(3, )
(4, ) 2 00 1 75
(4, )

67. Basic Facts & Procedures
Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning.

68. 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.

69. It is my job to teach:
Reading
Writing

70. Reading Assign reading Explicitly introduce vocabulary & notation
Preview reading
Connect reading
Check understanding of reading
Correct their understanding
Use paper & pencil

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

72. 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

73. 2nd Essential - Note taking

74. Note Taking Researchers - #1 Memory Aid - Writing it Down
Complete homework assignment
Prepare for unit test
Prepare for high-stakes tests

75. Rules and examples

76. Title
Date
Objective
Vocabulary
& Notation
Pattern
Development
Rule
Examples
Variation

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

79. Kinds of Questions
Directed
Echo
Cue
Conceptual

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

81. 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

82. Classroom Oral Recitation
Quadratic Formula

83. Practice
Guided
Group
Independent

84. 3rd Essential - Homework

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

86. Homework
Page 270, 1–32 odd

87. 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 – 33 multiples of 3

88. 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 –33 multiples of 3

89. Reviews
  Recently taught material
Long term review

90. Student Assessment

91. Assessing Student Work
What do your students know?
How do you know they know it?

92. 1 + 4 3 = 7 12

93. 5 + 24 7 18 = 18 3 = 24 4
Reducing Method 18/24 = 3/4
18 x 4
= 72
24 x 3
= 72
CD = 72

94. 5 15 = 24 72 7 28 18 24 = 3 4 + = 18 72 43 72

95. 4th Essential- Test Preparation
Test what you say you value:
Instruction – Assessment – Balance
Cumulative Questions
Practice Tests - Parallel construction
Setting a Date

96. Memory Aids
Help your students remember

97. 5th Essential - Tests
Form A ~ Form B

98. Organizing Student Learning
Making the connection -
Instruction to
Note taking to
Homework to
Test Preparation to
Tests

99. Organizing Student Learning
Helps students focus and study more effectively and efficiently resulting in increased student achievement

100. 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.

101. 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

102. 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

103. 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

104. 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 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.
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.

105. 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.

106. 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?

107. Questions
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?

108. Plan
Specific
Measurable
Achievable
Relevant
Timely